1State Key Laboratory of Rail Traffic Control and Safety Beijing Jiaotong University Beijing 100044 China2School of Traffic and Transportation Beijing Jiaotong University Beijing 100044 China3Department of Mechanical Engineering University of Alberta Edmonton AB Canada T6G 2R34School of Automation Nanjing University of Science and Technology Nanjing Jiangsu 210094 China5School of Mechanical Engineering Southwest Jiaotong University Chengdu Sichuan 610031 China
Correspondence should be addressed to Yuejian Chen yuejian1ualbertaca
Received 10 February 2016 Revised 9 March 2016 Accepted 5 April 2016
Academic Editor Rafael Morales
Copyright copy 2016 Xiaoqing Cheng et alThis is an open access article distributed under theCreativeCommonsAttribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited
The online detection of wheelset size has important implications for ensuring the safety of railway operation and decreasing themaintenance costs Based on laser displacement sensors (LDS) a novel online detection system of the wheel size is proposed usingonly six two-dimensional LDS and two one-dimensional LDS The calculation principles of tread profile and wheel diameter aregiven as well as the calibration method Errors induced by wheel-rail vibration misalignment sensor noise S-shape running andwheelset differential are also analyzed After system implementation field experiments were performed using both standard wheeland several real trains It turns out that the detection uncertainty of flange width and height is 01mm and wheel diameter 03mmwhich can meet the requirements of maintenance
1 Introduction
Wheel and rail interact with each other by designed pro-files and geometric parameters The wear of the profilesignificantly influences the dynamic performance of railwayvehicles and even leads to derailment in a massive stage [1]Therefore at the very beginning of railway transportationmeasuring and ensuring of wheel-rail interactions are afundamental issue [2]With the continuous increasing of axleload train speed andhigher reliability requirement this issueattracts more attention than ever
According to the charge-coupled device (UIC) 510-2code the geometric parameters of wheelset that need to bemeasured consist of diameter and tread profile managed byflange width and flange height [3] Varieties of measuringtechniques have appeared such as specially designed calipershand-on automatic scanner and online detection system [4]
At the earlier stage the caliper is an effective tool formeasuring wheelset size because of the advantage of thesimple operation However it has shortages of high labor
intensity and fluctuated accuracy depends on the skillfulnessof workers Meanwhile calipers a contact measuring toolwill inevitably undermine the measuring wheel causingcertain damage
After that advanced artificial caliper has emerged withapplying noncontact technology One recognized tool isMiniProf Wheel System developed by Greenwood Engineer-ing [5] The MiniProf Wheel System is magnetically attachedto the wheel It provides the calculation of wear parametersand is also capable of measuring the flange and taper linediameter on wheels Due to the benefits of utilizing computeranalysis overall efficiency is increased but this system stilltakes more than five minutes to measure a single car not tomention the whole train Medianu et al [6] also developed ahand-on scanning system for tread profile This system usesone-dimensional LDS (1D-LDS) driven by worn gear to scantread profile On the whole those hand-on systems requirethe train to remain static or even dismantled facing a greatchallenge of detection efficiency
Hindawi Publishing CorporationJournal of SensorsVolume 2016 Article ID 9507213 15 pageshttpdxdoiorg10115520169507213
2 Journal of Sensors
A widely distinguished technology is online detectionsystem which has the advantages of noncontact high effi-ciency and high accuracy The high efficiency is realized bydynamic measurement namely a train passes the measure-ment system at a certain speed There are some commercialcompanies such as MERMEC Group [7] IEM Inc [8] andKLD Labs Inc [9] selling wheelset detection systems onthe market These systems mainly utilize structured laserlight and charge-coupled device (CCD) image processingtechnology Chen et al [10] and Gong et al [11] proposeda structured laser light and CCD based online detectionsystem for tread profile and diameter respectively In theirresearch two pairs of structured laser light and CCD areadopted to recover the inner and outer profiles of each wheeland register them by the iterative closest point algorithmIn diameter detection the cycloid constraint is utilized toobtain a wide distribution of the contact points Even thoughmany possible factors that cause the error are considered thesystem still lacks real data validation and statistical detectionuncertainty analysis Mian et al [12] provided an opticalevaluation method for railway wheelset with installing imagecameras along at least one circumference of the wheel Such asystem can be of high price with somany optical sensors Gaoet al [13] utilized a pair of line structured laser light and CCDto obtain multiple contact points via repeated shooting Thismethod needed to measure the speed of the train preciselyand the space interval of the points was decided by thespeed and the time interval of shooting Zhang et al [14]used only one CCD camera to capture the image of thelight profile of the wheelset and in the meantime the treadprofile is illuminated by a linear laser Overall the structure ofstructured laser light and CCD based system seems to be toocomplex Such a structure also brings about difficulty in thecalibration of those systemsThe combination of structures ofstructured laser light and CCD is also sensitive to the harshenvironment with vibration and light
Apart from the structured laser light and CCD sensorsLDS can provide more satisfactory results The LDS is aspecial kind of structured light-vision measurement sensorwhere the photoelectrical detector and laser light sourceare assembled providing benefits like easy installation andno need to calibrate intrinsic parameters online Russianscientists [15] reported their innovative laser sensor claimingthat 1D-LDS can be enough for measuring tread profileThen they [16] further derived a mathematical calculationregarding wheel diameter detection However the methodneeds a high precise train speed and time interval of shootingGao et al [17] utilized one 1D-LDS and two eddy currentsensors to detect the wheel diameter Wu and Chen [18] usedhigh-speed CCD and 1D-LDS to measure the diameter andthe accuracy was within 12mm Zhang et al [19] used two1D-LDS and a position sensor to detect the wheel diameterand meanwhile wavelet analysis is used to eliminate thesignal noise Triangle geometry was the main computationalalgorithm in the LDS method These systems do not need aprecise train speed and time interval of shooting anymoreHowever the 1D-LDS methods mentioned above needed thedot laser to be strictly projected at the contact point on the
Flange width
Flan
ge h
eigh
t
al
m
n
L
u
v
o
10mm
70mm
Figure 1 Schematic of measuring target
wheel treadThat is difficult to achieve because of the S-shapemotion of the wheelset
Aiming at LDS based detection system the authorspreviously proposed an online detection system using eight2D-LDS to detect the wheel diameter and tread profile[20] The system utilized a digital IO card to generatedigital synchronous signals which guarantee simultaneousworking of all sensors The 2D-LDS sensors are relativelyof a high price and in the previous system some of the2D-LDS are actually not frequently used In this paperthe authors replaced several 2D-LDS sensors with 1D-LDSSix 2D-LDS and two 1D-LDS are implemented in this newsystem Working simultaneously the data collected from allthe sensors are processed and then wheel diameter andtread profile are calculated Errors induced by wheel-railvibration sensor noise misalignment S-shape running andwheelset diameter differential are also analyzed At last afterthe system is implemented the field test is carried out bystandard wheelset test and real train test
2 System Principle
21 Measuring Target Figure 1 shows a typical wear treadprofile [21] We define the coordinate 119906119900V as the tread profilepanel across the wheel center The inner side of the wheelas shown in black line 119897 in Figure 1 has no wear-out anddeformation when there is wheel-rail contact 119871 is the wheelhub thickness namely the distance from the inner side to theouter side of the wheel The base point a which is the centerof the vertical wheel load and is considered to be the diameterpoint of the wheel is minus70mm away from the line 119897 along 119906-axisThe base pointm which is the center of the lateral wheelload is minus10mm away from base point a along V-axisThe basepoint n is the vertex point of the wheel rim The tread profileis somehow complex so that the condition of tread profile isusually evaluated by flangewidth andheightTheflangewidthis defined by the width between base line 119897 and base pointmalong 119906-axis and the flange height is defined by the distancebetween base point a and vertex point n along V-axis
22 System Layout Thepresented wheelset size online detec-tion system depends on LDS sensors Figure 2 shows thesystem layoutThe system consists of six 2D-LDS and two 1D-LDS each of which is installed below the track to measure
Journal of Sensors 3
Wheelset
L4
L2
Support
Pedestal
Laser panel
precision clock signal
Data acquisition
port
IPC
Optical fiber To server
Data
softwareprocessing
Sensor fixture
All eight sensors
L3
2D-LDS
1D-LDS
2D-LDS
2D-LDS
L1
1kHz high-
Figure 2 Schematic diagram of sensors installation
both sides of the tread profile and diameter They can bedivided into two groups because the left side and right sideare mirrored Taking the left side LDS as an example the 2D-LDS L1 and L3 together with 1D-LDS L2 measure the wheeldiameter by three pointsrsquo principle The 2D-LDS L3 and L4measure the tread profile
Both the 2D and 1D laser sensors are based on lasertriangulationmeasurement principle and aremade up of laserdiode and a CCD linear sensor element The emitted laserforms a laser belt on the wheel tread and then the laser isreflected to the CCD linear inductive components Inside thesensor there is an integrated circuit unit to process the opticaldisplacement data and to obtain the tread and flange profilecoordinates Based on the principle that the output pointsof the LDS are originated from the laser emitting source inapplication the laser emitting source should be regarded asthe origin of the scanning coordinate The signal from allthe sensors is transmitted to IPC through data acquisitionport A digital IO card is utilized to produce precisely a1 kHz square signal in order to ensure all sensors to completethe task of acquiring the tread profile synchronously Thesensors begin to collect the data on the decline of the squarewave signal and then transmit the data to the IPC throughdata acquisition port for the subsequent processThe sampledsignal is analyzed in data processing software and finally the
condition of each wheel is decided There is also an opticalfiber in the IPC so that the condition of each wheel can betransmitted to distant depot office All the sensors are fixed byspecial designedmechanical sensor fixture so that the sensorscan be installed in certain space position The fixtures aresupported by the well manufactured mechanical structureThe whole system is finally connected with the ground by thepedestal
In addition the system also consists of several accessorialtypes of equipment that have not been shown in systemlayout figure which are wheel position sensor and automatictrain identification antennaThree wheel position sensors areinstalled beside the outside of the rail Along the rail the firstone is used to detect the arriving moment of the first wheelaxis of a train and hence to trigger subsequent hardwarefacilities the second one is used to trigger the scanning ofall laser sensors the last one is used to detect the leavingmoment of the last wheel axis of a train and hence to closethe subsequent hardware facilities
23 Static Tread Profile Calculation Principle Taking the leftside LDS as an example we define world coordinate frame(WCF) 119900-119909119910119911 and LDS scanning coordinates 119900(1)-119909(1)119910(1)119911(1)119900(2)-119909(2)119910(2)119911(2) 119900(3)-119909(3)119910(3)119911(3) and 119900(4)-119909(4)119910(4)119911(4) for L1
4 Journal of Sensors
o
y
WCF
x
z
y(1)
z(1)
o(1)
y(2)
z(2)
o(2)
x(2)
y(3)
o(3)x(3)
y(4)
o(4)
x(4)
Figure 3 Coordinates set
L2 L3 and L4 respectively As shown in Figure 3 thescanning coordinates take the origin of laser light as thecoordinate origin the equal angle bisector of the trianglelaser panel as 119910-axis and the direction in triangle laser panelorthogonal with 119910-axis as 119909-axis and finally use right-handrule to determine 119911-axisThe coordinates of the output pointsare in the scanning coordinate system of the sensor
The wheelset is assumed to be in the right position and toremain staticThe scanning coordinate of L3 and L4 is rotatedby two angles from the WCF namely angles 120572 and 120573 withrespect to 119909-axis and 119910-axis The tread profile is measuredby L3 and L4 and the scanning panels of L3 and L4 arethe same The tread profile can be measured in tread profilepanel constituted by L3 and L4 So as shown in Figure 4(a)only angle 120573 is considered when measuring tread profileBecause of angle 120573 the output line is distorted and needsto be transformed into physical profile According to theinstallation angles 1205733 and 1205734 the output data is transformedby
119906(3)
119899 =radic119909(3)2
119899 + 119910(3)2
119899 sin (120579 + 1205733)
= 119909(3)
119899 cos1205733 + 119910(3)
119899 sin1205733
V(3)119899 = radic119909(3)2
119899 + 119910(3)2
119899 cos (120579 + 1205733)
= 119910(3)
119899 cos1205733 minus 119909(3)
119899 sin1205733
(1)
119906(4)
119899 =radic119909(4)2
119899 + 119910(4)2
119899 sin (1205791015840 minus 1205734)
= 119909(4)
119899 cos1205732 minus 119910(4)
119899 sin1205732
V(4)119899 = radic119909(4)2
119899 + 119910(4)2
119899 cos (1205791015840 minus 1205734)
= 119910(4)
119899 cos1205732 + 119909(4)
119899 sin1205732
(2)
where (119909(3)119899 119910(3)119899 ) and (119909
(4)119899 119910(4)119899 ) are detected dot in LDS
scanning coordinates 119900(3)-119909(3)119910(3)119911(3) and 119900(4)-119909(4)119910(4)119911(4) 120579 isthe angle between 119910(3)-axis and the line that connects origin119900(3) and detected dot 1205791015840 is the angle between 119910(4)-axis andthe line that connects origin 119900(4) and detected dot (119906(3)119899 V
(3)119899 )
is the coordinate value of detected dot in the new coordinate119906(3)119900(3)V(3) and (119906(4)119899 V
(4)119899 ) is the coordinate value of detected
dot in the new coordinate 119906(4)119900(4)V(4) as wellAfter transformation the scanned lines in two different
coordinates 119906(3)119900(3)V(3) and 119906(4)119900(4)V(4) need to be mergedinto one coordinate We define the coordinate 119906(3)119900(3)V(3) astread profile base coordinate 119906119900V and move all the data from119906(4)119900(4)V(4) into 119906119900V by (3) as shown in Figure 4(b) Hence
119906119899 = 119906(4)
119899 + Δ119906
V119899 = V(4)119899 + ΔV(3)
Journal of Sensors 5
u
v
(a) (b)
v(3)
u(3)
v(4)
u(4)o(4)
y(3)
o(3)o(3)
x(3)
y(4)
1205733
1205734 120579120579998400
Figure 4 (a) Coordinate transformation of L4 and coordinate transformation of L3 (b) Moving all the data from 119906(4)119900(4)V(4) to 119906119900V
where (119906119899 V119899) is the dot in tread profile base coordinate 119906119900VΔ119906 and ΔV are the offset from 119906
(4)119900(4)V(4) to 119906119900V
As we know flange width flange height and wheeldiameter are determined by several base points and base lineThe output points from sensors are discrete so base points am and n are more likely not in one of the scanned pointsThe output points are also polluted with sensor noise whichinduced more detection uncertainty when we directly regardit as the base points Over here curve fitting is used forextracting the base point as well as the base lineThrough thismethod the coordinate value of base points can be preciselyextracted and the sensor noise can also be eliminated to someextent It is difficult to use a single curve to fit all the treaddue to the complexity of tread contour Therefore fittingdiscrete points of each base point within a certain range isapplied to improve the accuracy of the extracted base pointcoordinate value The common method of curve fitting isthe least square method [22] The least square method usesa given set of measured data to get the functional relation119891(119909 1198860 1198861 119886119899) between the variable 119909 and the variable 119910based on the principle of least squares Then the weightedsum of squaresrsquo value of the residual 119890119896 between the fittingfunction and the actual measured value at each point can beminimal which means 119865 in (4) is minimal
119865 =
119868
sum
119894=0
120596 (119909119894) (119891119894 minus 119910119894)2 (4)
where 120596(119909119894) ge 0 is the weight which reflects the notionthat the data (119909119894 119910119894) accounts for the proportion in theexperiment 119868 denotes the number of data points Accordingto the tread profile features and experimental researchfourth-order polynomial 119910 = sum4119894=0 119886119894119909
4minus119894 is selected to fit eachsubsection curve based on the least square method
With curve fitting technique four lines in total are fittedin order to extract the coordinate value of base points a mandn As shown in Figure 5 at first the inner side of thewheelhas no wear-out and deformation when there is wheel-railcontact so base line 119897 is fitted by selecting all the data pointsin the inner side of the wheelThe base point a is 70mm awayfrom the base line 119897 along 119906-axis Then the green line is fittedin order to extract base point a by selecting data points within
a certain range of base point aThe red line and yellow line arealso fitted by the same method in order to extract base pointsm and n respectively
After four lines are obtained the precise coordinate valueof all base points can be determined To this end the flangeheight and flange width are calculated as follows
119865119908 = 119906119897 minus 119906119898
119865ℎ = V119899 minus V119886(5)
where 119865119908 is flange width 119865ℎ is flange height 119906119897 is the 119906-axiscoordinate value of base line 119897 119906119898 is the 119906-axis coordinatevalue of base pointm V119899 is the V-axis coordinate value of basepoint n V119886 is the V-axis coordinate value of base point a
24 Static Wheel Diameter Calculation Principle Wheeldiameter is detected by 2D-L1 1D-L2 and 2D-L3 Each oneof the LDS measures one point in the circular wheel so thatthe wheel diameter can be determined by three points
The wheelset is assumed to be in the right position andto remain static The coordinates of the output points arein the scanning coordinate system of the sensor Similarto tread profile calculation the coordinate transformation
6 Journal of Sensors
o
y
WCF
x
z
v (1)
u(1)o(1)
y(2)
v(2)
o(2)
u(2)
u(3)o(3)
v (3)
x(4)
duoff
Figure 6 Scanning coordinates of 2D-L1 1D-L2 and 2D-L3 after coordinate transformation
y
z
o
Wheel
c3
c (x0 y0)
c1
c2 l1
l2
l3
1205722
12057211205723
P1 (y1 z1)
P2 (y2 z2)
P3 (y3 z3)lowast
lowast
lowast
(a)
a
o(2)
u(3)
o(3)
v (3)c3Fc
doff
(b)
Figure 7 Wheel diameter calculation principle in two dimensions (a) sight along the 119909-axis scanning coordinates of 2D-L1 1D-L2 and2D-L3 after transformation (b) sight in the 119906(3)119900(3)V(3) coordinate
was conducted and the scanning coordinates 119906(1)119900(1)V(1)119906(2)119900(2)V(2) and 119906(3)119900(3)V(3) for 2D-L1 1D-L2 and 2D-L3
respectively have been obtained Figure 6 shows the scanningcoordinates of 2D-L1 1D-L2 and 2D-L3 after coordinatetransformation Notice that 119906(2)119900(2)V(2) is still the same as119910(2)119900(2)119911(2) because of the installation position of 1D-L2
Figure 6 also shows the offset 119889off between the origin of thecoordinate 119906(3)119900(3)V(3) and laser scanning line of L2 in 119906(2)-axis Among three points the two points detected by 2D-L1and 2D-L3 are extracted from the 2D profiles The offset 119889offis the 119906(2)-axis coordinate value to extract the points in theflange circle from two-dimensional profile This offset 119889off isdetermined by sensor installation
Figure 7 shows the wheel diameter calculation princi-ple in two dimensions where (a) shows the principle that
three points determine a diameter in 119910119900119911 WCF and (b)shows extracting the point in the flange circle among two-dimensional profile and the final wheel diameter distancesubtraction by 119865119888 From Figure 7(a) the installation of eachLDS is modeled as three parameters in 119910119900119911 WCF whichare the position Pi(119910119894 119911119894) and angle 120572119894 They determinethe position of laser origin and the direction of detectionrespectively The angle 1205722 for 1D-L2 is designed as 1205872 Thepositions P1 and P3 are designed as symmetric with respectto the scanning line of 1D-L2 as well as the angles 1205721 and1205723 Even though many of the parameters are designed tobe equal for instance 1199111 = 1199113 the real parameters willvary after engineering implementation due to errors suchas installation error and manufacturing error Thus thisnine-parameter model is proposed for diameter calculation
Journal of Sensors 7
because it can describe all the possible errors The realinstallation parameters are obtained through calibration aslater described Moreover the distances 1198971 1198972 and 1198973 aredetected from three LDS sensors The three points c1 c2and c3 are in the flange of wheel detected by three sensorsrespectively The point c(1199100 1199110) is the origin of the detectedwheel which is calculated by three points c1 c2 and c3
According to Figures 6 and 7(a) the first information wecan get from the LDS sensors is the laser scanned distances1198971 1198972 and 1198973 1198972 is directly detected by 1D-L2 1198971 and 1198973 areextracted from the 2D profiles detected by 2D-L1 and 2D-L3 respectively To extract 1198971 and 1198973 we need to find thecorrect points in the two-dimensional tread profile As shownin Figures 6 and 7(b) the point that determines 1198971 and 1198973should be in the 119906-axis value of offset 119889off Similar to detectingtread profile we use the same curve fitting method to obtaina curve in the contour of the wheel in the 119906119900V coordinate thatis denoted by V = 1198913(119906) When the curve line is obtained1198973 = V3 = 1198913(119889off ) namely the V-axis value of curve 1198913(119906)
when 119906 = 119889off Similarly 1198971 is detected by 2D-LDS L1 usingthe same method as deciding 1198973
Once the laser scanned distances 1198971 1198972 and 1198973 aredetermined we get the three points c1 c2 and c3 in WCFcoordinate 119910119900119911 by
1199101198881
= 1199101 + 1198971 sin1205721
1199111198881
= 1199111 + 1198971 cos1205721
1199101198882
= 1199102 + 1198972 sin1205722
1199111198882
= 1199112 + 1198972 cos1205722
1199101198883
= 1199103 + 1198973 sin1205723
1199111198883
= 1199113 + 1198973 cos1205723
(6)
Based on three points c1 c2 and c3 the wheel center c(1199100 1199110)is determined by
1199100 =
(1199111198881
minus 1199111198883
) (11991021198881
minus 11991021198882
+ 11991121198881
minus 11991121198882
) minus (1199111198881
minus 1199111198882
) (11991021198881
minus 11991021198883
+ 11991121198881
minus 11991121198883
)
2 (1199101198881
minus 1199101198882
) (1199111198881
minus 1199111198883
) minus 2 (1199101198881
minus 1199101198883
) (1199111198881
minus 1199111198882
)
1199110 =
(1199101198881
minus 1199101198882
) (11991021198881
minus 11991021198883
+ 11991121198881
minus 11991121198883
) minus (1199101198881
minus 1199101198883
) (11991021198881
minus 11991021198882
+ 11991121198881
minus 11991121198882
)
2 (1199101198881
minus 1199101198882
) (1199111198881
minus 1199111198883
) minus 2 (1199101198881
minus 1199101198883
) (1199111198881
minus 1199111198882
)
(7)
and the wheel diameter119863119903 is determined by
119863119903 = 2 sdotradic(1199100)
2+ (1199110 minus 119911119888
2
)
2 (8)
From Figure 7(b) 119865119888 is the distance between points c3 anda along V-axis The wheel diameter detected by the previousthree points is somewhere in the contour circle governed bythe 1D-L2 only The point a is considered to be the diameterpoint of the wheel which is minus70mm away from the innerside of the wheel In order to obtain the final wheel diameterwe need to further subtract the distance 119865119888 from the wheeldiameter
119863 = 119863119903 minus 2119865119888 (9)
where119865119888 is the distance between point c3 and point a in V-axis(as shown in Figure 7(b)) namely 119865119888 = V119886 minus V119888
3
25 Dynamics Detection The calculation principles shownabove are in static case When the train passes dynam-ically multiscans can be obtained and the misalignmentphenomenon caused from wheel passing will occur
For tread profile detection ideally the laser light panel ofL3 and L4 is assumed to include the center of the measuredwheel In dynamics detection it is impossible to meet thatassumption for all measured wheels due to the moving ofwheel and the discrete sampling of LDS signal Basicallyif the laser light panel does not include the center of themeasured wheel the detected profile is horizontally stretched
along V-axis That will lead to the increase of detected flangeheight and flange width This phenomenon is called themisalignment between the laser panel and the detectiontarget [9]
Figure 8 shows the dynamics positions of thewheel centerand laser panel constituted by L3 and L4 in two-dimensionalWCF The wheel moves forward with a constant speed of V1198741 1198742 and 119874119894 are the center of wheel diameter circle underdifferent positions The laser panel has an installation angle1205723 with respect to 119910-axis which can be determined as 119911 =tan1205723 sdot 119910 in WCF The center points of wheel diameter circleare calculated by (7) 119889119894 denote the distance between 119894th wheelcenter point and the laser panel
Theoretically for every 119894th position of the wheel thedistance 119889119894 from the wheel center c(1199100
119894
1199110119894
) to the laser panelcan be determined by point to the distance formula as follows
When the distance 119889119894 equals zero the wheel center c(1199100119894
1199110119894
)
is in the laser panel where the flange height and flange widthhave no stretching On the other hand the bigger the distance119889119894 is the farther away the wheel center c(1199100
119894
1199110119894
) is from thelaser panel
It is worthmentioning that the LDSworks when the anglebetween laser light and detected surface is within a certainrange and the angle is influenced by laser wavelength surface
8 Journal of Sensors
y
z
Laser panel
Rail
Wheelv
Scanned section
O1 O2
d1 d22120579
120579
120579
1205723
Oi
di
L3 L4lowast
Figure 8 Dynamics position of the wheel center
smoothness surface material and so forth [23] It is assumedthat the angle 120579 (as shown in Figure 8) is the largest angleat which the LDS can still receive effective scan When thewheel is moving out of the detection range the LDS will beunable to scanThus the scanned sectionwill be the arcwith acentral angle of 2120579 and all the tread profiles and diameters arescanned from this section For most LDS sensors the angle 120579can reach up to 45∘ so the system can measure 90∘ arc of thewheel Correspondingly the maximum value of the distance119889119894 is 119877 sin 120579 where 119877 is the wheel radius
The misalignment phenomenon will bring about certainerror to the profile detection Among all the effective scanswe must select those scans where the induced error isacceptable In this paper the error induced in the tread profiledetection is analyzed in Section 3 As a result the error isdirectly proportional to the distance 119889119894 So we set up a certainthreshold 119870119901 When the distance 119889119894 lt 119870119901 the detectedtread profile can be regarded as useful profiles where the errorinduced by the misalignment phenomenon is negligible Thethreshold 119870119901 is firstly obtained through error analysis andalso is adjustable according to the field experiment Due tothe benefits from the high sampling frequency of the LDSsensors 119872 times of scans can be obtained for a wheelsetThen we can remove the bulky error first and performaverage operation to get the final wheel flange and wheelwidth as follows
119865119908119891
=
1
119872
119872
sum
119894=1
119865119908119894
119865ℎ119891
=
1
119872
119872
sum
119894=1
119865ℎ119894
(11)
where 119865119908119894
and 119865ℎ119894
are the flange width and flange height in119894th scan respectively 119865119908
119891
and 119865ℎ119891
are the final flange widthand flange height respectively The average operation herecan reduce the final error caused by Gaussian sensor noise
For wheel diameter detection the three points thatdetermine the wheel diameter are always in the contourcircle Thus the calculation results will not be influenced by
different wheel positions However 119865119888119894
in every 119894th scan willstill be stretched and bring about some error Similarly weselect a set of scans by comparing whether the distance 119889119894is smaller than a certain threshold 119870119889 or not When 119889119894 lt119870119889 the error induced in the detected 119865119888 is negligible Thetwo thresholds 119870119889 and 119870119901 might be different because ofthe different detection error requirements for tread profileand wheel diameter In this way 119873 times of scans can beobtained Then we can remove the bulky error first andperform average algorithm to get the final wheel diameter asfollows
119863119891 =1
119873
119873
sum
119894=1
119863119894 (12)
where 119863119894 is the wheel diameter in 119894th scan 119863119891 is the finalwheel diameter
26 Calibration The measuring and calculating of treadprofile and wheel diameter depend on many installationparameters Regarding tread profile calculation they are theangle 1205733 in (1) angle 1205734 in (2) and the offset Δ119906 and offsetΔV in (3) For wheel diameter they are the offset 119889off betweenthe origin of the coordinate 119906119900V and laser scanning line of L2in 119906(2)-axis the angles 1205721 1205722 and 1205723 and the positions P1P2 and P3 in (6) When the LDS are installed and fixed it isimpossible for those parameters to be the same with designedvalues because of the manufacture error of mechanical partsand installation accuracy So calibration is certainly needed
During the calibration process for tread profile detectiona standard wheel is placed on the rail over the detection sys-tem and then the offset and rotation angle of the coordinatetransformation matrix can be determined In terms of theangles 1205733 and 1205734 the calibrated accurate value is to makesure the inner and outer panels of the wheel are vertical Forthe offset Δ119906 the calibrated accurate value is to make surethe detected wheel hub thickness equals the standard wheelhub thickness and the offset ΔV is to make sure the scannedprofiles from two LDS coincide with each other
As for the calibration process for wheel diameter a setof new ground wheelsets is used The ground wheelset iswith different diameters that are 770mm 790mm 810mmand 840mm We set the minimization function 119891(119909) as thesquared summation of detected diameters subtracted by realdiameter That is
min 119891 (119909) =
119869
sum
119894=1
1003816100381610038161003816119863119894 minus 119863119903
1003816100381610038161003816
2 (13)
where 119863 is the detected diameter according to wheel diam-eter calibration principle 119863119903 is the real diameters 119909 =
[119889off 1205721 1205721 1205723 1199101 1199111 1199102 1199112 1199103 1199113] is the variables to be cali-brated 119869 denotes the number of ground wheelsets MATLABhas provided such tools to solve those optimization problemsOver here we use fmincon function to minimize the functionand the constraints in terms of the variables are also givenaccording to real physical ranges Finally the optimal valuesof the parameters can be obtained These values are assumedto be the real values that the implemented system has andhave been further put into use in system service
Journal of Sensors 9
3 Detection Error Analysis
In this section we consider four factors which are railvibration sensor noise misalignment and wheel inclinationcaused by wheel S-shape running and the differential ofdiameters
31 Wheel-Rail Vibration Wheel-rail vibration is the firstfactor that we considered In our system all the sensorsare well fixed by the mechanical support and mechanicalpedestal that has no direct contact with rail So the wheel-railvibrationwill not directly transmit to the sensors and insteadthe wheel-rail vibration has to transmit to the ground of thedepot and then transmit to the sensors through mechanicalsupport andmechanical pedestalThe vibration of the groundis on a lower level the maximum of acceleration is only04m2s [24] in Guangzhou metro depot and it is alsoattenuated by the mechanical pedestal We also measuredthe maximum of acceleration of mechanical support duringtrain passing which is only 02m2s So the change of theposition of the sensors due to the wheel-rail vibration in oursystemcanbeneglected Furthermore all the laser sensors arecapturing data simultaneously and the exposure time of theLDS is within 50 microseconds The vibration of the wheelwill not cause considerable movement within such a shorttime Overall the system is assumed to be reliable againstwheel-rail vibration
32 Misalignment As previously mentioned in Section 2Dynamics Detection if the laser light panel does not includethe center of the measured wheel the detected profile is hor-izontally stretched along V-axis This phenomenon is calledthe misalignment between the laser panel and the detectiontarget which will lead to the increase of the detected flangeheight and flange width Chen et al [10] derived a geometricmodel regarding howmany errors will be generated for flangeheight when wheel position varies The error 119890 of the flangeheight is
where 119877 is the wheel radius 119877119862 is the radius in the wheel rim119889 is the distance from the wheel center to the laser panel asdescribed in Section 2
On the basis of this geometric model when we know howmuch the error of the flange height is the errors of the flangewidth can be derived accordingly For different wear wheelsthe profiles aswell as the fitted line for lateral contact pointmare certainly different To illustrate the massiveness of errorshere we chose the same wheel where the fitted line for lateralcontact point m is V = 119891(119906) We obtain the inverse function119906 = 119892(V) and stretch it horizontally by a factor of (119865ℎ + 119890)119865ℎSo the stretched curve line is
119906 = 1198922 (V) = 119892(V119865ℎ
(119865ℎ + 119890)) (15)
Eventually the error of flange width is 120578 = 1198922(10)minus119865119908 where119865119908 is the original flange width
Error of flange heightError of flange width
0
01
02
03
04
05
06
07
08
Caus
ed er
ror (
mm
)
10 20 30 40 500d (mm)
Figure 9 The error of flange width and flange height with respectto various wheel positions
Theoretically from (14) and (15) we know that the smallerthe value of 119877 is the larger the error 119890 is So we chosethe largest standard wheelset with 119877 = 385mm and 119877119862 =399mm Figure 9 shows the error of flange height and flangewidth induced from misalignment in this case The distance119889 varies from 0mm to 50mmwith an interval of 1mm FromFigure 9 the error of flange height is lower than the error offlange width So we focus on the error of flange width here
In our system the sampling frequency of all LDS is 1 kHzand the maximum speed of the train in the depot is 36 kmhThemaximum of sampling step size along the railΔ119904 = 1ms times10ms = 10mmWhen we set the threshold119870119901 (as describedin Section 25) as 20mm the total measuring distance alongthe rail can be 58mm so that at least 119872 = 5 times ofefficient scans can be detected The corresponding errors areless than 01mm for flange width after taking the average ofthese 5 efficient scansThus the system can performdetectionnormally against themisalignment error benefitting from thehigh sampling frequency
33 Sensor Noise The LDS cannot be ideally accurate Themeasuring accuracy is influenced by temperature the rough-ness of the measured surface and so forth
In order to obtain the quantitative influence for profiledetection we built a 3D model in SolidWorks tools andextracted ideal sensor output points of standard inner andouter tread profiles In this model the standard wheel islocated in the position where the center of the wheel is inthe laser panel So the misalignment phenomenon will notaffect tread profile detection The wheel is in static positionso the simulated sensor output points are all from one scanMoreover the parameters that need to be calibrated areideally accurate To imitate the real situation Gaussian noiseis added to these coordinate valuesThemean of noise is zeroand the standard deviation is varied from 0 to 1mm with an
10 Journal of Sensors
X 03Y 01251
Flange widthFlange height
0
01
02
03
04
05
06
07Ca
used
erro
r (m
m)
02 04 06 08 10Noise level (mm)
Figure 10 The RMS error of flange height and flange width causedby different sensor noise level
interval of 01mm For each noise level 500 experiments arecarried out and the RMS error is calculated The RMS errorof flange height and flange width results caused by differentnoise level is shown in Figure 10 The caused error to flangeheight and flange width is approximately half of the sensornoise level This can be explained by the curve line fittingmethod that has taken more laser points into account andthus has reduced the random noise Because the flange heightis determined by two points the curve line fittingmethod hasat least reduced the randomerror into a quarter of the originalsensor noise
The 2D-LDS we chose is LJ-V7300 from KEYENCEwhich has a full-scale resolution of 01FS and a temper-ature drift of 001 FS∘C The detection range in 119910-axis is300 plusmn 145mm and in 119909-axis is 110mm to 240mm whichformed as a trapezoid The point in 119909-axis is fixed thus onlysensor noise in 119910-axis needs to be considered with full scaleof 290mm So accordingly the RMS error caused to theprofile coordinate noise in 119910-axis which is denoted by 120575 isless than 032mm which only leads to an error of 013mmboth to flange height and to flange width Taking dynamicsdetection effect into account the final error is reduced by120575119891 = 120575
radic5 = 0058mm with at least119873 = 5 times of efficientscans The error caused by sensor noise can be acceptable
Regarding the error of wheel diameter it can be theoreti-cally derived by the theorem of error propagation [25] Theresolution of each sensor is denoted by 1205751 1205752 and 1205753 Weobtain 120575119863 by taking differential of (6)ndash(9) as follows
120575119863 = plusmnradic(1205751
120597119863
1205971198971
)
2
+ (1205752
120597119863
1205971198972
)
2
+ (1205753
120597119863
1205971198973
)
2
(16)
We have chosen two 2D-LDS and one 1D-LDS to detect thewheel diameter and the two 2D-LDS are installed symmet-rically For systematic installation we have 1205751(1205971198631205971198971) =
1205753(1205971198631205971198973) Moreover the analytical function of particle
derivative will be too complex to derive So we consider aspecial case where
where the target wheel diameter is 119863 = 840mm and theorigin of the wheel is located in the origin of 119910119900119911WCF Morecalculation details can be found in the Appendix Finally wehave
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(18)
The 1D-LDS we chose is LK-G8085 from KEYENCE whichhas linearity of 005FS and a temperature drift of 001FS∘C So according to the full scale of 30mm the reso-lution of 1D-LDS 1205752 = 0018mm Based upon the findingthat the curve line fitting method has at least reduced therandom error into a quarter of the original sensor noise1205751 = 0075mm Finally 120575119863 is less than 0372mm Takingdynamics detection effect into account the final error 120575119863
119891
=
120575119863radic5 = 017mm The error caused by sensor noise can be
acceptable
34 Wheel Inclination Caused by Wheelset S-Shape RunningandDifferential ofWheel Diameter In engineering thewheelwill be inclined because of wheelset S-shape running and thedifferential of wheel diameter The wheelset S-shape runningis one kind of self-induced vibration due to the slope in thewheel trade When it is S-shape running the wheel panelwill have a certain angle with respect to 119910119900119911 panel in WCFdenoted by 120579119904 as shown in Figure 11(a) The differentialof wheel diameter in a wheelset is at different wear levelin the left and right wheel mainly induced from differentmassiveness of wear in the circuit of wheelset turning andunbalanced loading Similarly it will bring a certain angleabout the wheel panel with respect to the 119910119900119911 panel in WCFThe angle is denoted by 120579119889 as shown in Figure 11(b)
For wheel diameter detection because we only considerthe calculation in two dimensions an error will be generatedwhen we still regard the detected three points in a circle toactually be in an ellipse Considering the existence of angles120579119904 and 120579119889 we have the equation of ellipse as follows
1199102
(119877 sdot cos 120579119904)2+
1199112
1198772= 1
1199102
1198772+
1199112
(119877 sdot cos 120579119889)2= 1
(19)
Journal of Sensors 11
x
y
z
0
Ellipse wheel
Wheelset withS-shape running
120579s
(a)
x
y
z Ellipse wheel
Wheelset with differential of diameter
120579d
(b)
Figure 11 Mathematical illustration (a) Wheel S-shape running and (b) differential of wheel diameter
Similar towhenwe analyze sensor noise we consider a specialcase as (17) the origin of the target wheel is located in theorigin of 119910119900119911WCFThe real three points are
1198881(119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198882 (0 minus119877)
1198883(minus119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198881(119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
1198882 (0 minus119877 sdot cos 120579119889)
1198883(minus119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
(20)
Theoretically the larger the radius of the wheel is the biggerthe error is So we chose 119877 = 420mm and generated threepoints then using (7) we calculated the wheel diameter witherror Subtracting the real diameter we have the error withrespect to angle as shown in Figure 12 The effect of S-shaperunning caused angle has a relatively higher influence on thewheel diameter calculation
Based on the experience from Guangzhou Metro Cor-poration the differential of diameter in a wheelset shouldbe controlled under 2mm Considering the track gauge of1350mm the angle induced from the differential of diameter
S-shape runningWheel diameter differential
0
001
002
003
004
005
006
Caus
ed er
ror t
o di
amet
er (m
m)
01 02 03 04 050120579 (∘)
Figure 12 Wheel diameter errors
in a wheelset is less than 0001∘ thus the error can be ignoredAs for wheel S-shape running themaximum angle is 01∘ [26]when the speed of the train is under 36 kmhwhich will causean error not larger than 0005mm
4 Experimental Validation
41 System Implementation Theauthors previously proposedan online detection system using eight 2D-LDS [19] Thenew online detection system is installed in the same storageline of Guangzhou metro vehicle depot as the old systemso that comparison can be conducted In order to savefund only the left side namely half of the system has been
12 Journal of Sensors
(a) (b)
Figure 13 Field test (a) Standard wheel test and (b) real train test
Table 1 Standard wheelset detection the results of repeatedmeasurementsmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
implemented During the system implementation three-dimensional inclinometer and special rail gauge are used tocontrol the position of the mechanical support After thesystem is installed the calibration described in Section 2has been conducted to obtain the geometric parameters fortread profile calibration and diameter calculation As shownin Figure 13 the field test is carried out by a standard wheelsetand real train
42 Standard Wheelset The standard wheelset is a new pro-duced wheelset without any wear and diameter differentialThe manufacturing geometric size is as follows wheel diam-eter = 840mm flange height = 28mm and flange width =32mm One can also assume to have lower possibility of S-shape running because of zero external load The standardwheelset has been placed on the rail and passed through thedetection system This test has been carried out 6 times toverify both the detection and the repeatability of the systemComparing with the old system the results of this system areshown in Table 1
From Table 1 the mean values of the flange height andflange width detected by the old and the new system are very
close to each other which means the system error can beignored The standard deviation which also can be denotedas detection uncertainty of the new system measurement isslightly smaller than of the old system That may result fromthe lower effect frommisalignment as described in Section 3due to the higher sampling frequency that we used in the newsystem Detection uncertainty of not greater than 005mm intread profile measurement is acceptable for the engineeringrequirements As for wheel diameter detection the meanvalues are also close to each other The standard deviation ofthe new systemmeasurement is slightly higher than of the oldsystemThis may result from the replacement of 1D-LDS thathas brought about higher sensor noise to the middle pointamong three pointswithout curve fitting techniqueHoweverdetection uncertainty of less than 03mm is also acceptable inengineering
43 Real Train Detection Test Real train test also performs6 times of repeated detection to statistically evaluate theperformance of the system The train speed is controlledunder 36 kmh In the train we chose there are 4 new groundwheelsets in a car of the train Under the consideration thatthe ground new wheel is not out of roundness which hasan effect on the analysis results we selected the ground newwheel as our target wheel
Table 2 shows the mean and standard deviation value ofmeasurement The biggest differential value of mean flangeheight appears in 1 wheel and for mean flange width appearsin 3 wheel The difference does not exceed 015mm As forwheel diameter the biggest differential value 016mmappearsin 3 wheelThemean value of six times of repeated detectionis consistent with the standard wheelset test In terms ofstandard deviation the value is less than 01mm for flangewidth and flange height and 03mm for wheel diameterThe standard deviation of wheel diameter is relatively higherthan in standard wheelset test On the contrary the standarddeviation of flange width and flange height is relatively lowerthan in the old system That is also consistent with standard
Journal of Sensors 13
Table 2 Real train test the mean and standard deviation value of detected measurementmm
Wheelnumber
Mean flange height SD flange height Mean flange width SD flange width Mean wheeldiameter SD wheel diameter
Old New Old New Old New Old New Old New Old New1 2818 2803 0046 0060 2954 2943 0091 0062 80052 80150 0201 03012 2809 2811 0078 0040 2940 2929 0056 0028 80112 80096 0128 02863 2797 2791 0076 0033 2992 3006 0075 0056 80187 80166 0090 01794 2807 2805 0063 0053 2983 2988 0076 0088 80178 80201 0192 0282
Table 3 Real train test wheel 2 the result of repeated measure-mentmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
