Research ArticleA Real-Time Pothole Detection Approach for IntelligentTransportation System
Hsiu-Wen Wang1 Chi-Hua Chen2 Ding-Yuan Cheng3 Chun-Hao Lin2 and Chi-Chun Lo1
1 Institute of Information Management National Chiao Tung University Hsinchu 300 Taiwan2Telecommunication Laboratories Chunghwa Telecom Co Ltd Taoyuan 326 Taiwan3Department of Information Management Hwa Hsia University of Technology New Taipei 235 Taiwan
Correspondence should be addressed to Chi-Hua Chen chihua0826gmailcom
Received 14 August 2014 Revised 4 December 2014 Accepted 9 December 2014
Academic Editor Jung-Fa Tsai
Copyright copy 2015 Hsiu-WenWang 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
In recent years fast economic growth and rapid technology advance have led to significant impact on the quality of traditionaltransport system Intelligent transportation system (ITS) which aims to improve the transport system has becomemore and morepopular Furthermore improving the safety of traffic is an important issue of ITS and the pothole on the road causes serious harm todriversrsquo safety Therefore driversrsquo safety may be improved with the establishment of real-time pothole detection system for sharingthe pothole informationMoreover using themobile device to detect potholes has beenmore popular in recent yearsThis approachcan detect potholes with lower cost in a comprehensive environment This study proposes a pothole detection method based onthe mobile sensing The accelerometer data is normalized by Euler angle computation and is adopted in the pothole detectionalgorithm to obtain the pothole information Moreover the spatial interpolation method is used to reduce the location errors fromglobal positioning system (GPS) data In experiments the results show that the proposed approach can precisely detect potholeswithout false-positives and the higher accuracy is performed by the proposed approachTherefore the proposed real-time potholedetection approach can be used to improve the safety of traffic for ITS
1 Introduction
In recent years fast economic growth and rapid technologyadvance have led to significant impact on the quality oftraditional transport system Intelligent transportation sys-tem (ITS) which aims to improve the transport system hasbecome more and more popular For the safety of trafficroad users often feel uncomfortable when they drive onthe rough roads especially the potholes on the road Inaccordance with the statistics from the Ministry of Justicein Taiwan the national compensation money is about 240million dollars from 2008 to 2011 [1] The pothole on theroad causes serious harm to driversrsquo safetyTherefore driversrsquosafety may be improved with the establishment of real-timepothole detection system for sharing the pothole information
Moreover more and more sensors which include G-sensors electronic compass gyroscope global positioningsystem (GPS) microphone and cameras are equipped in
mobile device (eg smartphone and iPad) Several applica-tions use these sensors inmobile devices and combinemobilesensing techniques to solve problems such as social network[2] healthcare [3] environment monitoring [4] and trafficinformation [5] Therefore using the mobile device based onmobile sensing techniques to detect potholes is suitable andconvenient
This study proposes a pothole detection method basedon the mobile sensing and shares the pothole informationwith road users and government For this purpose themobile device should be equipped with G-sensors and GPSto collect accelerometer data and location information Theaccelerometer data is normalized by Euler angle computationand is adopted in the pothole detection algorithm to obtainthe pothole information Moreover the spatial interpolationmethod is used to reduce the location errors from GPS dataThen the pothole information is made public to improve thesafety of traffic
Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015 Article ID 869627 7 pageshttpdxdoiorg1011552015869627
2 Mathematical Problems in Engineering
The remainder of the paper is organized as followsSection 2 presents and discusses the various techniques ofimage recognition method and mobile sensing method forpothole detection In Section 3 this study proposes a real-time pothole detectionmethod based onmobile sensingThisstudy also illustrates the experiment results and analyses inSection 4 Finally this study concludes the paper in Section 5