wheelset test The standard deviation of wheel diameter inreal train test is supposed to be higher than in the standardwheelset test because of several assumptions One factor isthe higher possibility of S-shape running because of heavyaxial load On the other hand the wheelset that is in service isalso more polluted with rust than standard wheelset causingmore detection uncertainty However the standard deviationfrom real train test also does not exceed 03mm which isconsistent with standard wheelset test This may result fromthe lower train speed during the test which leads to lowerpossibility of S-shape running Meanwhile the rusty wheelcontour is also not in a massive stage Tables 3 and 4 show theresult of repeated measurement for wheels numbers 2 and 3respectively In each detection the results remain the sameand no gross error appears
Overall detection uncertainties for tread profile andwheel diameter are less than 01mmand 03mm respectivelyThe results show that the detection system has a highaccuracy which can meet the requirements of maintenanceoperation
5 Conclusion
This paper based on LDS proposed a novel on-track detec-tion system of the wheel size using only six 2D-LDS and two1D-LDS Errors induced bywheel-rail vibration sensor noisemisalignment S-shape running and wheelset differential arealso analyzed After the system is implemented real dataexperiments including standard wheel test and real traindetection test were performed It turns out that the detectionuncertainty of flange width and height is 01mm and wheeldiameter 03mm which can meet the requirements of main-tenanceThis system can be further used for different types ofrailway transportation which provides a new solution for thewheel size detection technology
To provide more benefits the target wheel diameter is 119863 =
840mm and the origin of the wheel is located in the originof 119910119900119911WCF as shown in Figure 14 In this special case therelevant geometric values are 1198881(minus19802mm minus19802mm)1198882(0mm 420mm) 1198883(19802mm minus19802mm) 1198971 = 280mm1198972 = 180mm and 1198973 = 280mm
According to (8) and (9) we get the particle derivative asfollows
120597119863
1205971198971
=
120597119863
1205971199100
1205971199100
1205971198971
+
120597119863
1205971199110
1205971199110
1205971198971
120597119863
1205971198972
=
120597119863
1205971199100
1205971199100
1205971198972
+
120597119863
1205971199110
1205971199110
1205971198972
+
120597119863
1205971199111198882
1205971199111198882
1205971198972
(A2)
14 Journal of Sensors
2D-L1
1D-L2
2D-L3
y
z
o
45∘45∘ c1l1
l2
l3
c2
c3 lowast
lowast
lowast
Figure 14 A special case
Taking the derivative of diameter 119863 with respect to 1199100 1199110and 119911119888
2
according to (8) and substituting (1199100 1199110) = (0 0) and1199111198882
= 180mm we have
120597119863
1205971199100
=
21199100
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199110
=
2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199111198882
=
minus2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
= 2
(A3)
Furthermore based upon (7) we get
1205971199100
1205971198971
=
1205971199100
1205971199101198881
1205971199101198881
1205971198971
+
1205971199100
1205971199111198881
1205971199111198881
1205971198971
1205971199110
1205971198971
=
1205971199110
1205971199101198881
1205971199101198881
1205971198971
+
1205971199110
1205971199111198881
1205971199111198881
1205971198971
1205971199100
1205971198972
=
1205971199100
1205971199111198882
1205971199111198882
1205971198972
1205971199110
1205971198972
=
1205971199110
1205971199111198882
1205971199111198882
1205971198972
1205971199100
1205971198973
=
1205971199100
1205971199101198883
1205971199101198883
1205971198973
+
1205971199100
1205971199111198883
1205971199111198883
1205971198973
1205971199110
1205971198973
=
1205971199110
1205971199101198883
1205971199101198883
1205971198973
+
1205971199110
1205971199111198883
1205971199111198883
1205971198973
(A4)
When calculating particle derivative of (1199100 1199110) with respectto three points 1198881 1198882 and 1198883 in WCF we assume that allparameters are with the geometric values in this special case
Then we substitute the ideal geometric values of this variableand we obtain
1205971199100
1205971199101198881
= 05
1205971199100
1205971199111198881
= 05
1205971199110
1205971199101198881
= minus12071
1205971199110
1205971199111198881
= minus12071
1205971199100
1205971199111198882
= 0
1205971199110
1205971199111198882
= 34142
1205971199100
1205971199101198883
= 05
1205971199100
1205971199111198883
= minus05
1205971199110
1205971199101198883
= 12071
1205971199110
1205971199111198883
= minus12071
1205971199101198881
1205971198971
=
1
radic2
1205971199111198881
1205971198971
=
1
radic2
1205971199111198882
1205971198972
= minus1
1205971199101198883
1205971198973
= minus
1
radic2
1205971199111198883
1205971198973
=
1
radic2
(A5)
Finally substituting (A5) into (A4) and then substituting(A4) and (A3) into (A2) we have
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(A6)
Competing Interests
The authors declare that they have no competing interests
Journal of Sensors 15
Acknowledgments
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
A widely distinguished technology is online detectionsystem which has the advantages of noncontact high effi-ciency and high accuracy The high efficiency is realized bydynamic measurement namely a train passes the measure-ment system at a certain speed There are some commercialcompanies such as MERMEC Group [7] IEM Inc [8] andKLD Labs Inc [9] selling wheelset detection systems onthe market These systems mainly utilize structured laserlight and charge-coupled device (CCD) image processingtechnology Chen et al [10] and Gong et al [11] proposeda structured laser light and CCD based online detectionsystem for tread profile and diameter respectively In theirresearch two pairs of structured laser light and CCD areadopted to recover the inner and outer profiles of each wheeland register them by the iterative closest point algorithmIn diameter detection the cycloid constraint is utilized toobtain a wide distribution of the contact points Even thoughmany possible factors that cause the error are considered thesystem still lacks real data validation and statistical detectionuncertainty analysis Mian et al [12] provided an opticalevaluation method for railway wheelset with installing imagecameras along at least one circumference of the wheel Such asystem can be of high price with somany optical sensors Gaoet al [13] utilized a pair of line structured laser light and CCDto obtain multiple contact points via repeated shooting Thismethod needed to measure the speed of the train preciselyand the space interval of the points was decided by thespeed and the time interval of shooting Zhang et al [14]used only one CCD camera to capture the image of thelight profile of the wheelset and in the meantime the treadprofile is illuminated by a linear laser Overall the structure ofstructured laser light and CCD based system seems to be toocomplex Such a structure also brings about difficulty in thecalibration of those systemsThe combination of structures ofstructured laser light and CCD is also sensitive to the harshenvironment with vibration and light
Apart from the structured laser light and CCD sensorsLDS can provide more satisfactory results The LDS is aspecial kind of structured light-vision measurement sensorwhere the photoelectrical detector and laser light sourceare assembled providing benefits like easy installation andno need to calibrate intrinsic parameters online Russianscientists [15] reported their innovative laser sensor claimingthat 1D-LDS can be enough for measuring tread profileThen they [16] further derived a mathematical calculationregarding wheel diameter detection However the methodneeds a high precise train speed and time interval of shootingGao et al [17] utilized one 1D-LDS and two eddy currentsensors to detect the wheel diameter Wu and Chen [18] usedhigh-speed CCD and 1D-LDS to measure the diameter andthe accuracy was within 12mm Zhang et al [19] used two1D-LDS and a position sensor to detect the wheel diameterand meanwhile wavelet analysis is used to eliminate thesignal noise Triangle geometry was the main computationalalgorithm in the LDS method These systems do not need aprecise train speed and time interval of shooting anymoreHowever the 1D-LDS methods mentioned above needed thedot laser to be strictly projected at the contact point on the
Flange width
Flan
ge h
eigh
t
al
m
n
L
u
v
o
10mm
70mm
Figure 1 Schematic of measuring target
wheel treadThat is difficult to achieve because of the S-shapemotion of the wheelset
Aiming at LDS based detection system the authorspreviously proposed an online detection system using eight2D-LDS to detect the wheel diameter and tread profile[20] The system utilized a digital IO card to generatedigital synchronous signals which guarantee simultaneousworking of all sensors The 2D-LDS sensors are relativelyof a high price and in the previous system some of the2D-LDS are actually not frequently used In this paperthe authors replaced several 2D-LDS sensors with 1D-LDSSix 2D-LDS and two 1D-LDS are implemented in this newsystem Working simultaneously the data collected from allthe sensors are processed and then wheel diameter andtread profile are calculated Errors induced by wheel-railvibration sensor noise misalignment S-shape running andwheelset diameter differential are also analyzed At last afterthe system is implemented the field test is carried out bystandard wheelset test and real train test
2 System Principle
21 Measuring Target Figure 1 shows a typical wear treadprofile [21] We define the coordinate 119906119900V as the tread profilepanel across the wheel center The inner side of the wheelas shown in black line 119897 in Figure 1 has no wear-out anddeformation when there is wheel-rail contact 119871 is the wheelhub thickness namely the distance from the inner side to theouter side of the wheel The base point a which is the centerof the vertical wheel load and is considered to be the diameterpoint of the wheel is minus70mm away from the line 119897 along 119906-axisThe base pointm which is the center of the lateral wheelload is minus10mm away from base point a along V-axisThe basepoint n is the vertex point of the wheel rim The tread profileis somehow complex so that the condition of tread profile isusually evaluated by flangewidth andheightTheflangewidthis defined by the width between base line 119897 and base pointmalong 119906-axis and the flange height is defined by the distancebetween base point a and vertex point n along V-axis
22 System Layout Thepresented wheelset size online detec-tion system depends on LDS sensors Figure 2 shows thesystem layoutThe system consists of six 2D-LDS and two 1D-LDS each of which is installed below the track to measure
Journal of Sensors 3
Wheelset
L4
L2
Support
Pedestal
Laser panel
precision clock signal
Data acquisition
port
IPC
Optical fiber To server
Data
softwareprocessing
Sensor fixture
All eight sensors
L3
2D-LDS
1D-LDS
2D-LDS
2D-LDS
L1
1kHz high-
Figure 2 Schematic diagram of sensors installation
both sides of the tread profile and diameter They can bedivided into two groups because the left side and right sideare mirrored Taking the left side LDS as an example the 2D-LDS L1 and L3 together with 1D-LDS L2 measure the wheeldiameter by three pointsrsquo principle The 2D-LDS L3 and L4measure the tread profile
Both the 2D and 1D laser sensors are based on lasertriangulationmeasurement principle and aremade up of laserdiode and a CCD linear sensor element The emitted laserforms a laser belt on the wheel tread and then the laser isreflected to the CCD linear inductive components Inside thesensor there is an integrated circuit unit to process the opticaldisplacement data and to obtain the tread and flange profilecoordinates Based on the principle that the output pointsof the LDS are originated from the laser emitting source inapplication the laser emitting source should be regarded asthe origin of the scanning coordinate The signal from allthe sensors is transmitted to IPC through data acquisitionport A digital IO card is utilized to produce precisely a1 kHz square signal in order to ensure all sensors to completethe task of acquiring the tread profile synchronously Thesensors begin to collect the data on the decline of the squarewave signal and then transmit the data to the IPC throughdata acquisition port for the subsequent processThe sampledsignal is analyzed in data processing software and finally the
condition of each wheel is decided There is also an opticalfiber in the IPC so that the condition of each wheel can betransmitted to distant depot office All the sensors are fixed byspecial designedmechanical sensor fixture so that the sensorscan be installed in certain space position The fixtures aresupported by the well manufactured mechanical structureThe whole system is finally connected with the ground by thepedestal
In addition the system also consists of several accessorialtypes of equipment that have not been shown in systemlayout figure which are wheel position sensor and automatictrain identification antennaThree wheel position sensors areinstalled beside the outside of the rail Along the rail the firstone is used to detect the arriving moment of the first wheelaxis of a train and hence to trigger subsequent hardwarefacilities the second one is used to trigger the scanning ofall laser sensors the last one is used to detect the leavingmoment of the last wheel axis of a train and hence to closethe subsequent hardware facilities
23 Static Tread Profile Calculation Principle Taking the leftside LDS as an example we define world coordinate frame(WCF) 119900-119909119910119911 and LDS scanning coordinates 119900(1)-119909(1)119910(1)119911(1)119900(2)-119909(2)119910(2)119911(2) 119900(3)-119909(3)119910(3)119911(3) and 119900(4)-119909(4)119910(4)119911(4) for L1
4 Journal of Sensors
o
y
WCF
x
z
y(1)
z(1)
o(1)
y(2)
z(2)
o(2)
x(2)
y(3)
o(3)x(3)
y(4)
o(4)
x(4)
Figure 3 Coordinates set
L2 L3 and L4 respectively As shown in Figure 3 thescanning coordinates take the origin of laser light as thecoordinate origin the equal angle bisector of the trianglelaser panel as 119910-axis and the direction in triangle laser panelorthogonal with 119910-axis as 119909-axis and finally use right-handrule to determine 119911-axisThe coordinates of the output pointsare in the scanning coordinate system of the sensor
The wheelset is assumed to be in the right position and toremain staticThe scanning coordinate of L3 and L4 is rotatedby two angles from the WCF namely angles 120572 and 120573 withrespect to 119909-axis and 119910-axis The tread profile is measuredby L3 and L4 and the scanning panels of L3 and L4 arethe same The tread profile can be measured in tread profilepanel constituted by L3 and L4 So as shown in Figure 4(a)only angle 120573 is considered when measuring tread profileBecause of angle 120573 the output line is distorted and needsto be transformed into physical profile According to theinstallation angles 1205733 and 1205734 the output data is transformedby
119906(3)
119899 =radic119909(3)2
119899 + 119910(3)2
119899 sin (120579 + 1205733)
= 119909(3)
119899 cos1205733 + 119910(3)
119899 sin1205733
V(3)119899 = radic119909(3)2
119899 + 119910(3)2
119899 cos (120579 + 1205733)
= 119910(3)
119899 cos1205733 minus 119909(3)
119899 sin1205733
(1)
119906(4)
119899 =radic119909(4)2
119899 + 119910(4)2
119899 sin (1205791015840 minus 1205734)
= 119909(4)
119899 cos1205732 minus 119910(4)
119899 sin1205732
V(4)119899 = radic119909(4)2
119899 + 119910(4)2
119899 cos (1205791015840 minus 1205734)
= 119910(4)
119899 cos1205732 + 119909(4)
119899 sin1205732
(2)
where (119909(3)119899 119910(3)119899 ) and (119909
(4)119899 119910(4)119899 ) are detected dot in LDS
scanning coordinates 119900(3)-119909(3)119910(3)119911(3) and 119900(4)-119909(4)119910(4)119911(4) 120579 isthe angle between 119910(3)-axis and the line that connects origin119900(3) and detected dot 1205791015840 is the angle between 119910(4)-axis andthe line that connects origin 119900(4) and detected dot (119906(3)119899 V
(3)119899 )
is the coordinate value of detected dot in the new coordinate119906(3)119900(3)V(3) and (119906(4)119899 V
(4)119899 ) is the coordinate value of detected
dot in the new coordinate 119906(4)119900(4)V(4) as wellAfter transformation the scanned lines in two different
coordinates 119906(3)119900(3)V(3) and 119906(4)119900(4)V(4) need to be mergedinto one coordinate We define the coordinate 119906(3)119900(3)V(3) astread profile base coordinate 119906119900V and move all the data from119906(4)119900(4)V(4) into 119906119900V by (3) as shown in Figure 4(b) Hence
119906119899 = 119906(4)
119899 + Δ119906
V119899 = V(4)119899 + ΔV(3)
Journal of Sensors 5
u
v
(a) (b)
v(3)
u(3)
v(4)
u(4)o(4)
y(3)
o(3)o(3)
x(3)
y(4)
1205733
1205734 120579120579998400
Figure 4 (a) Coordinate transformation of L4 and coordinate transformation of L3 (b) Moving all the data from 119906(4)119900(4)V(4) to 119906119900V
where (119906119899 V119899) is the dot in tread profile base coordinate 119906119900VΔ119906 and ΔV are the offset from 119906
(4)119900(4)V(4) to 119906119900V
As we know flange width flange height and wheeldiameter are determined by several base points and base lineThe output points from sensors are discrete so base points am and n are more likely not in one of the scanned pointsThe output points are also polluted with sensor noise whichinduced more detection uncertainty when we directly regardit as the base points Over here curve fitting is used forextracting the base point as well as the base lineThrough thismethod the coordinate value of base points can be preciselyextracted and the sensor noise can also be eliminated to someextent It is difficult to use a single curve to fit all the treaddue to the complexity of tread contour Therefore fittingdiscrete points of each base point within a certain range isapplied to improve the accuracy of the extracted base pointcoordinate value The common method of curve fitting isthe least square method [22] The least square method usesa given set of measured data to get the functional relation119891(119909 1198860 1198861 119886119899) between the variable 119909 and the variable 119910based on the principle of least squares Then the weightedsum of squaresrsquo value of the residual 119890119896 between the fittingfunction and the actual measured value at each point can beminimal which means 119865 in (4) is minimal
119865 =
119868
sum
119894=0
120596 (119909119894) (119891119894 minus 119910119894)2 (4)
where 120596(119909119894) ge 0 is the weight which reflects the notionthat the data (119909119894 119910119894) accounts for the proportion in theexperiment 119868 denotes the number of data points Accordingto the tread profile features and experimental researchfourth-order polynomial 119910 = sum4119894=0 119886119894119909
4minus119894 is selected to fit eachsubsection curve based on the least square method
With curve fitting technique four lines in total are fittedin order to extract the coordinate value of base points a mandn As shown in Figure 5 at first the inner side of thewheelhas no wear-out and deformation when there is wheel-railcontact so base line 119897 is fitted by selecting all the data pointsin the inner side of the wheelThe base point a is 70mm awayfrom the base line 119897 along 119906-axis Then the green line is fittedin order to extract base point a by selecting data points within
a certain range of base point aThe red line and yellow line arealso fitted by the same method in order to extract base pointsm and n respectively
After four lines are obtained the precise coordinate valueof all base points can be determined To this end the flangeheight and flange width are calculated as follows
119865119908 = 119906119897 minus 119906119898
119865ℎ = V119899 minus V119886(5)
where 119865119908 is flange width 119865ℎ is flange height 119906119897 is the 119906-axiscoordinate value of base line 119897 119906119898 is the 119906-axis coordinatevalue of base pointm V119899 is the V-axis coordinate value of basepoint n V119886 is the V-axis coordinate value of base point a
24 Static Wheel Diameter Calculation Principle Wheeldiameter is detected by 2D-L1 1D-L2 and 2D-L3 Each oneof the LDS measures one point in the circular wheel so thatthe wheel diameter can be determined by three points
The wheelset is assumed to be in the right position andto remain static The coordinates of the output points arein the scanning coordinate system of the sensor Similarto tread profile calculation the coordinate transformation
6 Journal of Sensors
o
y
WCF
x
z
v (1)
u(1)o(1)
y(2)
v(2)
o(2)
u(2)
u(3)o(3)
v (3)
x(4)
duoff
Figure 6 Scanning coordinates of 2D-L1 1D-L2 and 2D-L3 after coordinate transformation
y
z
o
Wheel
c3
c (x0 y0)
c1
c2 l1
l2
l3
1205722
12057211205723
P1 (y1 z1)
P2 (y2 z2)
P3 (y3 z3)lowast
lowast
lowast
(a)
a
o(2)
u(3)
o(3)
v (3)c3Fc
doff
(b)
Figure 7 Wheel diameter calculation principle in two dimensions (a) sight along the 119909-axis scanning coordinates of 2D-L1 1D-L2 and2D-L3 after transformation (b) sight in the 119906(3)119900(3)V(3) coordinate
was conducted and the scanning coordinates 119906(1)119900(1)V(1)119906(2)119900(2)V(2) and 119906(3)119900(3)V(3) for 2D-L1 1D-L2 and 2D-L3
respectively have been obtained Figure 6 shows the scanningcoordinates of 2D-L1 1D-L2 and 2D-L3 after coordinatetransformation Notice that 119906(2)119900(2)V(2) is still the same as119910(2)119900(2)119911(2) because of the installation position of 1D-L2
Figure 6 also shows the offset 119889off between the origin of thecoordinate 119906(3)119900(3)V(3) and laser scanning line of L2 in 119906(2)-axis Among three points the two points detected by 2D-L1and 2D-L3 are extracted from the 2D profiles The offset 119889offis the 119906(2)-axis coordinate value to extract the points in theflange circle from two-dimensional profile This offset 119889off isdetermined by sensor installation
Figure 7 shows the wheel diameter calculation princi-ple in two dimensions where (a) shows the principle that
three points determine a diameter in 119910119900119911 WCF and (b)shows extracting the point in the flange circle among two-dimensional profile and the final wheel diameter distancesubtraction by 119865119888 From Figure 7(a) the installation of eachLDS is modeled as three parameters in 119910119900119911 WCF whichare the position Pi(119910119894 119911119894) and angle 120572119894 They determinethe position of laser origin and the direction of detectionrespectively The angle 1205722 for 1D-L2 is designed as 1205872 Thepositions P1 and P3 are designed as symmetric with respectto the scanning line of 1D-L2 as well as the angles 1205721 and1205723 Even though many of the parameters are designed tobe equal for instance 1199111 = 1199113 the real parameters willvary after engineering implementation due to errors suchas installation error and manufacturing error Thus thisnine-parameter model is proposed for diameter calculation
Journal of Sensors 7
because it can describe all the possible errors The realinstallation parameters are obtained through calibration aslater described Moreover the distances 1198971 1198972 and 1198973 aredetected from three LDS sensors The three points c1 c2and c3 are in the flange of wheel detected by three sensorsrespectively The point c(1199100 1199110) is the origin of the detectedwheel which is calculated by three points c1 c2 and c3
According to Figures 6 and 7(a) the first information wecan get from the LDS sensors is the laser scanned distances1198971 1198972 and 1198973 1198972 is directly detected by 1D-L2 1198971 and 1198973 areextracted from the 2D profiles detected by 2D-L1 and 2D-L3 respectively To extract 1198971 and 1198973 we need to find thecorrect points in the two-dimensional tread profile As shownin Figures 6 and 7(b) the point that determines 1198971 and 1198973should be in the 119906-axis value of offset 119889off Similar to detectingtread profile we use the same curve fitting method to obtaina curve in the contour of the wheel in the 119906119900V coordinate thatis denoted by V = 1198913(119906) When the curve line is obtained1198973 = V3 = 1198913(119889off ) namely the V-axis value of curve 1198913(119906)
when 119906 = 119889off Similarly 1198971 is detected by 2D-LDS L1 usingthe same method as deciding 1198973
Once the laser scanned distances 1198971 1198972 and 1198973 aredetermined we get the three points c1 c2 and c3 in WCFcoordinate 119910119900119911 by
1199101198881
= 1199101 + 1198971 sin1205721
1199111198881
= 1199111 + 1198971 cos1205721
1199101198882
= 1199102 + 1198972 sin1205722
1199111198882
= 1199112 + 1198972 cos1205722
1199101198883
= 1199103 + 1198973 sin1205723
1199111198883
= 1199113 + 1198973 cos1205723
(6)
Based on three points c1 c2 and c3 the wheel center c(1199100 1199110)is determined by
1199100 =
(1199111198881
minus 1199111198883
) (11991021198881
minus 11991021198882
+ 11991121198881
minus 11991121198882
) minus (1199111198881
minus 1199111198882
) (11991021198881
minus 11991021198883
+ 11991121198881
minus 11991121198883
)
2 (1199101198881
minus 1199101198882
) (1199111198881
minus 1199111198883
) minus 2 (1199101198881
minus 1199101198883
) (1199111198881
minus 1199111198882
)
1199110 =
(1199101198881
minus 1199101198882
) (11991021198881
minus 11991021198883
+ 11991121198881
minus 11991121198883
) minus (1199101198881
minus 1199101198883
) (11991021198881
minus 11991021198882
+ 11991121198881
minus 11991121198882
)
2 (1199101198881
minus 1199101198882
) (1199111198881
minus 1199111198883
) minus 2 (1199101198881
minus 1199101198883
) (1199111198881
minus 1199111198882
)
(7)
and the wheel diameter119863119903 is determined by
119863119903 = 2 sdotradic(1199100)
2+ (1199110 minus 119911119888
2
)
2 (8)
From Figure 7(b) 119865119888 is the distance between points c3 anda along V-axis The wheel diameter detected by the previousthree points is somewhere in the contour circle governed bythe 1D-L2 only The point a is considered to be the diameterpoint of the wheel which is minus70mm away from the innerside of the wheel In order to obtain the final wheel diameterwe need to further subtract the distance 119865119888 from the wheeldiameter
119863 = 119863119903 minus 2119865119888 (9)
where119865119888 is the distance between point c3 and point a in V-axis(as shown in Figure 7(b)) namely 119865119888 = V119886 minus V119888
3
25 Dynamics Detection The calculation principles shownabove are in static case When the train passes dynam-ically multiscans can be obtained and the misalignmentphenomenon caused from wheel passing will occur
For tread profile detection ideally the laser light panel ofL3 and L4 is assumed to include the center of the measuredwheel In dynamics detection it is impossible to meet thatassumption for all measured wheels due to the moving ofwheel and the discrete sampling of LDS signal Basicallyif the laser light panel does not include the center of themeasured wheel the detected profile is horizontally stretched
along V-axis That will lead to the increase of detected flangeheight and flange width This phenomenon is called themisalignment between the laser panel and the detectiontarget [9]
Figure 8 shows the dynamics positions of thewheel centerand laser panel constituted by L3 and L4 in two-dimensionalWCF The wheel moves forward with a constant speed of V1198741 1198742 and 119874119894 are the center of wheel diameter circle underdifferent positions The laser panel has an installation angle1205723 with respect to 119910-axis which can be determined as 119911 =tan1205723 sdot 119910 in WCF The center points of wheel diameter circleare calculated by (7) 119889119894 denote the distance between 119894th wheelcenter point and the laser panel
Theoretically for every 119894th position of the wheel thedistance 119889119894 from the wheel center c(1199100
119894
1199110119894
) to the laser panelcan be determined by point to the distance formula as follows
When the distance 119889119894 equals zero the wheel center c(1199100119894
1199110119894
)
is in the laser panel where the flange height and flange widthhave no stretching On the other hand the bigger the distance119889119894 is the farther away the wheel center c(1199100
119894
1199110119894
) is from thelaser panel
It is worthmentioning that the LDSworks when the anglebetween laser light and detected surface is within a certainrange and the angle is influenced by laser wavelength surface
8 Journal of Sensors
y
z
Laser panel
Rail
Wheelv
Scanned section
O1 O2
d1 d22120579
120579
120579
1205723
Oi
di
L3 L4lowast
Figure 8 Dynamics position of the wheel center
smoothness surface material and so forth [23] It is assumedthat the angle 120579 (as shown in Figure 8) is the largest angleat which the LDS can still receive effective scan When thewheel is moving out of the detection range the LDS will beunable to scanThus the scanned sectionwill be the arcwith acentral angle of 2120579 and all the tread profiles and diameters arescanned from this section For most LDS sensors the angle 120579can reach up to 45∘ so the system can measure 90∘ arc of thewheel Correspondingly the maximum value of the distance119889119894 is 119877 sin 120579 where 119877 is the wheel radius
The misalignment phenomenon will bring about certainerror to the profile detection Among all the effective scanswe must select those scans where the induced error isacceptable In this paper the error induced in the tread profiledetection is analyzed in Section 3 As a result the error isdirectly proportional to the distance 119889119894 So we set up a certainthreshold 119870119901 When the distance 119889119894 lt 119870119901 the detectedtread profile can be regarded as useful profiles where the errorinduced by the misalignment phenomenon is negligible Thethreshold 119870119901 is firstly obtained through error analysis andalso is adjustable according to the field experiment Due tothe benefits from the high sampling frequency of the LDSsensors 119872 times of scans can be obtained for a wheelsetThen we can remove the bulky error first and performaverage operation to get the final wheel flange and wheelwidth as follows
119865119908119891
=
1
119872
119872
sum
119894=1
119865119908119894
119865ℎ119891
=
1
119872
119872
sum
119894=1
119865ℎ119894
(11)
where 119865119908119894
and 119865ℎ119894
are the flange width and flange height in119894th scan respectively 119865119908
119891
and 119865ℎ119891
are the final flange widthand flange height respectively The average operation herecan reduce the final error caused by Gaussian sensor noise
For wheel diameter detection the three points thatdetermine the wheel diameter are always in the contourcircle Thus the calculation results will not be influenced by
different wheel positions However 119865119888119894
in every 119894th scan willstill be stretched and bring about some error Similarly weselect a set of scans by comparing whether the distance 119889119894is smaller than a certain threshold 119870119889 or not When 119889119894 lt119870119889 the error induced in the detected 119865119888 is negligible Thetwo thresholds 119870119889 and 119870119901 might be different because ofthe different detection error requirements for tread profileand wheel diameter In this way 119873 times of scans can beobtained Then we can remove the bulky error first andperform average algorithm to get the final wheel diameter asfollows
119863119891 =1
119873
119873
sum
119894=1
119863119894 (12)
where 119863119894 is the wheel diameter in 119894th scan 119863119891 is the finalwheel diameter
26 Calibration The measuring and calculating of treadprofile and wheel diameter depend on many installationparameters Regarding tread profile calculation they are theangle 1205733 in (1) angle 1205734 in (2) and the offset Δ119906 and offsetΔV in (3) For wheel diameter they are the offset 119889off betweenthe origin of the coordinate 119906119900V and laser scanning line of L2in 119906(2)-axis the angles 1205721 1205722 and 1205723 and the positions P1P2 and P3 in (6) When the LDS are installed and fixed it isimpossible for those parameters to be the same with designedvalues because of the manufacture error of mechanical partsand installation accuracy So calibration is certainly needed
During the calibration process for tread profile detectiona standard wheel is placed on the rail over the detection sys-tem and then the offset and rotation angle of the coordinatetransformation matrix can be determined In terms of theangles 1205733 and 1205734 the calibrated accurate value is to makesure the inner and outer panels of the wheel are vertical Forthe offset Δ119906 the calibrated accurate value is to make surethe detected wheel hub thickness equals the standard wheelhub thickness and the offset ΔV is to make sure the scannedprofiles from two LDS coincide with each other
As for the calibration process for wheel diameter a setof new ground wheelsets is used The ground wheelset iswith different diameters that are 770mm 790mm 810mmand 840mm We set the minimization function 119891(119909) as thesquared summation of detected diameters subtracted by realdiameter That is
min 119891 (119909) =
119869
sum
119894=1
1003816100381610038161003816119863119894 minus 119863119903
1003816100381610038161003816
2 (13)
where 119863 is the detected diameter according to wheel diam-eter calibration principle 119863119903 is the real diameters 119909 =
[119889off 1205721 1205721 1205723 1199101 1199111 1199102 1199112 1199103 1199113] is the variables to be cali-brated 119869 denotes the number of ground wheelsets MATLABhas provided such tools to solve those optimization problemsOver here we use fmincon function to minimize the functionand the constraints in terms of the variables are also givenaccording to real physical ranges Finally the optimal valuesof the parameters can be obtained These values are assumedto be the real values that the implemented system has andhave been further put into use in system service
Journal of Sensors 9
3 Detection Error Analysis
In this section we consider four factors which are railvibration sensor noise misalignment and wheel inclinationcaused by wheel S-shape running and the differential ofdiameters
31 Wheel-Rail Vibration Wheel-rail vibration is the firstfactor that we considered In our system all the sensorsare well fixed by the mechanical support and mechanicalpedestal that has no direct contact with rail So the wheel-railvibrationwill not directly transmit to the sensors and insteadthe wheel-rail vibration has to transmit to the ground of thedepot and then transmit to the sensors through mechanicalsupport andmechanical pedestalThe vibration of the groundis on a lower level the maximum of acceleration is only04m2s [24] in Guangzhou metro depot and it is alsoattenuated by the mechanical pedestal We also measuredthe maximum of acceleration of mechanical support duringtrain passing which is only 02m2s So the change of theposition of the sensors due to the wheel-rail vibration in oursystemcanbeneglected Furthermore all the laser sensors arecapturing data simultaneously and the exposure time of theLDS is within 50 microseconds The vibration of the wheelwill not cause considerable movement within such a shorttime Overall the system is assumed to be reliable againstwheel-rail vibration
32 Misalignment As previously mentioned in Section 2Dynamics Detection if the laser light panel does not includethe center of the measured wheel the detected profile is hor-izontally stretched along V-axis This phenomenon is calledthe misalignment between the laser panel and the detectiontarget which will lead to the increase of the detected flangeheight and flange width Chen et al [10] derived a geometricmodel regarding howmany errors will be generated for flangeheight when wheel position varies The error 119890 of the flangeheight is
where 119877 is the wheel radius 119877119862 is the radius in the wheel rim119889 is the distance from the wheel center to the laser panel asdescribed in Section 2
On the basis of this geometric model when we know howmuch the error of the flange height is the errors of the flangewidth can be derived accordingly For different wear wheelsthe profiles aswell as the fitted line for lateral contact pointmare certainly different To illustrate the massiveness of errorshere we chose the same wheel where the fitted line for lateralcontact point m is V = 119891(119906) We obtain the inverse function119906 = 119892(V) and stretch it horizontally by a factor of (119865ℎ + 119890)119865ℎSo the stretched curve line is
119906 = 1198922 (V) = 119892(V119865ℎ
(119865ℎ + 119890)) (15)
Eventually the error of flange width is 120578 = 1198922(10)minus119865119908 where119865119908 is the original flange width
Error of flange heightError of flange width
0
01
02
03
04
05
06
07
08
Caus
ed er
ror (
mm
)
10 20 30 40 500d (mm)
Figure 9 The error of flange width and flange height with respectto various wheel positions
Theoretically from (14) and (15) we know that the smallerthe value of 119877 is the larger the error 119890 is So we chosethe largest standard wheelset with 119877 = 385mm and 119877119862 =399mm Figure 9 shows the error of flange height and flangewidth induced from misalignment in this case The distance119889 varies from 0mm to 50mmwith an interval of 1mm FromFigure 9 the error of flange height is lower than the error offlange width So we focus on the error of flange width here
In our system the sampling frequency of all LDS is 1 kHzand the maximum speed of the train in the depot is 36 kmhThemaximum of sampling step size along the railΔ119904 = 1ms times10ms = 10mmWhen we set the threshold119870119901 (as describedin Section 25) as 20mm the total measuring distance alongthe rail can be 58mm so that at least 119872 = 5 times ofefficient scans can be detected The corresponding errors areless than 01mm for flange width after taking the average ofthese 5 efficient scansThus the system can performdetectionnormally against themisalignment error benefitting from thehigh sampling frequency
33 Sensor Noise The LDS cannot be ideally accurate Themeasuring accuracy is influenced by temperature the rough-ness of the measured surface and so forth
In order to obtain the quantitative influence for profiledetection we built a 3D model in SolidWorks tools andextracted ideal sensor output points of standard inner andouter tread profiles In this model the standard wheel islocated in the position where the center of the wheel is inthe laser panel So the misalignment phenomenon will notaffect tread profile detection The wheel is in static positionso the simulated sensor output points are all from one scanMoreover the parameters that need to be calibrated areideally accurate To imitate the real situation Gaussian noiseis added to these coordinate valuesThemean of noise is zeroand the standard deviation is varied from 0 to 1mm with an
10 Journal of Sensors
X 03Y 01251
Flange widthFlange height
0
01
02
03
04
05
06
07Ca
used
erro
r (m
m)
02 04 06 08 10Noise level (mm)
Figure 10 The RMS error of flange height and flange width causedby different sensor noise level
interval of 01mm For each noise level 500 experiments arecarried out and the RMS error is calculated The RMS errorof flange height and flange width results caused by differentnoise level is shown in Figure 10 The caused error to flangeheight and flange width is approximately half of the sensornoise level This can be explained by the curve line fittingmethod that has taken more laser points into account andthus has reduced the random noise Because the flange heightis determined by two points the curve line fittingmethod hasat least reduced the randomerror into a quarter of the originalsensor noise
The 2D-LDS we chose is LJ-V7300 from KEYENCEwhich has a full-scale resolution of 01FS and a temper-ature drift of 001 FS∘C The detection range in 119910-axis is300 plusmn 145mm and in 119909-axis is 110mm to 240mm whichformed as a trapezoid The point in 119909-axis is fixed thus onlysensor noise in 119910-axis needs to be considered with full scaleof 290mm So accordingly the RMS error caused to theprofile coordinate noise in 119910-axis which is denoted by 120575 isless than 032mm which only leads to an error of 013mmboth to flange height and to flange width Taking dynamicsdetection effect into account the final error is reduced by120575119891 = 120575
radic5 = 0058mm with at least119873 = 5 times of efficientscans The error caused by sensor noise can be acceptable
Regarding the error of wheel diameter it can be theoreti-cally derived by the theorem of error propagation [25] Theresolution of each sensor is denoted by 1205751 1205752 and 1205753 Weobtain 120575119863 by taking differential of (6)ndash(9) as follows
120575119863 = plusmnradic(1205751
120597119863
1205971198971
)
2
+ (1205752
120597119863
1205971198972
)
2
+ (1205753
120597119863
1205971198973
)
2
(16)
We have chosen two 2D-LDS and one 1D-LDS to detect thewheel diameter and the two 2D-LDS are installed symmet-rically For systematic installation we have 1205751(1205971198631205971198971) =
1205753(1205971198631205971198973) Moreover the analytical function of particle
derivative will be too complex to derive So we consider aspecial case where
where the target wheel diameter is 119863 = 840mm and theorigin of the wheel is located in the origin of 119910119900119911WCF Morecalculation details can be found in the Appendix Finally wehave
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(18)
The 1D-LDS we chose is LK-G8085 from KEYENCE whichhas linearity of 005FS and a temperature drift of 001FS∘C So according to the full scale of 30mm the reso-lution of 1D-LDS 1205752 = 0018mm Based upon the findingthat the curve line fitting method has at least reduced therandom error into a quarter of the original sensor noise1205751 = 0075mm Finally 120575119863 is less than 0372mm Takingdynamics detection effect into account the final error 120575119863
119891
=
120575119863radic5 = 017mm The error caused by sensor noise can be
acceptable
34 Wheel Inclination Caused by Wheelset S-Shape RunningandDifferential ofWheel Diameter In engineering thewheelwill be inclined because of wheelset S-shape running and thedifferential of wheel diameter The wheelset S-shape runningis one kind of self-induced vibration due to the slope in thewheel trade When it is S-shape running the wheel panelwill have a certain angle with respect to 119910119900119911 panel in WCFdenoted by 120579119904 as shown in Figure 11(a) The differentialof wheel diameter in a wheelset is at different wear levelin the left and right wheel mainly induced from differentmassiveness of wear in the circuit of wheelset turning andunbalanced loading Similarly it will bring a certain angleabout the wheel panel with respect to the 119910119900119911 panel in WCFThe angle is denoted by 120579119889 as shown in Figure 11(b)
For wheel diameter detection because we only considerthe calculation in two dimensions an error will be generatedwhen we still regard the detected three points in a circle toactually be in an ellipse Considering the existence of angles120579119904 and 120579119889 we have the equation of ellipse as follows
1199102
(119877 sdot cos 120579119904)2+
1199112
1198772= 1
1199102
1198772+
1199112
(119877 sdot cos 120579119889)2= 1
(19)
Journal of Sensors 11
x
y
z
0
Ellipse wheel
Wheelset withS-shape running
120579s
(a)
x
y
z Ellipse wheel
Wheelset with differential of diameter
120579d
(b)
Figure 11 Mathematical illustration (a) Wheel S-shape running and (b) differential of wheel diameter
Similar towhenwe analyze sensor noise we consider a specialcase as (17) the origin of the target wheel is located in theorigin of 119910119900119911WCFThe real three points are
1198881(119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198882 (0 minus119877)
1198883(minus119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198881(119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
1198882 (0 minus119877 sdot cos 120579119889)
1198883(minus119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
(20)
Theoretically the larger the radius of the wheel is the biggerthe error is So we chose 119877 = 420mm and generated threepoints then using (7) we calculated the wheel diameter witherror Subtracting the real diameter we have the error withrespect to angle as shown in Figure 12 The effect of S-shaperunning caused angle has a relatively higher influence on thewheel diameter calculation
Based on the experience from Guangzhou Metro Cor-poration the differential of diameter in a wheelset shouldbe controlled under 2mm Considering the track gauge of1350mm the angle induced from the differential of diameter
S-shape runningWheel diameter differential
0
001
002
003
004
005
006
Caus
ed er
ror t
o di
amet
er (m
m)
01 02 03 04 050120579 (∘)
Figure 12 Wheel diameter errors
in a wheelset is less than 0001∘ thus the error can be ignoredAs for wheel S-shape running themaximum angle is 01∘ [26]when the speed of the train is under 36 kmhwhich will causean error not larger than 0005mm
4 Experimental Validation
41 System Implementation Theauthors previously proposedan online detection system using eight 2D-LDS [19] Thenew online detection system is installed in the same storageline of Guangzhou metro vehicle depot as the old systemso that comparison can be conducted In order to savefund only the left side namely half of the system has been
12 Journal of Sensors
(a) (b)
Figure 13 Field test (a) Standard wheel test and (b) real train test
Table 1 Standard wheelset detection the results of repeatedmeasurementsmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
implemented During the system implementation three-dimensional inclinometer and special rail gauge are used tocontrol the position of the mechanical support After thesystem is installed the calibration described in Section 2has been conducted to obtain the geometric parameters fortread profile calibration and diameter calculation As shownin Figure 13 the field test is carried out by a standard wheelsetand real train
42 Standard Wheelset The standard wheelset is a new pro-duced wheelset without any wear and diameter differentialThe manufacturing geometric size is as follows wheel diam-eter = 840mm flange height = 28mm and flange width =32mm One can also assume to have lower possibility of S-shape running because of zero external load The standardwheelset has been placed on the rail and passed through thedetection system This test has been carried out 6 times toverify both the detection and the repeatability of the systemComparing with the old system the results of this system areshown in Table 1
From Table 1 the mean values of the flange height andflange width detected by the old and the new system are very
close to each other which means the system error can beignored The standard deviation which also can be denotedas detection uncertainty of the new system measurement isslightly smaller than of the old system That may result fromthe lower effect frommisalignment as described in Section 3due to the higher sampling frequency that we used in the newsystem Detection uncertainty of not greater than 005mm intread profile measurement is acceptable for the engineeringrequirements As for wheel diameter detection the meanvalues are also close to each other The standard deviation ofthe new systemmeasurement is slightly higher than of the oldsystemThis may result from the replacement of 1D-LDS thathas brought about higher sensor noise to the middle pointamong three pointswithout curve fitting techniqueHoweverdetection uncertainty of less than 03mm is also acceptable inengineering
43 Real Train Detection Test Real train test also performs6 times of repeated detection to statistically evaluate theperformance of the system The train speed is controlledunder 36 kmh In the train we chose there are 4 new groundwheelsets in a car of the train Under the consideration thatthe ground new wheel is not out of roundness which hasan effect on the analysis results we selected the ground newwheel as our target wheel
Table 2 shows the mean and standard deviation value ofmeasurement The biggest differential value of mean flangeheight appears in 1 wheel and for mean flange width appearsin 3 wheel The difference does not exceed 015mm As forwheel diameter the biggest differential value 016mmappearsin 3 wheelThemean value of six times of repeated detectionis consistent with the standard wheelset test In terms ofstandard deviation the value is less than 01mm for flangewidth and flange height and 03mm for wheel diameterThe standard deviation of wheel diameter is relatively higherthan in standard wheelset test On the contrary the standarddeviation of flange width and flange height is relatively lowerthan in the old system That is also consistent with standard
Journal of Sensors 13
Table 2 Real train test the mean and standard deviation value of detected measurementmm
Wheelnumber
Mean flange height SD flange height Mean flange width SD flange width Mean wheeldiameter SD wheel diameter
Old New Old New Old New Old New Old New Old New1 2818 2803 0046 0060 2954 2943 0091 0062 80052 80150 0201 03012 2809 2811 0078 0040 2940 2929 0056 0028 80112 80096 0128 02863 2797 2791 0076 0033 2992 3006 0075 0056 80187 80166 0090 01794 2807 2805 0063 0053 2983 2988 0076 0088 80178 80201 0192 0282
Table 3 Real train test wheel 2 the result of repeated measure-mentmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
wheelset test The standard deviation of wheel diameter inreal train test is supposed to be higher than in the standardwheelset test because of several assumptions One factor isthe higher possibility of S-shape running because of heavyaxial load On the other hand the wheelset that is in service isalso more polluted with rust than standard wheelset causingmore detection uncertainty However the standard deviationfrom real train test also does not exceed 03mm which isconsistent with standard wheelset test This may result fromthe lower train speed during the test which leads to lowerpossibility of S-shape running Meanwhile the rusty wheelcontour is also not in a massive stage Tables 3 and 4 show theresult of repeated measurement for wheels numbers 2 and 3respectively In each detection the results remain the sameand no gross error appears
Overall detection uncertainties for tread profile andwheel diameter are less than 01mmand 03mm respectivelyThe results show that the detection system has a highaccuracy which can meet the requirements of maintenanceoperation
5 Conclusion
This paper based on LDS proposed a novel on-track detec-tion system of the wheel size using only six 2D-LDS and two1D-LDS Errors induced bywheel-rail vibration sensor noisemisalignment S-shape running and wheelset differential arealso analyzed After the system is implemented real dataexperiments including standard wheel test and real traindetection test were performed It turns out that the detectionuncertainty of flange width and height is 01mm and wheeldiameter 03mm which can meet the requirements of main-tenanceThis system can be further used for different types ofrailway transportation which provides a new solution for thewheel size detection technology
To provide more benefits the target wheel diameter is 119863 =
840mm and the origin of the wheel is located in the originof 119910119900119911WCF as shown in Figure 14 In this special case therelevant geometric values are 1198881(minus19802mm minus19802mm)1198882(0mm 420mm) 1198883(19802mm minus19802mm) 1198971 = 280mm1198972 = 180mm and 1198973 = 280mm
According to (8) and (9) we get the particle derivative asfollows
120597119863
1205971198971
=
120597119863
1205971199100
1205971199100
1205971198971
+
120597119863
1205971199110
1205971199110
1205971198971
120597119863
1205971198972
=
120597119863
1205971199100
1205971199100
1205971198972
+
120597119863
1205971199110
1205971199110
1205971198972
+
120597119863
1205971199111198882
1205971199111198882
1205971198972
(A2)
14 Journal of Sensors
2D-L1
1D-L2
2D-L3
y
z
o
45∘45∘ c1l1
l2
l3
c2
c3 lowast
lowast
lowast
Figure 14 A special case
Taking the derivative of diameter 119863 with respect to 1199100 1199110and 119911119888
2
according to (8) and substituting (1199100 1199110) = (0 0) and1199111198882
= 180mm we have
120597119863
1205971199100
=
21199100
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199110
=
2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199111198882
=
minus2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
= 2
(A3)
Furthermore based upon (7) we get
1205971199100
1205971198971
=
1205971199100
1205971199101198881
1205971199101198881
1205971198971
+
1205971199100
1205971199111198881
1205971199111198881
1205971198971
1205971199110
1205971198971
=
1205971199110
1205971199101198881
1205971199101198881
1205971198971
+
1205971199110
1205971199111198881
1205971199111198881
1205971198971
1205971199100
1205971198972
=
1205971199100
1205971199111198882
1205971199111198882
1205971198972
1205971199110
1205971198972
=
1205971199110
1205971199111198882
1205971199111198882
1205971198972
1205971199100
1205971198973
=
1205971199100
1205971199101198883
1205971199101198883
1205971198973
+
1205971199100
1205971199111198883
1205971199111198883
1205971198973
1205971199110
1205971198973
=
1205971199110
1205971199101198883
1205971199101198883
1205971198973
+
1205971199110
1205971199111198883
1205971199111198883
1205971198973
(A4)
When calculating particle derivative of (1199100 1199110) with respectto three points 1198881 1198882 and 1198883 in WCF we assume that allparameters are with the geometric values in this special case
Then we substitute the ideal geometric values of this variableand we obtain
1205971199100
1205971199101198881
= 05
1205971199100
1205971199111198881
= 05
1205971199110
1205971199101198881
= minus12071
1205971199110
1205971199111198881
= minus12071
1205971199100
1205971199111198882
= 0
1205971199110
1205971199111198882
= 34142
1205971199100
1205971199101198883
= 05
1205971199100
1205971199111198883
= minus05
1205971199110
1205971199101198883
= 12071
1205971199110
1205971199111198883
= minus12071
1205971199101198881
1205971198971
=
1
radic2
1205971199111198881
1205971198971
=
1
radic2
1205971199111198882
1205971198972
= minus1
1205971199101198883
1205971198973
= minus
1
radic2
1205971199111198883
1205971198973
=
1
radic2
(A5)
Finally substituting (A5) into (A4) and then substituting(A4) and (A3) into (A2) we have
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(A6)
Competing Interests
The authors declare that they have no competing interests
Journal of Sensors 15
Acknowledgments
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
Figure 2 Schematic diagram of sensors installation
both sides of the tread profile and diameter They can bedivided into two groups because the left side and right sideare mirrored Taking the left side LDS as an example the 2D-LDS L1 and L3 together with 1D-LDS L2 measure the wheeldiameter by three pointsrsquo principle The 2D-LDS L3 and L4measure the tread profile
Both the 2D and 1D laser sensors are based on lasertriangulationmeasurement principle and aremade up of laserdiode and a CCD linear sensor element The emitted laserforms a laser belt on the wheel tread and then the laser isreflected to the CCD linear inductive components Inside thesensor there is an integrated circuit unit to process the opticaldisplacement data and to obtain the tread and flange profilecoordinates Based on the principle that the output pointsof the LDS are originated from the laser emitting source inapplication the laser emitting source should be regarded asthe origin of the scanning coordinate The signal from allthe sensors is transmitted to IPC through data acquisitionport A digital IO card is utilized to produce precisely a1 kHz square signal in order to ensure all sensors to completethe task of acquiring the tread profile synchronously Thesensors begin to collect the data on the decline of the squarewave signal and then transmit the data to the IPC throughdata acquisition port for the subsequent processThe sampledsignal is analyzed in data processing software and finally the
condition of each wheel is decided There is also an opticalfiber in the IPC so that the condition of each wheel can betransmitted to distant depot office All the sensors are fixed byspecial designedmechanical sensor fixture so that the sensorscan be installed in certain space position The fixtures aresupported by the well manufactured mechanical structureThe whole system is finally connected with the ground by thepedestal
In addition the system also consists of several accessorialtypes of equipment that have not been shown in systemlayout figure which are wheel position sensor and automatictrain identification antennaThree wheel position sensors areinstalled beside the outside of the rail Along the rail the firstone is used to detect the arriving moment of the first wheelaxis of a train and hence to trigger subsequent hardwarefacilities the second one is used to trigger the scanning ofall laser sensors the last one is used to detect the leavingmoment of the last wheel axis of a train and hence to closethe subsequent hardware facilities
23 Static Tread Profile Calculation Principle Taking the leftside LDS as an example we define world coordinate frame(WCF) 119900-119909119910119911 and LDS scanning coordinates 119900(1)-119909(1)119910(1)119911(1)119900(2)-119909(2)119910(2)119911(2) 119900(3)-119909(3)119910(3)119911(3) and 119900(4)-119909(4)119910(4)119911(4) for L1
4 Journal of Sensors
o
y
WCF
x
z
y(1)
z(1)
o(1)
y(2)
z(2)
o(2)
x(2)
y(3)
o(3)x(3)
y(4)
o(4)
x(4)
Figure 3 Coordinates set
L2 L3 and L4 respectively As shown in Figure 3 thescanning coordinates take the origin of laser light as thecoordinate origin the equal angle bisector of the trianglelaser panel as 119910-axis and the direction in triangle laser panelorthogonal with 119910-axis as 119909-axis and finally use right-handrule to determine 119911-axisThe coordinates of the output pointsare in the scanning coordinate system of the sensor
The wheelset is assumed to be in the right position and toremain staticThe scanning coordinate of L3 and L4 is rotatedby two angles from the WCF namely angles 120572 and 120573 withrespect to 119909-axis and 119910-axis The tread profile is measuredby L3 and L4 and the scanning panels of L3 and L4 arethe same The tread profile can be measured in tread profilepanel constituted by L3 and L4 So as shown in Figure 4(a)only angle 120573 is considered when measuring tread profileBecause of angle 120573 the output line is distorted and needsto be transformed into physical profile According to theinstallation angles 1205733 and 1205734 the output data is transformedby
119906(3)
119899 =radic119909(3)2
119899 + 119910(3)2
119899 sin (120579 + 1205733)
= 119909(3)
119899 cos1205733 + 119910(3)
119899 sin1205733
V(3)119899 = radic119909(3)2
119899 + 119910(3)2
119899 cos (120579 + 1205733)
= 119910(3)
119899 cos1205733 minus 119909(3)
119899 sin1205733
(1)
119906(4)
119899 =radic119909(4)2
119899 + 119910(4)2
119899 sin (1205791015840 minus 1205734)
= 119909(4)
119899 cos1205732 minus 119910(4)
119899 sin1205732
V(4)119899 = radic119909(4)2
119899 + 119910(4)2
119899 cos (1205791015840 minus 1205734)
= 119910(4)
119899 cos1205732 + 119909(4)
119899 sin1205732
(2)
where (119909(3)119899 119910(3)119899 ) and (119909
(4)119899 119910(4)119899 ) are detected dot in LDS
scanning coordinates 119900(3)-119909(3)119910(3)119911(3) and 119900(4)-119909(4)119910(4)119911(4) 120579 isthe angle between 119910(3)-axis and the line that connects origin119900(3) and detected dot 1205791015840 is the angle between 119910(4)-axis andthe line that connects origin 119900(4) and detected dot (119906(3)119899 V
(3)119899 )
is the coordinate value of detected dot in the new coordinate119906(3)119900(3)V(3) and (119906(4)119899 V
(4)119899 ) is the coordinate value of detected
dot in the new coordinate 119906(4)119900(4)V(4) as wellAfter transformation the scanned lines in two different
coordinates 119906(3)119900(3)V(3) and 119906(4)119900(4)V(4) need to be mergedinto one coordinate We define the coordinate 119906(3)119900(3)V(3) astread profile base coordinate 119906119900V and move all the data from119906(4)119900(4)V(4) into 119906119900V by (3) as shown in Figure 4(b) Hence
119906119899 = 119906(4)
119899 + Δ119906
V119899 = V(4)119899 + ΔV(3)
Journal of Sensors 5
u
v
(a) (b)
v(3)
u(3)
v(4)
u(4)o(4)
y(3)
o(3)o(3)
x(3)
y(4)
1205733
1205734 120579120579998400
Figure 4 (a) Coordinate transformation of L4 and coordinate transformation of L3 (b) Moving all the data from 119906(4)119900(4)V(4) to 119906119900V
where (119906119899 V119899) is the dot in tread profile base coordinate 119906119900VΔ119906 and ΔV are the offset from 119906
(4)119900(4)V(4) to 119906119900V
As we know flange width flange height and wheeldiameter are determined by several base points and base lineThe output points from sensors are discrete so base points am and n are more likely not in one of the scanned pointsThe output points are also polluted with sensor noise whichinduced more detection uncertainty when we directly regardit as the base points Over here curve fitting is used forextracting the base point as well as the base lineThrough thismethod the coordinate value of base points can be preciselyextracted and the sensor noise can also be eliminated to someextent It is difficult to use a single curve to fit all the treaddue to the complexity of tread contour Therefore fittingdiscrete points of each base point within a certain range isapplied to improve the accuracy of the extracted base pointcoordinate value The common method of curve fitting isthe least square method [22] The least square method usesa given set of measured data to get the functional relation119891(119909 1198860 1198861 119886119899) between the variable 119909 and the variable 119910based on the principle of least squares Then the weightedsum of squaresrsquo value of the residual 119890119896 between the fittingfunction and the actual measured value at each point can beminimal which means 119865 in (4) is minimal
119865 =
119868
sum
119894=0
120596 (119909119894) (119891119894 minus 119910119894)2 (4)
where 120596(119909119894) ge 0 is the weight which reflects the notionthat the data (119909119894 119910119894) accounts for the proportion in theexperiment 119868 denotes the number of data points Accordingto the tread profile features and experimental researchfourth-order polynomial 119910 = sum4119894=0 119886119894119909
4minus119894 is selected to fit eachsubsection curve based on the least square method
With curve fitting technique four lines in total are fittedin order to extract the coordinate value of base points a mandn As shown in Figure 5 at first the inner side of thewheelhas no wear-out and deformation when there is wheel-railcontact so base line 119897 is fitted by selecting all the data pointsin the inner side of the wheelThe base point a is 70mm awayfrom the base line 119897 along 119906-axis Then the green line is fittedin order to extract base point a by selecting data points within
a certain range of base point aThe red line and yellow line arealso fitted by the same method in order to extract base pointsm and n respectively
After four lines are obtained the precise coordinate valueof all base points can be determined To this end the flangeheight and flange width are calculated as follows
119865119908 = 119906119897 minus 119906119898
119865ℎ = V119899 minus V119886(5)
where 119865119908 is flange width 119865ℎ is flange height 119906119897 is the 119906-axiscoordinate value of base line 119897 119906119898 is the 119906-axis coordinatevalue of base pointm V119899 is the V-axis coordinate value of basepoint n V119886 is the V-axis coordinate value of base point a
24 Static Wheel Diameter Calculation Principle Wheeldiameter is detected by 2D-L1 1D-L2 and 2D-L3 Each oneof the LDS measures one point in the circular wheel so thatthe wheel diameter can be determined by three points
The wheelset is assumed to be in the right position andto remain static The coordinates of the output points arein the scanning coordinate system of the sensor Similarto tread profile calculation the coordinate transformation
6 Journal of Sensors
o
y
WCF
x
z
v (1)
u(1)o(1)
y(2)
v(2)
o(2)
u(2)
u(3)o(3)
v (3)
x(4)
duoff
Figure 6 Scanning coordinates of 2D-L1 1D-L2 and 2D-L3 after coordinate transformation
y
z
o
Wheel
c3
c (x0 y0)
c1
c2 l1
l2
l3
1205722
12057211205723
P1 (y1 z1)
P2 (y2 z2)
P3 (y3 z3)lowast
lowast
lowast
(a)
a
o(2)
u(3)
o(3)
v (3)c3Fc
doff
(b)
Figure 7 Wheel diameter calculation principle in two dimensions (a) sight along the 119909-axis scanning coordinates of 2D-L1 1D-L2 and2D-L3 after transformation (b) sight in the 119906(3)119900(3)V(3) coordinate
was conducted and the scanning coordinates 119906(1)119900(1)V(1)119906(2)119900(2)V(2) and 119906(3)119900(3)V(3) for 2D-L1 1D-L2 and 2D-L3
respectively have been obtained Figure 6 shows the scanningcoordinates of 2D-L1 1D-L2 and 2D-L3 after coordinatetransformation Notice that 119906(2)119900(2)V(2) is still the same as119910(2)119900(2)119911(2) because of the installation position of 1D-L2
Figure 6 also shows the offset 119889off between the origin of thecoordinate 119906(3)119900(3)V(3) and laser scanning line of L2 in 119906(2)-axis Among three points the two points detected by 2D-L1and 2D-L3 are extracted from the 2D profiles The offset 119889offis the 119906(2)-axis coordinate value to extract the points in theflange circle from two-dimensional profile This offset 119889off isdetermined by sensor installation
Figure 7 shows the wheel diameter calculation princi-ple in two dimensions where (a) shows the principle that
three points determine a diameter in 119910119900119911 WCF and (b)shows extracting the point in the flange circle among two-dimensional profile and the final wheel diameter distancesubtraction by 119865119888 From Figure 7(a) the installation of eachLDS is modeled as three parameters in 119910119900119911 WCF whichare the position Pi(119910119894 119911119894) and angle 120572119894 They determinethe position of laser origin and the direction of detectionrespectively The angle 1205722 for 1D-L2 is designed as 1205872 Thepositions P1 and P3 are designed as symmetric with respectto the scanning line of 1D-L2 as well as the angles 1205721 and1205723 Even though many of the parameters are designed tobe equal for instance 1199111 = 1199113 the real parameters willvary after engineering implementation due to errors suchas installation error and manufacturing error Thus thisnine-parameter model is proposed for diameter calculation
Journal of Sensors 7
because it can describe all the possible errors The realinstallation parameters are obtained through calibration aslater described Moreover the distances 1198971 1198972 and 1198973 aredetected from three LDS sensors The three points c1 c2and c3 are in the flange of wheel detected by three sensorsrespectively The point c(1199100 1199110) is the origin of the detectedwheel which is calculated by three points c1 c2 and c3
According to Figures 6 and 7(a) the first information wecan get from the LDS sensors is the laser scanned distances1198971 1198972 and 1198973 1198972 is directly detected by 1D-L2 1198971 and 1198973 areextracted from the 2D profiles detected by 2D-L1 and 2D-L3 respectively To extract 1198971 and 1198973 we need to find thecorrect points in the two-dimensional tread profile As shownin Figures 6 and 7(b) the point that determines 1198971 and 1198973should be in the 119906-axis value of offset 119889off Similar to detectingtread profile we use the same curve fitting method to obtaina curve in the contour of the wheel in the 119906119900V coordinate thatis denoted by V = 1198913(119906) When the curve line is obtained1198973 = V3 = 1198913(119889off ) namely the V-axis value of curve 1198913(119906)
when 119906 = 119889off Similarly 1198971 is detected by 2D-LDS L1 usingthe same method as deciding 1198973
Once the laser scanned distances 1198971 1198972 and 1198973 aredetermined we get the three points c1 c2 and c3 in WCFcoordinate 119910119900119911 by
1199101198881
= 1199101 + 1198971 sin1205721
1199111198881
= 1199111 + 1198971 cos1205721
1199101198882
= 1199102 + 1198972 sin1205722
1199111198882
= 1199112 + 1198972 cos1205722
1199101198883
= 1199103 + 1198973 sin1205723
1199111198883
= 1199113 + 1198973 cos1205723
(6)
Based on three points c1 c2 and c3 the wheel center c(1199100 1199110)is determined by
1199100 =
(1199111198881
minus 1199111198883
) (11991021198881
minus 11991021198882
+ 11991121198881
minus 11991121198882
) minus (1199111198881
minus 1199111198882
) (11991021198881
minus 11991021198883
+ 11991121198881
minus 11991121198883
)
2 (1199101198881
minus 1199101198882
) (1199111198881
minus 1199111198883
) minus 2 (1199101198881
minus 1199101198883
) (1199111198881
minus 1199111198882
)
1199110 =
(1199101198881
minus 1199101198882
) (11991021198881
minus 11991021198883
+ 11991121198881
minus 11991121198883
) minus (1199101198881
minus 1199101198883
) (11991021198881
minus 11991021198882
+ 11991121198881
minus 11991121198882
)
2 (1199101198881
minus 1199101198882
) (1199111198881
minus 1199111198883
) minus 2 (1199101198881
minus 1199101198883
) (1199111198881
minus 1199111198882
)
(7)
and the wheel diameter119863119903 is determined by
119863119903 = 2 sdotradic(1199100)
2+ (1199110 minus 119911119888
2
)
2 (8)
From Figure 7(b) 119865119888 is the distance between points c3 anda along V-axis The wheel diameter detected by the previousthree points is somewhere in the contour circle governed bythe 1D-L2 only The point a is considered to be the diameterpoint of the wheel which is minus70mm away from the innerside of the wheel In order to obtain the final wheel diameterwe need to further subtract the distance 119865119888 from the wheeldiameter
119863 = 119863119903 minus 2119865119888 (9)
where119865119888 is the distance between point c3 and point a in V-axis(as shown in Figure 7(b)) namely 119865119888 = V119886 minus V119888
3
25 Dynamics Detection The calculation principles shownabove are in static case When the train passes dynam-ically multiscans can be obtained and the misalignmentphenomenon caused from wheel passing will occur
For tread profile detection ideally the laser light panel ofL3 and L4 is assumed to include the center of the measuredwheel In dynamics detection it is impossible to meet thatassumption for all measured wheels due to the moving ofwheel and the discrete sampling of LDS signal Basicallyif the laser light panel does not include the center of themeasured wheel the detected profile is horizontally stretched
along V-axis That will lead to the increase of detected flangeheight and flange width This phenomenon is called themisalignment between the laser panel and the detectiontarget [9]
Figure 8 shows the dynamics positions of thewheel centerand laser panel constituted by L3 and L4 in two-dimensionalWCF The wheel moves forward with a constant speed of V1198741 1198742 and 119874119894 are the center of wheel diameter circle underdifferent positions The laser panel has an installation angle1205723 with respect to 119910-axis which can be determined as 119911 =tan1205723 sdot 119910 in WCF The center points of wheel diameter circleare calculated by (7) 119889119894 denote the distance between 119894th wheelcenter point and the laser panel
Theoretically for every 119894th position of the wheel thedistance 119889119894 from the wheel center c(1199100
119894
1199110119894
) to the laser panelcan be determined by point to the distance formula as follows
When the distance 119889119894 equals zero the wheel center c(1199100119894
1199110119894
)
is in the laser panel where the flange height and flange widthhave no stretching On the other hand the bigger the distance119889119894 is the farther away the wheel center c(1199100
119894
1199110119894
) is from thelaser panel
It is worthmentioning that the LDSworks when the anglebetween laser light and detected surface is within a certainrange and the angle is influenced by laser wavelength surface
8 Journal of Sensors
y
z
Laser panel
Rail
Wheelv
Scanned section
O1 O2
d1 d22120579
120579
120579
1205723
Oi
di
L3 L4lowast
Figure 8 Dynamics position of the wheel center
smoothness surface material and so forth [23] It is assumedthat the angle 120579 (as shown in Figure 8) is the largest angleat which the LDS can still receive effective scan When thewheel is moving out of the detection range the LDS will beunable to scanThus the scanned sectionwill be the arcwith acentral angle of 2120579 and all the tread profiles and diameters arescanned from this section For most LDS sensors the angle 120579can reach up to 45∘ so the system can measure 90∘ arc of thewheel Correspondingly the maximum value of the distance119889119894 is 119877 sin 120579 where 119877 is the wheel radius
The misalignment phenomenon will bring about certainerror to the profile detection Among all the effective scanswe must select those scans where the induced error isacceptable In this paper the error induced in the tread profiledetection is analyzed in Section 3 As a result the error isdirectly proportional to the distance 119889119894 So we set up a certainthreshold 119870119901 When the distance 119889119894 lt 119870119901 the detectedtread profile can be regarded as useful profiles where the errorinduced by the misalignment phenomenon is negligible Thethreshold 119870119901 is firstly obtained through error analysis andalso is adjustable according to the field experiment Due tothe benefits from the high sampling frequency of the LDSsensors 119872 times of scans can be obtained for a wheelsetThen we can remove the bulky error first and performaverage operation to get the final wheel flange and wheelwidth as follows
119865119908119891
=
1
119872
119872
sum
119894=1
119865119908119894
119865ℎ119891
=
1
119872
119872
sum
119894=1
119865ℎ119894
(11)
where 119865119908119894
and 119865ℎ119894
are the flange width and flange height in119894th scan respectively 119865119908
119891
and 119865ℎ119891
are the final flange widthand flange height respectively The average operation herecan reduce the final error caused by Gaussian sensor noise
For wheel diameter detection the three points thatdetermine the wheel diameter are always in the contourcircle Thus the calculation results will not be influenced by
different wheel positions However 119865119888119894
in every 119894th scan willstill be stretched and bring about some error Similarly weselect a set of scans by comparing whether the distance 119889119894is smaller than a certain threshold 119870119889 or not When 119889119894 lt119870119889 the error induced in the detected 119865119888 is negligible Thetwo thresholds 119870119889 and 119870119901 might be different because ofthe different detection error requirements for tread profileand wheel diameter In this way 119873 times of scans can beobtained Then we can remove the bulky error first andperform average algorithm to get the final wheel diameter asfollows
119863119891 =1
119873
119873
sum
119894=1
119863119894 (12)
where 119863119894 is the wheel diameter in 119894th scan 119863119891 is the finalwheel diameter
26 Calibration The measuring and calculating of treadprofile and wheel diameter depend on many installationparameters Regarding tread profile calculation they are theangle 1205733 in (1) angle 1205734 in (2) and the offset Δ119906 and offsetΔV in (3) For wheel diameter they are the offset 119889off betweenthe origin of the coordinate 119906119900V and laser scanning line of L2in 119906(2)-axis the angles 1205721 1205722 and 1205723 and the positions P1P2 and P3 in (6) When the LDS are installed and fixed it isimpossible for those parameters to be the same with designedvalues because of the manufacture error of mechanical partsand installation accuracy So calibration is certainly needed
During the calibration process for tread profile detectiona standard wheel is placed on the rail over the detection sys-tem and then the offset and rotation angle of the coordinatetransformation matrix can be determined In terms of theangles 1205733 and 1205734 the calibrated accurate value is to makesure the inner and outer panels of the wheel are vertical Forthe offset Δ119906 the calibrated accurate value is to make surethe detected wheel hub thickness equals the standard wheelhub thickness and the offset ΔV is to make sure the scannedprofiles from two LDS coincide with each other
As for the calibration process for wheel diameter a setof new ground wheelsets is used The ground wheelset iswith different diameters that are 770mm 790mm 810mmand 840mm We set the minimization function 119891(119909) as thesquared summation of detected diameters subtracted by realdiameter That is
min 119891 (119909) =
119869
sum
119894=1
1003816100381610038161003816119863119894 minus 119863119903
1003816100381610038161003816
2 (13)
where 119863 is the detected diameter according to wheel diam-eter calibration principle 119863119903 is the real diameters 119909 =
[119889off 1205721 1205721 1205723 1199101 1199111 1199102 1199112 1199103 1199113] is the variables to be cali-brated 119869 denotes the number of ground wheelsets MATLABhas provided such tools to solve those optimization problemsOver here we use fmincon function to minimize the functionand the constraints in terms of the variables are also givenaccording to real physical ranges Finally the optimal valuesof the parameters can be obtained These values are assumedto be the real values that the implemented system has andhave been further put into use in system service
Journal of Sensors 9
3 Detection Error Analysis
In this section we consider four factors which are railvibration sensor noise misalignment and wheel inclinationcaused by wheel S-shape running and the differential ofdiameters
31 Wheel-Rail Vibration Wheel-rail vibration is the firstfactor that we considered In our system all the sensorsare well fixed by the mechanical support and mechanicalpedestal that has no direct contact with rail So the wheel-railvibrationwill not directly transmit to the sensors and insteadthe wheel-rail vibration has to transmit to the ground of thedepot and then transmit to the sensors through mechanicalsupport andmechanical pedestalThe vibration of the groundis on a lower level the maximum of acceleration is only04m2s [24] in Guangzhou metro depot and it is alsoattenuated by the mechanical pedestal We also measuredthe maximum of acceleration of mechanical support duringtrain passing which is only 02m2s So the change of theposition of the sensors due to the wheel-rail vibration in oursystemcanbeneglected Furthermore all the laser sensors arecapturing data simultaneously and the exposure time of theLDS is within 50 microseconds The vibration of the wheelwill not cause considerable movement within such a shorttime Overall the system is assumed to be reliable againstwheel-rail vibration
32 Misalignment As previously mentioned in Section 2Dynamics Detection if the laser light panel does not includethe center of the measured wheel the detected profile is hor-izontally stretched along V-axis This phenomenon is calledthe misalignment between the laser panel and the detectiontarget which will lead to the increase of the detected flangeheight and flange width Chen et al [10] derived a geometricmodel regarding howmany errors will be generated for flangeheight when wheel position varies The error 119890 of the flangeheight is
where 119877 is the wheel radius 119877119862 is the radius in the wheel rim119889 is the distance from the wheel center to the laser panel asdescribed in Section 2
On the basis of this geometric model when we know howmuch the error of the flange height is the errors of the flangewidth can be derived accordingly For different wear wheelsthe profiles aswell as the fitted line for lateral contact pointmare certainly different To illustrate the massiveness of errorshere we chose the same wheel where the fitted line for lateralcontact point m is V = 119891(119906) We obtain the inverse function119906 = 119892(V) and stretch it horizontally by a factor of (119865ℎ + 119890)119865ℎSo the stretched curve line is
119906 = 1198922 (V) = 119892(V119865ℎ
(119865ℎ + 119890)) (15)
Eventually the error of flange width is 120578 = 1198922(10)minus119865119908 where119865119908 is the original flange width
Error of flange heightError of flange width
0
01
02
03
04
05
06
07
08
Caus
ed er
ror (
mm
)
10 20 30 40 500d (mm)
Figure 9 The error of flange width and flange height with respectto various wheel positions
Theoretically from (14) and (15) we know that the smallerthe value of 119877 is the larger the error 119890 is So we chosethe largest standard wheelset with 119877 = 385mm and 119877119862 =399mm Figure 9 shows the error of flange height and flangewidth induced from misalignment in this case The distance119889 varies from 0mm to 50mmwith an interval of 1mm FromFigure 9 the error of flange height is lower than the error offlange width So we focus on the error of flange width here
In our system the sampling frequency of all LDS is 1 kHzand the maximum speed of the train in the depot is 36 kmhThemaximum of sampling step size along the railΔ119904 = 1ms times10ms = 10mmWhen we set the threshold119870119901 (as describedin Section 25) as 20mm the total measuring distance alongthe rail can be 58mm so that at least 119872 = 5 times ofefficient scans can be detected The corresponding errors areless than 01mm for flange width after taking the average ofthese 5 efficient scansThus the system can performdetectionnormally against themisalignment error benefitting from thehigh sampling frequency
33 Sensor Noise The LDS cannot be ideally accurate Themeasuring accuracy is influenced by temperature the rough-ness of the measured surface and so forth
In order to obtain the quantitative influence for profiledetection we built a 3D model in SolidWorks tools andextracted ideal sensor output points of standard inner andouter tread profiles In this model the standard wheel islocated in the position where the center of the wheel is inthe laser panel So the misalignment phenomenon will notaffect tread profile detection The wheel is in static positionso the simulated sensor output points are all from one scanMoreover the parameters that need to be calibrated areideally accurate To imitate the real situation Gaussian noiseis added to these coordinate valuesThemean of noise is zeroand the standard deviation is varied from 0 to 1mm with an
10 Journal of Sensors
X 03Y 01251
Flange widthFlange height
0
01
02
03
04
05
06
07Ca
used
erro
r (m
m)
02 04 06 08 10Noise level (mm)
Figure 10 The RMS error of flange height and flange width causedby different sensor noise level
interval of 01mm For each noise level 500 experiments arecarried out and the RMS error is calculated The RMS errorof flange height and flange width results caused by differentnoise level is shown in Figure 10 The caused error to flangeheight and flange width is approximately half of the sensornoise level This can be explained by the curve line fittingmethod that has taken more laser points into account andthus has reduced the random noise Because the flange heightis determined by two points the curve line fittingmethod hasat least reduced the randomerror into a quarter of the originalsensor noise
The 2D-LDS we chose is LJ-V7300 from KEYENCEwhich has a full-scale resolution of 01FS and a temper-ature drift of 001 FS∘C The detection range in 119910-axis is300 plusmn 145mm and in 119909-axis is 110mm to 240mm whichformed as a trapezoid The point in 119909-axis is fixed thus onlysensor noise in 119910-axis needs to be considered with full scaleof 290mm So accordingly the RMS error caused to theprofile coordinate noise in 119910-axis which is denoted by 120575 isless than 032mm which only leads to an error of 013mmboth to flange height and to flange width Taking dynamicsdetection effect into account the final error is reduced by120575119891 = 120575
radic5 = 0058mm with at least119873 = 5 times of efficientscans The error caused by sensor noise can be acceptable
Regarding the error of wheel diameter it can be theoreti-cally derived by the theorem of error propagation [25] Theresolution of each sensor is denoted by 1205751 1205752 and 1205753 Weobtain 120575119863 by taking differential of (6)ndash(9) as follows
120575119863 = plusmnradic(1205751
120597119863
1205971198971
)
2
+ (1205752
120597119863
1205971198972
)
2
+ (1205753
120597119863
1205971198973
)
2
(16)
We have chosen two 2D-LDS and one 1D-LDS to detect thewheel diameter and the two 2D-LDS are installed symmet-rically For systematic installation we have 1205751(1205971198631205971198971) =
1205753(1205971198631205971198973) Moreover the analytical function of particle
derivative will be too complex to derive So we consider aspecial case where
where the target wheel diameter is 119863 = 840mm and theorigin of the wheel is located in the origin of 119910119900119911WCF Morecalculation details can be found in the Appendix Finally wehave
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(18)
The 1D-LDS we chose is LK-G8085 from KEYENCE whichhas linearity of 005FS and a temperature drift of 001FS∘C So according to the full scale of 30mm the reso-lution of 1D-LDS 1205752 = 0018mm Based upon the findingthat the curve line fitting method has at least reduced therandom error into a quarter of the original sensor noise1205751 = 0075mm Finally 120575119863 is less than 0372mm Takingdynamics detection effect into account the final error 120575119863
119891
=
120575119863radic5 = 017mm The error caused by sensor noise can be
acceptable
34 Wheel Inclination Caused by Wheelset S-Shape RunningandDifferential ofWheel Diameter In engineering thewheelwill be inclined because of wheelset S-shape running and thedifferential of wheel diameter The wheelset S-shape runningis one kind of self-induced vibration due to the slope in thewheel trade When it is S-shape running the wheel panelwill have a certain angle with respect to 119910119900119911 panel in WCFdenoted by 120579119904 as shown in Figure 11(a) The differentialof wheel diameter in a wheelset is at different wear levelin the left and right wheel mainly induced from differentmassiveness of wear in the circuit of wheelset turning andunbalanced loading Similarly it will bring a certain angleabout the wheel panel with respect to the 119910119900119911 panel in WCFThe angle is denoted by 120579119889 as shown in Figure 11(b)
For wheel diameter detection because we only considerthe calculation in two dimensions an error will be generatedwhen we still regard the detected three points in a circle toactually be in an ellipse Considering the existence of angles120579119904 and 120579119889 we have the equation of ellipse as follows
1199102
(119877 sdot cos 120579119904)2+
1199112
1198772= 1
1199102
1198772+
1199112
(119877 sdot cos 120579119889)2= 1
(19)
Journal of Sensors 11
x
y
z
0
Ellipse wheel
Wheelset withS-shape running
120579s
(a)
x
y
z Ellipse wheel
Wheelset with differential of diameter
120579d
(b)
Figure 11 Mathematical illustration (a) Wheel S-shape running and (b) differential of wheel diameter
Similar towhenwe analyze sensor noise we consider a specialcase as (17) the origin of the target wheel is located in theorigin of 119910119900119911WCFThe real three points are
1198881(119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198882 (0 minus119877)
1198883(minus119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198881(119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
1198882 (0 minus119877 sdot cos 120579119889)
1198883(minus119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
(20)
Theoretically the larger the radius of the wheel is the biggerthe error is So we chose 119877 = 420mm and generated threepoints then using (7) we calculated the wheel diameter witherror Subtracting the real diameter we have the error withrespect to angle as shown in Figure 12 The effect of S-shaperunning caused angle has a relatively higher influence on thewheel diameter calculation
Based on the experience from Guangzhou Metro Cor-poration the differential of diameter in a wheelset shouldbe controlled under 2mm Considering the track gauge of1350mm the angle induced from the differential of diameter
S-shape runningWheel diameter differential
0
001
002
003
004
005
006
Caus
ed er
ror t
o di
amet
er (m
m)
01 02 03 04 050120579 (∘)
Figure 12 Wheel diameter errors
in a wheelset is less than 0001∘ thus the error can be ignoredAs for wheel S-shape running themaximum angle is 01∘ [26]when the speed of the train is under 36 kmhwhich will causean error not larger than 0005mm
4 Experimental Validation
41 System Implementation Theauthors previously proposedan online detection system using eight 2D-LDS [19] Thenew online detection system is installed in the same storageline of Guangzhou metro vehicle depot as the old systemso that comparison can be conducted In order to savefund only the left side namely half of the system has been
12 Journal of Sensors
(a) (b)
Figure 13 Field test (a) Standard wheel test and (b) real train test
Table 1 Standard wheelset detection the results of repeatedmeasurementsmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
implemented During the system implementation three-dimensional inclinometer and special rail gauge are used tocontrol the position of the mechanical support After thesystem is installed the calibration described in Section 2has been conducted to obtain the geometric parameters fortread profile calibration and diameter calculation As shownin Figure 13 the field test is carried out by a standard wheelsetand real train
42 Standard Wheelset The standard wheelset is a new pro-duced wheelset without any wear and diameter differentialThe manufacturing geometric size is as follows wheel diam-eter = 840mm flange height = 28mm and flange width =32mm One can also assume to have lower possibility of S-shape running because of zero external load The standardwheelset has been placed on the rail and passed through thedetection system This test has been carried out 6 times toverify both the detection and the repeatability of the systemComparing with the old system the results of this system areshown in Table 1
From Table 1 the mean values of the flange height andflange width detected by the old and the new system are very
close to each other which means the system error can beignored The standard deviation which also can be denotedas detection uncertainty of the new system measurement isslightly smaller than of the old system That may result fromthe lower effect frommisalignment as described in Section 3due to the higher sampling frequency that we used in the newsystem Detection uncertainty of not greater than 005mm intread profile measurement is acceptable for the engineeringrequirements As for wheel diameter detection the meanvalues are also close to each other The standard deviation ofthe new systemmeasurement is slightly higher than of the oldsystemThis may result from the replacement of 1D-LDS thathas brought about higher sensor noise to the middle pointamong three pointswithout curve fitting techniqueHoweverdetection uncertainty of less than 03mm is also acceptable inengineering
43 Real Train Detection Test Real train test also performs6 times of repeated detection to statistically evaluate theperformance of the system The train speed is controlledunder 36 kmh In the train we chose there are 4 new groundwheelsets in a car of the train Under the consideration thatthe ground new wheel is not out of roundness which hasan effect on the analysis results we selected the ground newwheel as our target wheel
Table 2 shows the mean and standard deviation value ofmeasurement The biggest differential value of mean flangeheight appears in 1 wheel and for mean flange width appearsin 3 wheel The difference does not exceed 015mm As forwheel diameter the biggest differential value 016mmappearsin 3 wheelThemean value of six times of repeated detectionis consistent with the standard wheelset test In terms ofstandard deviation the value is less than 01mm for flangewidth and flange height and 03mm for wheel diameterThe standard deviation of wheel diameter is relatively higherthan in standard wheelset test On the contrary the standarddeviation of flange width and flange height is relatively lowerthan in the old system That is also consistent with standard
Journal of Sensors 13
Table 2 Real train test the mean and standard deviation value of detected measurementmm
Wheelnumber
Mean flange height SD flange height Mean flange width SD flange width Mean wheeldiameter SD wheel diameter
Old New Old New Old New Old New Old New Old New1 2818 2803 0046 0060 2954 2943 0091 0062 80052 80150 0201 03012 2809 2811 0078 0040 2940 2929 0056 0028 80112 80096 0128 02863 2797 2791 0076 0033 2992 3006 0075 0056 80187 80166 0090 01794 2807 2805 0063 0053 2983 2988 0076 0088 80178 80201 0192 0282
Table 3 Real train test wheel 2 the result of repeated measure-mentmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
wheelset test The standard deviation of wheel diameter inreal train test is supposed to be higher than in the standardwheelset test because of several assumptions One factor isthe higher possibility of S-shape running because of heavyaxial load On the other hand the wheelset that is in service isalso more polluted with rust than standard wheelset causingmore detection uncertainty However the standard deviationfrom real train test also does not exceed 03mm which isconsistent with standard wheelset test This may result fromthe lower train speed during the test which leads to lowerpossibility of S-shape running Meanwhile the rusty wheelcontour is also not in a massive stage Tables 3 and 4 show theresult of repeated measurement for wheels numbers 2 and 3respectively In each detection the results remain the sameand no gross error appears
Overall detection uncertainties for tread profile andwheel diameter are less than 01mmand 03mm respectivelyThe results show that the detection system has a highaccuracy which can meet the requirements of maintenanceoperation
5 Conclusion
This paper based on LDS proposed a novel on-track detec-tion system of the wheel size using only six 2D-LDS and two1D-LDS Errors induced bywheel-rail vibration sensor noisemisalignment S-shape running and wheelset differential arealso analyzed After the system is implemented real dataexperiments including standard wheel test and real traindetection test were performed It turns out that the detectionuncertainty of flange width and height is 01mm and wheeldiameter 03mm which can meet the requirements of main-tenanceThis system can be further used for different types ofrailway transportation which provides a new solution for thewheel size detection technology
To provide more benefits the target wheel diameter is 119863 =
840mm and the origin of the wheel is located in the originof 119910119900119911WCF as shown in Figure 14 In this special case therelevant geometric values are 1198881(minus19802mm minus19802mm)1198882(0mm 420mm) 1198883(19802mm minus19802mm) 1198971 = 280mm1198972 = 180mm and 1198973 = 280mm
According to (8) and (9) we get the particle derivative asfollows
120597119863
1205971198971
=
120597119863
1205971199100
1205971199100
1205971198971
+
120597119863
1205971199110
1205971199110
1205971198971
120597119863
1205971198972
=
120597119863
1205971199100
1205971199100
1205971198972
+
120597119863
1205971199110
1205971199110
1205971198972
+
120597119863
1205971199111198882
1205971199111198882
1205971198972
(A2)
14 Journal of Sensors
2D-L1
1D-L2
2D-L3
y
z
o
45∘45∘ c1l1
l2
l3
c2
c3 lowast
lowast
lowast
Figure 14 A special case
Taking the derivative of diameter 119863 with respect to 1199100 1199110and 119911119888
2
according to (8) and substituting (1199100 1199110) = (0 0) and1199111198882
= 180mm we have
120597119863
1205971199100
=
21199100
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199110
=
2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199111198882
=
minus2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
= 2
(A3)
Furthermore based upon (7) we get
1205971199100
1205971198971
=
1205971199100
1205971199101198881
1205971199101198881
1205971198971
+
1205971199100
1205971199111198881
1205971199111198881
1205971198971
1205971199110