2 Related Work
Some pothole detection methods have been proposed andcan be classified into two groups image recognition methodand mobile sensing method The advantages and short-comings of these methods are presented in the followingsubsections
21 Image Recognition Method Yu and Salari proposed apothole detection approach based on laser imaging tech-niques to collect road information Then the artificial neuralnetwork algorithm (ANN) was used to analyze the roadinformation and detect potholes [6] However this approachwhich requires a big computation power to recognize thelaser images is unsuitable for mobile devices
Lin and Liu used the support vector machine algorithm(SVM) to analyze images about road information for potholedetection [7] Although this approach can provide highaccuracy a big computation power is required for imagerecognition Therefore this approach is also unsuitable formobile devices
22 Mobile Sensing Method For BusNet project the G-sensor and GPS are equipped in the on-board unit (OBU) inbus to collect accelerometer data and location informationThese data can be sent to data processing center via wirelessnetworks and data processing center can analyze these datato check whether the vectors of accelerometer data exceed thethresholds for pothole detection [8] However this approachrequires that the batch accelerometer data is sent whenbus enters the bus station Therefore this approach cannotprovide real-time pothole detection information
The pothole patrol system which was proposed by aproject team from Massachusetts Institute of Technologycombined G-sensor and GPS This system analyzed the 119909-axis accelerometer data and 119911-axis accelerometer data andequipped five data filters which include (1) speed (2) high-pass (3) 119911-peak (4) 119909119911-ratio and (5) speed versus 119911 ratio[9] Although these data filters can detect potholes only 119911-peak of data filter can obtain the precise pothole informationHowever high misjudgment of 119911-peak of data filters with thesurge of road
Nericell project used a smartphone based on WindowsMobile operation system which is equipped with G-sensorandGPS to collect and analyze accelerometer data for potholedetection [10] However the smartphone in this projectshould be equipped with the specific angle Furthermore thisproject only considered analyzing 119911-axis accelerometer datawith high misjudgment
Mednis et al proposed four pothole detection approacheswhich include (1) Z-THRESH approach (2) Z-DIFFapproach (3) STDEV-Z approach and (4)G-ZEROapproachto analyze the accelerometer data [11] The accelerometerdata in this study is obtained from Tmote sensors TexasInstruments controllers and Analog Devices G-sensors [12]However the results of Z-THRESH approach and G-ZEROapproach would be influenced by peak value to generatemore false-positives The results of Z-DIFF approach andSTDEV-Z approach are dependent on frequency and timingTherefore the design and comparisons of these approachesfor mobile device require to be investigated
23 Summary In summary due to the requirement of bigcomputation power for image recognition method too manyresources are allocated for this method to be an efficiencymobile device Therefore mobile sensing method is moresuitable to detect potholes for mobile device However pre-vious pothole detection approaches based on mobile sensingonly considered one threshold to detect pothole and highfalse-positives are obtained from these approaches Conse-quently this study considers Mednisrsquos approaches [11] andproposes a real-time pothole detection method to improvethe accuracy of pothole detection method
3 Real-Time Pothole Detection Method
The proposed real-time pothole detection method based onmobile sensing includes three steps (1) accelerometer datanormalization (2) pothole detection approaches and (3)pothole location determination
31 Problem Definition Some shortcomings are in previouspothole detection methods as follows (1) mobile deviceshould be equipped with the specific angle (2) high false-positives may be generated with considering only one thresh-old for pothole detection (3) the precise pothole location hasnot been investigated
Therefore this study proposes a real-time pothole detec-tion method based on mobile sensing to collect and normal-ize the accelerometer data from mobile device for free angleestablishment Furthermore a pothole detection algorithm isproposed to consider several thresholds and combine severalpothole detection approaches for pothole detection accuracyimprovement Finally the space interpolation method isadopted to determine pothole location for leaving shortcom-ings
32 Accelerometer Data Normalization For solving the lim-itation of the specific angle in previous pothole detectionapproaches this study uses Euler angle formulas to nor-malize the three-axis accelerometer data The Euler anglesdescribe the vector set in 3-dimensional Euclidean spacethree parameters and represent a sequence of three elementalrotations For example Figure 1 shows that the vector set ofaccelerometer data is defined as 1199091015840 1199101015840 1199111015840The 119909101584011991010158401199111015840 systemrotates about the 1199091015840-axis by angle 120572 The 1199101015840-axis is now atangle 120572 with respect to the 119910-axis and the 1199111015840-axis is nowat angle 120572 with respect to the 119911-axis In accordance with
Mathematical Problems in Engineering 3
z
z998400
y
y998400
120572
x = x998400
Figure 1 A case study of Euler angles (the 119909101584011991010158401199111015840 system rotatesabout the 1199091015840-axis by angle 120572)
Euler angle formulas the vector set 119909 119910 119911 can be calculatedby adopting the values of vector set 1199091015840 1199101015840 1199111015840 and angle 120572(shown in formulas (1)) Furthermore the vector of each axiscan be calculated by using Euler angle formulas when thesystem rotates about the 1199101015840-axis by angle 120573 and 1199111015840-axis byangle 120574 (shown in formulas (2))Therefore the vector of eachaxis with 0 degree angle is referred to as baseline in this studyIn runtime stage the vector set 119909 119910 119911 can be calculatedby adopting the vector set of baseline and rotation angle foraccelerometer data normalization
[119909 119910 119911] = [119909101584011991010158401199111015840][
[
1 0 0
0 cos120572 minus sin1205720 sin120572 cos120572
]
]
119909 = 1199091015840
119910 = 1199101015840times (cos120572) + 1199111015840 times (sin120572)
119911 = 1199101015840times (minus sin120572) + 1199111015840 times (cos120572)
(1)
[119909 119910 119911] = [119909101584011991010158401199111015840][
[
cos120573 0 sin1205730 1 0
minus sin120573 0 cos120573]
]
119909 = 1199091015840times (cos120573) + 1199111015840 times (minus sin120573)
119910 = 1199101015840
119911 = 1199091015840times (sin120573) + 1199111015840 times (cos120573)
[119909 119910 119911] = [119909101584011991010158401199111015840][
[
cos 120574 minus sin 120574 0sin 120574 cos 120574 0
0 0 1
]
]
119909 = 1199091015840times (cos 120574) + 1199101015840 times (sin 120574)
119910 = 1199091015840times (minus sin 120574) + 1199101015840 times (cos 120574)
119911 = 1199111015840
(2)
33 Pothole Detection Approaches This study considers theprevious four pothole detection approaches and proposes apothole detection algorithm to combine these approachesfor pothole detection improvement The notations of theseapproaches are defined and summarized in Notations
331 The First Pothole Detection Approach Z-THRESH TheZ-THRESH approach considers the minimum value of 119911-axis accelerometer data as the threshold to detect potholeThe value of 119911-axis accelerometer data is aboutminus980065ms2when the G-sensor is laid horizontally Moreover the valueof 119911-axis accelerometer data is lower than minus980065ms2when the G-sensor is dropped off Therefore the 119911-axisaccelerometer data drops off quickly when the car entersa pothole Then 119911-axis accelerometer data increases whenthe car leaves a pothole Therefore this study considers thelowest value of 119911-axis accelerometer data through a pothole inexperimental runs Furthermore the maximum value of theminimum value of 119911-axis accelerometer data in each run isselected as the threshold 120579