1205971198971
=
1205971199110
1205971199101198881
1205971199101198881
1205971198971
+
1205971199110
1205971199111198881
1205971199111198881
1205971198971
1205971199100
1205971198972
=
1205971199100
1205971199111198882
1205971199111198882
1205971198972
1205971199110
1205971198972
=
1205971199110
1205971199111198882
1205971199111198882
1205971198972
1205971199100
1205971198973
=
1205971199100
1205971199101198883
1205971199101198883
1205971198973
+
1205971199100
1205971199111198883
1205971199111198883
1205971198973
1205971199110
1205971198973
=
1205971199110
1205971199101198883
1205971199101198883
1205971198973
+
1205971199110
1205971199111198883
1205971199111198883
1205971198973
(A4)
When calculating particle derivative of (1199100 1199110) with respectto three points 1198881 1198882 and 1198883 in WCF we assume that allparameters are with the geometric values in this special case
Then we substitute the ideal geometric values of this variableand we obtain
1205971199100
1205971199101198881
= 05
1205971199100
1205971199111198881
= 05
1205971199110
1205971199101198881
= minus12071
1205971199110
1205971199111198881
= minus12071
1205971199100
1205971199111198882
= 0
1205971199110
1205971199111198882
= 34142
1205971199100
1205971199101198883
= 05
1205971199100
1205971199111198883
= minus05
1205971199110
1205971199101198883
= 12071
1205971199110
1205971199111198883
= minus12071
1205971199101198881
1205971198971
=
1
radic2
1205971199111198881
1205971198971
=
1
radic2
1205971199111198882
1205971198972
= minus1
1205971199101198883
1205971198973
= minus
1
radic2
1205971199111198883
1205971198973
=
1
radic2
(A5)
Finally substituting (A5) into (A4) and then substituting(A4) and (A3) into (A2) we have
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(A6)
Competing Interests
The authors declare that they have no competing interests
Journal of Sensors 15
Acknowledgments
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
L2 L3 and L4 respectively As shown in Figure 3 thescanning coordinates take the origin of laser light as thecoordinate origin the equal angle bisector of the trianglelaser panel as 119910-axis and the direction in triangle laser panelorthogonal with 119910-axis as 119909-axis and finally use right-handrule to determine 119911-axisThe coordinates of the output pointsare in the scanning coordinate system of the sensor
The wheelset is assumed to be in the right position and toremain staticThe scanning coordinate of L3 and L4 is rotatedby two angles from the WCF namely angles 120572 and 120573 withrespect to 119909-axis and 119910-axis The tread profile is measuredby L3 and L4 and the scanning panels of L3 and L4 arethe same The tread profile can be measured in tread profilepanel constituted by L3 and L4 So as shown in Figure 4(a)only angle 120573 is considered when measuring tread profileBecause of angle 120573 the output line is distorted and needsto be transformed into physical profile According to theinstallation angles 1205733 and 1205734 the output data is transformedby
119906(3)
119899 =radic119909(3)2
119899 + 119910(3)2
119899 sin (120579 + 1205733)
= 119909(3)
119899 cos1205733 + 119910(3)
119899 sin1205733
V(3)119899 = radic119909(3)2
119899 + 119910(3)2
119899 cos (120579 + 1205733)
= 119910(3)
119899 cos1205733 minus 119909(3)
119899 sin1205733
(1)
119906(4)
119899 =radic119909(4)2
119899 + 119910(4)2
119899 sin (1205791015840 minus 1205734)
= 119909(4)
119899 cos1205732 minus 119910(4)
119899 sin1205732
V(4)119899 = radic119909(4)2
119899 + 119910(4)2
119899 cos (1205791015840 minus 1205734)
= 119910(4)
119899 cos1205732 + 119909(4)
119899 sin1205732
(2)
where (119909(3)119899 119910(3)119899 ) and (119909
(4)119899 119910(4)119899 ) are detected dot in LDS
scanning coordinates 119900(3)-119909(3)119910(3)119911(3) and 119900(4)-119909(4)119910(4)119911(4) 120579 isthe angle between 119910(3)-axis and the line that connects origin119900(3) and detected dot 1205791015840 is the angle between 119910(4)-axis andthe line that connects origin 119900(4) and detected dot (119906(3)119899 V
(3)119899 )
is the coordinate value of detected dot in the new coordinate119906(3)119900(3)V(3) and (119906(4)119899 V
(4)119899 ) is the coordinate value of detected
dot in the new coordinate 119906(4)119900(4)V(4) as wellAfter transformation the scanned lines in two different
coordinates 119906(3)119900(3)V(3) and 119906(4)119900(4)V(4) need to be mergedinto one coordinate We define the coordinate 119906(3)119900(3)V(3) astread profile base coordinate 119906119900V and move all the data from119906(4)119900(4)V(4) into 119906119900V by (3) as shown in Figure 4(b) Hence
119906119899 = 119906(4)
119899 + Δ119906
V119899 = V(4)119899 + ΔV(3)
Journal of Sensors 5
u
v
(a) (b)
v(3)
u(3)
v(4)
u(4)o(4)
y(3)
o(3)o(3)
x(3)
y(4)
1205733
1205734 120579120579998400
Figure 4 (a) Coordinate transformation of L4 and coordinate transformation of L3 (b) Moving all the data from 119906(4)119900(4)V(4) to 119906119900V
where (119906119899 V119899) is the dot in tread profile base coordinate 119906119900VΔ119906 and ΔV are the offset from 119906
(4)119900(4)V(4) to 119906119900V
As we know flange width flange height and wheeldiameter are determined by several base points and base lineThe output points from sensors are discrete so base points am and n are more likely not in one of the scanned pointsThe output points are also polluted with sensor noise whichinduced more detection uncertainty when we directly regardit as the base points Over here curve fitting is used forextracting the base point as well as the base lineThrough thismethod the coordinate value of base points can be preciselyextracted and the sensor noise can also be eliminated to someextent It is difficult to use a single curve to fit all the treaddue to the complexity of tread contour Therefore fittingdiscrete points of each base point within a certain range isapplied to improve the accuracy of the extracted base pointcoordinate value The common method of curve fitting isthe least square method [22] The least square method usesa given set of measured data to get the functional relation119891(119909 1198860 1198861 119886119899) between the variable 119909 and the variable 119910based on the principle of least squares Then the weightedsum of squaresrsquo value of the residual 119890119896 between the fittingfunction and the actual measured value at each point can beminimal which means 119865 in (4) is minimal
119865 =
119868
sum
119894=0
120596 (119909119894) (119891119894 minus 119910119894)2 (4)
where 120596(119909119894) ge 0 is the weight which reflects the notionthat the data (119909119894 119910119894) accounts for the proportion in theexperiment 119868 denotes the number of data points Accordingto the tread profile features and experimental researchfourth-order polynomial 119910 = sum4119894=0 119886119894119909
4minus119894 is selected to fit eachsubsection curve based on the least square method
With curve fitting technique four lines in total are fittedin order to extract the coordinate value of base points a mandn As shown in Figure 5 at first the inner side of thewheelhas no wear-out and deformation when there is wheel-railcontact so base line 119897 is fitted by selecting all the data pointsin the inner side of the wheelThe base point a is 70mm awayfrom the base line 119897 along 119906-axis Then the green line is fittedin order to extract base point a by selecting data points within
a certain range of base point aThe red line and yellow line arealso fitted by the same method in order to extract base pointsm and n respectively
After four lines are obtained the precise coordinate valueof all base points can be determined To this end the flangeheight and flange width are calculated as follows
119865119908 = 119906119897 minus 119906119898
119865ℎ = V119899 minus V119886(5)
where 119865119908 is flange width 119865ℎ is flange height 119906119897 is the 119906-axiscoordinate value of base line 119897 119906119898 is the 119906-axis coordinatevalue of base pointm V119899 is the V-axis coordinate value of basepoint n V119886 is the V-axis coordinate value of base point a
24 Static Wheel Diameter Calculation Principle Wheeldiameter is detected by 2D-L1 1D-L2 and 2D-L3 Each oneof the LDS measures one point in the circular wheel so thatthe wheel diameter can be determined by three points
The wheelset is assumed to be in the right position andto remain static The coordinates of the output points arein the scanning coordinate system of the sensor Similarto tread profile calculation the coordinate transformation
6 Journal of Sensors
o
y
WCF
x
z
v (1)
u(1)o(1)
y(2)
v(2)
o(2)
u(2)
u(3)o(3)
v (3)
x(4)
duoff
Figure 6 Scanning coordinates of 2D-L1 1D-L2 and 2D-L3 after coordinate transformation
y
z
o
Wheel
c3
c (x0 y0)
c1
c2 l1
l2
l3
1205722
12057211205723
P1 (y1 z1)
P2 (y2 z2)
P3 (y3 z3)lowast
lowast
lowast
(a)
a
o(2)
u(3)
o(3)
v (3)c3Fc
doff
(b)
Figure 7 Wheel diameter calculation principle in two dimensions (a) sight along the 119909-axis scanning coordinates of 2D-L1 1D-L2 and2D-L3 after transformation (b) sight in the 119906(3)119900(3)V(3) coordinate
was conducted and the scanning coordinates 119906(1)119900(1)V(1)119906(2)119900(2)V(2) and 119906(3)119900(3)V(3) for 2D-L1 1D-L2 and 2D-L3
respectively have been obtained Figure 6 shows the scanningcoordinates of 2D-L1 1D-L2 and 2D-L3 after coordinatetransformation Notice that 119906(2)119900(2)V(2) is still the same as119910(2)119900(2)119911(2) because of the installation position of 1D-L2
Figure 6 also shows the offset 119889off between the origin of thecoordinate 119906(3)119900(3)V(3) and laser scanning line of L2 in 119906(2)-axis Among three points the two points detected by 2D-L1and 2D-L3 are extracted from the 2D profiles The offset 119889offis the 119906(2)-axis coordinate value to extract the points in theflange circle from two-dimensional profile This offset 119889off isdetermined by sensor installation
Figure 7 shows the wheel diameter calculation princi-ple in two dimensions where (a) shows the principle that
three points determine a diameter in 119910119900119911 WCF and (b)shows extracting the point in the flange circle among two-dimensional profile and the final wheel diameter distancesubtraction by 119865119888 From Figure 7(a) the installation of eachLDS is modeled as three parameters in 119910119900119911 WCF whichare the position Pi(119910119894 119911119894) and angle 120572119894 They determinethe position of laser origin and the direction of detectionrespectively The angle 1205722 for 1D-L2 is designed as 1205872 Thepositions P1 and P3 are designed as symmetric with respectto the scanning line of 1D-L2 as well as the angles 1205721 and1205723 Even though many of the parameters are designed tobe equal for instance 1199111 = 1199113 the real parameters willvary after engineering implementation due to errors suchas installation error and manufacturing error Thus thisnine-parameter model is proposed for diameter calculation
Journal of Sensors 7
because it can describe all the possible errors The realinstallation parameters are obtained through calibration aslater described Moreover the distances 1198971 1198972 and 1198973 aredetected from three LDS sensors The three points c1 c2and c3 are in the flange of wheel detected by three sensorsrespectively The point c(1199100 1199110) is the origin of the detectedwheel which is calculated by three points c1 c2 and c3
According to Figures 6 and 7(a) the first information wecan get from the LDS sensors is the laser scanned distances1198971 1198972 and 1198973 1198972 is directly detected by 1D-L2 1198971 and 1198973 areextracted from the 2D profiles detected by 2D-L1 and 2D-L3 respectively To extract 1198971 and 1198973 we need to find thecorrect points in the two-dimensional tread profile As shownin Figures 6 and 7(b) the point that determines 1198971 and 1198973should be in the 119906-axis value of offset 119889off Similar to detectingtread profile we use the same curve fitting method to obtaina curve in the contour of the wheel in the 119906119900V coordinate thatis denoted by V = 1198913(119906) When the curve line is obtained1198973 = V3 = 1198913(119889off ) namely the V-axis value of curve 1198913(119906)
when 119906 = 119889off Similarly 1198971 is detected by 2D-LDS L1 usingthe same method as deciding 1198973
Once the laser scanned distances 1198971 1198972 and 1198973 aredetermined we get the three points c1 c2 and c3 in WCFcoordinate 119910119900119911 by
1199101198881
= 1199101 + 1198971 sin1205721
1199111198881
= 1199111 + 1198971 cos1205721
1199101198882
= 1199102 + 1198972 sin1205722
1199111198882
= 1199112 + 1198972 cos1205722
1199101198883
= 1199103 + 1198973 sin1205723
1199111198883
= 1199113 + 1198973 cos1205723
(6)
Based on three points c1 c2 and c3 the wheel center c(1199100 1199110)is determined by
1199100 =
(1199111198881
minus 1199111198883
) (11991021198881
minus 11991021198882
+ 11991121198881
minus 11991121198882
) minus (1199111198881
minus 1199111198882
) (11991021198881
minus 11991021198883
+ 11991121198881
minus 11991121198883
)
2 (1199101198881
minus 1199101198882
) (1199111198881
minus 1199111198883
) minus 2 (1199101198881
minus 1199101198883
) (1199111198881
minus 1199111198882
)
1199110 =
(1199101198881
minus 1199101198882
) (11991021198881
minus 11991021198883
+ 11991121198881
minus 11991121198883
) minus (1199101198881
minus 1199101198883
) (11991021198881
minus 11991021198882
+ 11991121198881
minus 11991121198882
)
2 (1199101198881
minus 1199101198882
) (1199111198881
minus 1199111198883
) minus 2 (1199101198881
minus 1199101198883
) (1199111198881
minus 1199111198882
)
(7)
and the wheel diameter119863119903 is determined by
119863119903 = 2 sdotradic(1199100)
2+ (1199110 minus 119911119888
2
)
2 (8)
From Figure 7(b) 119865119888 is the distance between points c3 anda along V-axis The wheel diameter detected by the previousthree points is somewhere in the contour circle governed bythe 1D-L2 only The point a is considered to be the diameterpoint of the wheel which is minus70mm away from the innerside of the wheel In order to obtain the final wheel diameterwe need to further subtract the distance 119865119888 from the wheeldiameter
119863 = 119863119903 minus 2119865119888 (9)
where119865119888 is the distance between point c3 and point a in V-axis(as shown in Figure 7(b)) namely 119865119888 = V119886 minus V119888
3
25 Dynamics Detection The calculation principles shownabove are in static case When the train passes dynam-ically multiscans can be obtained and the misalignmentphenomenon caused from wheel passing will occur
For tread profile detection ideally the laser light panel ofL3 and L4 is assumed to include the center of the measuredwheel In dynamics detection it is impossible to meet thatassumption for all measured wheels due to the moving ofwheel and the discrete sampling of LDS signal Basicallyif the laser light panel does not include the center of themeasured wheel the detected profile is horizontally stretched
along V-axis That will lead to the increase of detected flangeheight and flange width This phenomenon is called themisalignment between the laser panel and the detectiontarget [9]
Figure 8 shows the dynamics positions of thewheel centerand laser panel constituted by L3 and L4 in two-dimensionalWCF The wheel moves forward with a constant speed of V1198741 1198742 and 119874119894 are the center of wheel diameter circle underdifferent positions The laser panel has an installation angle1205723 with respect to 119910-axis which can be determined as 119911 =tan1205723 sdot 119910 in WCF The center points of wheel diameter circleare calculated by (7) 119889119894 denote the distance between 119894th wheelcenter point and the laser panel
Theoretically for every 119894th position of the wheel thedistance 119889119894 from the wheel center c(1199100
119894
1199110119894
) to the laser panelcan be determined by point to the distance formula as follows
When the distance 119889119894 equals zero the wheel center c(1199100119894
1199110119894
)
is in the laser panel where the flange height and flange widthhave no stretching On the other hand the bigger the distance119889119894 is the farther away the wheel center c(1199100
119894
1199110119894
) is from thelaser panel
It is worthmentioning that the LDSworks when the anglebetween laser light and detected surface is within a certainrange and the angle is influenced by laser wavelength surface
8 Journal of Sensors
y
z
Laser panel
Rail
Wheelv
Scanned section
O1 O2
d1 d22120579
120579
120579
1205723
Oi
di
L3 L4lowast
Figure 8 Dynamics position of the wheel center
smoothness surface material and so forth [23] It is assumedthat the angle 120579 (as shown in Figure 8) is the largest angleat which the LDS can still receive effective scan When thewheel is moving out of the detection range the LDS will beunable to scanThus the scanned sectionwill be the arcwith acentral angle of 2120579 and all the tread profiles and diameters arescanned from this section For most LDS sensors the angle 120579can reach up to 45∘ so the system can measure 90∘ arc of thewheel Correspondingly the maximum value of the distance119889119894 is 119877 sin 120579 where 119877 is the wheel radius
The misalignment phenomenon will bring about certainerror to the profile detection Among all the effective scanswe must select those scans where the induced error isacceptable In this paper the error induced in the tread profiledetection is analyzed in Section 3 As a result the error isdirectly proportional to the distance 119889119894 So we set up a certainthreshold 119870119901 When the distance 119889119894 lt 119870119901 the detectedtread profile can be regarded as useful profiles where the errorinduced by the misalignment phenomenon is negligible Thethreshold 119870119901 is firstly obtained through error analysis andalso is adjustable according to the field experiment Due tothe benefits from the high sampling frequency of the LDSsensors 119872 times of scans can be obtained for a wheelsetThen we can remove the bulky error first and performaverage operation to get the final wheel flange and wheelwidth as follows
119865119908119891
=
1
119872
119872
sum
119894=1
119865119908119894
119865ℎ119891
=
1
119872
119872
sum
119894=1
119865ℎ119894
(11)
where 119865119908119894
and 119865ℎ119894
are the flange width and flange height in119894th scan respectively 119865119908
119891
and 119865ℎ119891
are the final flange widthand flange height respectively The average operation herecan reduce the final error caused by Gaussian sensor noise
For wheel diameter detection the three points thatdetermine the wheel diameter are always in the contourcircle Thus the calculation results will not be influenced by
different wheel positions However 119865119888119894
in every 119894th scan willstill be stretched and bring about some error Similarly weselect a set of scans by comparing whether the distance 119889119894is smaller than a certain threshold 119870119889 or not When 119889119894 lt119870119889 the error induced in the detected 119865119888 is negligible Thetwo thresholds 119870119889 and 119870119901 might be different because ofthe different detection error requirements for tread profileand wheel diameter In this way 119873 times of scans can beobtained Then we can remove the bulky error first andperform average algorithm to get the final wheel diameter asfollows
119863119891 =1
119873
119873
sum
119894=1
119863119894 (12)
where 119863119894 is the wheel diameter in 119894th scan 119863119891 is the finalwheel diameter
26 Calibration The measuring and calculating of treadprofile and wheel diameter depend on many installationparameters Regarding tread profile calculation they are theangle 1205733 in (1) angle 1205734 in (2) and the offset Δ119906 and offsetΔV in (3) For wheel diameter they are the offset 119889off betweenthe origin of the coordinate 119906119900V and laser scanning line of L2in 119906(2)-axis the angles 1205721 1205722 and 1205723 and the positions P1P2 and P3 in (6) When the LDS are installed and fixed it isimpossible for those parameters to be the same with designedvalues because of the manufacture error of mechanical partsand installation accuracy So calibration is certainly needed
During the calibration process for tread profile detectiona standard wheel is placed on the rail over the detection sys-tem and then the offset and rotation angle of the coordinatetransformation matrix can be determined In terms of theangles 1205733 and 1205734 the calibrated accurate value is to makesure the inner and outer panels of the wheel are vertical Forthe offset Δ119906 the calibrated accurate value is to make surethe detected wheel hub thickness equals the standard wheelhub thickness and the offset ΔV is to make sure the scannedprofiles from two LDS coincide with each other
As for the calibration process for wheel diameter a setof new ground wheelsets is used The ground wheelset iswith different diameters that are 770mm 790mm 810mmand 840mm We set the minimization function 119891(119909) as thesquared summation of detected diameters subtracted by realdiameter That is
min 119891 (119909) =
119869
sum
119894=1
1003816100381610038161003816119863119894 minus 119863119903
1003816100381610038161003816
2 (13)
where 119863 is the detected diameter according to wheel diam-eter calibration principle 119863119903 is the real diameters 119909 =
[119889off 1205721 1205721 1205723 1199101 1199111 1199102 1199112 1199103 1199113] is the variables to be cali-brated 119869 denotes the number of ground wheelsets MATLABhas provided such tools to solve those optimization problemsOver here we use fmincon function to minimize the functionand the constraints in terms of the variables are also givenaccording to real physical ranges Finally the optimal valuesof the parameters can be obtained These values are assumedto be the real values that the implemented system has andhave been further put into use in system service
Journal of Sensors 9
3 Detection Error Analysis
In this section we consider four factors which are railvibration sensor noise misalignment and wheel inclinationcaused by wheel S-shape running and the differential ofdiameters
31 Wheel-Rail Vibration Wheel-rail vibration is the firstfactor that we considered In our system all the sensorsare well fixed by the mechanical support and mechanicalpedestal that has no direct contact with rail So the wheel-railvibrationwill not directly transmit to the sensors and insteadthe wheel-rail vibration has to transmit to the ground of thedepot and then transmit to the sensors through mechanicalsupport andmechanical pedestalThe vibration of the groundis on a lower level the maximum of acceleration is only04m2s [24] in Guangzhou metro depot and it is alsoattenuated by the mechanical pedestal We also measuredthe maximum of acceleration of mechanical support duringtrain passing which is only 02m2s So the change of theposition of the sensors due to the wheel-rail vibration in oursystemcanbeneglected Furthermore all the laser sensors arecapturing data simultaneously and the exposure time of theLDS is within 50 microseconds The vibration of the wheelwill not cause considerable movement within such a shorttime Overall the system is assumed to be reliable againstwheel-rail vibration
32 Misalignment As previously mentioned in Section 2Dynamics Detection if the laser light panel does not includethe center of the measured wheel the detected profile is hor-izontally stretched along V-axis This phenomenon is calledthe misalignment between the laser panel and the detectiontarget which will lead to the increase of the detected flangeheight and flange width Chen et al [10] derived a geometricmodel regarding howmany errors will be generated for flangeheight when wheel position varies The error 119890 of the flangeheight is
where 119877 is the wheel radius 119877119862 is the radius in the wheel rim119889 is the distance from the wheel center to the laser panel asdescribed in Section 2
On the basis of this geometric model when we know howmuch the error of the flange height is the errors of the flangewidth can be derived accordingly For different wear wheelsthe profiles aswell as the fitted line for lateral contact pointmare certainly different To illustrate the massiveness of errorshere we chose the same wheel where the fitted line for lateralcontact point m is V = 119891(119906) We obtain the inverse function119906 = 119892(V) and stretch it horizontally by a factor of (119865ℎ + 119890)119865ℎSo the stretched curve line is
119906 = 1198922 (V) = 119892(V119865ℎ
(119865ℎ + 119890)) (15)
Eventually the error of flange width is 120578 = 1198922(10)minus119865119908 where119865119908 is the original flange width
Error of flange heightError of flange width
0
01
02
03
04
05
06
07
08
Caus
ed er
ror (
mm
)
10 20 30 40 500d (mm)
Figure 9 The error of flange width and flange height with respectto various wheel positions
Theoretically from (14) and (15) we know that the smallerthe value of 119877 is the larger the error 119890 is So we chosethe largest standard wheelset with 119877 = 385mm and 119877119862 =399mm Figure 9 shows the error of flange height and flangewidth induced from misalignment in this case The distance119889 varies from 0mm to 50mmwith an interval of 1mm FromFigure 9 the error of flange height is lower than the error offlange width So we focus on the error of flange width here
In our system the sampling frequency of all LDS is 1 kHzand the maximum speed of the train in the depot is 36 kmhThemaximum of sampling step size along the railΔ119904 = 1ms times10ms = 10mmWhen we set the threshold119870119901 (as describedin Section 25) as 20mm the total measuring distance alongthe rail can be 58mm so that at least 119872 = 5 times ofefficient scans can be detected The corresponding errors areless than 01mm for flange width after taking the average ofthese 5 efficient scansThus the system can performdetectionnormally against themisalignment error benefitting from thehigh sampling frequency
33 Sensor Noise The LDS cannot be ideally accurate Themeasuring accuracy is influenced by temperature the rough-ness of the measured surface and so forth
In order to obtain the quantitative influence for profiledetection we built a 3D model in SolidWorks tools andextracted ideal sensor output points of standard inner andouter tread profiles In this model the standard wheel islocated in the position where the center of the wheel is inthe laser panel So the misalignment phenomenon will notaffect tread profile detection The wheel is in static positionso the simulated sensor output points are all from one scanMoreover the parameters that need to be calibrated areideally accurate To imitate the real situation Gaussian noiseis added to these coordinate valuesThemean of noise is zeroand the standard deviation is varied from 0 to 1mm with an
10 Journal of Sensors
X 03Y 01251
Flange widthFlange height
0
01
02
03
04
05
06
07Ca
used
erro
r (m
m)
02 04 06 08 10Noise level (mm)
Figure 10 The RMS error of flange height and flange width causedby different sensor noise level
interval of 01mm For each noise level 500 experiments arecarried out and the RMS error is calculated The RMS errorof flange height and flange width results caused by differentnoise level is shown in Figure 10 The caused error to flangeheight and flange width is approximately half of the sensornoise level This can be explained by the curve line fittingmethod that has taken more laser points into account andthus has reduced the random noise Because the flange heightis determined by two points the curve line fittingmethod hasat least reduced the randomerror into a quarter of the originalsensor noise
The 2D-LDS we chose is LJ-V7300 from KEYENCEwhich has a full-scale resolution of 01FS and a temper-ature drift of 001 FS∘C The detection range in 119910-axis is300 plusmn 145mm and in 119909-axis is 110mm to 240mm whichformed as a trapezoid The point in 119909-axis is fixed thus onlysensor noise in 119910-axis needs to be considered with full scaleof 290mm So accordingly the RMS error caused to theprofile coordinate noise in 119910-axis which is denoted by 120575 isless than 032mm which only leads to an error of 013mmboth to flange height and to flange width Taking dynamicsdetection effect into account the final error is reduced by120575119891 = 120575
radic5 = 0058mm with at least119873 = 5 times of efficientscans The error caused by sensor noise can be acceptable
Regarding the error of wheel diameter it can be theoreti-cally derived by the theorem of error propagation [25] Theresolution of each sensor is denoted by 1205751 1205752 and 1205753 Weobtain 120575119863 by taking differential of (6)ndash(9) as follows
120575119863 = plusmnradic(1205751
120597119863
1205971198971
)
2
+ (1205752
120597119863
1205971198972
)
2
+ (1205753
120597119863
1205971198973
)
2
(16)
We have chosen two 2D-LDS and one 1D-LDS to detect thewheel diameter and the two 2D-LDS are installed symmet-rically For systematic installation we have 1205751(1205971198631205971198971) =
1205753(1205971198631205971198973) Moreover the analytical function of particle
derivative will be too complex to derive So we consider aspecial case where
where the target wheel diameter is 119863 = 840mm and theorigin of the wheel is located in the origin of 119910119900119911WCF Morecalculation details can be found in the Appendix Finally wehave
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(18)
The 1D-LDS we chose is LK-G8085 from KEYENCE whichhas linearity of 005FS and a temperature drift of 001FS∘C So according to the full scale of 30mm the reso-lution of 1D-LDS 1205752 = 0018mm Based upon the findingthat the curve line fitting method has at least reduced therandom error into a quarter of the original sensor noise1205751 = 0075mm Finally 120575119863 is less than 0372mm Takingdynamics detection effect into account the final error 120575119863
119891
=
120575119863radic5 = 017mm The error caused by sensor noise can be
acceptable
34 Wheel Inclination Caused by Wheelset S-Shape RunningandDifferential ofWheel Diameter In engineering thewheelwill be inclined because of wheelset S-shape running and thedifferential of wheel diameter The wheelset S-shape runningis one kind of self-induced vibration due to the slope in thewheel trade When it is S-shape running the wheel panelwill have a certain angle with respect to 119910119900119911 panel in WCFdenoted by 120579119904 as shown in Figure 11(a) The differentialof wheel diameter in a wheelset is at different wear levelin the left and right wheel mainly induced from differentmassiveness of wear in the circuit of wheelset turning andunbalanced loading Similarly it will bring a certain angleabout the wheel panel with respect to the 119910119900119911 panel in WCFThe angle is denoted by 120579119889 as shown in Figure 11(b)
For wheel diameter detection because we only considerthe calculation in two dimensions an error will be generatedwhen we still regard the detected three points in a circle toactually be in an ellipse Considering the existence of angles120579119904 and 120579119889 we have the equation of ellipse as follows
1199102
(119877 sdot cos 120579119904)2+
1199112
1198772= 1
1199102
1198772+
1199112
(119877 sdot cos 120579119889)2= 1
(19)
Journal of Sensors 11
x
y
z
0
Ellipse wheel
Wheelset withS-shape running
120579s
(a)
x
y
z Ellipse wheel
Wheelset with differential of diameter
120579d
(b)
Figure 11 Mathematical illustration (a) Wheel S-shape running and (b) differential of wheel diameter
Similar towhenwe analyze sensor noise we consider a specialcase as (17) the origin of the target wheel is located in theorigin of 119910119900119911WCFThe real three points are
1198881(119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198882 (0 minus119877)
1198883(minus119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198881(119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
1198882 (0 minus119877 sdot cos 120579119889)
1198883(minus119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
(20)
Theoretically the larger the radius of the wheel is the biggerthe error is So we chose 119877 = 420mm and generated threepoints then using (7) we calculated the wheel diameter witherror Subtracting the real diameter we have the error withrespect to angle as shown in Figure 12 The effect of S-shaperunning caused angle has a relatively higher influence on thewheel diameter calculation
Based on the experience from Guangzhou Metro Cor-poration the differential of diameter in a wheelset shouldbe controlled under 2mm Considering the track gauge of1350mm the angle induced from the differential of diameter
S-shape runningWheel diameter differential
0
001
002
003
004
005
006
Caus
ed er
ror t
o di
amet
er (m
m)
01 02 03 04 050120579 (∘)
Figure 12 Wheel diameter errors
in a wheelset is less than 0001∘ thus the error can be ignoredAs for wheel S-shape running themaximum angle is 01∘ [26]when the speed of the train is under 36 kmhwhich will causean error not larger than 0005mm
4 Experimental Validation
41 System Implementation Theauthors previously proposedan online detection system using eight 2D-LDS [19] Thenew online detection system is installed in the same storageline of Guangzhou metro vehicle depot as the old systemso that comparison can be conducted In order to savefund only the left side namely half of the system has been
12 Journal of Sensors
(a) (b)
Figure 13 Field test (a) Standard wheel test and (b) real train test
Table 1 Standard wheelset detection the results of repeatedmeasurementsmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
implemented During the system implementation three-dimensional inclinometer and special rail gauge are used tocontrol the position of the mechanical support After thesystem is installed the calibration described in Section 2has been conducted to obtain the geometric parameters fortread profile calibration and diameter calculation As shownin Figure 13 the field test is carried out by a standard wheelsetand real train
42 Standard Wheelset The standard wheelset is a new pro-duced wheelset without any wear and diameter differentialThe manufacturing geometric size is as follows wheel diam-eter = 840mm flange height = 28mm and flange width =32mm One can also assume to have lower possibility of S-shape running because of zero external load The standardwheelset has been placed on the rail and passed through thedetection system This test has been carried out 6 times toverify both the detection and the repeatability of the systemComparing with the old system the results of this system areshown in Table 1
From Table 1 the mean values of the flange height andflange width detected by the old and the new system are very
close to each other which means the system error can beignored The standard deviation which also can be denotedas detection uncertainty of the new system measurement isslightly smaller than of the old system That may result fromthe lower effect frommisalignment as described in Section 3due to the higher sampling frequency that we used in the newsystem Detection uncertainty of not greater than 005mm intread profile measurement is acceptable for the engineeringrequirements As for wheel diameter detection the meanvalues are also close to each other The standard deviation ofthe new systemmeasurement is slightly higher than of the oldsystemThis may result from the replacement of 1D-LDS thathas brought about higher sensor noise to the middle pointamong three pointswithout curve fitting techniqueHoweverdetection uncertainty of less than 03mm is also acceptable inengineering
43 Real Train Detection Test Real train test also performs6 times of repeated detection to statistically evaluate theperformance of the system The train speed is controlledunder 36 kmh In the train we chose there are 4 new groundwheelsets in a car of the train Under the consideration thatthe ground new wheel is not out of roundness which hasan effect on the analysis results we selected the ground newwheel as our target wheel
Table 2 shows the mean and standard deviation value ofmeasurement The biggest differential value of mean flangeheight appears in 1 wheel and for mean flange width appearsin 3 wheel The difference does not exceed 015mm As forwheel diameter the biggest differential value 016mmappearsin 3 wheelThemean value of six times of repeated detectionis consistent with the standard wheelset test In terms ofstandard deviation the value is less than 01mm for flangewidth and flange height and 03mm for wheel diameterThe standard deviation of wheel diameter is relatively higherthan in standard wheelset test On the contrary the standarddeviation of flange width and flange height is relatively lowerthan in the old system That is also consistent with standard
Journal of Sensors 13
Table 2 Real train test the mean and standard deviation value of detected measurementmm
Wheelnumber
Mean flange height SD flange height Mean flange width SD flange width Mean wheeldiameter SD wheel diameter
Old New Old New Old New Old New Old New Old New1 2818 2803 0046 0060 2954 2943 0091 0062 80052 80150 0201 03012 2809 2811 0078 0040 2940 2929 0056 0028 80112 80096 0128 02863 2797 2791 0076 0033 2992 3006 0075 0056 80187 80166 0090 01794 2807 2805 0063 0053 2983 2988 0076 0088 80178 80201 0192 0282
Table 3 Real train test wheel 2 the result of repeated measure-mentmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
wheelset test The standard deviation of wheel diameter inreal train test is supposed to be higher than in the standardwheelset test because of several assumptions One factor isthe higher possibility of S-shape running because of heavyaxial load On the other hand the wheelset that is in service isalso more polluted with rust than standard wheelset causingmore detection uncertainty However the standard deviationfrom real train test also does not exceed 03mm which isconsistent with standard wheelset test This may result fromthe lower train speed during the test which leads to lowerpossibility of S-shape running Meanwhile the rusty wheelcontour is also not in a massive stage Tables 3 and 4 show theresult of repeated measurement for wheels numbers 2 and 3respectively In each detection the results remain the sameand no gross error appears
Overall detection uncertainties for tread profile andwheel diameter are less than 01mmand 03mm respectivelyThe results show that the detection system has a highaccuracy which can meet the requirements of maintenanceoperation
5 Conclusion
This paper based on LDS proposed a novel on-track detec-tion system of the wheel size using only six 2D-LDS and two1D-LDS Errors induced bywheel-rail vibration sensor noisemisalignment S-shape running and wheelset differential arealso analyzed After the system is implemented real dataexperiments including standard wheel test and real traindetection test were performed It turns out that the detectionuncertainty of flange width and height is 01mm and wheeldiameter 03mm which can meet the requirements of main-tenanceThis system can be further used for different types ofrailway transportation which provides a new solution for thewheel size detection technology
To provide more benefits the target wheel diameter is 119863 =
840mm and the origin of the wheel is located in the originof 119910119900119911WCF as shown in Figure 14 In this special case therelevant geometric values are 1198881(minus19802mm minus19802mm)1198882(0mm 420mm) 1198883(19802mm minus19802mm) 1198971 = 280mm1198972 = 180mm and 1198973 = 280mm
According to (8) and (9) we get the particle derivative asfollows
120597119863
1205971198971
=
120597119863
1205971199100
1205971199100
1205971198971
+
120597119863
1205971199110
1205971199110
1205971198971
120597119863
1205971198972
=
120597119863
1205971199100
1205971199100
1205971198972
+
120597119863
1205971199110
1205971199110
1205971198972
+
120597119863
1205971199111198882
1205971199111198882
1205971198972
(A2)
14 Journal of Sensors
2D-L1
1D-L2
2D-L3
y
z
o
45∘45∘ c1l1
l2
l3
c2
c3 lowast
lowast
lowast
Figure 14 A special case
Taking the derivative of diameter 119863 with respect to 1199100 1199110and 119911119888
2
according to (8) and substituting (1199100 1199110) = (0 0) and1199111198882
= 180mm we have
120597119863
1205971199100
=
21199100
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199110
=
2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199111198882
=
minus2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
= 2
(A3)
Furthermore based upon (7) we get
1205971199100
1205971198971
=
1205971199100
1205971199101198881
1205971199101198881
1205971198971
+
1205971199100
1205971199111198881
1205971199111198881
1205971198971
1205971199110
1205971198971
=
1205971199110
1205971199101198881
1205971199101198881
1205971198971
+
1205971199110
1205971199111198881
1205971199111198881
1205971198971
1205971199100
1205971198972
=
1205971199100
1205971199111198882
1205971199111198882
1205971198972
1205971199110
1205971198972
=
1205971199110
1205971199111198882
1205971199111198882
1205971198972
1205971199100
1205971198973
=
1205971199100
1205971199101198883
1205971199101198883
1205971198973
+
1205971199100
1205971199111198883
1205971199111198883
1205971198973
1205971199110
1205971198973
=
1205971199110
1205971199101198883
1205971199101198883
1205971198973
+
1205971199110
1205971199111198883
1205971199111198883
1205971198973
(A4)
When calculating particle derivative of (1199100 1199110) with respectto three points 1198881 1198882 and 1198883 in WCF we assume that allparameters are with the geometric values in this special case
Then we substitute the ideal geometric values of this variableand we obtain
1205971199100
1205971199101198881
= 05
1205971199100
1205971199111198881
= 05
1205971199110
1205971199101198881
= minus12071
1205971199110
1205971199111198881
= minus12071
1205971199100
1205971199111198882
= 0
1205971199110
1205971199111198882
= 34142
1205971199100
1205971199101198883
= 05
1205971199100
1205971199111198883
= minus05
1205971199110
1205971199101198883
= 12071
1205971199110
1205971199111198883
= minus12071
1205971199101198881
1205971198971
=
1
radic2
1205971199111198881
1205971198971
=
1
radic2
1205971199111198882
1205971198972
= minus1
1205971199101198883
1205971198973
= minus
1
radic2
1205971199111198883
1205971198973
=
1
radic2
(A5)
Finally substituting (A5) into (A4) and then substituting(A4) and (A3) into (A2) we have
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(A6)
Competing Interests
The authors declare that they have no competing interests
Journal of Sensors 15
Acknowledgments
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
Figure 4 (a) Coordinate transformation of L4 and coordinate transformation of L3 (b) Moving all the data from 119906(4)119900(4)V(4) to 119906119900V
where (119906119899 V119899) is the dot in tread profile base coordinate 119906119900VΔ119906 and ΔV are the offset from 119906
(4)119900(4)V(4) to 119906119900V
As we know flange width flange height and wheeldiameter are determined by several base points and base lineThe output points from sensors are discrete so base points am and n are more likely not in one of the scanned pointsThe output points are also polluted with sensor noise whichinduced more detection uncertainty when we directly regardit as the base points Over here curve fitting is used forextracting the base point as well as the base lineThrough thismethod the coordinate value of base points can be preciselyextracted and the sensor noise can also be eliminated to someextent It is difficult to use a single curve to fit all the treaddue to the complexity of tread contour Therefore fittingdiscrete points of each base point within a certain range isapplied to improve the accuracy of the extracted base pointcoordinate value The common method of curve fitting isthe least square method [22] The least square method usesa given set of measured data to get the functional relation119891(119909 1198860 1198861 119886119899) between the variable 119909 and the variable 119910based on the principle of least squares Then the weightedsum of squaresrsquo value of the residual 119890119896 between the fittingfunction and the actual measured value at each point can beminimal which means 119865 in (4) is minimal
119865 =
119868
sum
119894=0
120596 (119909119894) (119891119894 minus 119910119894)2 (4)
where 120596(119909119894) ge 0 is the weight which reflects the notionthat the data (119909119894 119910119894) accounts for the proportion in theexperiment 119868 denotes the number of data points Accordingto the tread profile features and experimental researchfourth-order polynomial 119910 = sum4119894=0 119886119894119909
4minus119894 is selected to fit eachsubsection curve based on the least square method
With curve fitting technique four lines in total are fittedin order to extract the coordinate value of base points a mandn As shown in Figure 5 at first the inner side of thewheelhas no wear-out and deformation when there is wheel-railcontact so base line 119897 is fitted by selecting all the data pointsin the inner side of the wheelThe base point a is 70mm awayfrom the base line 119897 along 119906-axis Then the green line is fittedin order to extract base point a by selecting data points within
a certain range of base point aThe red line and yellow line arealso fitted by the same method in order to extract base pointsm and n respectively
After four lines are obtained the precise coordinate valueof all base points can be determined To this end the flangeheight and flange width are calculated as follows
119865119908 = 119906119897 minus 119906119898
119865ℎ = V119899 minus V119886(5)
where 119865119908 is flange width 119865ℎ is flange height 119906119897 is the 119906-axiscoordinate value of base line 119897 119906119898 is the 119906-axis coordinatevalue of base pointm V119899 is the V-axis coordinate value of basepoint n V119886 is the V-axis coordinate value of base point a
24 Static Wheel Diameter Calculation Principle Wheeldiameter is detected by 2D-L1 1D-L2 and 2D-L3 Each oneof the LDS measures one point in the circular wheel so thatthe wheel diameter can be determined by three points
The wheelset is assumed to be in the right position andto remain static The coordinates of the output points arein the scanning coordinate system of the sensor Similarto tread profile calculation the coordinate transformation
6 Journal of Sensors
o
y
WCF
x
z
v (1)
u(1)o(1)
y(2)
v(2)
o(2)
u(2)
u(3)o(3)
v (3)
x(4)
duoff
Figure 6 Scanning coordinates of 2D-L1 1D-L2 and 2D-L3 after coordinate transformation
y
z
o
Wheel
c3
c (x0 y0)
c1
c2 l1
l2
l3
1205722
12057211205723
P1 (y1 z1)
P2 (y2 z2)
P3 (y3 z3)lowast
lowast
lowast
(a)
a
o(2)
u(3)
o(3)
v (3)c3Fc
doff
(b)
Figure 7 Wheel diameter calculation principle in two dimensions (a) sight along the 119909-axis scanning coordinates of 2D-L1 1D-L2 and2D-L3 after transformation (b) sight in the 119906(3)119900(3)V(3) coordinate
was conducted and the scanning coordinates 119906(1)119900(1)V(1)119906(2)119900(2)V(2) and 119906(3)119900(3)V(3) for 2D-L1 1D-L2 and 2D-L3
respectively have been obtained Figure 6 shows the scanningcoordinates of 2D-L1 1D-L2 and 2D-L3 after coordinatetransformation Notice that 119906(2)119900(2)V(2) is still the same as119910(2)119900(2)119911(2) because of the installation position of 1D-L2
Figure 6 also shows the offset 119889off between the origin of thecoordinate 119906(3)119900(3)V(3) and laser scanning line of L2 in 119906(2)-axis Among three points the two points detected by 2D-L1and 2D-L3 are extracted from the 2D profiles The offset 119889offis the 119906(2)-axis coordinate value to extract the points in theflange circle from two-dimensional profile This offset 119889off isdetermined by sensor installation
Figure 7 shows the wheel diameter calculation princi-ple in two dimensions where (a) shows the principle that
three points determine a diameter in 119910119900119911 WCF and (b)shows extracting the point in the flange circle among two-dimensional profile and the final wheel diameter distancesubtraction by 119865119888 From Figure 7(a) the installation of eachLDS is modeled as three parameters in 119910119900119911 WCF whichare the position Pi(119910119894 119911119894) and angle 120572119894 They determinethe position of laser origin and the direction of detectionrespectively The angle 1205722 for 1D-L2 is designed as 1205872 Thepositions P1 and P3 are designed as symmetric with respectto the scanning line of 1D-L2 as well as the angles 1205721 and1205723 Even though many of the parameters are designed tobe equal for instance 1199111 = 1199113 the real parameters willvary after engineering implementation due to errors suchas installation error and manufacturing error Thus thisnine-parameter model is proposed for diameter calculation
Journal of Sensors 7
because it can describe all the possible errors The realinstallation parameters are obtained through calibration aslater described Moreover the distances 1198971 1198972 and 1198973 aredetected from three LDS sensors The three points c1 c2and c3 are in the flange of wheel detected by three sensorsrespectively The point c(1199100 1199110) is the origin of the detectedwheel which is calculated by three points c1 c2 and c3
According to Figures 6 and 7(a) the first information wecan get from the LDS sensors is the laser scanned distances1198971 1198972 and 1198973 1198972 is directly detected by 1D-L2 1198971 and 1198973 areextracted from the 2D profiles detected by 2D-L1 and 2D-L3 respectively To extract 1198971 and 1198973 we need to find thecorrect points in the two-dimensional tread profile As shownin Figures 6 and 7(b) the point that determines 1198971 and 1198973should be in the 119906-axis value of offset 119889off Similar to detectingtread profile we use the same curve fitting method to obtaina curve in the contour of the wheel in the 119906119900V coordinate thatis denoted by V = 1198913(119906) When the curve line is obtained1198973 = V3 = 1198913(119889off ) namely the V-axis value of curve 1198913(119906)
when 119906 = 119889off Similarly 1198971 is detected by 2D-LDS L1 usingthe same method as deciding 1198973
Once the laser scanned distances 1198971 1198972 and 1198973 aredetermined we get the three points c1 c2 and c3 in WCFcoordinate 119910119900119911 by
1199101198881
= 1199101 + 1198971 sin1205721
1199111198881
= 1199111 + 1198971 cos1205721
1199101198882
= 1199102 + 1198972 sin1205722
1199111198882
= 1199112 + 1198972 cos1205722
1199101198883
= 1199103 + 1198973 sin1205723
1199111198883
= 1199113 + 1198973 cos1205723
(6)
Based on three points c1 c2 and c3 the wheel center c(1199100 1199110)is determined by
1199100 =
(1199111198881
minus 1199111198883
) (11991021198881
minus 11991021198882
+ 11991121198881
minus 11991121198882
) minus (1199111198881
minus 1199111198882
) (11991021198881
minus 11991021198883
+ 11991121198881
minus 11991121198883
)
2 (1199101198881
minus 1199101198882
) (1199111198881
minus 1199111198883
) minus 2 (1199101198881
minus 1199101198883
) (1199111198881
minus 1199111198882
)
1199110 =
(1199101198881
minus 1199101198882
) (11991021198881
minus 11991021198883
+ 11991121198881
minus 11991121198883
) minus (1199101198881
minus 1199101198883
) (11991021198881
minus 11991021198882
+ 11991121198881
minus 11991121198882
)
2 (1199101198881
minus 1199101198882
) (1199111198881
minus 1199111198883
) minus 2 (1199101198881
minus 1199101198883
) (1199111198881
minus 1199111198882
)
(7)
and the wheel diameter119863119903 is determined by
119863119903 = 2 sdotradic(1199100)
2+ (1199110 minus 119911119888
2
)
2 (8)
From Figure 7(b) 119865119888 is the distance between points c3 anda along V-axis The wheel diameter detected by the previousthree points is somewhere in the contour circle governed bythe 1D-L2 only The point a is considered to be the diameterpoint of the wheel which is minus70mm away from the innerside of the wheel In order to obtain the final wheel diameterwe need to further subtract the distance 119865119888 from the wheeldiameter
119863 = 119863119903 minus 2119865119888 (9)
where119865119888 is the distance between point c3 and point a in V-axis(as shown in Figure 7(b)) namely 119865119888 = V119886 minus V119888
3
25 Dynamics Detection The calculation principles shownabove are in static case When the train passes dynam-ically multiscans can be obtained and the misalignmentphenomenon caused from wheel passing will occur
For tread profile detection ideally the laser light panel ofL3 and L4 is assumed to include the center of the measuredwheel In dynamics detection it is impossible to meet thatassumption for all measured wheels due to the moving ofwheel and the discrete sampling of LDS signal Basicallyif the laser light panel does not include the center of themeasured wheel the detected profile is horizontally stretched
along V-axis That will lead to the increase of detected flangeheight and flange width This phenomenon is called themisalignment between the laser panel and the detectiontarget [9]
Figure 8 shows the dynamics positions of thewheel centerand laser panel constituted by L3 and L4 in two-dimensionalWCF The wheel moves forward with a constant speed of V1198741 1198742 and 119874119894 are the center of wheel diameter circle underdifferent positions The laser panel has an installation angle1205723 with respect to 119910-axis which can be determined as 119911 =tan1205723 sdot 119910 in WCF The center points of wheel diameter circleare calculated by (7) 119889119894 denote the distance between 119894th wheelcenter point and the laser panel
Theoretically for every 119894th position of the wheel thedistance 119889119894 from the wheel center c(1199100
119894
1199110119894
) to the laser panelcan be determined by point to the distance formula as follows
When the distance 119889119894 equals zero the wheel center c(1199100119894
1199110119894
)
is in the laser panel where the flange height and flange widthhave no stretching On the other hand the bigger the distance119889119894 is the farther away the wheel center c(1199100
119894
1199110119894
) is from thelaser panel
It is worthmentioning that the LDSworks when the anglebetween laser light and detected surface is within a certainrange and the angle is influenced by laser wavelength surface
8 Journal of Sensors
y
z
Laser panel
Rail
Wheelv
Scanned section
O1 O2
d1 d22120579
120579
120579
1205723
Oi
di
L3 L4lowast
Figure 8 Dynamics position of the wheel center
smoothness surface material and so forth [23] It is assumedthat the angle 120579 (as shown in Figure 8) is the largest angleat which the LDS can still receive effective scan When thewheel is moving out of the detection range the LDS will beunable to scanThus the scanned sectionwill be the arcwith acentral angle of 2120579 and all the tread profiles and diameters arescanned from this section For most LDS sensors the angle 120579can reach up to 45∘ so the system can measure 90∘ arc of thewheel Correspondingly the maximum value of the distance119889119894 is 119877 sin 120579 where 119877 is the wheel radius
The misalignment phenomenon will bring about certainerror to the profile detection Among all the effective scanswe must select those scans where the induced error isacceptable In this paper the error induced in the tread profiledetection is analyzed in Section 3 As a result the error isdirectly proportional to the distance 119889119894 So we set up a certainthreshold 119870119901 When the distance 119889119894 lt 119870119901 the detectedtread profile can be regarded as useful profiles where the errorinduced by the misalignment phenomenon is negligible Thethreshold 119870119901 is firstly obtained through error analysis andalso is adjustable according to the field experiment Due tothe benefits from the high sampling frequency of the LDSsensors 119872 times of scans can be obtained for a wheelsetThen we can remove the bulky error first and performaverage operation to get the final wheel flange and wheelwidth as follows
119865119908119891
=
1
119872
119872
sum
119894=1
119865119908119894
119865ℎ119891
=
1
119872
119872
sum
119894=1
119865ℎ119894
(11)
where 119865119908119894
and 119865ℎ119894
are the flange width and flange height in119894th scan respectively 119865119908
119891
and 119865ℎ119891
are the final flange widthand flange height respectively The average operation herecan reduce the final error caused by Gaussian sensor noise
For wheel diameter detection the three points thatdetermine the wheel diameter are always in the contourcircle Thus the calculation results will not be influenced by
different wheel positions However 119865119888119894
in every 119894th scan willstill be stretched and bring about some error Similarly weselect a set of scans by comparing whether the distance 119889119894is smaller than a certain threshold 119870119889 or not When 119889119894 lt119870119889 the error induced in the detected 119865119888 is negligible Thetwo thresholds 119870119889 and 119870119901 might be different because ofthe different detection error requirements for tread profileand wheel diameter In this way 119873 times of scans can beobtained Then we can remove the bulky error first andperform average algorithm to get the final wheel diameter asfollows
119863119891 =1
119873
119873
sum
119894=1
119863119894 (12)
where 119863119894 is the wheel diameter in 119894th scan 119863119891 is the finalwheel diameter
26 Calibration The measuring and calculating of treadprofile and wheel diameter depend on many installationparameters Regarding tread profile calculation they are theangle 1205733 in (1) angle 1205734 in (2) and the offset Δ119906 and offsetΔV in (3) For wheel diameter they are the offset 119889off betweenthe origin of the coordinate 119906119900V and laser scanning line of L2in 119906(2)-axis the angles 1205721 1205722 and 1205723 and the positions P1P2 and P3 in (6) When the LDS are installed and fixed it isimpossible for those parameters to be the same with designedvalues because of the manufacture error of mechanical partsand installation accuracy So calibration is certainly needed
During the calibration process for tread profile detectiona standard wheel is placed on the rail over the detection sys-tem and then the offset and rotation angle of the coordinatetransformation matrix can be determined In terms of theangles 1205733 and 1205734 the calibrated accurate value is to makesure the inner and outer panels of the wheel are vertical Forthe offset Δ119906 the calibrated accurate value is to make surethe detected wheel hub thickness equals the standard wheelhub thickness and the offset ΔV is to make sure the scannedprofiles from two LDS coincide with each other
As for the calibration process for wheel diameter a setof new ground wheelsets is used The ground wheelset iswith different diameters that are 770mm 790mm 810mmand 840mm We set the minimization function 119891(119909) as thesquared summation of detected diameters subtracted by realdiameter That is
min 119891 (119909) =
119869
sum
119894=1
1003816100381610038161003816119863119894 minus 119863119903
1003816100381610038161003816
2 (13)
where 119863 is the detected diameter according to wheel diam-eter calibration principle 119863119903 is the real diameters 119909 =
[119889off 1205721 1205721 1205723 1199101 1199111 1199102 1199112 1199103 1199113] is the variables to be cali-brated 119869 denotes the number of ground wheelsets MATLABhas provided such tools to solve those optimization problemsOver here we use fmincon function to minimize the functionand the constraints in terms of the variables are also givenaccording to real physical ranges Finally the optimal valuesof the parameters can be obtained These values are assumedto be the real values that the implemented system has andhave been further put into use in system service
Journal of Sensors 9
3 Detection Error Analysis
In this section we consider four factors which are railvibration sensor noise misalignment and wheel inclinationcaused by wheel S-shape running and the differential ofdiameters
31 Wheel-Rail Vibration Wheel-rail vibration is the firstfactor that we considered In our system all the sensorsare well fixed by the mechanical support and mechanicalpedestal that has no direct contact with rail So the wheel-railvibrationwill not directly transmit to the sensors and insteadthe wheel-rail vibration has to transmit to the ground of thedepot and then transmit to the sensors through mechanicalsupport andmechanical pedestalThe vibration of the groundis on a lower level the maximum of acceleration is only04m2s [24] in Guangzhou metro depot and it is alsoattenuated by the mechanical pedestal We also measuredthe maximum of acceleration of mechanical support duringtrain passing which is only 02m2s So the change of theposition of the sensors due to the wheel-rail vibration in oursystemcanbeneglected Furthermore all the laser sensors arecapturing data simultaneously and the exposure time of theLDS is within 50 microseconds The vibration of the wheelwill not cause considerable movement within such a shorttime Overall the system is assumed to be reliable againstwheel-rail vibration
32 Misalignment As previously mentioned in Section 2Dynamics Detection if the laser light panel does not includethe center of the measured wheel the detected profile is hor-izontally stretched along V-axis This phenomenon is calledthe misalignment between the laser panel and the detectiontarget which will lead to the increase of the detected flangeheight and flange width Chen et al [10] derived a geometricmodel regarding howmany errors will be generated for flangeheight when wheel position varies The error 119890 of the flangeheight is
where 119877 is the wheel radius 119877119862 is the radius in the wheel rim119889 is the distance from the wheel center to the laser panel asdescribed in Section 2
On the basis of this geometric model when we know howmuch the error of the flange height is the errors of the flangewidth can be derived accordingly For different wear wheelsthe profiles aswell as the fitted line for lateral contact pointmare certainly different To illustrate the massiveness of errorshere we chose the same wheel where the fitted line for lateralcontact point m is V = 119891(119906) We obtain the inverse function119906 = 119892(V) and stretch it horizontally by a factor of (119865ℎ + 119890)119865ℎSo the stretched curve line is
119906 = 1198922 (V) = 119892(V119865ℎ
(119865ℎ + 119890)) (15)
Eventually the error of flange width is 120578 = 1198922(10)minus119865119908 where119865119908 is the original flange width
Error of flange heightError of flange width
0
01
02
03
04
05
06
07
08
Caus
ed er
ror (
mm
)
10 20 30 40 500d (mm)
Figure 9 The error of flange width and flange height with respectto various wheel positions
Theoretically from (14) and (15) we know that the smallerthe value of 119877 is the larger the error 119890 is So we chosethe largest standard wheelset with 119877 = 385mm and 119877119862 =399mm Figure 9 shows the error of flange height and flangewidth induced from misalignment in this case The distance119889 varies from 0mm to 50mmwith an interval of 1mm FromFigure 9 the error of flange height is lower than the error offlange width So we focus on the error of flange width here
In our system the sampling frequency of all LDS is 1 kHzand the maximum speed of the train in the depot is 36 kmhThemaximum of sampling step size along the railΔ119904 = 1ms times10ms = 10mmWhen we set the threshold119870119901 (as describedin Section 25) as 20mm the total measuring distance alongthe rail can be 58mm so that at least 119872 = 5 times ofefficient scans can be detected The corresponding errors areless than 01mm for flange width after taking the average ofthese 5 efficient scansThus the system can performdetectionnormally against themisalignment error benefitting from thehigh sampling frequency
33 Sensor Noise The LDS cannot be ideally accurate Themeasuring accuracy is influenced by temperature the rough-ness of the measured surface and so forth
In order to obtain the quantitative influence for profiledetection we built a 3D model in SolidWorks tools andextracted ideal sensor output points of standard inner andouter tread profiles In this model the standard wheel islocated in the position where the center of the wheel is inthe laser panel So the misalignment phenomenon will notaffect tread profile detection The wheel is in static positionso the simulated sensor output points are all from one scanMoreover the parameters that need to be calibrated areideally accurate To imitate the real situation Gaussian noiseis added to these coordinate valuesThemean of noise is zeroand the standard deviation is varied from 0 to 1mm with an
10 Journal of Sensors
X 03Y 01251
Flange widthFlange height
0
01
02
03
04
05
06
07Ca
used
erro
r (m
m)
02 04 06 08 10Noise level (mm)
Figure 10 The RMS error of flange height and flange width causedby different sensor noise level
interval of 01mm For each noise level 500 experiments arecarried out and the RMS error is calculated The RMS errorof flange height and flange width results caused by differentnoise level is shown in Figure 10 The caused error to flangeheight and flange width is approximately half of the sensornoise level This can be explained by the curve line fittingmethod that has taken more laser points into account andthus has reduced the random noise Because the flange heightis determined by two points the curve line fittingmethod hasat least reduced the randomerror into a quarter of the originalsensor noise
The 2D-LDS we chose is LJ-V7300 from KEYENCEwhich has a full-scale resolution of 01FS and a temper-ature drift of 001 FS∘C The detection range in 119910-axis is300 plusmn 145mm and in 119909-axis is 110mm to 240mm whichformed as a trapezoid The point in 119909-axis is fixed thus onlysensor noise in 119910-axis needs to be considered with full scaleof 290mm So accordingly the RMS error caused to theprofile coordinate noise in 119910-axis which is denoted by 120575 isless than 032mm which only leads to an error of 013mmboth to flange height and to flange width Taking dynamicsdetection effect into account the final error is reduced by120575119891 = 120575
radic5 = 0058mm with at least119873 = 5 times of efficientscans The error caused by sensor noise can be acceptable
Regarding the error of wheel diameter it can be theoreti-cally derived by the theorem of error propagation [25] Theresolution of each sensor is denoted by 1205751 1205752 and 1205753 Weobtain 120575119863 by taking differential of (6)ndash(9) as follows
120575119863 = plusmnradic(1205751
120597119863
1205971198971
)
2
+ (1205752
120597119863
1205971198972
)
2
+ (1205753
120597119863
1205971198973
)
2
(16)
We have chosen two 2D-LDS and one 1D-LDS to detect thewheel diameter and the two 2D-LDS are installed symmet-rically For systematic installation we have 1205751(1205971198631205971198971) =
1205753(1205971198631205971198973) Moreover the analytical function of particle
derivative will be too complex to derive So we consider aspecial case where
where the target wheel diameter is 119863 = 840mm and theorigin of the wheel is located in the origin of 119910119900119911WCF Morecalculation details can be found in the Appendix Finally wehave
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(18)
The 1D-LDS we chose is LK-G8085 from KEYENCE whichhas linearity of 005FS and a temperature drift of 001FS∘C So according to the full scale of 30mm the reso-lution of 1D-LDS 1205752 = 0018mm Based upon the findingthat the curve line fitting method has at least reduced therandom error into a quarter of the original sensor noise1205751 = 0075mm Finally 120575119863 is less than 0372mm Takingdynamics detection effect into account the final error 120575119863
119891
=
120575119863radic5 = 017mm The error caused by sensor noise can be
acceptable
34 Wheel Inclination Caused by Wheelset S-Shape RunningandDifferential ofWheel Diameter In engineering thewheelwill be inclined because of wheelset S-shape running and thedifferential of wheel diameter The wheelset S-shape runningis one kind of self-induced vibration due to the slope in thewheel trade When it is S-shape running the wheel panelwill have a certain angle with respect to 119910119900119911 panel in WCFdenoted by 120579119904 as shown in Figure 11(a) The differentialof wheel diameter in a wheelset is at different wear levelin the left and right wheel mainly induced from differentmassiveness of wear in the circuit of wheelset turning andunbalanced loading Similarly it will bring a certain angleabout the wheel panel with respect to the 119910119900119911 panel in WCFThe angle is denoted by 120579119889 as shown in Figure 11(b)
For wheel diameter detection because we only considerthe calculation in two dimensions an error will be generatedwhen we still regard the detected three points in a circle toactually be in an ellipse Considering the existence of angles120579119904 and 120579119889 we have the equation of ellipse as follows
1199102
(119877 sdot cos 120579119904)2+
1199112
1198772= 1
1199102
1198772+
1199112
(119877 sdot cos 120579119889)2= 1
(19)
Journal of Sensors 11
x
y
z
0
Ellipse wheel
Wheelset withS-shape running
120579s
(a)
x
y
z Ellipse wheel
Wheelset with differential of diameter
120579d
(b)
Figure 11 Mathematical illustration (a) Wheel S-shape running and (b) differential of wheel diameter
Similar towhenwe analyze sensor noise we consider a specialcase as (17) the origin of the target wheel is located in theorigin of 119910119900119911WCFThe real three points are
1198881(119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198882 (0 minus119877)
1198883(minus119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198881(119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
1198882 (0 minus119877 sdot cos 120579119889)
1198883(minus119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
(20)
Theoretically the larger the radius of the wheel is the biggerthe error is So we chose 119877 = 420mm and generated threepoints then using (7) we calculated the wheel diameter witherror Subtracting the real diameter we have the error withrespect to angle as shown in Figure 12 The effect of S-shaperunning caused angle has a relatively higher influence on thewheel diameter calculation
Based on the experience from Guangzhou Metro Cor-poration the differential of diameter in a wheelset shouldbe controlled under 2mm Considering the track gauge of1350mm the angle induced from the differential of diameter
S-shape runningWheel diameter differential
0
001
002
003
004
005
006
Caus
ed er
ror t
o di
amet
er (m
m)
01 02 03 04 050120579 (∘)
Figure 12 Wheel diameter errors
in a wheelset is less than 0001∘ thus the error can be ignoredAs for wheel S-shape running themaximum angle is 01∘ [26]when the speed of the train is under 36 kmhwhich will causean error not larger than 0005mm
4 Experimental Validation
41 System Implementation Theauthors previously proposedan online detection system using eight 2D-LDS [19] Thenew online detection system is installed in the same storageline of Guangzhou metro vehicle depot as the old systemso that comparison can be conducted In order to savefund only the left side namely half of the system has been
12 Journal of Sensors
(a) (b)
Figure 13 Field test (a) Standard wheel test and (b) real train test
Table 1 Standard wheelset detection the results of repeatedmeasurementsmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
implemented During the system implementation three-dimensional inclinometer and special rail gauge are used tocontrol the position of the mechanical support After thesystem is installed the calibration described in Section 2has been conducted to obtain the geometric parameters fortread profile calibration and diameter calculation As shownin Figure 13 the field test is carried out by a standard wheelsetand real train
42 Standard Wheelset The standard wheelset is a new pro-duced wheelset without any wear and diameter differentialThe manufacturing geometric size is as follows wheel diam-eter = 840mm flange height = 28mm and flange width =32mm One can also assume to have lower possibility of S-shape running because of zero external load The standardwheelset has been placed on the rail and passed through thedetection system This test has been carried out 6 times toverify both the detection and the repeatability of the systemComparing with the old system the results of this system areshown in Table 1
From Table 1 the mean values of the flange height andflange width detected by the old and the new system are very
close to each other which means the system error can beignored The standard deviation which also can be denotedas detection uncertainty of the new system measurement isslightly smaller than of the old system That may result fromthe lower effect frommisalignment as described in Section 3due to the higher sampling frequency that we used in the newsystem Detection uncertainty of not greater than 005mm intread profile measurement is acceptable for the engineeringrequirements As for wheel diameter detection the meanvalues are also close to each other The standard deviation ofthe new systemmeasurement is slightly higher than of the oldsystemThis may result from the replacement of 1D-LDS thathas brought about higher sensor noise to the middle pointamong three pointswithout curve fitting techniqueHoweverdetection uncertainty of less than 03mm is also acceptable inengineering
43 Real Train Detection Test Real train test also performs6 times of repeated detection to statistically evaluate theperformance of the system The train speed is controlledunder 36 kmh In the train we chose there are 4 new groundwheelsets in a car of the train Under the consideration thatthe ground new wheel is not out of roundness which hasan effect on the analysis results we selected the ground newwheel as our target wheel
Table 2 shows the mean and standard deviation value ofmeasurement The biggest differential value of mean flangeheight appears in 1 wheel and for mean flange width appearsin 3 wheel The difference does not exceed 015mm As forwheel diameter the biggest differential value 016mmappearsin 3 wheelThemean value of six times of repeated detectionis consistent with the standard wheelset test In terms ofstandard deviation the value is less than 01mm for flangewidth and flange height and 03mm for wheel diameterThe standard deviation of wheel diameter is relatively higherthan in standard wheelset test On the contrary the standarddeviation of flange width and flange height is relatively lowerthan in the old system That is also consistent with standard
Journal of Sensors 13
Table 2 Real train test the mean and standard deviation value of detected measurementmm
Wheelnumber
Mean flange height SD flange height Mean flange width SD flange width Mean wheeldiameter SD wheel diameter
Old New Old New Old New Old New Old New Old New1 2818 2803 0046 0060 2954 2943 0091 0062 80052 80150 0201 03012 2809 2811 0078 0040 2940 2929 0056 0028 80112 80096 0128 02863 2797 2791 0076 0033 2992 3006 0075 0056 80187 80166 0090 01794 2807 2805 0063 0053 2983 2988 0076 0088 80178 80201 0192 0282
Table 3 Real train test wheel 2 the result of repeated measure-mentmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
wheelset test The standard deviation of wheel diameter inreal train test is supposed to be higher than in the standardwheelset test because of several assumptions One factor isthe higher possibility of S-shape running because of heavyaxial load On the other hand the wheelset that is in service isalso more polluted with rust than standard wheelset causingmore detection uncertainty However the standard deviationfrom real train test also does not exceed 03mm which isconsistent with standard wheelset test This may result fromthe lower train speed during the test which leads to lowerpossibility of S-shape running Meanwhile the rusty wheelcontour is also not in a massive stage Tables 3 and 4 show theresult of repeated measurement for wheels numbers 2 and 3respectively In each detection the results remain the sameand no gross error appears
Overall detection uncertainties for tread profile andwheel diameter are less than 01mmand 03mm respectivelyThe results show that the detection system has a highaccuracy which can meet the requirements of maintenanceoperation
5 Conclusion
This paper based on LDS proposed a novel on-track detec-tion system of the wheel size using only six 2D-LDS and two1D-LDS Errors induced bywheel-rail vibration sensor noisemisalignment S-shape running and wheelset differential arealso analyzed After the system is implemented real dataexperiments including standard wheel test and real traindetection test were performed It turns out that the detectionuncertainty of flange width and height is 01mm and wheeldiameter 03mm which can meet the requirements of main-tenanceThis system can be further used for different types ofrailway transportation which provides a new solution for thewheel size detection technology
To provide more benefits the target wheel diameter is 119863 =
840mm and the origin of the wheel is located in the originof 119910119900119911WCF as shown in Figure 14 In this special case therelevant geometric values are 1198881(minus19802mm minus19802mm)1198882(0mm 420mm) 1198883(19802mm minus19802mm) 1198971 = 280mm1198972 = 180mm and 1198973 = 280mm
According to (8) and (9) we get the particle derivative asfollows
120597119863
1205971198971
=
120597119863
1205971199100
1205971199100
1205971198971
+
120597119863
1205971199110
1205971199110
1205971198971
120597119863
1205971198972
=
120597119863
1205971199100
1205971199100
1205971198972
+
120597119863
1205971199110
1205971199110
1205971198972
+
120597119863
1205971199111198882
1205971199111198882
1205971198972
(A2)
14 Journal of Sensors
2D-L1
1D-L2
2D-L3
y
z
o
45∘45∘ c1l1
l2
l3
c2
c3 lowast
lowast
lowast
Figure 14 A special case
Taking the derivative of diameter 119863 with respect to 1199100 1199110and 119911119888
2
according to (8) and substituting (1199100 1199110) = (0 0) and1199111198882
= 180mm we have
120597119863
1205971199100
=
21199100
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199110
=
2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199111198882
=
minus2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
= 2
(A3)
Furthermore based upon (7) we get
1205971199100
1205971198971
=
1205971199100
1205971199101198881
1205971199101198881
1205971198971
+
1205971199100
1205971199111198881
1205971199111198881
1205971198971
1205971199110
1205971198971
=
1205971199110
1205971199101198881
1205971199101198881
1205971198971
+
1205971199110
1205971199111198881
1205971199111198881
1205971198971
1205971199100
1205971198972
=
1205971199100
1205971199111198882
1205971199111198882
1205971198972
1205971199110
1205971198972
=
1205971199110
1205971199111198882
1205971199111198882
1205971198972
1205971199100
1205971198973
=
1205971199100
1205971199101198883
1205971199101198883
1205971198973
+
1205971199100
1205971199111198883
1205971199111198883
1205971198973
1205971199110
1205971198973
=
1205971199110
1205971199101198883
1205971199101198883
1205971198973
+
1205971199110
1205971199111198883
1205971199111198883
1205971198973
(A4)
When calculating particle derivative of (1199100 1199110) with respectto three points 1198881 1198882 and 1198883 in WCF we assume that allparameters are with the geometric values in this special case
Then we substitute the ideal geometric values of this variableand we obtain
1205971199100
1205971199101198881
= 05
1205971199100
1205971199111198881
= 05
1205971199110
1205971199101198881
= minus12071
1205971199110
1205971199111198881
= minus12071
1205971199100
1205971199111198882
= 0
1205971199110
1205971199111198882
= 34142
1205971199100
1205971199101198883
= 05
1205971199100
1205971199111198883
= minus05
1205971199110
1205971199101198883
= 12071
1205971199110
1205971199111198883
= minus12071
1205971199101198881
1205971198971
=
1
radic2
1205971199111198881
1205971198971
=
1
radic2
1205971199111198882
1205971198972
= minus1
1205971199101198883
1205971198973
= minus
1
radic2
1205971199111198883
1205971198973
=
1
radic2
(A5)
Finally substituting (A5) into (A4) and then substituting(A4) and (A3) into (A2) we have
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(A6)
Competing Interests
The authors declare that they have no competing interests
Journal of Sensors 15
Acknowledgments
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
Figure 6 Scanning coordinates of 2D-L1 1D-L2 and 2D-L3 after coordinate transformation
y
z
o
Wheel
c3
c (x0 y0)
c1
c2 l1
l2
l3
1205722
12057211205723
P1 (y1 z1)
P2 (y2 z2)
P3 (y3 z3)lowast
lowast
lowast
(a)
a
o(2)
u(3)
o(3)
v (3)c3Fc
doff
(b)
Figure 7 Wheel diameter calculation principle in two dimensions (a) sight along the 119909-axis scanning coordinates of 2D-L1 1D-L2 and2D-L3 after transformation (b) sight in the 119906(3)119900(3)V(3) coordinate
was conducted and the scanning coordinates 119906(1)119900(1)V(1)119906(2)119900(2)V(2) and 119906(3)119900(3)V(3) for 2D-L1 1D-L2 and 2D-L3
respectively have been obtained Figure 6 shows the scanningcoordinates of 2D-L1 1D-L2 and 2D-L3 after coordinatetransformation Notice that 119906(2)119900(2)V(2) is still the same as119910(2)119900(2)119911(2) because of the installation position of 1D-L2
Figure 6 also shows the offset 119889off between the origin of thecoordinate 119906(3)119900(3)V(3) and laser scanning line of L2 in 119906(2)-axis Among three points the two points detected by 2D-L1and 2D-L3 are extracted from the 2D profiles The offset 119889offis the 119906(2)-axis coordinate value to extract the points in theflange circle from two-dimensional profile This offset 119889off isdetermined by sensor installation
Figure 7 shows the wheel diameter calculation princi-ple in two dimensions where (a) shows the principle that
three points determine a diameter in 119910119900119911 WCF and (b)shows extracting the point in the flange circle among two-dimensional profile and the final wheel diameter distancesubtraction by 119865119888 From Figure 7(a) the installation of eachLDS is modeled as three parameters in 119910119900119911 WCF whichare the position Pi(119910119894 119911119894) and angle 120572119894 They determinethe position of laser origin and the direction of detectionrespectively The angle 1205722 for 1D-L2 is designed as 1205872 Thepositions P1 and P3 are designed as symmetric with respectto the scanning line of 1D-L2 as well as the angles 1205721 and1205723 Even though many of the parameters are designed tobe equal for instance 1199111 = 1199113 the real parameters willvary after engineering implementation due to errors suchas installation error and manufacturing error Thus thisnine-parameter model is proposed for diameter calculation
Journal of Sensors 7
because it can describe all the possible errors The realinstallation parameters are obtained through calibration aslater described Moreover the distances 1198971 1198972 and 1198973 aredetected from three LDS sensors The three points c1 c2and c3 are in the flange of wheel detected by three sensorsrespectively The point c(1199100 1199110) is the origin of the detectedwheel which is calculated by three points c1 c2 and c3
According to Figures 6 and 7(a) the first information wecan get from the LDS sensors is the laser scanned distances1198971 1198972 and 1198973 1198972 is directly detected by 1D-L2 1198971 and 1198973 areextracted from the 2D profiles detected by 2D-L1 and 2D-L3 respectively To extract 1198971 and 1198973 we need to find thecorrect points in the two-dimensional tread profile As shownin Figures 6 and 7(b) the point that determines 1198971 and 1198973should be in the 119906-axis value of offset 119889off Similar to detectingtread profile we use the same curve fitting method to obtaina curve in the contour of the wheel in the 119906119900V coordinate thatis denoted by V = 1198913(119906) When the curve line is obtained1198973 = V3 = 1198913(119889off ) namely the V-axis value of curve 1198913(119906)
when 119906 = 119889off Similarly 1198971 is detected by 2D-LDS L1 usingthe same method as deciding 1198973
Once the laser scanned distances 1198971 1198972 and 1198973 aredetermined we get the three points c1 c2 and c3 in WCFcoordinate 119910119900119911 by
1199101198881
= 1199101 + 1198971 sin1205721
1199111198881
= 1199111 + 1198971 cos1205721
1199101198882
= 1199102 + 1198972 sin1205722
1199111198882
= 1199112 + 1198972 cos1205722
1199101198883
= 1199103 + 1198973 sin1205723
1199111198883
= 1199113 + 1198973 cos1205723
(6)
Based on three points c1 c2 and c3 the wheel center c(1199100 1199110)is determined by
1199100 =
(1199111198881
minus 1199111198883
) (11991021198881
minus 11991021198882
+ 11991121198881
minus 11991121198882
) minus (1199111198881
minus 1199111198882
) (11991021198881
minus 11991021198883
+ 11991121198881
minus 11991121198883
)
2 (1199101198881
minus 1199101198882
) (1199111198881
minus 1199111198883
) minus 2 (1199101198881
minus 1199101198883
) (1199111198881
minus 1199111198882
)
1199110 =
(1199101198881
minus 1199101198882
) (11991021198881
minus 11991021198883
+ 11991121198881
minus 11991121198883
) minus (1199101198881
minus 1199101198883
) (11991021198881
minus 11991021198882
+ 11991121198881
minus 11991121198882
)
2 (1199101198881
minus 1199101198882
) (1199111198881
minus 1199111198883
) minus 2 (1199101198881
minus 1199101198883
) (1199111198881
minus 1199111198882
)
(7)
and the wheel diameter119863119903 is determined by
119863119903 = 2 sdotradic(1199100)
2+ (1199110 minus 119911119888
2
)
2 (8)
From Figure 7(b) 119865119888 is the distance between points c3 anda along V-axis The wheel diameter detected by the previousthree points is somewhere in the contour circle governed bythe 1D-L2 only The point a is considered to be the diameterpoint of the wheel which is minus70mm away from the innerside of the wheel In order to obtain the final wheel diameterwe need to further subtract the distance 119865119888 from the wheeldiameter
119863 = 119863119903 minus 2119865119888 (9)
where119865119888 is the distance between point c3 and point a in V-axis(as shown in Figure 7(b)) namely 119865119888 = V119886 minus V119888
3
25 Dynamics Detection The calculation principles shownabove are in static case When the train passes dynam-ically multiscans can be obtained and the misalignmentphenomenon caused from wheel passing will occur
For tread profile detection ideally the laser light panel ofL3 and L4 is assumed to include the center of the measuredwheel In dynamics detection it is impossible to meet thatassumption for all measured wheels due to the moving ofwheel and the discrete sampling of LDS signal Basicallyif the laser light panel does not include the center of themeasured wheel the detected profile is horizontally stretched
along V-axis That will lead to the increase of detected flangeheight and flange width This phenomenon is called themisalignment between the laser panel and the detectiontarget [9]
Figure 8 shows the dynamics positions of thewheel centerand laser panel constituted by L3 and L4 in two-dimensionalWCF The wheel moves forward with a constant speed of V1198741 1198742 and 119874119894 are the center of wheel diameter circle underdifferent positions The laser panel has an installation angle1205723 with respect to 119910-axis which can be determined as 119911 =tan1205723 sdot 119910 in WCF The center points of wheel diameter circleare calculated by (7) 119889119894 denote the distance between 119894th wheelcenter point and the laser panel
Theoretically for every 119894th position of the wheel thedistance 119889119894 from the wheel center c(1199100
119894
1199110119894
) to the laser panelcan be determined by point to the distance formula as follows
When the distance 119889119894 equals zero the wheel center c(1199100119894
1199110119894
)
is in the laser panel where the flange height and flange widthhave no stretching On the other hand the bigger the distance119889119894 is the farther away the wheel center c(1199100
119894
1199110119894
) is from thelaser panel
It is worthmentioning that the LDSworks when the anglebetween laser light and detected surface is within a certainrange and the angle is influenced by laser wavelength surface
8 Journal of Sensors
y
z
Laser panel
Rail
Wheelv
Scanned section
O1 O2
d1 d22120579
120579
120579
1205723
Oi
di
L3 L4lowast
Figure 8 Dynamics position of the wheel center
smoothness surface material and so forth [23] It is assumedthat the angle 120579 (as shown in Figure 8) is the largest angleat which the LDS can still receive effective scan When thewheel is moving out of the detection range the LDS will beunable to scanThus the scanned sectionwill be the arcwith acentral angle of 2120579 and all the tread profiles and diameters arescanned from this section For most LDS sensors the angle 120579can reach up to 45∘ so the system can measure 90∘ arc of thewheel Correspondingly the maximum value of the distance119889119894 is 119877 sin 120579 where 119877 is the wheel radius
The misalignment phenomenon will bring about certainerror to the profile detection Among all the effective scanswe must select those scans where the induced error isacceptable In this paper the error induced in the tread profiledetection is analyzed in Section 3 As a result the error isdirectly proportional to the distance 119889119894 So we set up a certainthreshold 119870119901 When the distance 119889119894 lt 119870119901 the detectedtread profile can be regarded as useful profiles where the errorinduced by the misalignment phenomenon is negligible Thethreshold 119870119901 is firstly obtained through error analysis andalso is adjustable according to the field experiment Due tothe benefits from the high sampling frequency of the LDSsensors 119872 times of scans can be obtained for a wheelsetThen we can remove the bulky error first and performaverage operation to get the final wheel flange and wheelwidth as follows
119865119908119891
=
1
119872
119872
sum
119894=1
119865119908119894
119865ℎ119891
=
1
119872
119872
sum
119894=1
119865ℎ119894
(11)
where 119865119908119894
and 119865ℎ119894
are the flange width and flange height in119894th scan respectively 119865119908
119891
and 119865ℎ119891
are the final flange widthand flange height respectively The average operation herecan reduce the final error caused by Gaussian sensor noise
For wheel diameter detection the three points thatdetermine the wheel diameter are always in the contourcircle Thus the calculation results will not be influenced by
different wheel positions However 119865119888119894
in every 119894th scan willstill be stretched and bring about some error Similarly weselect a set of scans by comparing whether the distance 119889119894is smaller than a certain threshold 119870119889 or not When 119889119894 lt119870119889 the error induced in the detected 119865119888 is negligible Thetwo thresholds 119870119889 and 119870119901 might be different because ofthe different detection error requirements for tread profileand wheel diameter In this way 119873 times of scans can beobtained Then we can remove the bulky error first andperform average algorithm to get the final wheel diameter asfollows
119863119891 =1
119873
119873
sum
119894=1
119863119894 (12)
where 119863119894 is the wheel diameter in 119894th scan 119863119891 is the finalwheel diameter
26 Calibration The measuring and calculating of treadprofile and wheel diameter depend on many installationparameters Regarding tread profile calculation they are theangle 1205733 in (1) angle 1205734 in (2) and the offset Δ119906 and offsetΔV in (3) For wheel diameter they are the offset 119889off betweenthe origin of the coordinate 119906119900V and laser scanning line of L2in 119906(2)-axis the angles 1205721 1205722 and 1205723 and the positions P1P2 and P3 in (6) When the LDS are installed and fixed it isimpossible for those parameters to be the same with designedvalues because of the manufacture error of mechanical partsand installation accuracy So calibration is certainly needed
During the calibration process for tread profile detectiona standard wheel is placed on the rail over the detection sys-tem and then the offset and rotation angle of the coordinatetransformation matrix can be determined In terms of theangles 1205733 and 1205734 the calibrated accurate value is to makesure the inner and outer panels of the wheel are vertical Forthe offset Δ119906 the calibrated accurate value is to make surethe detected wheel hub thickness equals the standard wheelhub thickness and the offset ΔV is to make sure the scannedprofiles from two LDS coincide with each other
As for the calibration process for wheel diameter a setof new ground wheelsets is used The ground wheelset iswith different diameters that are 770mm 790mm 810mmand 840mm We set the minimization function 119891(119909) as thesquared summation of detected diameters subtracted by realdiameter That is
min 119891 (119909) =
119869
sum
119894=1
1003816100381610038161003816119863119894 minus 119863119903
1003816100381610038161003816
2 (13)
where 119863 is the detected diameter according to wheel diam-eter calibration principle 119863119903 is the real diameters 119909 =
[119889off 1205721 1205721 1205723 1199101 1199111 1199102 1199112 1199103 1199113] is the variables to be cali-brated 119869 denotes the number of ground wheelsets MATLABhas provided such tools to solve those optimization problemsOver here we use fmincon function to minimize the functionand the constraints in terms of the variables are also givenaccording to real physical ranges Finally the optimal valuesof the parameters can be obtained These values are assumedto be the real values that the implemented system has andhave been further put into use in system service
Journal of Sensors 9
3 Detection Error Analysis
In this section we consider four factors which are railvibration sensor noise misalignment and wheel inclinationcaused by wheel S-shape running and the differential ofdiameters
31 Wheel-Rail Vibration Wheel-rail vibration is the firstfactor that we considered In our system all the sensorsare well fixed by the mechanical support and mechanicalpedestal that has no direct contact with rail So the wheel-railvibrationwill not directly transmit to the sensors and insteadthe wheel-rail vibration has to transmit to the ground of thedepot and then transmit to the sensors through mechanicalsupport andmechanical pedestalThe vibration of the groundis on a lower level the maximum of acceleration is only04m2s [24] in Guangzhou metro depot and it is alsoattenuated by the mechanical pedestal We also measuredthe maximum of acceleration of mechanical support duringtrain passing which is only 02m2s So the change of theposition of the sensors due to the wheel-rail vibration in oursystemcanbeneglected Furthermore all the laser sensors arecapturing data simultaneously and the exposure time of theLDS is within 50 microseconds The vibration of the wheelwill not cause considerable movement within such a shorttime Overall the system is assumed to be reliable againstwheel-rail vibration
32 Misalignment As previously mentioned in Section 2Dynamics Detection if the laser light panel does not includethe center of the measured wheel the detected profile is hor-izontally stretched along V-axis This phenomenon is calledthe misalignment between the laser panel and the detectiontarget which will lead to the increase of the detected flangeheight and flange width Chen et al [10] derived a geometricmodel regarding howmany errors will be generated for flangeheight when wheel position varies The error 119890 of the flangeheight is
where 119877 is the wheel radius 119877119862 is the radius in the wheel rim119889 is the distance from the wheel center to the laser panel asdescribed in Section 2
On the basis of this geometric model when we know howmuch the error of the flange height is the errors of the flangewidth can be derived accordingly For different wear wheelsthe profiles aswell as the fitted line for lateral contact pointmare certainly different To illustrate the massiveness of errorshere we chose the same wheel where the fitted line for lateralcontact point m is V = 119891(119906) We obtain the inverse function119906 = 119892(V) and stretch it horizontally by a factor of (119865ℎ + 119890)119865ℎSo the stretched curve line is
119906 = 1198922 (V) = 119892(V119865ℎ
(119865ℎ + 119890)) (15)