1which is suitable to detect pothole
for each experimental run (shown in formula (3)) In runtimestage the value of119891
1(119892119886119894119895) is 1 when the value of 119892
119886119894119895is lower
than 1205791for pothole detection (shown in formula (4))
The value of threshold is
1205791= max119886=11le119894le119899119894isin119873
min119890119894le119895le119897119894 119895isin119873
119892119886119894119895 (3)
Detection function is
1198911(119892119886119894119895) =
1 if 119892119886119894119895le 1205791
0 others
where 119886 = 1 1 le 119894 le 119899 119894 isin 119873 119895 isin 119873
(4)
332 The Second Pothole Detection Approach Z-DIFF TheZ-DIFF approach considers the maximum difference of twoconsecutive 119911-axis accelerometer records as the thresholdto detect pothole Due to much decreasing and increasingof 119911-axis accelerometer data through a pothole the velocityof variation of 119911-axis accelerometer data between time 119905
119894119895minus1
and time 119905119894119895
is calculated and used to detect potholeTherefore this study retrieves the largest value of velocity ofvariation of 119911-axis accelerometer data through a pothole inexperimental runs Furthermore the minimum value of themaximum value of variation velocity in each run is selectedas the threshold 120579
2which is suitable to detect pothole for
each experimental run (shown in formula (5)) In runtimestage the value of 119891
2(119892119886119894119895) is 1 when the value of |119892
119886119894119895minus
119892119886119894119895minus1
|(119905119894119895minus 119905119894119895minus1) is larger than 120579
2for pothole detection
(shown in formula (6)) However the limitation of thisapproach is difficult to determine the time difference between119905119894119895minus1
and 119905119894119895 and the accuracy of this approach is influenced
by this time differenceThe value of threshold is
1205792= min119886=11le119894le119899119894isin119873
max119890119894le119895le119897119894 119895isin119873
10038161003816100381610038161003816119892119886119894119895minus 119892119886119894119895minus1
10038161003816100381610038161003816
119905119894119895minus 119905119894119895minus1
(5)
4 Mathematical Problems in Engineering
Detection function is
1198912(119892119886119894119895) =
1 if10038161003816100381610038161003816119892119886119894119895minus 119892119886119894119895minus1
10038161003816100381610038161003816
119905119894119895minus 119905119894119895minus1
ge 1205792
0 others
where 119886 = 1 1 le 119894 le 119899 119894 isin 119873 119895 ge 1 119895 isin 119873
(6)
333 The Third Pothole Detection Approach STDEV(Z)The STDEV(Z) approach considers the maximum standarddeviation of 119911-axis accelerometer data as the threshold todetect pothole Due to the perturbation motion of 119911-axisaccelerometer data through a pothole the standard deviationof 119911-axis accelerometer data during 119870 records is calculatedand used to detect potholeTherefore this study gets themax-imum value of standard deviation of 119911-axis accelerometerdata through a pothole in experimental runs Furthermorethe minimum value of the maximum value of standarddeviation in each run is selected as the threshold 120579
3which is
suitable to detect pothole for each experimental run (shownin formula (7)) In runtime stage the value of 119891
3(119892119886119894119895) is 1
when the value of radicsum119895119896=119895minus119870+1
(119892119886119894119896minus 120583119894119895)2119870 is larger than
1205793for pothole detection (shown in formula (8)) However
the limitation of this approach is difficult to determine thevalue of119870which means time period and the accuracy of thisapproach is influenced by this time period
The value of threshold is
1205793= min119886=11le119894le119899119894isin119873
max119890119894le119895le119897119894 119895isin119873
radicsum119895
119896=119895minus119870+1(119892119886119894119896minus 120583119894119895)
2
119870
where 120583119894119895=
sum119895
119896=119895minus119870+1119892119886119894119896
119870
(7)
Detection function is
1198913(119892119886119894119895) =
1 if radicsum119895
119896=119895minus119870+1(119892119886119894119896minus 120583119894119895)
2
119870
ge 1205793