Eventually the error of flange width is 120578 = 1198922(10)minus119865119908 where119865119908 is the original flange width
Error of flange heightError of flange width
0
01
02
03
04
05
06
07
08
Caus
ed er
ror (
mm
)
10 20 30 40 500d (mm)
Figure 9 The error of flange width and flange height with respectto various wheel positions
Theoretically from (14) and (15) we know that the smallerthe value of 119877 is the larger the error 119890 is So we chosethe largest standard wheelset with 119877 = 385mm and 119877119862 =399mm Figure 9 shows the error of flange height and flangewidth induced from misalignment in this case The distance119889 varies from 0mm to 50mmwith an interval of 1mm FromFigure 9 the error of flange height is lower than the error offlange width So we focus on the error of flange width here
In our system the sampling frequency of all LDS is 1 kHzand the maximum speed of the train in the depot is 36 kmhThemaximum of sampling step size along the railΔ119904 = 1ms times10ms = 10mmWhen we set the threshold119870119901 (as describedin Section 25) as 20mm the total measuring distance alongthe rail can be 58mm so that at least 119872 = 5 times ofefficient scans can be detected The corresponding errors areless than 01mm for flange width after taking the average ofthese 5 efficient scansThus the system can performdetectionnormally against themisalignment error benefitting from thehigh sampling frequency
33 Sensor Noise The LDS cannot be ideally accurate Themeasuring accuracy is influenced by temperature the rough-ness of the measured surface and so forth
In order to obtain the quantitative influence for profiledetection we built a 3D model in SolidWorks tools andextracted ideal sensor output points of standard inner andouter tread profiles In this model the standard wheel islocated in the position where the center of the wheel is inthe laser panel So the misalignment phenomenon will notaffect tread profile detection The wheel is in static positionso the simulated sensor output points are all from one scanMoreover the parameters that need to be calibrated areideally accurate To imitate the real situation Gaussian noiseis added to these coordinate valuesThemean of noise is zeroand the standard deviation is varied from 0 to 1mm with an
10 Journal of Sensors
X 03Y 01251
Flange widthFlange height
0
01
02
03
04
05
06
07Ca
used
erro
r (m
m)
02 04 06 08 10Noise level (mm)
Figure 10 The RMS error of flange height and flange width causedby different sensor noise level
interval of 01mm For each noise level 500 experiments arecarried out and the RMS error is calculated The RMS errorof flange height and flange width results caused by differentnoise level is shown in Figure 10 The caused error to flangeheight and flange width is approximately half of the sensornoise level This can be explained by the curve line fittingmethod that has taken more laser points into account andthus has reduced the random noise Because the flange heightis determined by two points the curve line fittingmethod hasat least reduced the randomerror into a quarter of the originalsensor noise
The 2D-LDS we chose is LJ-V7300 from KEYENCEwhich has a full-scale resolution of 01FS and a temper-ature drift of 001 FS∘C The detection range in 119910-axis is300 plusmn 145mm and in 119909-axis is 110mm to 240mm whichformed as a trapezoid The point in 119909-axis is fixed thus onlysensor noise in 119910-axis needs to be considered with full scaleof 290mm So accordingly the RMS error caused to theprofile coordinate noise in 119910-axis which is denoted by 120575 isless than 032mm which only leads to an error of 013mmboth to flange height and to flange width Taking dynamicsdetection effect into account the final error is reduced by120575119891 = 120575
radic5 = 0058mm with at least119873 = 5 times of efficientscans The error caused by sensor noise can be acceptable
Regarding the error of wheel diameter it can be theoreti-cally derived by the theorem of error propagation [25] Theresolution of each sensor is denoted by 1205751 1205752 and 1205753 Weobtain 120575119863 by taking differential of (6)ndash(9) as follows
120575119863 = plusmnradic(1205751
120597119863
1205971198971
)
2
+ (1205752
120597119863
1205971198972
)
2
+ (1205753
120597119863
1205971198973
)
2
(16)
We have chosen two 2D-LDS and one 1D-LDS to detect thewheel diameter and the two 2D-LDS are installed symmet-rically For systematic installation we have 1205751(1205971198631205971198971) =
1205753(1205971198631205971198973) Moreover the analytical function of particle
derivative will be too complex to derive So we consider aspecial case where
where the target wheel diameter is 119863 = 840mm and theorigin of the wheel is located in the origin of 119910119900119911WCF Morecalculation details can be found in the Appendix Finally wehave
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(18)
The 1D-LDS we chose is LK-G8085 from KEYENCE whichhas linearity of 005FS and a temperature drift of 001FS∘C So according to the full scale of 30mm the reso-lution of 1D-LDS 1205752 = 0018mm Based upon the findingthat the curve line fitting method has at least reduced therandom error into a quarter of the original sensor noise1205751 = 0075mm Finally 120575119863 is less than 0372mm Takingdynamics detection effect into account the final error 120575119863
119891
=
120575119863radic5 = 017mm The error caused by sensor noise can be
acceptable
34 Wheel Inclination Caused by Wheelset S-Shape RunningandDifferential ofWheel Diameter In engineering thewheelwill be inclined because of wheelset S-shape running and thedifferential of wheel diameter The wheelset S-shape runningis one kind of self-induced vibration due to the slope in thewheel trade When it is S-shape running the wheel panelwill have a certain angle with respect to 119910119900119911 panel in WCFdenoted by 120579119904 as shown in Figure 11(a) The differentialof wheel diameter in a wheelset is at different wear levelin the left and right wheel mainly induced from differentmassiveness of wear in the circuit of wheelset turning andunbalanced loading Similarly it will bring a certain angleabout the wheel panel with respect to the 119910119900119911 panel in WCFThe angle is denoted by 120579119889 as shown in Figure 11(b)
For wheel diameter detection because we only considerthe calculation in two dimensions an error will be generatedwhen we still regard the detected three points in a circle toactually be in an ellipse Considering the existence of angles120579119904 and 120579119889 we have the equation of ellipse as follows
1199102
(119877 sdot cos 120579119904)2+
1199112
1198772= 1
1199102
1198772+
1199112
(119877 sdot cos 120579119889)2= 1
(19)
Journal of Sensors 11
x
y
z
0
Ellipse wheel
Wheelset withS-shape running
120579s
(a)
x
y
z Ellipse wheel
Wheelset with differential of diameter
120579d
(b)
Figure 11 Mathematical illustration (a) Wheel S-shape running and (b) differential of wheel diameter
Similar towhenwe analyze sensor noise we consider a specialcase as (17) the origin of the target wheel is located in theorigin of 119910119900119911WCFThe real three points are
1198881(119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198882 (0 minus119877)
1198883(minus119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198881(119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
1198882 (0 minus119877 sdot cos 120579119889)
1198883(minus119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
(20)
Theoretically the larger the radius of the wheel is the biggerthe error is So we chose 119877 = 420mm and generated threepoints then using (7) we calculated the wheel diameter witherror Subtracting the real diameter we have the error withrespect to angle as shown in Figure 12 The effect of S-shaperunning caused angle has a relatively higher influence on thewheel diameter calculation
Based on the experience from Guangzhou Metro Cor-poration the differential of diameter in a wheelset shouldbe controlled under 2mm Considering the track gauge of1350mm the angle induced from the differential of diameter
S-shape runningWheel diameter differential
0
001
002
003
004
005
006
Caus
ed er
ror t
o di
amet
er (m
m)
01 02 03 04 050120579 (∘)
Figure 12 Wheel diameter errors
in a wheelset is less than 0001∘ thus the error can be ignoredAs for wheel S-shape running themaximum angle is 01∘ [26]when the speed of the train is under 36 kmhwhich will causean error not larger than 0005mm
4 Experimental Validation
41 System Implementation Theauthors previously proposedan online detection system using eight 2D-LDS [19] Thenew online detection system is installed in the same storageline of Guangzhou metro vehicle depot as the old systemso that comparison can be conducted In order to savefund only the left side namely half of the system has been
12 Journal of Sensors
(a) (b)
Figure 13 Field test (a) Standard wheel test and (b) real train test
Table 1 Standard wheelset detection the results of repeatedmeasurementsmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
implemented During the system implementation three-dimensional inclinometer and special rail gauge are used tocontrol the position of the mechanical support After thesystem is installed the calibration described in Section 2has been conducted to obtain the geometric parameters fortread profile calibration and diameter calculation As shownin Figure 13 the field test is carried out by a standard wheelsetand real train
42 Standard Wheelset The standard wheelset is a new pro-duced wheelset without any wear and diameter differentialThe manufacturing geometric size is as follows wheel diam-eter = 840mm flange height = 28mm and flange width =32mm One can also assume to have lower possibility of S-shape running because of zero external load The standardwheelset has been placed on the rail and passed through thedetection system This test has been carried out 6 times toverify both the detection and the repeatability of the systemComparing with the old system the results of this system areshown in Table 1
From Table 1 the mean values of the flange height andflange width detected by the old and the new system are very
close to each other which means the system error can beignored The standard deviation which also can be denotedas detection uncertainty of the new system measurement isslightly smaller than of the old system That may result fromthe lower effect frommisalignment as described in Section 3due to the higher sampling frequency that we used in the newsystem Detection uncertainty of not greater than 005mm intread profile measurement is acceptable for the engineeringrequirements As for wheel diameter detection the meanvalues are also close to each other The standard deviation ofthe new systemmeasurement is slightly higher than of the oldsystemThis may result from the replacement of 1D-LDS thathas brought about higher sensor noise to the middle pointamong three pointswithout curve fitting techniqueHoweverdetection uncertainty of less than 03mm is also acceptable inengineering
43 Real Train Detection Test Real train test also performs6 times of repeated detection to statistically evaluate theperformance of the system The train speed is controlledunder 36 kmh In the train we chose there are 4 new groundwheelsets in a car of the train Under the consideration thatthe ground new wheel is not out of roundness which hasan effect on the analysis results we selected the ground newwheel as our target wheel
Table 2 shows the mean and standard deviation value ofmeasurement The biggest differential value of mean flangeheight appears in 1 wheel and for mean flange width appearsin 3 wheel The difference does not exceed 015mm As forwheel diameter the biggest differential value 016mmappearsin 3 wheelThemean value of six times of repeated detectionis consistent with the standard wheelset test In terms ofstandard deviation the value is less than 01mm for flangewidth and flange height and 03mm for wheel diameterThe standard deviation of wheel diameter is relatively higherthan in standard wheelset test On the contrary the standarddeviation of flange width and flange height is relatively lowerthan in the old system That is also consistent with standard
Journal of Sensors 13
Table 2 Real train test the mean and standard deviation value of detected measurementmm
Wheelnumber
Mean flange height SD flange height Mean flange width SD flange width Mean wheeldiameter SD wheel diameter
Old New Old New Old New Old New Old New Old New1 2818 2803 0046 0060 2954 2943 0091 0062 80052 80150 0201 03012 2809 2811 0078 0040 2940 2929 0056 0028 80112 80096 0128 02863 2797 2791 0076 0033 2992 3006 0075 0056 80187 80166 0090 01794 2807 2805 0063 0053 2983 2988 0076 0088 80178 80201 0192 0282
Table 3 Real train test wheel 2 the result of repeated measure-mentmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
wheelset test The standard deviation of wheel diameter inreal train test is supposed to be higher than in the standardwheelset test because of several assumptions One factor isthe higher possibility of S-shape running because of heavyaxial load On the other hand the wheelset that is in service isalso more polluted with rust than standard wheelset causingmore detection uncertainty However the standard deviationfrom real train test also does not exceed 03mm which isconsistent with standard wheelset test This may result fromthe lower train speed during the test which leads to lowerpossibility of S-shape running Meanwhile the rusty wheelcontour is also not in a massive stage Tables 3 and 4 show theresult of repeated measurement for wheels numbers 2 and 3respectively In each detection the results remain the sameand no gross error appears
Overall detection uncertainties for tread profile andwheel diameter are less than 01mmand 03mm respectivelyThe results show that the detection system has a highaccuracy which can meet the requirements of maintenanceoperation
5 Conclusion
This paper based on LDS proposed a novel on-track detec-tion system of the wheel size using only six 2D-LDS and two1D-LDS Errors induced bywheel-rail vibration sensor noisemisalignment S-shape running and wheelset differential arealso analyzed After the system is implemented real dataexperiments including standard wheel test and real traindetection test were performed It turns out that the detectionuncertainty of flange width and height is 01mm and wheeldiameter 03mm which can meet the requirements of main-tenanceThis system can be further used for different types ofrailway transportation which provides a new solution for thewheel size detection technology
To provide more benefits the target wheel diameter is 119863 =
840mm and the origin of the wheel is located in the originof 119910119900119911WCF as shown in Figure 14 In this special case therelevant geometric values are 1198881(minus19802mm minus19802mm)1198882(0mm 420mm) 1198883(19802mm minus19802mm) 1198971 = 280mm1198972 = 180mm and 1198973 = 280mm
According to (8) and (9) we get the particle derivative asfollows
120597119863
1205971198971
=
120597119863
1205971199100
1205971199100
1205971198971
+
120597119863
1205971199110
1205971199110
1205971198971
120597119863
1205971198972
=
120597119863
1205971199100
1205971199100
1205971198972
+
120597119863
1205971199110
1205971199110
1205971198972
+
120597119863
1205971199111198882
1205971199111198882
1205971198972
(A2)
14 Journal of Sensors
2D-L1
1D-L2
2D-L3
y
z
o
45∘45∘ c1l1
l2
l3
c2
c3 lowast
lowast
lowast
Figure 14 A special case
Taking the derivative of diameter 119863 with respect to 1199100 1199110and 119911119888
2
according to (8) and substituting (1199100 1199110) = (0 0) and1199111198882
= 180mm we have
120597119863
1205971199100
=
21199100
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199110
=
2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199111198882
=
minus2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
= 2
(A3)
Furthermore based upon (7) we get
1205971199100
1205971198971
=
1205971199100
1205971199101198881
1205971199101198881
1205971198971
+
1205971199100
1205971199111198881
1205971199111198881
1205971198971
1205971199110
1205971198971
=
1205971199110
1205971199101198881
1205971199101198881
1205971198971
+
1205971199110
1205971199111198881
1205971199111198881
1205971198971
1205971199100
1205971198972
=
1205971199100
1205971199111198882
1205971199111198882
1205971198972
1205971199110
1205971198972
=
1205971199110
1205971199111198882
1205971199111198882
1205971198972
1205971199100
1205971198973
=
1205971199100
1205971199101198883
1205971199101198883
1205971198973
+
1205971199100
1205971199111198883
1205971199111198883
1205971198973
1205971199110
1205971198973
=
1205971199110
1205971199101198883
1205971199101198883
1205971198973
+
1205971199110
1205971199111198883
1205971199111198883
1205971198973
(A4)
When calculating particle derivative of (1199100 1199110) with respectto three points 1198881 1198882 and 1198883 in WCF we assume that allparameters are with the geometric values in this special case
Then we substitute the ideal geometric values of this variableand we obtain
1205971199100
1205971199101198881
= 05
1205971199100
1205971199111198881
= 05
1205971199110
1205971199101198881
= minus12071
1205971199110
1205971199111198881
= minus12071
1205971199100
1205971199111198882
= 0
1205971199110
1205971199111198882
= 34142
1205971199100
1205971199101198883
= 05
1205971199100
1205971199111198883
= minus05
1205971199110
1205971199101198883
= 12071
1205971199110
1205971199111198883
= minus12071
1205971199101198881
1205971198971
=
1
radic2
1205971199111198881
1205971198971
=
1
radic2
1205971199111198882
1205971198972
= minus1
1205971199101198883
1205971198973
= minus
1
radic2
1205971199111198883
1205971198973
=
1
radic2
(A5)
Finally substituting (A5) into (A4) and then substituting(A4) and (A3) into (A2) we have
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(A6)
Competing Interests
The authors declare that they have no competing interests
Journal of Sensors 15
Acknowledgments
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
because it can describe all the possible errors The realinstallation parameters are obtained through calibration aslater described Moreover the distances 1198971 1198972 and 1198973 aredetected from three LDS sensors The three points c1 c2and c3 are in the flange of wheel detected by three sensorsrespectively The point c(1199100 1199110) is the origin of the detectedwheel which is calculated by three points c1 c2 and c3
According to Figures 6 and 7(a) the first information wecan get from the LDS sensors is the laser scanned distances1198971 1198972 and 1198973 1198972 is directly detected by 1D-L2 1198971 and 1198973 areextracted from the 2D profiles detected by 2D-L1 and 2D-L3 respectively To extract 1198971 and 1198973 we need to find thecorrect points in the two-dimensional tread profile As shownin Figures 6 and 7(b) the point that determines 1198971 and 1198973should be in the 119906-axis value of offset 119889off Similar to detectingtread profile we use the same curve fitting method to obtaina curve in the contour of the wheel in the 119906119900V coordinate thatis denoted by V = 1198913(119906) When the curve line is obtained1198973 = V3 = 1198913(119889off ) namely the V-axis value of curve 1198913(119906)
when 119906 = 119889off Similarly 1198971 is detected by 2D-LDS L1 usingthe same method as deciding 1198973
Once the laser scanned distances 1198971 1198972 and 1198973 aredetermined we get the three points c1 c2 and c3 in WCFcoordinate 119910119900119911 by
1199101198881
= 1199101 + 1198971 sin1205721
1199111198881
= 1199111 + 1198971 cos1205721
1199101198882
= 1199102 + 1198972 sin1205722
1199111198882
= 1199112 + 1198972 cos1205722
1199101198883
= 1199103 + 1198973 sin1205723
1199111198883
= 1199113 + 1198973 cos1205723
(6)
Based on three points c1 c2 and c3 the wheel center c(1199100 1199110)is determined by
1199100 =
(1199111198881
minus 1199111198883
) (11991021198881
minus 11991021198882
+ 11991121198881
minus 11991121198882
) minus (1199111198881
minus 1199111198882
) (11991021198881
minus 11991021198883
+ 11991121198881
minus 11991121198883
)
2 (1199101198881
minus 1199101198882
) (1199111198881
minus 1199111198883
) minus 2 (1199101198881
minus 1199101198883
) (1199111198881
minus 1199111198882
)
1199110 =
(1199101198881
minus 1199101198882
) (11991021198881
minus 11991021198883
+ 11991121198881
minus 11991121198883
) minus (1199101198881
minus 1199101198883
) (11991021198881
minus 11991021198882
+ 11991121198881
minus 11991121198882
)
2 (1199101198881
minus 1199101198882
) (1199111198881
minus 1199111198883
) minus 2 (1199101198881
minus 1199101198883
) (1199111198881
minus 1199111198882
)
(7)
and the wheel diameter119863119903 is determined by
119863119903 = 2 sdotradic(1199100)
2+ (1199110 minus 119911119888
2
)
2 (8)
From Figure 7(b) 119865119888 is the distance between points c3 anda along V-axis The wheel diameter detected by the previousthree points is somewhere in the contour circle governed bythe 1D-L2 only The point a is considered to be the diameterpoint of the wheel which is minus70mm away from the innerside of the wheel In order to obtain the final wheel diameterwe need to further subtract the distance 119865119888 from the wheeldiameter
119863 = 119863119903 minus 2119865119888 (9)
where119865119888 is the distance between point c3 and point a in V-axis(as shown in Figure 7(b)) namely 119865119888 = V119886 minus V119888
3
25 Dynamics Detection The calculation principles shownabove are in static case When the train passes dynam-ically multiscans can be obtained and the misalignmentphenomenon caused from wheel passing will occur
For tread profile detection ideally the laser light panel ofL3 and L4 is assumed to include the center of the measuredwheel In dynamics detection it is impossible to meet thatassumption for all measured wheels due to the moving ofwheel and the discrete sampling of LDS signal Basicallyif the laser light panel does not include the center of themeasured wheel the detected profile is horizontally stretched
along V-axis That will lead to the increase of detected flangeheight and flange width This phenomenon is called themisalignment between the laser panel and the detectiontarget [9]
Figure 8 shows the dynamics positions of thewheel centerand laser panel constituted by L3 and L4 in two-dimensionalWCF The wheel moves forward with a constant speed of V1198741 1198742 and 119874119894 are the center of wheel diameter circle underdifferent positions The laser panel has an installation angle1205723 with respect to 119910-axis which can be determined as 119911 =tan1205723 sdot 119910 in WCF The center points of wheel diameter circleare calculated by (7) 119889119894 denote the distance between 119894th wheelcenter point and the laser panel
Theoretically for every 119894th position of the wheel thedistance 119889119894 from the wheel center c(1199100
119894
1199110119894
) to the laser panelcan be determined by point to the distance formula as follows
When the distance 119889119894 equals zero the wheel center c(1199100119894
1199110119894
)
is in the laser panel where the flange height and flange widthhave no stretching On the other hand the bigger the distance119889119894 is the farther away the wheel center c(1199100
119894
1199110119894
) is from thelaser panel
It is worthmentioning that the LDSworks when the anglebetween laser light and detected surface is within a certainrange and the angle is influenced by laser wavelength surface
8 Journal of Sensors
y
z
Laser panel
Rail
Wheelv
Scanned section
O1 O2
d1 d22120579
120579
120579
1205723
Oi
di
L3 L4lowast
Figure 8 Dynamics position of the wheel center
smoothness surface material and so forth [23] It is assumedthat the angle 120579 (as shown in Figure 8) is the largest angleat which the LDS can still receive effective scan When thewheel is moving out of the detection range the LDS will beunable to scanThus the scanned sectionwill be the arcwith acentral angle of 2120579 and all the tread profiles and diameters arescanned from this section For most LDS sensors the angle 120579can reach up to 45∘ so the system can measure 90∘ arc of thewheel Correspondingly the maximum value of the distance119889119894 is 119877 sin 120579 where 119877 is the wheel radius
The misalignment phenomenon will bring about certainerror to the profile detection Among all the effective scanswe must select those scans where the induced error isacceptable In this paper the error induced in the tread profiledetection is analyzed in Section 3 As a result the error isdirectly proportional to the distance 119889119894 So we set up a certainthreshold 119870119901 When the distance 119889119894 lt 119870119901 the detectedtread profile can be regarded as useful profiles where the errorinduced by the misalignment phenomenon is negligible Thethreshold 119870119901 is firstly obtained through error analysis andalso is adjustable according to the field experiment Due tothe benefits from the high sampling frequency of the LDSsensors 119872 times of scans can be obtained for a wheelsetThen we can remove the bulky error first and performaverage operation to get the final wheel flange and wheelwidth as follows
119865119908119891
=
1
119872
119872
sum
119894=1
119865119908119894
119865ℎ119891
=
1
119872
119872
sum
119894=1
119865ℎ119894
(11)
where 119865119908119894
and 119865ℎ119894
are the flange width and flange height in119894th scan respectively 119865119908
119891
and 119865ℎ119891
are the final flange widthand flange height respectively The average operation herecan reduce the final error caused by Gaussian sensor noise
For wheel diameter detection the three points thatdetermine the wheel diameter are always in the contourcircle Thus the calculation results will not be influenced by
different wheel positions However 119865119888119894
in every 119894th scan willstill be stretched and bring about some error Similarly weselect a set of scans by comparing whether the distance 119889119894is smaller than a certain threshold 119870119889 or not When 119889119894 lt119870119889 the error induced in the detected 119865119888 is negligible Thetwo thresholds 119870119889 and 119870119901 might be different because ofthe different detection error requirements for tread profileand wheel diameter In this way 119873 times of scans can beobtained Then we can remove the bulky error first andperform average algorithm to get the final wheel diameter asfollows
119863119891 =1
119873
119873
sum
119894=1
119863119894 (12)
where 119863119894 is the wheel diameter in 119894th scan 119863119891 is the finalwheel diameter
26 Calibration The measuring and calculating of treadprofile and wheel diameter depend on many installationparameters Regarding tread profile calculation they are theangle 1205733 in (1) angle 1205734 in (2) and the offset Δ119906 and offsetΔV in (3) For wheel diameter they are the offset 119889off betweenthe origin of the coordinate 119906119900V and laser scanning line of L2in 119906(2)-axis the angles 1205721 1205722 and 1205723 and the positions P1P2 and P3 in (6) When the LDS are installed and fixed it isimpossible for those parameters to be the same with designedvalues because of the manufacture error of mechanical partsand installation accuracy So calibration is certainly needed
During the calibration process for tread profile detectiona standard wheel is placed on the rail over the detection sys-tem and then the offset and rotation angle of the coordinatetransformation matrix can be determined In terms of theangles 1205733 and 1205734 the calibrated accurate value is to makesure the inner and outer panels of the wheel are vertical Forthe offset Δ119906 the calibrated accurate value is to make surethe detected wheel hub thickness equals the standard wheelhub thickness and the offset ΔV is to make sure the scannedprofiles from two LDS coincide with each other
As for the calibration process for wheel diameter a setof new ground wheelsets is used The ground wheelset iswith different diameters that are 770mm 790mm 810mmand 840mm We set the minimization function 119891(119909) as thesquared summation of detected diameters subtracted by realdiameter That is
min 119891 (119909) =
119869
sum
119894=1
1003816100381610038161003816119863119894 minus 119863119903
1003816100381610038161003816
2 (13)
where 119863 is the detected diameter according to wheel diam-eter calibration principle 119863119903 is the real diameters 119909 =
[119889off 1205721 1205721 1205723 1199101 1199111 1199102 1199112 1199103 1199113] is the variables to be cali-brated 119869 denotes the number of ground wheelsets MATLABhas provided such tools to solve those optimization problemsOver here we use fmincon function to minimize the functionand the constraints in terms of the variables are also givenaccording to real physical ranges Finally the optimal valuesof the parameters can be obtained These values are assumedto be the real values that the implemented system has andhave been further put into use in system service
Journal of Sensors 9
3 Detection Error Analysis
In this section we consider four factors which are railvibration sensor noise misalignment and wheel inclinationcaused by wheel S-shape running and the differential ofdiameters
31 Wheel-Rail Vibration Wheel-rail vibration is the firstfactor that we considered In our system all the sensorsare well fixed by the mechanical support and mechanicalpedestal that has no direct contact with rail So the wheel-railvibrationwill not directly transmit to the sensors and insteadthe wheel-rail vibration has to transmit to the ground of thedepot and then transmit to the sensors through mechanicalsupport andmechanical pedestalThe vibration of the groundis on a lower level the maximum of acceleration is only04m2s [24] in Guangzhou metro depot and it is alsoattenuated by the mechanical pedestal We also measuredthe maximum of acceleration of mechanical support duringtrain passing which is only 02m2s So the change of theposition of the sensors due to the wheel-rail vibration in oursystemcanbeneglected Furthermore all the laser sensors arecapturing data simultaneously and the exposure time of theLDS is within 50 microseconds The vibration of the wheelwill not cause considerable movement within such a shorttime Overall the system is assumed to be reliable againstwheel-rail vibration
32 Misalignment As previously mentioned in Section 2Dynamics Detection if the laser light panel does not includethe center of the measured wheel the detected profile is hor-izontally stretched along V-axis This phenomenon is calledthe misalignment between the laser panel and the detectiontarget which will lead to the increase of the detected flangeheight and flange width Chen et al [10] derived a geometricmodel regarding howmany errors will be generated for flangeheight when wheel position varies The error 119890 of the flangeheight is
where 119877 is the wheel radius 119877119862 is the radius in the wheel rim119889 is the distance from the wheel center to the laser panel asdescribed in Section 2
On the basis of this geometric model when we know howmuch the error of the flange height is the errors of the flangewidth can be derived accordingly For different wear wheelsthe profiles aswell as the fitted line for lateral contact pointmare certainly different To illustrate the massiveness of errorshere we chose the same wheel where the fitted line for lateralcontact point m is V = 119891(119906) We obtain the inverse function119906 = 119892(V) and stretch it horizontally by a factor of (119865ℎ + 119890)119865ℎSo the stretched curve line is
119906 = 1198922 (V) = 119892(V119865ℎ
(119865ℎ + 119890)) (15)
Eventually the error of flange width is 120578 = 1198922(10)minus119865119908 where119865119908 is the original flange width
Error of flange heightError of flange width
0
01
02
03
04
05
06
07
08
Caus
ed er
ror (
mm
)
10 20 30 40 500d (mm)
Figure 9 The error of flange width and flange height with respectto various wheel positions
Theoretically from (14) and (15) we know that the smallerthe value of 119877 is the larger the error 119890 is So we chosethe largest standard wheelset with 119877 = 385mm and 119877119862 =399mm Figure 9 shows the error of flange height and flangewidth induced from misalignment in this case The distance119889 varies from 0mm to 50mmwith an interval of 1mm FromFigure 9 the error of flange height is lower than the error offlange width So we focus on the error of flange width here
In our system the sampling frequency of all LDS is 1 kHzand the maximum speed of the train in the depot is 36 kmhThemaximum of sampling step size along the railΔ119904 = 1ms times10ms = 10mmWhen we set the threshold119870119901 (as describedin Section 25) as 20mm the total measuring distance alongthe rail can be 58mm so that at least 119872 = 5 times ofefficient scans can be detected The corresponding errors areless than 01mm for flange width after taking the average ofthese 5 efficient scansThus the system can performdetectionnormally against themisalignment error benefitting from thehigh sampling frequency
33 Sensor Noise The LDS cannot be ideally accurate Themeasuring accuracy is influenced by temperature the rough-ness of the measured surface and so forth
In order to obtain the quantitative influence for profiledetection we built a 3D model in SolidWorks tools andextracted ideal sensor output points of standard inner andouter tread profiles In this model the standard wheel islocated in the position where the center of the wheel is inthe laser panel So the misalignment phenomenon will notaffect tread profile detection The wheel is in static positionso the simulated sensor output points are all from one scanMoreover the parameters that need to be calibrated areideally accurate To imitate the real situation Gaussian noiseis added to these coordinate valuesThemean of noise is zeroand the standard deviation is varied from 0 to 1mm with an
10 Journal of Sensors
X 03Y 01251
Flange widthFlange height
0
01
02
03
04
05
06
07Ca
used
erro
r (m
m)
02 04 06 08 10Noise level (mm)
Figure 10 The RMS error of flange height and flange width causedby different sensor noise level
interval of 01mm For each noise level 500 experiments arecarried out and the RMS error is calculated The RMS errorof flange height and flange width results caused by differentnoise level is shown in Figure 10 The caused error to flangeheight and flange width is approximately half of the sensornoise level This can be explained by the curve line fittingmethod that has taken more laser points into account andthus has reduced the random noise Because the flange heightis determined by two points the curve line fittingmethod hasat least reduced the randomerror into a quarter of the originalsensor noise
The 2D-LDS we chose is LJ-V7300 from KEYENCEwhich has a full-scale resolution of 01FS and a temper-ature drift of 001 FS∘C The detection range in 119910-axis is300 plusmn 145mm and in 119909-axis is 110mm to 240mm whichformed as a trapezoid The point in 119909-axis is fixed thus onlysensor noise in 119910-axis needs to be considered with full scaleof 290mm So accordingly the RMS error caused to theprofile coordinate noise in 119910-axis which is denoted by 120575 isless than 032mm which only leads to an error of 013mmboth to flange height and to flange width Taking dynamicsdetection effect into account the final error is reduced by120575119891 = 120575
radic5 = 0058mm with at least119873 = 5 times of efficientscans The error caused by sensor noise can be acceptable
Regarding the error of wheel diameter it can be theoreti-cally derived by the theorem of error propagation [25] Theresolution of each sensor is denoted by 1205751 1205752 and 1205753 Weobtain 120575119863 by taking differential of (6)ndash(9) as follows
120575119863 = plusmnradic(1205751
120597119863
1205971198971
)
2
+ (1205752
120597119863
1205971198972
)
2
+ (1205753
120597119863
1205971198973
)
2
(16)
We have chosen two 2D-LDS and one 1D-LDS to detect thewheel diameter and the two 2D-LDS are installed symmet-rically For systematic installation we have 1205751(1205971198631205971198971) =
1205753(1205971198631205971198973) Moreover the analytical function of particle
derivative will be too complex to derive So we consider aspecial case where
where the target wheel diameter is 119863 = 840mm and theorigin of the wheel is located in the origin of 119910119900119911WCF Morecalculation details can be found in the Appendix Finally wehave
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(18)
The 1D-LDS we chose is LK-G8085 from KEYENCE whichhas linearity of 005FS and a temperature drift of 001FS∘C So according to the full scale of 30mm the reso-lution of 1D-LDS 1205752 = 0018mm Based upon the findingthat the curve line fitting method has at least reduced therandom error into a quarter of the original sensor noise1205751 = 0075mm Finally 120575119863 is less than 0372mm Takingdynamics detection effect into account the final error 120575119863
119891
=
120575119863radic5 = 017mm The error caused by sensor noise can be
acceptable
34 Wheel Inclination Caused by Wheelset S-Shape RunningandDifferential ofWheel Diameter In engineering thewheelwill be inclined because of wheelset S-shape running and thedifferential of wheel diameter The wheelset S-shape runningis one kind of self-induced vibration due to the slope in thewheel trade When it is S-shape running the wheel panelwill have a certain angle with respect to 119910119900119911 panel in WCFdenoted by 120579119904 as shown in Figure 11(a) The differentialof wheel diameter in a wheelset is at different wear levelin the left and right wheel mainly induced from differentmassiveness of wear in the circuit of wheelset turning andunbalanced loading Similarly it will bring a certain angleabout the wheel panel with respect to the 119910119900119911 panel in WCFThe angle is denoted by 120579119889 as shown in Figure 11(b)
For wheel diameter detection because we only considerthe calculation in two dimensions an error will be generatedwhen we still regard the detected three points in a circle toactually be in an ellipse Considering the existence of angles120579119904 and 120579119889 we have the equation of ellipse as follows
1199102
(119877 sdot cos 120579119904)2+
1199112
1198772= 1
1199102
1198772+
1199112
(119877 sdot cos 120579119889)2= 1
(19)
Journal of Sensors 11
x
y
z
0
Ellipse wheel
Wheelset withS-shape running
120579s
(a)
x
y
z Ellipse wheel
Wheelset with differential of diameter
120579d
(b)
Figure 11 Mathematical illustration (a) Wheel S-shape running and (b) differential of wheel diameter
Similar towhenwe analyze sensor noise we consider a specialcase as (17) the origin of the target wheel is located in theorigin of 119910119900119911WCFThe real three points are
1198881(119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198882 (0 minus119877)
1198883(minus119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198881(119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
1198882 (0 minus119877 sdot cos 120579119889)
1198883(minus119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
(20)
Theoretically the larger the radius of the wheel is the biggerthe error is So we chose 119877 = 420mm and generated threepoints then using (7) we calculated the wheel diameter witherror Subtracting the real diameter we have the error withrespect to angle as shown in Figure 12 The effect of S-shaperunning caused angle has a relatively higher influence on thewheel diameter calculation
Based on the experience from Guangzhou Metro Cor-poration the differential of diameter in a wheelset shouldbe controlled under 2mm Considering the track gauge of1350mm the angle induced from the differential of diameter
S-shape runningWheel diameter differential
0
001
002
003
004
005
006
Caus
ed er
ror t
o di
amet
er (m
m)
01 02 03 04 050120579 (∘)
Figure 12 Wheel diameter errors
in a wheelset is less than 0001∘ thus the error can be ignoredAs for wheel S-shape running themaximum angle is 01∘ [26]when the speed of the train is under 36 kmhwhich will causean error not larger than 0005mm
4 Experimental Validation
41 System Implementation Theauthors previously proposedan online detection system using eight 2D-LDS [19] Thenew online detection system is installed in the same storageline of Guangzhou metro vehicle depot as the old systemso that comparison can be conducted In order to savefund only the left side namely half of the system has been
12 Journal of Sensors
(a) (b)
Figure 13 Field test (a) Standard wheel test and (b) real train test
Table 1 Standard wheelset detection the results of repeatedmeasurementsmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
implemented During the system implementation three-dimensional inclinometer and special rail gauge are used tocontrol the position of the mechanical support After thesystem is installed the calibration described in Section 2has been conducted to obtain the geometric parameters fortread profile calibration and diameter calculation As shownin Figure 13 the field test is carried out by a standard wheelsetand real train
42 Standard Wheelset The standard wheelset is a new pro-duced wheelset without any wear and diameter differentialThe manufacturing geometric size is as follows wheel diam-eter = 840mm flange height = 28mm and flange width =32mm One can also assume to have lower possibility of S-shape running because of zero external load The standardwheelset has been placed on the rail and passed through thedetection system This test has been carried out 6 times toverify both the detection and the repeatability of the systemComparing with the old system the results of this system areshown in Table 1
From Table 1 the mean values of the flange height andflange width detected by the old and the new system are very
close to each other which means the system error can beignored The standard deviation which also can be denotedas detection uncertainty of the new system measurement isslightly smaller than of the old system That may result fromthe lower effect frommisalignment as described in Section 3due to the higher sampling frequency that we used in the newsystem Detection uncertainty of not greater than 005mm intread profile measurement is acceptable for the engineeringrequirements As for wheel diameter detection the meanvalues are also close to each other The standard deviation ofthe new systemmeasurement is slightly higher than of the oldsystemThis may result from the replacement of 1D-LDS thathas brought about higher sensor noise to the middle pointamong three pointswithout curve fitting techniqueHoweverdetection uncertainty of less than 03mm is also acceptable inengineering
43 Real Train Detection Test Real train test also performs6 times of repeated detection to statistically evaluate theperformance of the system The train speed is controlledunder 36 kmh In the train we chose there are 4 new groundwheelsets in a car of the train Under the consideration thatthe ground new wheel is not out of roundness which hasan effect on the analysis results we selected the ground newwheel as our target wheel
Table 2 shows the mean and standard deviation value ofmeasurement The biggest differential value of mean flangeheight appears in 1 wheel and for mean flange width appearsin 3 wheel The difference does not exceed 015mm As forwheel diameter the biggest differential value 016mmappearsin 3 wheelThemean value of six times of repeated detectionis consistent with the standard wheelset test In terms ofstandard deviation the value is less than 01mm for flangewidth and flange height and 03mm for wheel diameterThe standard deviation of wheel diameter is relatively higherthan in standard wheelset test On the contrary the standarddeviation of flange width and flange height is relatively lowerthan in the old system That is also consistent with standard
Journal of Sensors 13
Table 2 Real train test the mean and standard deviation value of detected measurementmm
Wheelnumber
Mean flange height SD flange height Mean flange width SD flange width Mean wheeldiameter SD wheel diameter
Old New Old New Old New Old New Old New Old New1 2818 2803 0046 0060 2954 2943 0091 0062 80052 80150 0201 03012 2809 2811 0078 0040 2940 2929 0056 0028 80112 80096 0128 02863 2797 2791 0076 0033 2992 3006 0075 0056 80187 80166 0090 01794 2807 2805 0063 0053 2983 2988 0076 0088 80178 80201 0192 0282
Table 3 Real train test wheel 2 the result of repeated measure-mentmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
wheelset test The standard deviation of wheel diameter inreal train test is supposed to be higher than in the standardwheelset test because of several assumptions One factor isthe higher possibility of S-shape running because of heavyaxial load On the other hand the wheelset that is in service isalso more polluted with rust than standard wheelset causingmore detection uncertainty However the standard deviationfrom real train test also does not exceed 03mm which isconsistent with standard wheelset test This may result fromthe lower train speed during the test which leads to lowerpossibility of S-shape running Meanwhile the rusty wheelcontour is also not in a massive stage Tables 3 and 4 show theresult of repeated measurement for wheels numbers 2 and 3respectively In each detection the results remain the sameand no gross error appears
Overall detection uncertainties for tread profile andwheel diameter are less than 01mmand 03mm respectivelyThe results show that the detection system has a highaccuracy which can meet the requirements of maintenanceoperation
5 Conclusion
This paper based on LDS proposed a novel on-track detec-tion system of the wheel size using only six 2D-LDS and two1D-LDS Errors induced bywheel-rail vibration sensor noisemisalignment S-shape running and wheelset differential arealso analyzed After the system is implemented real dataexperiments including standard wheel test and real traindetection test were performed It turns out that the detectionuncertainty of flange width and height is 01mm and wheeldiameter 03mm which can meet the requirements of main-tenanceThis system can be further used for different types ofrailway transportation which provides a new solution for thewheel size detection technology
To provide more benefits the target wheel diameter is 119863 =
840mm and the origin of the wheel is located in the originof 119910119900119911WCF as shown in Figure 14 In this special case therelevant geometric values are 1198881(minus19802mm minus19802mm)1198882(0mm 420mm) 1198883(19802mm minus19802mm) 1198971 = 280mm1198972 = 180mm and 1198973 = 280mm
According to (8) and (9) we get the particle derivative asfollows
120597119863
1205971198971
=
120597119863
1205971199100
1205971199100
1205971198971
+
120597119863
1205971199110
1205971199110
1205971198971
120597119863
1205971198972
=
120597119863
1205971199100
1205971199100
1205971198972
+
120597119863
1205971199110
1205971199110
1205971198972
+
120597119863
1205971199111198882
1205971199111198882
1205971198972
(A2)
14 Journal of Sensors
2D-L1
1D-L2
2D-L3
y
z
o
45∘45∘ c1l1
l2
l3
c2
c3 lowast
lowast
lowast
Figure 14 A special case
Taking the derivative of diameter 119863 with respect to 1199100 1199110and 119911119888
2
according to (8) and substituting (1199100 1199110) = (0 0) and1199111198882
= 180mm we have
120597119863
1205971199100
=
21199100
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199110
=
2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199111198882
=
minus2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
= 2
(A3)
Furthermore based upon (7) we get
1205971199100
1205971198971
=
1205971199100
1205971199101198881
1205971199101198881
1205971198971
+
1205971199100
1205971199111198881
1205971199111198881
1205971198971
1205971199110
1205971198971
=
1205971199110
1205971199101198881
1205971199101198881
1205971198971
+
1205971199110
1205971199111198881
1205971199111198881
1205971198971
1205971199100
1205971198972
=
1205971199100
1205971199111198882
1205971199111198882
1205971198972
1205971199110
1205971198972
=
1205971199110
1205971199111198882
1205971199111198882
1205971198972
1205971199100
1205971198973
=
1205971199100
1205971199101198883
1205971199101198883
1205971198973
+
1205971199100
1205971199111198883
1205971199111198883
1205971198973
1205971199110
1205971198973
=
1205971199110
1205971199101198883
1205971199101198883
1205971198973
+
1205971199110
1205971199111198883
1205971199111198883
1205971198973
(A4)
When calculating particle derivative of (1199100 1199110) with respectto three points 1198881 1198882 and 1198883 in WCF we assume that allparameters are with the geometric values in this special case
Then we substitute the ideal geometric values of this variableand we obtain
1205971199100
1205971199101198881
= 05
1205971199100
1205971199111198881
= 05
1205971199110
1205971199101198881
= minus12071
1205971199110
1205971199111198881
= minus12071
1205971199100
1205971199111198882
= 0
1205971199110
1205971199111198882
= 34142
1205971199100
1205971199101198883
= 05
1205971199100
1205971199111198883
= minus05
1205971199110
1205971199101198883
= 12071
1205971199110
1205971199111198883
= minus12071
1205971199101198881
1205971198971
=
1
radic2
1205971199111198881
1205971198971
=
1
radic2
1205971199111198882
1205971198972
= minus1
1205971199101198883
1205971198973
= minus
1
radic2
1205971199111198883
1205971198973
=
1
radic2
(A5)
Finally substituting (A5) into (A4) and then substituting(A4) and (A3) into (A2) we have
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(A6)
Competing Interests
The authors declare that they have no competing interests
Journal of Sensors 15
Acknowledgments
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
smoothness surface material and so forth [23] It is assumedthat the angle 120579 (as shown in Figure 8) is the largest angleat which the LDS can still receive effective scan When thewheel is moving out of the detection range the LDS will beunable to scanThus the scanned sectionwill be the arcwith acentral angle of 2120579 and all the tread profiles and diameters arescanned from this section For most LDS sensors the angle 120579can reach up to 45∘ so the system can measure 90∘ arc of thewheel Correspondingly the maximum value of the distance119889119894 is 119877 sin 120579 where 119877 is the wheel radius
The misalignment phenomenon will bring about certainerror to the profile detection Among all the effective scanswe must select those scans where the induced error isacceptable In this paper the error induced in the tread profiledetection is analyzed in Section 3 As a result the error isdirectly proportional to the distance 119889119894 So we set up a certainthreshold 119870119901 When the distance 119889119894 lt 119870119901 the detectedtread profile can be regarded as useful profiles where the errorinduced by the misalignment phenomenon is negligible Thethreshold 119870119901 is firstly obtained through error analysis andalso is adjustable according to the field experiment Due tothe benefits from the high sampling frequency of the LDSsensors 119872 times of scans can be obtained for a wheelsetThen we can remove the bulky error first and performaverage operation to get the final wheel flange and wheelwidth as follows
119865119908119891
=
1
119872
119872
sum
119894=1
119865119908119894
119865ℎ119891
=
1
119872
119872
sum
119894=1
119865ℎ119894
(11)
where 119865119908119894
and 119865ℎ119894
are the flange width and flange height in119894th scan respectively 119865119908
119891
and 119865ℎ119891
are the final flange widthand flange height respectively The average operation herecan reduce the final error caused by Gaussian sensor noise
For wheel diameter detection the three points thatdetermine the wheel diameter are always in the contourcircle Thus the calculation results will not be influenced by
different wheel positions However 119865119888119894
in every 119894th scan willstill be stretched and bring about some error Similarly weselect a set of scans by comparing whether the distance 119889119894is smaller than a certain threshold 119870119889 or not When 119889119894 lt119870119889 the error induced in the detected 119865119888 is negligible Thetwo thresholds 119870119889 and 119870119901 might be different because ofthe different detection error requirements for tread profileand wheel diameter In this way 119873 times of scans can beobtained Then we can remove the bulky error first andperform average algorithm to get the final wheel diameter asfollows
119863119891 =1
119873
119873
sum
119894=1
119863119894 (12)
where 119863119894 is the wheel diameter in 119894th scan 119863119891 is the finalwheel diameter
26 Calibration The measuring and calculating of treadprofile and wheel diameter depend on many installationparameters Regarding tread profile calculation they are theangle 1205733 in (1) angle 1205734 in (2) and the offset Δ119906 and offsetΔV in (3) For wheel diameter they are the offset 119889off betweenthe origin of the coordinate 119906119900V and laser scanning line of L2in 119906(2)-axis the angles 1205721 1205722 and 1205723 and the positions P1P2 and P3 in (6) When the LDS are installed and fixed it isimpossible for those parameters to be the same with designedvalues because of the manufacture error of mechanical partsand installation accuracy So calibration is certainly needed
During the calibration process for tread profile detectiona standard wheel is placed on the rail over the detection sys-tem and then the offset and rotation angle of the coordinatetransformation matrix can be determined In terms of theangles 1205733 and 1205734 the calibrated accurate value is to makesure the inner and outer panels of the wheel are vertical Forthe offset Δ119906 the calibrated accurate value is to make surethe detected wheel hub thickness equals the standard wheelhub thickness and the offset ΔV is to make sure the scannedprofiles from two LDS coincide with each other
As for the calibration process for wheel diameter a setof new ground wheelsets is used The ground wheelset iswith different diameters that are 770mm 790mm 810mmand 840mm We set the minimization function 119891(119909) as thesquared summation of detected diameters subtracted by realdiameter That is
min 119891 (119909) =
119869
sum
119894=1
1003816100381610038161003816119863119894 minus 119863119903
1003816100381610038161003816
2 (13)
where 119863 is the detected diameter according to wheel diam-eter calibration principle 119863119903 is the real diameters 119909 =
[119889off 1205721 1205721 1205723 1199101 1199111 1199102 1199112 1199103 1199113] is the variables to be cali-brated 119869 denotes the number of ground wheelsets MATLABhas provided such tools to solve those optimization problemsOver here we use fmincon function to minimize the functionand the constraints in terms of the variables are also givenaccording to real physical ranges Finally the optimal valuesof the parameters can be obtained These values are assumedto be the real values that the implemented system has andhave been further put into use in system service
Journal of Sensors 9
3 Detection Error Analysis
In this section we consider four factors which are railvibration sensor noise misalignment and wheel inclinationcaused by wheel S-shape running and the differential ofdiameters
31 Wheel-Rail Vibration Wheel-rail vibration is the firstfactor that we considered In our system all the sensorsare well fixed by the mechanical support and mechanicalpedestal that has no direct contact with rail So the wheel-railvibrationwill not directly transmit to the sensors and insteadthe wheel-rail vibration has to transmit to the ground of thedepot and then transmit to the sensors through mechanicalsupport andmechanical pedestalThe vibration of the groundis on a lower level the maximum of acceleration is only04m2s [24] in Guangzhou metro depot and it is alsoattenuated by the mechanical pedestal We also measuredthe maximum of acceleration of mechanical support duringtrain passing which is only 02m2s So the change of theposition of the sensors due to the wheel-rail vibration in oursystemcanbeneglected Furthermore all the laser sensors arecapturing data simultaneously and the exposure time of theLDS is within 50 microseconds The vibration of the wheelwill not cause considerable movement within such a shorttime Overall the system is assumed to be reliable againstwheel-rail vibration
32 Misalignment As previously mentioned in Section 2Dynamics Detection if the laser light panel does not includethe center of the measured wheel the detected profile is hor-izontally stretched along V-axis This phenomenon is calledthe misalignment between the laser panel and the detectiontarget which will lead to the increase of the detected flangeheight and flange width Chen et al [10] derived a geometricmodel regarding howmany errors will be generated for flangeheight when wheel position varies The error 119890 of the flangeheight is
where 119877 is the wheel radius 119877119862 is the radius in the wheel rim119889 is the distance from the wheel center to the laser panel asdescribed in Section 2
On the basis of this geometric model when we know howmuch the error of the flange height is the errors of the flangewidth can be derived accordingly For different wear wheelsthe profiles aswell as the fitted line for lateral contact pointmare certainly different To illustrate the massiveness of errorshere we chose the same wheel where the fitted line for lateralcontact point m is V = 119891(119906) We obtain the inverse function119906 = 119892(V) and stretch it horizontally by a factor of (119865ℎ + 119890)119865ℎSo the stretched curve line is
119906 = 1198922 (V) = 119892(V119865ℎ
(119865ℎ + 119890)) (15)
Eventually the error of flange width is 120578 = 1198922(10)minus119865119908 where119865119908 is the original flange width
Error of flange heightError of flange width
0
01
02
03
04
05
06
07
08
Caus
ed er
ror (
mm
)
10 20 30 40 500d (mm)
Figure 9 The error of flange width and flange height with respectto various wheel positions
Theoretically from (14) and (15) we know that the smallerthe value of 119877 is the larger the error 119890 is So we chosethe largest standard wheelset with 119877 = 385mm and 119877119862 =399mm Figure 9 shows the error of flange height and flangewidth induced from misalignment in this case The distance119889 varies from 0mm to 50mmwith an interval of 1mm FromFigure 9 the error of flange height is lower than the error offlange width So we focus on the error of flange width here
In our system the sampling frequency of all LDS is 1 kHzand the maximum speed of the train in the depot is 36 kmhThemaximum of sampling step size along the railΔ119904 = 1ms times10ms = 10mmWhen we set the threshold119870119901 (as describedin Section 25) as 20mm the total measuring distance alongthe rail can be 58mm so that at least 119872 = 5 times ofefficient scans can be detected The corresponding errors areless than 01mm for flange width after taking the average ofthese 5 efficient scansThus the system can performdetectionnormally against themisalignment error benefitting from thehigh sampling frequency
33 Sensor Noise The LDS cannot be ideally accurate Themeasuring accuracy is influenced by temperature the rough-ness of the measured surface and so forth
In order to obtain the quantitative influence for profiledetection we built a 3D model in SolidWorks tools andextracted ideal sensor output points of standard inner andouter tread profiles In this model the standard wheel islocated in the position where the center of the wheel is inthe laser panel So the misalignment phenomenon will notaffect tread profile detection The wheel is in static positionso the simulated sensor output points are all from one scanMoreover the parameters that need to be calibrated areideally accurate To imitate the real situation Gaussian noiseis added to these coordinate valuesThemean of noise is zeroand the standard deviation is varied from 0 to 1mm with an
10 Journal of Sensors
X 03Y 01251
Flange widthFlange height
0
01
02
03
04
05
06
07Ca
used
erro
r (m
m)
02 04 06 08 10Noise level (mm)
Figure 10 The RMS error of flange height and flange width causedby different sensor noise level
interval of 01mm For each noise level 500 experiments arecarried out and the RMS error is calculated The RMS errorof flange height and flange width results caused by differentnoise level is shown in Figure 10 The caused error to flangeheight and flange width is approximately half of the sensornoise level This can be explained by the curve line fittingmethod that has taken more laser points into account andthus has reduced the random noise Because the flange heightis determined by two points the curve line fittingmethod hasat least reduced the randomerror into a quarter of the originalsensor noise
The 2D-LDS we chose is LJ-V7300 from KEYENCEwhich has a full-scale resolution of 01FS and a temper-ature drift of 001 FS∘C The detection range in 119910-axis is300 plusmn 145mm and in 119909-axis is 110mm to 240mm whichformed as a trapezoid The point in 119909-axis is fixed thus onlysensor noise in 119910-axis needs to be considered with full scaleof 290mm So accordingly the RMS error caused to theprofile coordinate noise in 119910-axis which is denoted by 120575 isless than 032mm which only leads to an error of 013mmboth to flange height and to flange width Taking dynamicsdetection effect into account the final error is reduced by120575119891 = 120575
radic5 = 0058mm with at least119873 = 5 times of efficientscans The error caused by sensor noise can be acceptable
Regarding the error of wheel diameter it can be theoreti-cally derived by the theorem of error propagation [25] Theresolution of each sensor is denoted by 1205751 1205752 and 1205753 Weobtain 120575119863 by taking differential of (6)ndash(9) as follows
120575119863 = plusmnradic(1205751
120597119863
1205971198971
)
2
+ (1205752
120597119863
1205971198972
)
2
+ (1205753
120597119863
1205971198973
)
2
(16)
We have chosen two 2D-LDS and one 1D-LDS to detect thewheel diameter and the two 2D-LDS are installed symmet-rically For systematic installation we have 1205751(1205971198631205971198971) =
1205753(1205971198631205971198973) Moreover the analytical function of particle
derivative will be too complex to derive So we consider aspecial case where
where the target wheel diameter is 119863 = 840mm and theorigin of the wheel is located in the origin of 119910119900119911WCF Morecalculation details can be found in the Appendix Finally wehave
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(18)
The 1D-LDS we chose is LK-G8085 from KEYENCE whichhas linearity of 005FS and a temperature drift of 001FS∘C So according to the full scale of 30mm the reso-lution of 1D-LDS 1205752 = 0018mm Based upon the findingthat the curve line fitting method has at least reduced therandom error into a quarter of the original sensor noise1205751 = 0075mm Finally 120575119863 is less than 0372mm Takingdynamics detection effect into account the final error 120575119863
119891
=
120575119863radic5 = 017mm The error caused by sensor noise can be
acceptable
34 Wheel Inclination Caused by Wheelset S-Shape RunningandDifferential ofWheel Diameter In engineering thewheelwill be inclined because of wheelset S-shape running and thedifferential of wheel diameter The wheelset S-shape runningis one kind of self-induced vibration due to the slope in thewheel trade When it is S-shape running the wheel panelwill have a certain angle with respect to 119910119900119911 panel in WCFdenoted by 120579119904 as shown in Figure 11(a) The differentialof wheel diameter in a wheelset is at different wear levelin the left and right wheel mainly induced from differentmassiveness of wear in the circuit of wheelset turning andunbalanced loading Similarly it will bring a certain angleabout the wheel panel with respect to the 119910119900119911 panel in WCFThe angle is denoted by 120579119889 as shown in Figure 11(b)
For wheel diameter detection because we only considerthe calculation in two dimensions an error will be generatedwhen we still regard the detected three points in a circle toactually be in an ellipse Considering the existence of angles120579119904 and 120579119889 we have the equation of ellipse as follows
1199102
(119877 sdot cos 120579119904)2+
1199112
1198772= 1
1199102
1198772+
1199112
(119877 sdot cos 120579119889)2= 1
(19)
Journal of Sensors 11
x
y
z
0
Ellipse wheel
Wheelset withS-shape running
120579s
(a)
x
y
z Ellipse wheel
Wheelset with differential of diameter
120579d
(b)
Figure 11 Mathematical illustration (a) Wheel S-shape running and (b) differential of wheel diameter
Similar towhenwe analyze sensor noise we consider a specialcase as (17) the origin of the target wheel is located in theorigin of 119910119900119911WCFThe real three points are
1198881(119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198882 (0 minus119877)
1198883(minus119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198881(119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
1198882 (0 minus119877 sdot cos 120579119889)
1198883(minus119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
(20)
Theoretically the larger the radius of the wheel is the biggerthe error is So we chose 119877 = 420mm and generated threepoints then using (7) we calculated the wheel diameter witherror Subtracting the real diameter we have the error withrespect to angle as shown in Figure 12 The effect of S-shaperunning caused angle has a relatively higher influence on thewheel diameter calculation
Based on the experience from Guangzhou Metro Cor-poration the differential of diameter in a wheelset shouldbe controlled under 2mm Considering the track gauge of1350mm the angle induced from the differential of diameter
S-shape runningWheel diameter differential
0
001
002
003
004
005
006
Caus
ed er
ror t
o di
amet
er (m
m)
01 02 03 04 050120579 (∘)
Figure 12 Wheel diameter errors
in a wheelset is less than 0001∘ thus the error can be ignoredAs for wheel S-shape running themaximum angle is 01∘ [26]when the speed of the train is under 36 kmhwhich will causean error not larger than 0005mm
4 Experimental Validation
41 System Implementation Theauthors previously proposedan online detection system using eight 2D-LDS [19] Thenew online detection system is installed in the same storageline of Guangzhou metro vehicle depot as the old systemso that comparison can be conducted In order to savefund only the left side namely half of the system has been
12 Journal of Sensors
(a) (b)
Figure 13 Field test (a) Standard wheel test and (b) real train test
Table 1 Standard wheelset detection the results of repeatedmeasurementsmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
implemented During the system implementation three-dimensional inclinometer and special rail gauge are used tocontrol the position of the mechanical support After thesystem is installed the calibration described in Section 2has been conducted to obtain the geometric parameters fortread profile calibration and diameter calculation As shownin Figure 13 the field test is carried out by a standard wheelsetand real train
42 Standard Wheelset The standard wheelset is a new pro-duced wheelset without any wear and diameter differentialThe manufacturing geometric size is as follows wheel diam-eter = 840mm flange height = 28mm and flange width =32mm One can also assume to have lower possibility of S-shape running because of zero external load The standardwheelset has been placed on the rail and passed through thedetection system This test has been carried out 6 times toverify both the detection and the repeatability of the systemComparing with the old system the results of this system areshown in Table 1
From Table 1 the mean values of the flange height andflange width detected by the old and the new system are very
close to each other which means the system error can beignored The standard deviation which also can be denotedas detection uncertainty of the new system measurement isslightly smaller than of the old system That may result fromthe lower effect frommisalignment as described in Section 3due to the higher sampling frequency that we used in the newsystem Detection uncertainty of not greater than 005mm intread profile measurement is acceptable for the engineeringrequirements As for wheel diameter detection the meanvalues are also close to each other The standard deviation ofthe new systemmeasurement is slightly higher than of the oldsystemThis may result from the replacement of 1D-LDS thathas brought about higher sensor noise to the middle pointamong three pointswithout curve fitting techniqueHoweverdetection uncertainty of less than 03mm is also acceptable inengineering
43 Real Train Detection Test Real train test also performs6 times of repeated detection to statistically evaluate theperformance of the system The train speed is controlledunder 36 kmh In the train we chose there are 4 new groundwheelsets in a car of the train Under the consideration thatthe ground new wheel is not out of roundness which hasan effect on the analysis results we selected the ground newwheel as our target wheel
Table 2 shows the mean and standard deviation value ofmeasurement The biggest differential value of mean flangeheight appears in 1 wheel and for mean flange width appearsin 3 wheel The difference does not exceed 015mm As forwheel diameter the biggest differential value 016mmappearsin 3 wheelThemean value of six times of repeated detectionis consistent with the standard wheelset test In terms ofstandard deviation the value is less than 01mm for flangewidth and flange height and 03mm for wheel diameterThe standard deviation of wheel diameter is relatively higherthan in standard wheelset test On the contrary the standarddeviation of flange width and flange height is relatively lowerthan in the old system That is also consistent with standard
Journal of Sensors 13
Table 2 Real train test the mean and standard deviation value of detected measurementmm
Wheelnumber
Mean flange height SD flange height Mean flange width SD flange width Mean wheeldiameter SD wheel diameter
Old New Old New Old New Old New Old New Old New1 2818 2803 0046 0060 2954 2943 0091 0062 80052 80150 0201 03012 2809 2811 0078 0040 2940 2929 0056 0028 80112 80096 0128 02863 2797 2791 0076 0033 2992 3006 0075 0056 80187 80166 0090 01794 2807 2805 0063 0053 2983 2988 0076 0088 80178 80201 0192 0282
Table 3 Real train test wheel 2 the result of repeated measure-mentmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
wheelset test The standard deviation of wheel diameter inreal train test is supposed to be higher than in the standardwheelset test because of several assumptions One factor isthe higher possibility of S-shape running because of heavyaxial load On the other hand the wheelset that is in service isalso more polluted with rust than standard wheelset causingmore detection uncertainty However the standard deviationfrom real train test also does not exceed 03mm which isconsistent with standard wheelset test This may result fromthe lower train speed during the test which leads to lowerpossibility of S-shape running Meanwhile the rusty wheelcontour is also not in a massive stage Tables 3 and 4 show theresult of repeated measurement for wheels numbers 2 and 3respectively In each detection the results remain the sameand no gross error appears
Overall detection uncertainties for tread profile andwheel diameter are less than 01mmand 03mm respectivelyThe results show that the detection system has a highaccuracy which can meet the requirements of maintenanceoperation
5 Conclusion
This paper based on LDS proposed a novel on-track detec-tion system of the wheel size using only six 2D-LDS and two1D-LDS Errors induced bywheel-rail vibration sensor noisemisalignment S-shape running and wheelset differential arealso analyzed After the system is implemented real dataexperiments including standard wheel test and real traindetection test were performed It turns out that the detectionuncertainty of flange width and height is 01mm and wheeldiameter 03mm which can meet the requirements of main-tenanceThis system can be further used for different types ofrailway transportation which provides a new solution for thewheel size detection technology
To provide more benefits the target wheel diameter is 119863 =
840mm and the origin of the wheel is located in the originof 119910119900119911WCF as shown in Figure 14 In this special case therelevant geometric values are 1198881(minus19802mm minus19802mm)1198882(0mm 420mm) 1198883(19802mm minus19802mm) 1198971 = 280mm1198972 = 180mm and 1198973 = 280mm
According to (8) and (9) we get the particle derivative asfollows
120597119863
1205971198971
=
120597119863
1205971199100
1205971199100
1205971198971
+
120597119863
1205971199110
1205971199110
1205971198971
120597119863
1205971198972
=
120597119863
1205971199100
1205971199100
1205971198972
+
120597119863
1205971199110
1205971199110
1205971198972
+
120597119863
1205971199111198882
1205971199111198882
1205971198972
(A2)
14 Journal of Sensors
2D-L1
1D-L2
2D-L3
y
z
o
45∘45∘ c1l1
l2
l3
c2
c3 lowast
lowast
lowast
Figure 14 A special case
Taking the derivative of diameter 119863 with respect to 1199100 1199110and 119911119888
2
according to (8) and substituting (1199100 1199110) = (0 0) and1199111198882
= 180mm we have
120597119863
1205971199100
=
21199100
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199110
=
2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199111198882
=
minus2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
= 2
(A3)
Furthermore based upon (7) we get
1205971199100
1205971198971
=
1205971199100
1205971199101198881
1205971199101198881
1205971198971
+
1205971199100
1205971199111198881
1205971199111198881
1205971198971
1205971199110
1205971198971
=
1205971199110
1205971199101198881
1205971199101198881
1205971198971
+
1205971199110
1205971199111198881
1205971199111198881
1205971198971
1205971199100
1205971198972
=
1205971199100
1205971199111198882
1205971199111198882
1205971198972
1205971199110
1205971198972
=
1205971199110
1205971199111198882
1205971199111198882
1205971198972
1205971199100
1205971198973
=
1205971199100
1205971199101198883
1205971199101198883
1205971198973
+
1205971199100
1205971199111198883
1205971199111198883
1205971198973
1205971199110
1205971198973
=
1205971199110
1205971199101198883
1205971199101198883
1205971198973
+
1205971199110
1205971199111198883
1205971199111198883
1205971198973
(A4)
When calculating particle derivative of (1199100 1199110) with respectto three points 1198881 1198882 and 1198883 in WCF we assume that allparameters are with the geometric values in this special case
Then we substitute the ideal geometric values of this variableand we obtain
1205971199100
1205971199101198881
= 05
1205971199100
1205971199111198881
= 05
1205971199110
1205971199101198881
= minus12071
1205971199110
1205971199111198881
= minus12071
1205971199100
1205971199111198882
= 0
1205971199110
1205971199111198882
= 34142
1205971199100
1205971199101198883
= 05
1205971199100
1205971199111198883
= minus05
1205971199110
1205971199101198883
= 12071
1205971199110
1205971199111198883
= minus12071
1205971199101198881
1205971198971
=
1
radic2
1205971199111198881
1205971198971
=
1
radic2
1205971199111198882
1205971198972
= minus1
1205971199101198883
1205971198973
= minus
1
radic2
1205971199111198883
1205971198973
=
1
radic2
(A5)
Finally substituting (A5) into (A4) and then substituting(A4) and (A3) into (A2) we have
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(A6)
Competing Interests
The authors declare that they have no competing interests
Journal of Sensors 15
Acknowledgments
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
In this section we consider four factors which are railvibration sensor noise misalignment and wheel inclinationcaused by wheel S-shape running and the differential ofdiameters
31 Wheel-Rail Vibration Wheel-rail vibration is the firstfactor that we considered In our system all the sensorsare well fixed by the mechanical support and mechanicalpedestal that has no direct contact with rail So the wheel-railvibrationwill not directly transmit to the sensors and insteadthe wheel-rail vibration has to transmit to the ground of thedepot and then transmit to the sensors through mechanicalsupport andmechanical pedestalThe vibration of the groundis on a lower level the maximum of acceleration is only04m2s [24] in Guangzhou metro depot and it is alsoattenuated by the mechanical pedestal We also measuredthe maximum of acceleration of mechanical support duringtrain passing which is only 02m2s So the change of theposition of the sensors due to the wheel-rail vibration in oursystemcanbeneglected Furthermore all the laser sensors arecapturing data simultaneously and the exposure time of theLDS is within 50 microseconds The vibration of the wheelwill not cause considerable movement within such a shorttime Overall the system is assumed to be reliable againstwheel-rail vibration
32 Misalignment As previously mentioned in Section 2Dynamics Detection if the laser light panel does not includethe center of the measured wheel the detected profile is hor-izontally stretched along V-axis This phenomenon is calledthe misalignment between the laser panel and the detectiontarget which will lead to the increase of the detected flangeheight and flange width Chen et al [10] derived a geometricmodel regarding howmany errors will be generated for flangeheight when wheel position varies The error 119890 of the flangeheight is
where 119877 is the wheel radius 119877119862 is the radius in the wheel rim119889 is the distance from the wheel center to the laser panel asdescribed in Section 2
On the basis of this geometric model when we know howmuch the error of the flange height is the errors of the flangewidth can be derived accordingly For different wear wheelsthe profiles aswell as the fitted line for lateral contact pointmare certainly different To illustrate the massiveness of errorshere we chose the same wheel where the fitted line for lateralcontact point m is V = 119891(119906) We obtain the inverse function119906 = 119892(V) and stretch it horizontally by a factor of (119865ℎ + 119890)119865ℎSo the stretched curve line is
119906 = 1198922 (V) = 119892(V119865ℎ
(119865ℎ + 119890)) (15)
Eventually the error of flange width is 120578 = 1198922(10)minus119865119908 where119865119908 is the original flange width
Error of flange heightError of flange width
0
01
02
03
04
05
06
07
08
Caus
ed er
ror (
mm
)
10 20 30 40 500d (mm)
Figure 9 The error of flange width and flange height with respectto various wheel positions
Theoretically from (14) and (15) we know that the smallerthe value of 119877 is the larger the error 119890 is So we chosethe largest standard wheelset with 119877 = 385mm and 119877119862 =399mm Figure 9 shows the error of flange height and flangewidth induced from misalignment in this case The distance119889 varies from 0mm to 50mmwith an interval of 1mm FromFigure 9 the error of flange height is lower than the error offlange width So we focus on the error of flange width here
In our system the sampling frequency of all LDS is 1 kHzand the maximum speed of the train in the depot is 36 kmhThemaximum of sampling step size along the railΔ119904 = 1ms times10ms = 10mmWhen we set the threshold119870119901 (as describedin Section 25) as 20mm the total measuring distance alongthe rail can be 58mm so that at least 119872 = 5 times ofefficient scans can be detected The corresponding errors areless than 01mm for flange width after taking the average ofthese 5 efficient scansThus the system can performdetectionnormally against themisalignment error benefitting from thehigh sampling frequency
33 Sensor Noise The LDS cannot be ideally accurate Themeasuring accuracy is influenced by temperature the rough-ness of the measured surface and so forth
In order to obtain the quantitative influence for profiledetection we built a 3D model in SolidWorks tools andextracted ideal sensor output points of standard inner andouter tread profiles In this model the standard wheel islocated in the position where the center of the wheel is inthe laser panel So the misalignment phenomenon will notaffect tread profile detection The wheel is in static positionso the simulated sensor output points are all from one scanMoreover the parameters that need to be calibrated areideally accurate To imitate the real situation Gaussian noiseis added to these coordinate valuesThemean of noise is zeroand the standard deviation is varied from 0 to 1mm with an
10 Journal of Sensors
X 03Y 01251
Flange widthFlange height
0
01
02
03
04
05
06
07Ca
used
erro
r (m
m)
02 04 06 08 10Noise level (mm)
Figure 10 The RMS error of flange height and flange width causedby different sensor noise level
interval of 01mm For each noise level 500 experiments arecarried out and the RMS error is calculated The RMS errorof flange height and flange width results caused by differentnoise level is shown in Figure 10 The caused error to flangeheight and flange width is approximately half of the sensornoise level This can be explained by the curve line fittingmethod that has taken more laser points into account andthus has reduced the random noise Because the flange heightis determined by two points the curve line fittingmethod hasat least reduced the randomerror into a quarter of the originalsensor noise
The 2D-LDS we chose is LJ-V7300 from KEYENCEwhich has a full-scale resolution of 01FS and a temper-ature drift of 001 FS∘C The detection range in 119910-axis is300 plusmn 145mm and in 119909-axis is 110mm to 240mm whichformed as a trapezoid The point in 119909-axis is fixed thus onlysensor noise in 119910-axis needs to be considered with full scaleof 290mm So accordingly the RMS error caused to theprofile coordinate noise in 119910-axis which is denoted by 120575 isless than 032mm which only leads to an error of 013mmboth to flange height and to flange width Taking dynamicsdetection effect into account the final error is reduced by120575119891 = 120575
radic5 = 0058mm with at least119873 = 5 times of efficientscans The error caused by sensor noise can be acceptable
Regarding the error of wheel diameter it can be theoreti-cally derived by the theorem of error propagation [25] Theresolution of each sensor is denoted by 1205751 1205752 and 1205753 Weobtain 120575119863 by taking differential of (6)ndash(9) as follows
120575119863 = plusmnradic(1205751
120597119863
1205971198971
)
2
+ (1205752
120597119863
1205971198972
)
2
+ (1205753
120597119863
1205971198973
)
2
(16)
We have chosen two 2D-LDS and one 1D-LDS to detect thewheel diameter and the two 2D-LDS are installed symmet-rically For systematic installation we have 1205751(1205971198631205971198971) =
1205753(1205971198631205971198973) Moreover the analytical function of particle
derivative will be too complex to derive So we consider aspecial case where
where the target wheel diameter is 119863 = 840mm and theorigin of the wheel is located in the origin of 119910119900119911WCF Morecalculation details can be found in the Appendix Finally wehave
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(18)
The 1D-LDS we chose is LK-G8085 from KEYENCE whichhas linearity of 005FS and a temperature drift of 001FS∘C So according to the full scale of 30mm the reso-lution of 1D-LDS 1205752 = 0018mm Based upon the findingthat the curve line fitting method has at least reduced therandom error into a quarter of the original sensor noise1205751 = 0075mm Finally 120575119863 is less than 0372mm Takingdynamics detection effect into account the final error 120575119863
119891
=
120575119863radic5 = 017mm The error caused by sensor noise can be
acceptable
34 Wheel Inclination Caused by Wheelset S-Shape RunningandDifferential ofWheel Diameter In engineering thewheelwill be inclined because of wheelset S-shape running and thedifferential of wheel diameter The wheelset S-shape runningis one kind of self-induced vibration due to the slope in thewheel trade When it is S-shape running the wheel panelwill have a certain angle with respect to 119910119900119911 panel in WCFdenoted by 120579119904 as shown in Figure 11(a) The differentialof wheel diameter in a wheelset is at different wear levelin the left and right wheel mainly induced from differentmassiveness of wear in the circuit of wheelset turning andunbalanced loading Similarly it will bring a certain angleabout the wheel panel with respect to the 119910119900119911 panel in WCFThe angle is denoted by 120579119889 as shown in Figure 11(b)
For wheel diameter detection because we only considerthe calculation in two dimensions an error will be generatedwhen we still regard the detected three points in a circle toactually be in an ellipse Considering the existence of angles120579119904 and 120579119889 we have the equation of ellipse as follows
1199102
(119877 sdot cos 120579119904)2+
1199112
1198772= 1
1199102
1198772+
1199112
(119877 sdot cos 120579119889)2= 1
(19)
Journal of Sensors 11
x
y
z
0
Ellipse wheel
Wheelset withS-shape running
120579s
(a)
x
y
z Ellipse wheel
Wheelset with differential of diameter
120579d
(b)
Figure 11 Mathematical illustration (a) Wheel S-shape running and (b) differential of wheel diameter
Similar towhenwe analyze sensor noise we consider a specialcase as (17) the origin of the target wheel is located in theorigin of 119910119900119911WCFThe real three points are
1198881(119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198882 (0 minus119877)
1198883(minus119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198881(119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
1198882 (0 minus119877 sdot cos 120579119889)
1198883(minus119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
(20)
Theoretically the larger the radius of the wheel is the biggerthe error is So we chose 119877 = 420mm and generated threepoints then using (7) we calculated the wheel diameter witherror Subtracting the real diameter we have the error withrespect to angle as shown in Figure 12 The effect of S-shaperunning caused angle has a relatively higher influence on thewheel diameter calculation
Based on the experience from Guangzhou Metro Cor-poration the differential of diameter in a wheelset shouldbe controlled under 2mm Considering the track gauge of1350mm the angle induced from the differential of diameter
S-shape runningWheel diameter differential
0
001
002
003
004
005
006
Caus
ed er
ror t
o di
amet
er (m
m)
01 02 03 04 050120579 (∘)
Figure 12 Wheel diameter errors
in a wheelset is less than 0001∘ thus the error can be ignoredAs for wheel S-shape running themaximum angle is 01∘ [26]when the speed of the train is under 36 kmhwhich will causean error not larger than 0005mm
4 Experimental Validation
41 System Implementation Theauthors previously proposedan online detection system using eight 2D-LDS [19] Thenew online detection system is installed in the same storageline of Guangzhou metro vehicle depot as the old systemso that comparison can be conducted In order to savefund only the left side namely half of the system has been
12 Journal of Sensors
(a) (b)
Figure 13 Field test (a) Standard wheel test and (b) real train test
Table 1 Standard wheelset detection the results of repeatedmeasurementsmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
implemented During the system implementation three-dimensional inclinometer and special rail gauge are used tocontrol the position of the mechanical support After thesystem is installed the calibration described in Section 2has been conducted to obtain the geometric parameters fortread profile calibration and diameter calculation As shownin Figure 13 the field test is carried out by a standard wheelsetand real train
42 Standard Wheelset The standard wheelset is a new pro-duced wheelset without any wear and diameter differentialThe manufacturing geometric size is as follows wheel diam-eter = 840mm flange height = 28mm and flange width =32mm One can also assume to have lower possibility of S-shape running because of zero external load The standardwheelset has been placed on the rail and passed through thedetection system This test has been carried out 6 times toverify both the detection and the repeatability of the systemComparing with the old system the results of this system areshown in Table 1
From Table 1 the mean values of the flange height andflange width detected by the old and the new system are very
close to each other which means the system error can beignored The standard deviation which also can be denotedas detection uncertainty of the new system measurement isslightly smaller than of the old system That may result fromthe lower effect frommisalignment as described in Section 3due to the higher sampling frequency that we used in the newsystem Detection uncertainty of not greater than 005mm intread profile measurement is acceptable for the engineeringrequirements As for wheel diameter detection the meanvalues are also close to each other The standard deviation ofthe new systemmeasurement is slightly higher than of the oldsystemThis may result from the replacement of 1D-LDS thathas brought about higher sensor noise to the middle pointamong three pointswithout curve fitting techniqueHoweverdetection uncertainty of less than 03mm is also acceptable inengineering
43 Real Train Detection Test Real train test also performs6 times of repeated detection to statistically evaluate theperformance of the system The train speed is controlledunder 36 kmh In the train we chose there are 4 new groundwheelsets in a car of the train Under the consideration thatthe ground new wheel is not out of roundness which hasan effect on the analysis results we selected the ground newwheel as our target wheel
Table 2 shows the mean and standard deviation value ofmeasurement The biggest differential value of mean flangeheight appears in 1 wheel and for mean flange width appearsin 3 wheel The difference does not exceed 015mm As forwheel diameter the biggest differential value 016mmappearsin 3 wheelThemean value of six times of repeated detectionis consistent with the standard wheelset test In terms ofstandard deviation the value is less than 01mm for flangewidth and flange height and 03mm for wheel diameterThe standard deviation of wheel diameter is relatively higherthan in standard wheelset test On the contrary the standarddeviation of flange width and flange height is relatively lowerthan in the old system That is also consistent with standard
Journal of Sensors 13
Table 2 Real train test the mean and standard deviation value of detected measurementmm
Wheelnumber
Mean flange height SD flange height Mean flange width SD flange width Mean wheeldiameter SD wheel diameter
Old New Old New Old New Old New Old New Old New1 2818 2803 0046 0060 2954 2943 0091 0062 80052 80150 0201 03012 2809 2811 0078 0040 2940 2929 0056 0028 80112 80096 0128 02863 2797 2791 0076 0033 2992 3006 0075 0056 80187 80166 0090 01794 2807 2805 0063 0053 2983 2988 0076 0088 80178 80201 0192 0282
Table 3 Real train test wheel 2 the result of repeated measure-mentmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
wheelset test The standard deviation of wheel diameter inreal train test is supposed to be higher than in the standardwheelset test because of several assumptions One factor isthe higher possibility of S-shape running because of heavyaxial load On the other hand the wheelset that is in service isalso more polluted with rust than standard wheelset causingmore detection uncertainty However the standard deviationfrom real train test also does not exceed 03mm which isconsistent with standard wheelset test This may result fromthe lower train speed during the test which leads to lowerpossibility of S-shape running Meanwhile the rusty wheelcontour is also not in a massive stage Tables 3 and 4 show theresult of repeated measurement for wheels numbers 2 and 3respectively In each detection the results remain the sameand no gross error appears
Overall detection uncertainties for tread profile andwheel diameter are less than 01mmand 03mm respectivelyThe results show that the detection system has a highaccuracy which can meet the requirements of maintenanceoperation
5 Conclusion
This paper based on LDS proposed a novel on-track detec-tion system of the wheel size using only six 2D-LDS and two1D-LDS Errors induced bywheel-rail vibration sensor noisemisalignment S-shape running and wheelset differential arealso analyzed After the system is implemented real dataexperiments including standard wheel test and real traindetection test were performed It turns out that the detectionuncertainty of flange width and height is 01mm and wheeldiameter 03mm which can meet the requirements of main-tenanceThis system can be further used for different types ofrailway transportation which provides a new solution for thewheel size detection technology
To provide more benefits the target wheel diameter is 119863 =
840mm and the origin of the wheel is located in the originof 119910119900119911WCF as shown in Figure 14 In this special case therelevant geometric values are 1198881(minus19802mm minus19802mm)1198882(0mm 420mm) 1198883(19802mm minus19802mm) 1198971 = 280mm1198972 = 180mm and 1198973 = 280mm
According to (8) and (9) we get the particle derivative asfollows
120597119863
1205971198971
=
120597119863
1205971199100
1205971199100
1205971198971
+
120597119863
1205971199110
1205971199110
1205971198971
120597119863
1205971198972
=
120597119863
1205971199100
1205971199100
1205971198972
+
120597119863
1205971199110
1205971199110
1205971198972
+
120597119863
1205971199111198882
1205971199111198882
1205971198972
(A2)
14 Journal of Sensors
2D-L1
1D-L2
2D-L3
y
z
o
45∘45∘ c1l1
l2
l3
c2
c3 lowast
lowast
lowast
Figure 14 A special case
Taking the derivative of diameter 119863 with respect to 1199100 1199110and 119911119888
2
according to (8) and substituting (1199100 1199110) = (0 0) and1199111198882
= 180mm we have
120597119863
1205971199100
=
21199100
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199110
=
2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199111198882
=
minus2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
= 2
(A3)
Furthermore based upon (7) we get
1205971199100
1205971198971
=
1205971199100
1205971199101198881
1205971199101198881
1205971198971
+
1205971199100
1205971199111198881
1205971199111198881
1205971198971
1205971199110
1205971198971
=
1205971199110
1205971199101198881
1205971199101198881
1205971198971
+
1205971199110
1205971199111198881
1205971199111198881
1205971198971
1205971199100
1205971198972
=
1205971199100
1205971199111198882
1205971199111198882
1205971198972
1205971199110
1205971198972
=
1205971199110
1205971199111198882
1205971199111198882
1205971198972
1205971199100
1205971198973
=
1205971199100
1205971199101198883
1205971199101198883
1205971198973
+
1205971199100
1205971199111198883
1205971199111198883
1205971198973
1205971199110
1205971198973
=
1205971199110
1205971199101198883
1205971199101198883
1205971198973
+
1205971199110
1205971199111198883
1205971199111198883
1205971198973
(A4)
When calculating particle derivative of (1199100 1199110) with respectto three points 1198881 1198882 and 1198883 in WCF we assume that allparameters are with the geometric values in this special case
Then we substitute the ideal geometric values of this variableand we obtain
1205971199100
1205971199101198881
= 05
1205971199100
1205971199111198881
= 05
1205971199110
1205971199101198881
= minus12071
1205971199110
1205971199111198881
= minus12071
1205971199100
1205971199111198882
= 0
1205971199110
1205971199111198882
= 34142
1205971199100
1205971199101198883
= 05
1205971199100
1205971199111198883
= minus05
1205971199110
1205971199101198883
= 12071
1205971199110
1205971199111198883
= minus12071
1205971199101198881
1205971198971
=
1
radic2
1205971199111198881
1205971198971
=
1
radic2
1205971199111198882
1205971198972
= minus1
1205971199101198883
1205971198973
= minus
1
radic2
1205971199111198883
1205971198973
=
1
radic2
(A5)
Finally substituting (A5) into (A4) and then substituting(A4) and (A3) into (A2) we have
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(A6)
Competing Interests
The authors declare that they have no competing interests
Journal of Sensors 15
Acknowledgments
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
Figure 10 The RMS error of flange height and flange width causedby different sensor noise level