0 others
where 119886 = 1 1 le 119894 le 119899 119894 isin 119873 119895 ge 119870
119895 isin 119873 120583119894119895=
sum119895
119896=119895minus119870+1119892119886119894119896
119870
(8)
334 The Fourth Pothole Detection Approach G-ZERO TheG-ZERO approach considers all three-axis accelerometerdata and selects a lower bound and upper bound to detectpothole for accuracy improvement When a car passesthrough a pothole all values of three-axis accelerometer dataare near to zero Therefore this study considers the largestvalue of three-axis accelerometer data through a pothole asa candidate of lower bound and the lowest value of three-axis accelerometer data through a pothole as a candidate ofupper bound Then the minimum value of the maximumvalue of three-axis accelerometer data in each run is selected
as the lower bound 12057941 and the maximum value of the
minimum value of three-axis accelerometer data in each runis selected as the upper bound 120579
42(shown in formulas (9)
and (10)) In runtime stage the value of 1198914(119892119886119894119895) is 1 when
the value of 119892119886119894119895
is larger than 12057941
and is lower than 12057942
forpothole detection (shown in formula (11))
The value of lower bound is
12057941= min119886isin1231le119894le119899119894isin119873
max119890119894le119895le119897119894 119895isin119873
119892119886119894119895 (9)
The value of upper bound is
12057942= max119886isin1231le119894le119899119894isin119873
min119890119894le119895le119897119894 119895isin119873
119892119886119894119895 (10)
Detection function is
1198914(119892119886119894119895) =
1 if 12057941le 119892119886119894119895le 12057942
0 others
where 119886 = 1 2 3 1 le 119894 le 119899 119894 isin 119873 119895 isin 119873
(11)
335 The Fifth Pothole Detection Approach ProposedApproach This subsection proposes a pothole detectionapproach which combines and improves the Z-THRESHand G-ZERO approaches to detect pothole Furthermorethe Z-DIFF and STDEV(Z) approaches are limited inaccordance with time differences and time periods sothese two approaches are not adopted The pseudocode ofthe proposed pothole detection approach is presented inAlgorithm 1The input parameters of this proposed approachare three-axis accelerometer data and the value of output is 1when the proposed pothole detection approach supposes thecar passed through a pothole In the proposed approach theparameter check method is used to record whether the valueof 1198911(119892119886119894119895) or 119891
4(119892119886119894119895) is 1 When one of Z-THRESH and
G-ZERO approaches supposes that the car passed througha pothole the timestamp 119905
119894119895is recorded and compared
with the parameter check time The value of output is 1 if119905119894119895-119888ℎ119890119888119896 119905119894119898119890 is smaller than 120576 seconds which means a
pothole is detected Furthermore the parameter check timecan be trained and learned by historical data from eachpractical run
34 Pothole Location Determination For pothole locationdetermination this study uses the space interpolationmethod to obtain precise pothole location Figure 2 showsthat two locations (ie 119871
1and 119871
2) and timestamps (ie 119905
1
and 1199052) obtained from GPS module are adopted in the space
interpolation method to determine the pothole location Thefunction 119889(119871
1 1198712) is defined as the distance between location
1198711and location 119871
2 Therefore the pothole location 119871
119901can be
determined by using
119889 (1198711 119871119901) =
119889 (1198711 1198712) times (1199052minus 1199051)
(1199053minus 1199051)
119889 (1198712 119871119901) =
119889 (1198711 1198712) times (1199053minus 1199052)
(1199053minus 1199051)
(12)
Mathematical Problems in Engineering 5
Input 119892119886119894119895
where 119886 = 1 2 3 1 le 119894 le 119899 119894 isin 119873 119895 isin 119873OutputThe value of output is 1 when the proposed pothole detection approach
supposes the car passed through a potholeSet check method = 0set check time = 0while (119895 isin 119873)
if (119905119894119895-check time) gt 120576 sec thencheck method = 0check time = 0
end ifif 1198911(1198921119894119895) = 1 then
if check method = 0 thencheck method = 1check time = 119905