interval of 01mm For each noise level 500 experiments arecarried out and the RMS error is calculated The RMS errorof flange height and flange width results caused by differentnoise level is shown in Figure 10 The caused error to flangeheight and flange width is approximately half of the sensornoise level This can be explained by the curve line fittingmethod that has taken more laser points into account andthus has reduced the random noise Because the flange heightis determined by two points the curve line fittingmethod hasat least reduced the randomerror into a quarter of the originalsensor noise
The 2D-LDS we chose is LJ-V7300 from KEYENCEwhich has a full-scale resolution of 01FS and a temper-ature drift of 001 FS∘C The detection range in 119910-axis is300 plusmn 145mm and in 119909-axis is 110mm to 240mm whichformed as a trapezoid The point in 119909-axis is fixed thus onlysensor noise in 119910-axis needs to be considered with full scaleof 290mm So accordingly the RMS error caused to theprofile coordinate noise in 119910-axis which is denoted by 120575 isless than 032mm which only leads to an error of 013mmboth to flange height and to flange width Taking dynamicsdetection effect into account the final error is reduced by120575119891 = 120575
radic5 = 0058mm with at least119873 = 5 times of efficientscans The error caused by sensor noise can be acceptable
Regarding the error of wheel diameter it can be theoreti-cally derived by the theorem of error propagation [25] Theresolution of each sensor is denoted by 1205751 1205752 and 1205753 Weobtain 120575119863 by taking differential of (6)ndash(9) as follows
120575119863 = plusmnradic(1205751
120597119863
1205971198971
)
2
+ (1205752
120597119863
1205971198972
)
2
+ (1205753
120597119863
1205971198973
)
2
(16)
We have chosen two 2D-LDS and one 1D-LDS to detect thewheel diameter and the two 2D-LDS are installed symmet-rically For systematic installation we have 1205751(1205971198631205971198971) =
1205753(1205971198631205971198973) Moreover the analytical function of particle
derivative will be too complex to derive So we consider aspecial case where
where the target wheel diameter is 119863 = 840mm and theorigin of the wheel is located in the origin of 119910119900119911WCF Morecalculation details can be found in the Appendix Finally wehave
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(18)
The 1D-LDS we chose is LK-G8085 from KEYENCE whichhas linearity of 005FS and a temperature drift of 001FS∘C So according to the full scale of 30mm the reso-lution of 1D-LDS 1205752 = 0018mm Based upon the findingthat the curve line fitting method has at least reduced therandom error into a quarter of the original sensor noise1205751 = 0075mm Finally 120575119863 is less than 0372mm Takingdynamics detection effect into account the final error 120575119863
119891
=
120575119863radic5 = 017mm The error caused by sensor noise can be
acceptable
34 Wheel Inclination Caused by Wheelset S-Shape RunningandDifferential ofWheel Diameter In engineering thewheelwill be inclined because of wheelset S-shape running and thedifferential of wheel diameter The wheelset S-shape runningis one kind of self-induced vibration due to the slope in thewheel trade When it is S-shape running the wheel panelwill have a certain angle with respect to 119910119900119911 panel in WCFdenoted by 120579119904 as shown in Figure 11(a) The differentialof wheel diameter in a wheelset is at different wear levelin the left and right wheel mainly induced from differentmassiveness of wear in the circuit of wheelset turning andunbalanced loading Similarly it will bring a certain angleabout the wheel panel with respect to the 119910119900119911 panel in WCFThe angle is denoted by 120579119889 as shown in Figure 11(b)
For wheel diameter detection because we only considerthe calculation in two dimensions an error will be generatedwhen we still regard the detected three points in a circle toactually be in an ellipse Considering the existence of angles120579119904 and 120579119889 we have the equation of ellipse as follows
1199102
(119877 sdot cos 120579119904)2+
1199112
1198772= 1
1199102
1198772+
1199112
(119877 sdot cos 120579119889)2= 1
(19)
Journal of Sensors 11
x
y
z
0
Ellipse wheel
Wheelset withS-shape running
120579s
(a)
x
y
z Ellipse wheel
Wheelset with differential of diameter
120579d
(b)
Figure 11 Mathematical illustration (a) Wheel S-shape running and (b) differential of wheel diameter
Similar towhenwe analyze sensor noise we consider a specialcase as (17) the origin of the target wheel is located in theorigin of 119910119900119911WCFThe real three points are
1198881(119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198882 (0 minus119877)
1198883(minus119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198881(119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
1198882 (0 minus119877 sdot cos 120579119889)
1198883(minus119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
(20)
Theoretically the larger the radius of the wheel is the biggerthe error is So we chose 119877 = 420mm and generated threepoints then using (7) we calculated the wheel diameter witherror Subtracting the real diameter we have the error withrespect to angle as shown in Figure 12 The effect of S-shaperunning caused angle has a relatively higher influence on thewheel diameter calculation
Based on the experience from Guangzhou Metro Cor-poration the differential of diameter in a wheelset shouldbe controlled under 2mm Considering the track gauge of1350mm the angle induced from the differential of diameter
S-shape runningWheel diameter differential
0
001
002
003
004
005
006
Caus
ed er
ror t
o di
amet
er (m
m)
01 02 03 04 050120579 (∘)
Figure 12 Wheel diameter errors
in a wheelset is less than 0001∘ thus the error can be ignoredAs for wheel S-shape running themaximum angle is 01∘ [26]when the speed of the train is under 36 kmhwhich will causean error not larger than 0005mm
4 Experimental Validation
41 System Implementation Theauthors previously proposedan online detection system using eight 2D-LDS [19] Thenew online detection system is installed in the same storageline of Guangzhou metro vehicle depot as the old systemso that comparison can be conducted In order to savefund only the left side namely half of the system has been
12 Journal of Sensors
(a) (b)
Figure 13 Field test (a) Standard wheel test and (b) real train test
Table 1 Standard wheelset detection the results of repeatedmeasurementsmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
implemented During the system implementation three-dimensional inclinometer and special rail gauge are used tocontrol the position of the mechanical support After thesystem is installed the calibration described in Section 2has been conducted to obtain the geometric parameters fortread profile calibration and diameter calculation As shownin Figure 13 the field test is carried out by a standard wheelsetand real train
42 Standard Wheelset The standard wheelset is a new pro-duced wheelset without any wear and diameter differentialThe manufacturing geometric size is as follows wheel diam-eter = 840mm flange height = 28mm and flange width =32mm One can also assume to have lower possibility of S-shape running because of zero external load The standardwheelset has been placed on the rail and passed through thedetection system This test has been carried out 6 times toverify both the detection and the repeatability of the systemComparing with the old system the results of this system areshown in Table 1
From Table 1 the mean values of the flange height andflange width detected by the old and the new system are very
close to each other which means the system error can beignored The standard deviation which also can be denotedas detection uncertainty of the new system measurement isslightly smaller than of the old system That may result fromthe lower effect frommisalignment as described in Section 3due to the higher sampling frequency that we used in the newsystem Detection uncertainty of not greater than 005mm intread profile measurement is acceptable for the engineeringrequirements As for wheel diameter detection the meanvalues are also close to each other The standard deviation ofthe new systemmeasurement is slightly higher than of the oldsystemThis may result from the replacement of 1D-LDS thathas brought about higher sensor noise to the middle pointamong three pointswithout curve fitting techniqueHoweverdetection uncertainty of less than 03mm is also acceptable inengineering
43 Real Train Detection Test Real train test also performs6 times of repeated detection to statistically evaluate theperformance of the system The train speed is controlledunder 36 kmh In the train we chose there are 4 new groundwheelsets in a car of the train Under the consideration thatthe ground new wheel is not out of roundness which hasan effect on the analysis results we selected the ground newwheel as our target wheel
Table 2 shows the mean and standard deviation value ofmeasurement The biggest differential value of mean flangeheight appears in 1 wheel and for mean flange width appearsin 3 wheel The difference does not exceed 015mm As forwheel diameter the biggest differential value 016mmappearsin 3 wheelThemean value of six times of repeated detectionis consistent with the standard wheelset test In terms ofstandard deviation the value is less than 01mm for flangewidth and flange height and 03mm for wheel diameterThe standard deviation of wheel diameter is relatively higherthan in standard wheelset test On the contrary the standarddeviation of flange width and flange height is relatively lowerthan in the old system That is also consistent with standard
Journal of Sensors 13
Table 2 Real train test the mean and standard deviation value of detected measurementmm
Wheelnumber
Mean flange height SD flange height Mean flange width SD flange width Mean wheeldiameter SD wheel diameter
Old New Old New Old New Old New Old New Old New1 2818 2803 0046 0060 2954 2943 0091 0062 80052 80150 0201 03012 2809 2811 0078 0040 2940 2929 0056 0028 80112 80096 0128 02863 2797 2791 0076 0033 2992 3006 0075 0056 80187 80166 0090 01794 2807 2805 0063 0053 2983 2988 0076 0088 80178 80201 0192 0282
Table 3 Real train test wheel 2 the result of repeated measure-mentmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
wheelset test The standard deviation of wheel diameter inreal train test is supposed to be higher than in the standardwheelset test because of several assumptions One factor isthe higher possibility of S-shape running because of heavyaxial load On the other hand the wheelset that is in service isalso more polluted with rust than standard wheelset causingmore detection uncertainty However the standard deviationfrom real train test also does not exceed 03mm which isconsistent with standard wheelset test This may result fromthe lower train speed during the test which leads to lowerpossibility of S-shape running Meanwhile the rusty wheelcontour is also not in a massive stage Tables 3 and 4 show theresult of repeated measurement for wheels numbers 2 and 3respectively In each detection the results remain the sameand no gross error appears
Overall detection uncertainties for tread profile andwheel diameter are less than 01mmand 03mm respectivelyThe results show that the detection system has a highaccuracy which can meet the requirements of maintenanceoperation
5 Conclusion
This paper based on LDS proposed a novel on-track detec-tion system of the wheel size using only six 2D-LDS and two1D-LDS Errors induced bywheel-rail vibration sensor noisemisalignment S-shape running and wheelset differential arealso analyzed After the system is implemented real dataexperiments including standard wheel test and real traindetection test were performed It turns out that the detectionuncertainty of flange width and height is 01mm and wheeldiameter 03mm which can meet the requirements of main-tenanceThis system can be further used for different types ofrailway transportation which provides a new solution for thewheel size detection technology
To provide more benefits the target wheel diameter is 119863 =
840mm and the origin of the wheel is located in the originof 119910119900119911WCF as shown in Figure 14 In this special case therelevant geometric values are 1198881(minus19802mm minus19802mm)1198882(0mm 420mm) 1198883(19802mm minus19802mm) 1198971 = 280mm1198972 = 180mm and 1198973 = 280mm
According to (8) and (9) we get the particle derivative asfollows
120597119863
1205971198971
=
120597119863
1205971199100
1205971199100
1205971198971
+
120597119863
1205971199110
1205971199110
1205971198971
120597119863
1205971198972
=
120597119863
1205971199100
1205971199100
1205971198972
+
120597119863
1205971199110
1205971199110
1205971198972
+
120597119863
1205971199111198882
1205971199111198882
1205971198972
(A2)
14 Journal of Sensors
2D-L1
1D-L2
2D-L3
y
z
o
45∘45∘ c1l1
l2
l3
c2
c3 lowast
lowast
lowast
Figure 14 A special case
Taking the derivative of diameter 119863 with respect to 1199100 1199110and 119911119888
2
according to (8) and substituting (1199100 1199110) = (0 0) and1199111198882
= 180mm we have
120597119863
1205971199100
=
21199100
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199110
=
2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199111198882
=
minus2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
= 2
(A3)
Furthermore based upon (7) we get
1205971199100
1205971198971
=
1205971199100
1205971199101198881
1205971199101198881
1205971198971
+
1205971199100
1205971199111198881
1205971199111198881
1205971198971
1205971199110
1205971198971
=
1205971199110
1205971199101198881
1205971199101198881
1205971198971
+
1205971199110
1205971199111198881
1205971199111198881
1205971198971
1205971199100
1205971198972
=
1205971199100
1205971199111198882
1205971199111198882
1205971198972
1205971199110
1205971198972
=
1205971199110
1205971199111198882
1205971199111198882
1205971198972
1205971199100
1205971198973
=
1205971199100
1205971199101198883
1205971199101198883
1205971198973
+
1205971199100
1205971199111198883
1205971199111198883
1205971198973
1205971199110
1205971198973
=
1205971199110
1205971199101198883
1205971199101198883
1205971198973
+
1205971199110
1205971199111198883
1205971199111198883
1205971198973
(A4)
When calculating particle derivative of (1199100 1199110) with respectto three points 1198881 1198882 and 1198883 in WCF we assume that allparameters are with the geometric values in this special case
Then we substitute the ideal geometric values of this variableand we obtain
1205971199100
1205971199101198881
= 05
1205971199100
1205971199111198881
= 05
1205971199110
1205971199101198881
= minus12071
1205971199110
1205971199111198881
= minus12071
1205971199100
1205971199111198882
= 0
1205971199110
1205971199111198882
= 34142
1205971199100
1205971199101198883
= 05
1205971199100
1205971199111198883
= minus05
1205971199110
1205971199101198883
= 12071
1205971199110
1205971199111198883
= minus12071
1205971199101198881
1205971198971
=
1
radic2
1205971199111198881
1205971198971
=
1
radic2
1205971199111198882
1205971198972
= minus1
1205971199101198883
1205971198973
= minus
1
radic2
1205971199111198883
1205971198973
=
1
radic2
(A5)
Finally substituting (A5) into (A4) and then substituting(A4) and (A3) into (A2) we have
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(A6)
Competing Interests
The authors declare that they have no competing interests
Journal of Sensors 15
Acknowledgments
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
Figure 11 Mathematical illustration (a) Wheel S-shape running and (b) differential of wheel diameter
Similar towhenwe analyze sensor noise we consider a specialcase as (17) the origin of the target wheel is located in theorigin of 119910119900119911WCFThe real three points are
1198881(119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198882 (0 minus119877)
1198883(minus119877 sdot cos 120579119904
radic(cos 120579119904)2+ 1
minus
119877 sdot cos 120579119904radic(cos 120579119904)
2+ 1
)
1198881(119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
1198882 (0 minus119877 sdot cos 120579119889)
1198883(minus119877 sdot cos 120579119889
radic(cos 120579119889)2+ 1
minus
119877 sdot cos 120579119889radic(cos 120579119889)
2+ 1
)
(20)
Theoretically the larger the radius of the wheel is the biggerthe error is So we chose 119877 = 420mm and generated threepoints then using (7) we calculated the wheel diameter witherror Subtracting the real diameter we have the error withrespect to angle as shown in Figure 12 The effect of S-shaperunning caused angle has a relatively higher influence on thewheel diameter calculation
Based on the experience from Guangzhou Metro Cor-poration the differential of diameter in a wheelset shouldbe controlled under 2mm Considering the track gauge of1350mm the angle induced from the differential of diameter
S-shape runningWheel diameter differential
0
001
002
003
004
005
006
Caus
ed er
ror t
o di
amet
er (m
m)
01 02 03 04 050120579 (∘)
Figure 12 Wheel diameter errors
in a wheelset is less than 0001∘ thus the error can be ignoredAs for wheel S-shape running themaximum angle is 01∘ [26]when the speed of the train is under 36 kmhwhich will causean error not larger than 0005mm
4 Experimental Validation
41 System Implementation Theauthors previously proposedan online detection system using eight 2D-LDS [19] Thenew online detection system is installed in the same storageline of Guangzhou metro vehicle depot as the old systemso that comparison can be conducted In order to savefund only the left side namely half of the system has been
12 Journal of Sensors
(a) (b)
Figure 13 Field test (a) Standard wheel test and (b) real train test
Table 1 Standard wheelset detection the results of repeatedmeasurementsmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
implemented During the system implementation three-dimensional inclinometer and special rail gauge are used tocontrol the position of the mechanical support After thesystem is installed the calibration described in Section 2has been conducted to obtain the geometric parameters fortread profile calibration and diameter calculation As shownin Figure 13 the field test is carried out by a standard wheelsetand real train
42 Standard Wheelset The standard wheelset is a new pro-duced wheelset without any wear and diameter differentialThe manufacturing geometric size is as follows wheel diam-eter = 840mm flange height = 28mm and flange width =32mm One can also assume to have lower possibility of S-shape running because of zero external load The standardwheelset has been placed on the rail and passed through thedetection system This test has been carried out 6 times toverify both the detection and the repeatability of the systemComparing with the old system the results of this system areshown in Table 1
From Table 1 the mean values of the flange height andflange width detected by the old and the new system are very
close to each other which means the system error can beignored The standard deviation which also can be denotedas detection uncertainty of the new system measurement isslightly smaller than of the old system That may result fromthe lower effect frommisalignment as described in Section 3due to the higher sampling frequency that we used in the newsystem Detection uncertainty of not greater than 005mm intread profile measurement is acceptable for the engineeringrequirements As for wheel diameter detection the meanvalues are also close to each other The standard deviation ofthe new systemmeasurement is slightly higher than of the oldsystemThis may result from the replacement of 1D-LDS thathas brought about higher sensor noise to the middle pointamong three pointswithout curve fitting techniqueHoweverdetection uncertainty of less than 03mm is also acceptable inengineering
43 Real Train Detection Test Real train test also performs6 times of repeated detection to statistically evaluate theperformance of the system The train speed is controlledunder 36 kmh In the train we chose there are 4 new groundwheelsets in a car of the train Under the consideration thatthe ground new wheel is not out of roundness which hasan effect on the analysis results we selected the ground newwheel as our target wheel
Table 2 shows the mean and standard deviation value ofmeasurement The biggest differential value of mean flangeheight appears in 1 wheel and for mean flange width appearsin 3 wheel The difference does not exceed 015mm As forwheel diameter the biggest differential value 016mmappearsin 3 wheelThemean value of six times of repeated detectionis consistent with the standard wheelset test In terms ofstandard deviation the value is less than 01mm for flangewidth and flange height and 03mm for wheel diameterThe standard deviation of wheel diameter is relatively higherthan in standard wheelset test On the contrary the standarddeviation of flange width and flange height is relatively lowerthan in the old system That is also consistent with standard
Journal of Sensors 13
Table 2 Real train test the mean and standard deviation value of detected measurementmm
Wheelnumber
Mean flange height SD flange height Mean flange width SD flange width Mean wheeldiameter SD wheel diameter
Old New Old New Old New Old New Old New Old New1 2818 2803 0046 0060 2954 2943 0091 0062 80052 80150 0201 03012 2809 2811 0078 0040 2940 2929 0056 0028 80112 80096 0128 02863 2797 2791 0076 0033 2992 3006 0075 0056 80187 80166 0090 01794 2807 2805 0063 0053 2983 2988 0076 0088 80178 80201 0192 0282
Table 3 Real train test wheel 2 the result of repeated measure-mentmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
wheelset test The standard deviation of wheel diameter inreal train test is supposed to be higher than in the standardwheelset test because of several assumptions One factor isthe higher possibility of S-shape running because of heavyaxial load On the other hand the wheelset that is in service isalso more polluted with rust than standard wheelset causingmore detection uncertainty However the standard deviationfrom real train test also does not exceed 03mm which isconsistent with standard wheelset test This may result fromthe lower train speed during the test which leads to lowerpossibility of S-shape running Meanwhile the rusty wheelcontour is also not in a massive stage Tables 3 and 4 show theresult of repeated measurement for wheels numbers 2 and 3respectively In each detection the results remain the sameand no gross error appears
Overall detection uncertainties for tread profile andwheel diameter are less than 01mmand 03mm respectivelyThe results show that the detection system has a highaccuracy which can meet the requirements of maintenanceoperation
5 Conclusion
This paper based on LDS proposed a novel on-track detec-tion system of the wheel size using only six 2D-LDS and two1D-LDS Errors induced bywheel-rail vibration sensor noisemisalignment S-shape running and wheelset differential arealso analyzed After the system is implemented real dataexperiments including standard wheel test and real traindetection test were performed It turns out that the detectionuncertainty of flange width and height is 01mm and wheeldiameter 03mm which can meet the requirements of main-tenanceThis system can be further used for different types ofrailway transportation which provides a new solution for thewheel size detection technology
To provide more benefits the target wheel diameter is 119863 =
840mm and the origin of the wheel is located in the originof 119910119900119911WCF as shown in Figure 14 In this special case therelevant geometric values are 1198881(minus19802mm minus19802mm)1198882(0mm 420mm) 1198883(19802mm minus19802mm) 1198971 = 280mm1198972 = 180mm and 1198973 = 280mm
According to (8) and (9) we get the particle derivative asfollows
120597119863
1205971198971
=
120597119863
1205971199100
1205971199100
1205971198971
+
120597119863
1205971199110
1205971199110
1205971198971
120597119863
1205971198972
=
120597119863
1205971199100
1205971199100
1205971198972
+
120597119863
1205971199110
1205971199110
1205971198972
+
120597119863
1205971199111198882
1205971199111198882
1205971198972
(A2)
14 Journal of Sensors
2D-L1
1D-L2
2D-L3
y
z
o
45∘45∘ c1l1
l2
l3
c2
c3 lowast
lowast
lowast
Figure 14 A special case
Taking the derivative of diameter 119863 with respect to 1199100 1199110and 119911119888
2
according to (8) and substituting (1199100 1199110) = (0 0) and1199111198882
= 180mm we have
120597119863
1205971199100
=
21199100
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199110
=
2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199111198882
=
minus2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
= 2
(A3)
Furthermore based upon (7) we get
1205971199100
1205971198971
=
1205971199100
1205971199101198881
1205971199101198881
1205971198971
+
1205971199100
1205971199111198881
1205971199111198881
1205971198971
1205971199110
1205971198971
=
1205971199110
1205971199101198881
1205971199101198881
1205971198971
+
1205971199110
1205971199111198881
1205971199111198881
1205971198971
1205971199100
1205971198972
=
1205971199100
1205971199111198882
1205971199111198882
1205971198972
1205971199110
1205971198972
=
1205971199110
1205971199111198882
1205971199111198882
1205971198972
1205971199100
1205971198973
=
1205971199100
1205971199101198883
1205971199101198883
1205971198973
+
1205971199100
1205971199111198883
1205971199111198883
1205971198973
1205971199110
1205971198973
=
1205971199110
1205971199101198883
1205971199101198883
1205971198973
+
1205971199110
1205971199111198883
1205971199111198883
1205971198973
(A4)
When calculating particle derivative of (1199100 1199110) with respectto three points 1198881 1198882 and 1198883 in WCF we assume that allparameters are with the geometric values in this special case
Then we substitute the ideal geometric values of this variableand we obtain
1205971199100
1205971199101198881
= 05
1205971199100
1205971199111198881
= 05
1205971199110
1205971199101198881
= minus12071
1205971199110
1205971199111198881
= minus12071
1205971199100
1205971199111198882
= 0
1205971199110
1205971199111198882
= 34142
1205971199100
1205971199101198883
= 05
1205971199100
1205971199111198883
= minus05
1205971199110
1205971199101198883
= 12071
1205971199110
1205971199111198883
= minus12071
1205971199101198881
1205971198971
=
1
radic2
1205971199111198881
1205971198971
=
1
radic2
1205971199111198882
1205971198972
= minus1
1205971199101198883
1205971198973
= minus
1
radic2
1205971199111198883
1205971198973
=
1
radic2
(A5)
Finally substituting (A5) into (A4) and then substituting(A4) and (A3) into (A2) we have
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(A6)
Competing Interests
The authors declare that they have no competing interests
Journal of Sensors 15
Acknowledgments
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
implemented During the system implementation three-dimensional inclinometer and special rail gauge are used tocontrol the position of the mechanical support After thesystem is installed the calibration described in Section 2has been conducted to obtain the geometric parameters fortread profile calibration and diameter calculation As shownin Figure 13 the field test is carried out by a standard wheelsetand real train
42 Standard Wheelset The standard wheelset is a new pro-duced wheelset without any wear and diameter differentialThe manufacturing geometric size is as follows wheel diam-eter = 840mm flange height = 28mm and flange width =32mm One can also assume to have lower possibility of S-shape running because of zero external load The standardwheelset has been placed on the rail and passed through thedetection system This test has been carried out 6 times toverify both the detection and the repeatability of the systemComparing with the old system the results of this system areshown in Table 1
From Table 1 the mean values of the flange height andflange width detected by the old and the new system are very
close to each other which means the system error can beignored The standard deviation which also can be denotedas detection uncertainty of the new system measurement isslightly smaller than of the old system That may result fromthe lower effect frommisalignment as described in Section 3due to the higher sampling frequency that we used in the newsystem Detection uncertainty of not greater than 005mm intread profile measurement is acceptable for the engineeringrequirements As for wheel diameter detection the meanvalues are also close to each other The standard deviation ofthe new systemmeasurement is slightly higher than of the oldsystemThis may result from the replacement of 1D-LDS thathas brought about higher sensor noise to the middle pointamong three pointswithout curve fitting techniqueHoweverdetection uncertainty of less than 03mm is also acceptable inengineering
43 Real Train Detection Test Real train test also performs6 times of repeated detection to statistically evaluate theperformance of the system The train speed is controlledunder 36 kmh In the train we chose there are 4 new groundwheelsets in a car of the train Under the consideration thatthe ground new wheel is not out of roundness which hasan effect on the analysis results we selected the ground newwheel as our target wheel
Table 2 shows the mean and standard deviation value ofmeasurement The biggest differential value of mean flangeheight appears in 1 wheel and for mean flange width appearsin 3 wheel The difference does not exceed 015mm As forwheel diameter the biggest differential value 016mmappearsin 3 wheelThemean value of six times of repeated detectionis consistent with the standard wheelset test In terms ofstandard deviation the value is less than 01mm for flangewidth and flange height and 03mm for wheel diameterThe standard deviation of wheel diameter is relatively higherthan in standard wheelset test On the contrary the standarddeviation of flange width and flange height is relatively lowerthan in the old system That is also consistent with standard
Journal of Sensors 13
Table 2 Real train test the mean and standard deviation value of detected measurementmm
Wheelnumber
Mean flange height SD flange height Mean flange width SD flange width Mean wheeldiameter SD wheel diameter
Old New Old New Old New Old New Old New Old New1 2818 2803 0046 0060 2954 2943 0091 0062 80052 80150 0201 03012 2809 2811 0078 0040 2940 2929 0056 0028 80112 80096 0128 02863 2797 2791 0076 0033 2992 3006 0075 0056 80187 80166 0090 01794 2807 2805 0063 0053 2983 2988 0076 0088 80178 80201 0192 0282
Table 3 Real train test wheel 2 the result of repeated measure-mentmm
Measurementtimes
Flange height Flange width Wheel diameterOld New Old New Old New
wheelset test The standard deviation of wheel diameter inreal train test is supposed to be higher than in the standardwheelset test because of several assumptions One factor isthe higher possibility of S-shape running because of heavyaxial load On the other hand the wheelset that is in service isalso more polluted with rust than standard wheelset causingmore detection uncertainty However the standard deviationfrom real train test also does not exceed 03mm which isconsistent with standard wheelset test This may result fromthe lower train speed during the test which leads to lowerpossibility of S-shape running Meanwhile the rusty wheelcontour is also not in a massive stage Tables 3 and 4 show theresult of repeated measurement for wheels numbers 2 and 3respectively In each detection the results remain the sameand no gross error appears
Overall detection uncertainties for tread profile andwheel diameter are less than 01mmand 03mm respectivelyThe results show that the detection system has a highaccuracy which can meet the requirements of maintenanceoperation
5 Conclusion
This paper based on LDS proposed a novel on-track detec-tion system of the wheel size using only six 2D-LDS and two1D-LDS Errors induced bywheel-rail vibration sensor noisemisalignment S-shape running and wheelset differential arealso analyzed After the system is implemented real dataexperiments including standard wheel test and real traindetection test were performed It turns out that the detectionuncertainty of flange width and height is 01mm and wheeldiameter 03mm which can meet the requirements of main-tenanceThis system can be further used for different types ofrailway transportation which provides a new solution for thewheel size detection technology
To provide more benefits the target wheel diameter is 119863 =
840mm and the origin of the wheel is located in the originof 119910119900119911WCF as shown in Figure 14 In this special case therelevant geometric values are 1198881(minus19802mm minus19802mm)1198882(0mm 420mm) 1198883(19802mm minus19802mm) 1198971 = 280mm1198972 = 180mm and 1198973 = 280mm
According to (8) and (9) we get the particle derivative asfollows
120597119863
1205971198971
=
120597119863
1205971199100
1205971199100
1205971198971
+
120597119863
1205971199110
1205971199110
1205971198971
120597119863
1205971198972
=
120597119863
1205971199100
1205971199100
1205971198972
+
120597119863
1205971199110
1205971199110
1205971198972
+
120597119863
1205971199111198882
1205971199111198882
1205971198972
(A2)
14 Journal of Sensors
2D-L1
1D-L2
2D-L3
y
z
o
45∘45∘ c1l1
l2
l3
c2
c3 lowast
lowast
lowast
Figure 14 A special case
Taking the derivative of diameter 119863 with respect to 1199100 1199110and 119911119888
2
according to (8) and substituting (1199100 1199110) = (0 0) and1199111198882
= 180mm we have
120597119863
1205971199100
=
21199100
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199110
=
2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199111198882
=
minus2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
= 2
(A3)
Furthermore based upon (7) we get
1205971199100
1205971198971
=
1205971199100
1205971199101198881
1205971199101198881
1205971198971
+
1205971199100
1205971199111198881
1205971199111198881
1205971198971
1205971199110
1205971198971
=
1205971199110
1205971199101198881
1205971199101198881
1205971198971
+
1205971199110
1205971199111198881
1205971199111198881
1205971198971
1205971199100
1205971198972
=
1205971199100
1205971199111198882
1205971199111198882
1205971198972
1205971199110
1205971198972
=
1205971199110
1205971199111198882
1205971199111198882
1205971198972
1205971199100
1205971198973
=
1205971199100
1205971199101198883
1205971199101198883
1205971198973
+
1205971199100
1205971199111198883
1205971199111198883
1205971198973
1205971199110
1205971198973
=
1205971199110
1205971199101198883
1205971199101198883
1205971198973
+
1205971199110
1205971199111198883
1205971199111198883
1205971198973
(A4)
When calculating particle derivative of (1199100 1199110) with respectto three points 1198881 1198882 and 1198883 in WCF we assume that allparameters are with the geometric values in this special case
Then we substitute the ideal geometric values of this variableand we obtain
1205971199100
1205971199101198881
= 05
1205971199100
1205971199111198881
= 05
1205971199110
1205971199101198881
= minus12071
1205971199110
1205971199111198881
= minus12071
1205971199100
1205971199111198882
= 0
1205971199110
1205971199111198882
= 34142
1205971199100
1205971199101198883
= 05
1205971199100
1205971199111198883
= minus05
1205971199110
1205971199101198883
= 12071
1205971199110
1205971199111198883
= minus12071
1205971199101198881
1205971198971
=
1
radic2
1205971199111198881
1205971198971
=
1
radic2
1205971199111198882
1205971198972
= minus1
1205971199101198883
1205971198973
= minus
1
radic2
1205971199111198883
1205971198973
=
1
radic2
(A5)
Finally substituting (A5) into (A4) and then substituting(A4) and (A3) into (A2) we have
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(A6)
Competing Interests
The authors declare that they have no competing interests
Journal of Sensors 15
Acknowledgments
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
wheelset test The standard deviation of wheel diameter inreal train test is supposed to be higher than in the standardwheelset test because of several assumptions One factor isthe higher possibility of S-shape running because of heavyaxial load On the other hand the wheelset that is in service isalso more polluted with rust than standard wheelset causingmore detection uncertainty However the standard deviationfrom real train test also does not exceed 03mm which isconsistent with standard wheelset test This may result fromthe lower train speed during the test which leads to lowerpossibility of S-shape running Meanwhile the rusty wheelcontour is also not in a massive stage Tables 3 and 4 show theresult of repeated measurement for wheels numbers 2 and 3respectively In each detection the results remain the sameand no gross error appears
Overall detection uncertainties for tread profile andwheel diameter are less than 01mmand 03mm respectivelyThe results show that the detection system has a highaccuracy which can meet the requirements of maintenanceoperation
5 Conclusion
This paper based on LDS proposed a novel on-track detec-tion system of the wheel size using only six 2D-LDS and two1D-LDS Errors induced bywheel-rail vibration sensor noisemisalignment S-shape running and wheelset differential arealso analyzed After the system is implemented real dataexperiments including standard wheel test and real traindetection test were performed It turns out that the detectionuncertainty of flange width and height is 01mm and wheeldiameter 03mm which can meet the requirements of main-tenanceThis system can be further used for different types ofrailway transportation which provides a new solution for thewheel size detection technology
To provide more benefits the target wheel diameter is 119863 =
840mm and the origin of the wheel is located in the originof 119910119900119911WCF as shown in Figure 14 In this special case therelevant geometric values are 1198881(minus19802mm minus19802mm)1198882(0mm 420mm) 1198883(19802mm minus19802mm) 1198971 = 280mm1198972 = 180mm and 1198973 = 280mm
According to (8) and (9) we get the particle derivative asfollows
120597119863
1205971198971
=
120597119863
1205971199100
1205971199100
1205971198971
+
120597119863
1205971199110
1205971199110
1205971198971
120597119863
1205971198972
=
120597119863
1205971199100
1205971199100
1205971198972
+
120597119863
1205971199110
1205971199110
1205971198972
+
120597119863
1205971199111198882
1205971199111198882
1205971198972
(A2)
14 Journal of Sensors
2D-L1
1D-L2
2D-L3
y
z
o
45∘45∘ c1l1
l2
l3
c2
c3 lowast
lowast
lowast
Figure 14 A special case
Taking the derivative of diameter 119863 with respect to 1199100 1199110and 119911119888
2
according to (8) and substituting (1199100 1199110) = (0 0) and1199111198882
= 180mm we have
120597119863
1205971199100
=
21199100
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199110
=
2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199111198882
=
minus2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
= 2
(A3)
Furthermore based upon (7) we get
1205971199100
1205971198971
=
1205971199100
1205971199101198881
1205971199101198881
1205971198971
+
1205971199100
1205971199111198881
1205971199111198881
1205971198971
1205971199110
1205971198971
=
1205971199110
1205971199101198881
1205971199101198881
1205971198971
+
1205971199110
1205971199111198881
1205971199111198881
1205971198971
1205971199100
1205971198972
=
1205971199100
1205971199111198882
1205971199111198882
1205971198972
1205971199110
1205971198972
=
1205971199110
1205971199111198882
1205971199111198882
1205971198972
1205971199100
1205971198973
=
1205971199100
1205971199101198883
1205971199101198883
1205971198973
+
1205971199100
1205971199111198883
1205971199111198883
1205971198973
1205971199110
1205971198973
=
1205971199110
1205971199101198883
1205971199101198883
1205971198973
+
1205971199110
1205971199111198883
1205971199111198883
1205971198973
(A4)
When calculating particle derivative of (1199100 1199110) with respectto three points 1198881 1198882 and 1198883 in WCF we assume that allparameters are with the geometric values in this special case
Then we substitute the ideal geometric values of this variableand we obtain
1205971199100
1205971199101198881
= 05
1205971199100
1205971199111198881
= 05
1205971199110
1205971199101198881
= minus12071
1205971199110
1205971199111198881
= minus12071
1205971199100
1205971199111198882
= 0
1205971199110
1205971199111198882
= 34142
1205971199100
1205971199101198883
= 05
1205971199100
1205971199111198883
= minus05
1205971199110
1205971199101198883
= 12071
1205971199110
1205971199111198883
= minus12071
1205971199101198881
1205971198971
=
1
radic2
1205971199111198881
1205971198971
=
1
radic2
1205971199111198882
1205971198972
= minus1
1205971199101198883
1205971198973
= minus
1
radic2
1205971199111198883
1205971198973
=
1
radic2
(A5)
Finally substituting (A5) into (A4) and then substituting(A4) and (A3) into (A2) we have
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(A6)
Competing Interests
The authors declare that they have no competing interests
Journal of Sensors 15
Acknowledgments
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
Taking the derivative of diameter 119863 with respect to 1199100 1199110and 119911119888
2
according to (8) and substituting (1199100 1199110) = (0 0) and1199111198882
= 180mm we have
120597119863
1205971199100
=
21199100
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199110
=
2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
=
1
180mm
120597119863
1205971199111198882
=
minus2 (1199110 minus 1199111198882
)
radic(1199100)2+ (1199110 minus 119911119888
2
)
2
= 2
(A3)
Furthermore based upon (7) we get
1205971199100
1205971198971
=
1205971199100
1205971199101198881
1205971199101198881
1205971198971
+
1205971199100
1205971199111198881
1205971199111198881
1205971198971
1205971199110
1205971198971
=
1205971199110
1205971199101198881
1205971199101198881
1205971198971
+
1205971199110
1205971199111198881
1205971199111198881
1205971198971
1205971199100
1205971198972
=
1205971199100
1205971199111198882
1205971199111198882
1205971198972
1205971199110
1205971198972
=
1205971199110
1205971199111198882
1205971199111198882
1205971198972
1205971199100
1205971198973
=
1205971199100
1205971199101198883
1205971199101198883
1205971198973
+
1205971199100
1205971199111198883
1205971199111198883
1205971198973
1205971199110
1205971198973
=
1205971199110
1205971199101198883
1205971199101198883
1205971198973
+
1205971199110
1205971199111198883
1205971199111198883
1205971198973
(A4)
When calculating particle derivative of (1199100 1199110) with respectto three points 1198881 1198882 and 1198883 in WCF we assume that allparameters are with the geometric values in this special case
Then we substitute the ideal geometric values of this variableand we obtain
1205971199100
1205971199101198881
= 05
1205971199100
1205971199111198881
= 05
1205971199110
1205971199101198881
= minus12071
1205971199110
1205971199111198881
= minus12071
1205971199100
1205971199111198882
= 0
1205971199110
1205971199111198882
= 34142
1205971199100
1205971199101198883
= 05
1205971199100
1205971199111198883
= minus05
1205971199110
1205971199101198883
= 12071
1205971199110
1205971199111198883
= minus12071
1205971199101198881
1205971198971
=
1
radic2
1205971199111198881
1205971198971
=
1
radic2
1205971199111198882
1205971198972
= minus1
1205971199101198883
1205971198973
= minus
1
radic2
1205971199111198883
1205971198973
=
1
radic2
(A5)
Finally substituting (A5) into (A4) and then substituting(A4) and (A3) into (A2) we have
120597119863
1205971198971
= minus34142
120597119863
1205971198972
= 48284
(A6)
Competing Interests
The authors declare that they have no competing interests
Journal of Sensors 15
Acknowledgments
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
This research was carried out under the NationalKey Research and Development Plan of China(2016YFB1200402) the Science and Technology Program ofGuangzhou (201508010010) and the Fundamental ResearchFunds for the Central Universities (AE89454) The fund isgreatly acknowledged Special thanks are due to Mr Jie Jiangfor his help in 3D design in SolidWorks
References
[1] Y Chen Z Xing J Li and Y Qin ldquoThe analysis of wheel-railvibration signal based on frequency slice wavelet transformrdquoin Proceedings of the 17th IEEE International Conference onIntelligent Transportation Systems (ITSC rsquo14) pp 1312ndash1316Qingdao China October 2014
[2] R Pohl A Erhard H-J Montag H-M Thomas and HWustenberg ldquoNDT techniques for railroad wheel and gaugecorner inspectionrdquo NDT amp E International vol 37 no 2 pp89ndash94 2004
[3] The International Union of Railways UIC 510-2 Code TrailingStock Wheels and Wheelsets Conditions Concerning the Useof Wheels of Various Diameters The International Union ofRailways Paris France 2004
[4] Z Zhang C Lu F Zhang Y Ren K Yang and Z Su ldquoAnovel method for non-contact measuring diameter parametersof wheelset based on wavelet analysisrdquoOptik vol 123 no 5 pp433ndash438 2012
[5] Web-1 2016 httpswwwgreenwooddkminiprofwheelphp[6] S O Medianu G A Rimbu D Lipcinski I Popovici and
D Strambeanu ldquoSystem for diagnosis of rolling profiles of therailway vehiclesrdquoMechanical Systems and Signal Processing vol48 no 1-2 pp 153ndash161 2014
file+measurement[10] X Chen J Sun Z Liu and G Zhang ldquoDynamic tread wear
measurement method for train wheels against vibrationsrdquoApplied Optics vol 54 no 17 pp 5270ndash5280 2015
[11] Z Gong J Sun and G Zhang ldquoDynamic structured-light mea-surement for wheel diameter based on the cycloid constraintrdquoApplied Optics vol 55 no 1 pp 198ndash207 2016
[12] Z F Mian J C Mullaney R MacAllister and T J SchneiderldquoOptical wheel evaluationrdquo US Patent No 7564569 2009
[13] Y Gao S Shao and Q Feng ldquoA new method for dynamicallymeasuring diameters of train wheels using line structured lightvisual sensorrdquo in Proceedings of the International Symposiumon Photonics and Optoelectronics (SOPO rsquo12) pp 1ndash4 IEEEShanghai China May 2012
[14] Z-F Zhang Z Gao Y-Y Liu et al ldquoComputer vision basedmethod and system for online measurement of geometricparameters of train wheel setsrdquo Sensors vol 12 no 1 pp 334ndash346 2012
[15] A N Baibakov K I Kuchinskii V I Paterikin S V Plotnikovand V V Sotnikov ldquoExperience in developing and usingautomated laser diagnostic equipment for the contactless mon-itoring of the parameters of freight car wheelsrdquo MeasurementTechniques vol 53 no 4 pp 444ndash448 2010
[16] Yu N Dubnishchev P Y Belousov O P Belousova and V VSotnikov ldquoOptical control of the radius of a wheel rolling on arailrdquo Optoelectronics Instrumentation and Data Processing vol48 no 1 pp 75ndash80 2012
[17] Y Gao Q Feng and J Cui ldquoA simple method for dynam-ically measuring the diameters of train wheels using a one-dimensional laser displacement transducerrdquo Optics and Lasersin Engineering vol 53 pp 158ndash163 2014
[18] KWu and J Chen ldquoDynamic measurement for wheel diameterof train based on high-speed CCD and laser displacementsensorsrdquo Sensor Letters vol 9 no 5 pp 2099ndash2103 2011
[19] Z Zhang Z Su Y Su and Z Gao ldquoDenoising of sensorsignals for the flange thickness measurement based on waveletanalysisrdquo OptikmdashInternational Journal for Light and ElectronOptics vol 122 no 8 pp 681ndash686 2011
[20] Z Xing Y Chen X Wang Y Qin and S Chen ldquoOnlinedetection system for wheel-set size of rail vehicle based on 2Dlaser displacement sensorsrdquoOptik vol 127 no 4 pp 1695ndash17022016
[21] CN-TB ldquoTread profile for locomotive and carrdquo 2003[22] A Ravindran K M Ragsdell and G V Reklaitis Engineering
Optimization Methods and Applications John Wiley amp SonsNew York NY USA 2nd edition 2006
[23] T J Ko J W Park H S Kim and S H Kim ldquoOn-machinemeasurement using a noncontact sensor based on a CADmodelrdquo The International Journal of Advanced ManufacturingTechnology vol 32 no 7-8 pp 739ndash746 2007
[24] C Zou YWang PWang and J Guo ldquoMeasurement of groundand nearby building vibration and noise induced by trains ina metro depotrdquo Science of the Total Environment vol 536 pp761ndash773 2015
[25] A J Wheeler and A R Ganji Introduction to EngineeringExperimentation Prentice Hall Upper Saddle River NJ USA3rd edition 2010
[26] A Qin M Su and Y Yao ldquoInfluence of hunting wave to lateralvibration of deck steel plate bridgesrdquo Journal of ShijiazhuangRailway Institute vol 20 no 1 pp 56ndash60 2007