119894119895
else if check method = 4 thenreturn 1
elsecheck time = 119905
119894119895
end ifend ifif 1198914(119892119886119894119895) = 1 then
if check method = 0 thencheck method = 4check time = 119905
119894119895
else if check method = 1 thenreturn 1
elsecheck time = 119905
119894119895
end ifend if
end while
Algorithm 1 The pseudocode of the proposed pothole detection approach
d(L1 L2) times (t2 minus t1)
(t3 minus t1)
d(L1 L2) times (t3 minus t2)
(t3 minus t1)
GPS locationL1 at time t1
GPS location L2 at time t3at time t2
Pothole location Lp
Figure 2 The space interpolation method for pothole locationdetermination
4 Experimental Results
This section discusses the analyses of experimental resultsfor accelerometer data normalization pothole detectionapproaches and pothole location determination
41 The Analyses of Accelerometer Data Normalization Forthe analyses of accelerometer data normalization this studygives two case studies which include (1) the mobile devicewith 0 degree angle as baseline (shown in Figure 3) and (2) themobile device with minus15 degree angle (ie the value of 120572 is minus15in Figure 1) (shown in Figure 4)Then the 119905-test and119865-test are
Figure 3 A case study of the mobile device with 0 degree angle asbaseline
used to verify the difference between the 119911-axis accelerometerdata of baseline in Case 1 and the 119911-axis accelerometer dataafter accelerometer data normalization in Case 2
This study uses two-tailed 119905-test to determine significanceof the difference between the mean of 119911-axis accelerometerdata of baseline in Case 1 (120583
1= minus98489) and the mean of 119911-
axis accelerometer data after accelerometer data normaliza-tion in Case 2 (120583
2= minus98476) The sample sizes of Case 1
and Case 2 are 60 Furthermore this study also uses 119865-test to
6 Mathematical Problems in Engineering
15∘
Figure 4 A case study of the mobile device with minus15 degree angle
determine significance of the difference between the varianceof 119911-axis accelerometer data of baseline in Case 1 (120590
1
2=
0000077) and the variance of 119911-axis accelerometer data afteraccelerometer data normalization in Case 2 (120590
2
2= 0000085)
Table 1 shows the 119905-test and 119865-test for the population meansand variances of samples in Case 1 and Case 2 Experimentalresults indicate that the null hypothesis (H0 120583
1= 1205832) in 119905-
test is accepted and another null hypothesis (H0 1205901= 1205902) in
119865-test is also accepted Therefore using Euler angle formulasto normalize the accelerometer data from mobile device issuitable for free angle establishment
42 The Accuracy of Pothole Detection Approach For theanalyses of accuracy of pothole detection approach thisstudy selects a pothole (length 58 cm weight 51 cm anddepth 6 cm) as a case study (shown in Figure 5) and 10runs in experiment environment The mean frequency ofaccelerometer data detection in G-sensor in mobile device is124 countssecondThe 119896-fold cross-validation [13] is used toverify the accuracy of pothole detection approach In exper-iments training and testing are performed 10 times (ie 119896 =10) In iteration 119894 the accelerometer data in 119894th run therapyis selected as the test corpus and the accelerometer datain other runs is collectively used to train the thresholds foreach approach Table 2 shows the comparisons ofZ-THRESHapproach Z-DIFF approach STDEV(Z) approach G-ZEROapproach and the proposed approach The results showthat the proposed approach can precisely detect potholeswithout false-positives and the accuracy of the proposedapproach is 100 Furthermore this study also implementedand compared common machine learning methods whichinclude ANN SVM and decision tree (DT) (shown inTable 3) Although these machine learning methods candetect potholes several false-positives are generated by them
43 The Error of Pothole Location Determination For theanalyses of error of pothole location determination thisstudy uses the accelerometer data and location informationfrom 10 runs in Section 42 to verify the space interpolationmethod The results show that the error of pothole locationdetermination is reduced from 1747 meters to 1174 metersafter using the space interpolation method Therefore thespace interpolation method is suitable to determinate theprecise pothole location
6 cm
51 cm
58 cm
Figure 5 A case study of a pothole in University Road HsinchuTaiwan
Table 1 The test results for accelerometer data with normalization
The value of 119911-axis accelerometer datamean (standard deviation)
The 0 degree angle(baseline) minus98489 (0000077)
The minus15 degree angle afternormalization minus98476 (0000085)
Table 2 The false positive of each pothole detection approach
Detectionmethod 119885-THRESH 119885-DIFF STDEV(119885) 119866-ZERO Proposed
methodFalse-positive 49 40 274 8 0
Table 3 The comparisons of different machine learning methods
Detection method ANN SVM DTFalse-positive 1626 255 282
5 Conclusions and Future Work
This study proposes a real-time pothole detection methodbased on the mobile sensing techniques This method usesEuler angle computation to normalize the accelerometer dataobtained from mobile device with free angle establishmentMoreover a pothole detection approach is proposed tobe combined with Z-THRESH and G-ZERO approachesfor reducing the false-positives of pothole detection Fur-thermore the spatial interpolation method is adopted toobtain precisely the location of pothole In experimentsthe results show that the proposed approach can preciselydetect potholes without false-positives and the accuracy ofthe proposed approach is 100Therefore the proposed real-time pothole detection approach can be used to improve thesafety of traffic for ITS
However the limitation of this study is sample size In thefuture more practical results will be retrieved and analyzedto deploy the proposed method everywhere Furthermoredue to the limited battery capacity of mobile device the issueabout saving of computation power can be investigated Agreen pothole detection approach is needed to reduce thefrequency of accelerometer data detectionwith high accuracyof pothole detection
Mathematical Problems in Engineering 7
Notations
119892119886119894119895
The acceleration of the 119886th axle of the 119895threcord in the 119894th run
119905119894119895 The timestamp of the 119895th record in the 119894th
run119899 The number of runs119890119894 The 119890
119894th entering pothole record in the 119894th
run119897119894 The 119897
119894th leaving pothole record in the 119894th
run119886 The coordinate axis of G-sensor in mobile
device (eg the value of 119886 is 1 whichmeans 119885-axis)
119891119898(sdot) The output of the119898th pothole detection
approach (eg the value of 1198911(sdot) is 1 when
the first pothole detection approachsupposes that the car passed through apothole)
119870 The third pothole detection approachrequires119870 records to calculate thestandard deviation
120579119898 The value of threshold for the119898th
approach12057941 The value of lower bound for the fourth
pothole detection approach12057942 The value of upper bound for the fourth
pothole detection approach
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The research is supported by the National Science Councilof Taiwan under Grants nos NSC 102-2622-H-009-001-CC3 NSC102-2410-H146-002-MY2 NSC 102-2410-H-009-052-MY3 and MOST 103-2622-H-009-001-CC3
References
[1] Ministry of Justice National Compensation Statistics andStatistics of Justice 2012 httpwwwmojgovtwctaspxItem=36988ampCtNode=11625ampmp=095
[2] E Miluzzo N D Lane K Fodor et al ldquoSensing meets mobilesocial networks The design implementation and evaluationof the CenceMe applicationrdquo in Proceedings of the 6th ACMConference on Embedded Networked Sensor Systems (SenSysrsquo08) pp 337ndash350 Raleigh Calif USA November 2008
[3] C-C Lo C-H Chen D-Y Cheng and H-Y Kung ldquoUbiqui-tous healthcare service system with context-awareness capabil-ity design and implementationrdquo Expert Systems with Applica-tions vol 38 no 4 pp 4416ndash4436 2011
[4] C I Wu H Y Kung C H Chen and L C Kuo ldquoAn intelligentslope disaster prediction andmonitoring system based onWSNand ANPrdquo Expert Systems with Applications vol 41 no 10 pp4554ndash4562 2014
[5] C-H Chen H-C Chang C-Y Su C-C Lo and H-F LinldquoTraffic speed estimation based on normal location updatesand call arrivals from cellular networksrdquo Simulation ModellingPractice andTheory vol 35 no 1 pp 26ndash33 2013
[6] X Yu and E Salari ldquoPavement pothole detection and severitymeasurement using laser imagingrdquo in Proceedings of the IEEEInternational Conference on ElectroInformation Technology(EIT rsquo11) pp 1ndash5 Mankato Minn USA May 2011
[7] J Lin and Y Liu ldquoPotholes detection based on SVM in thepavement distress imagerdquo in Proceedings of the 9th InternationalSymposium on Distributed Computing and Applications to Busi-ness Engineering and Science (DCABES rsquo10) pp 544ndash547 HongKong August 2010
[8] K de Zoysa C Keppitiyagama G P Seneviratne and W WA T Shihan ldquoA public transport system based sensor networkfor road surface condition monitoringrdquo in Proceedings of theWorkshop on Networked Systems for Developing Regions KyotoJapan August 2007
[9] J Eriksson L Girod B Hull R Newton S Madden andH Balakrishnan ldquoThe pothole patrol using a mobile sensornetwork for road surface monitoringrdquo in Proceedings of the 6thInternational Conference on Mobile Systems Applications andServices (MobiSys rsquo08) pp 29ndash39 June 2008
[10] P Mohan V N Padmanabhan and R Ramjee ldquoNericellrich monitoring of road and traffic conditions using mobilesmartphonesrdquo in Proceedings of the 6th ACM Conference onEmbedded Network Sensor Systems Raleigh NC USA 2008
[11] AMednis G Strazdins R Zviedris G Kanonirs and L SelavoldquoReal time pothole detection using Android smartphones withaccelerometersrdquo in Proceedings of the International Conferenceon Distributed Computing in Sensor Systems (DCOSS rsquo11) pp 1ndash6 IEEE Barcelona Spain June 2011
[12] R Zviedris A Elsts G Strazdins A Mednis and L SelavoldquoLynxNet wild animal monitoring using sensor networksrdquo inProceedings of the 4th International Conference on Real-worldWireless Sensor Networks Colombo Sri Lanka 2010
[13] J Han and M Kamber Data mining Concepts and TechniquesMorgan Kaufmann San Francisco Calif USA 2006
Submit your manuscripts athttpwwwhindawicom
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2 Mathematical Problems in Engineering
The remainder of the paper is organized as followsSection 2 presents and discusses the various techniques ofimage recognition method and mobile sensing method forpothole detection In Section 3 this study proposes a real-time pothole detectionmethod based onmobile sensingThisstudy also illustrates the experiment results and analyses inSection 4 Finally this study concludes the paper in Section 5
2 Related Work
Some pothole detection methods have been proposed andcan be classified into two groups image recognition methodand mobile sensing method The advantages and short-comings of these methods are presented in the followingsubsections
21 Image Recognition Method Yu and Salari proposed apothole detection approach based on laser imaging tech-niques to collect road information Then the artificial neuralnetwork algorithm (ANN) was used to analyze the roadinformation and detect potholes [6] However this approachwhich requires a big computation power to recognize thelaser images is unsuitable for mobile devices
Lin and Liu used the support vector machine algorithm(SVM) to analyze images about road information for potholedetection [7] Although this approach can provide highaccuracy a big computation power is required for imagerecognition Therefore this approach is also unsuitable formobile devices
22 Mobile Sensing Method For BusNet project the G-sensor and GPS are equipped in the on-board unit (OBU) inbus to collect accelerometer data and location informationThese data can be sent to data processing center via wirelessnetworks and data processing center can analyze these datato check whether the vectors of accelerometer data exceed thethresholds for pothole detection [8] However this approachrequires that the batch accelerometer data is sent whenbus enters the bus station Therefore this approach cannotprovide real-time pothole detection information
The pothole patrol system which was proposed by aproject team from Massachusetts Institute of Technologycombined G-sensor and GPS This system analyzed the 119909-axis accelerometer data and 119911-axis accelerometer data andequipped five data filters which include (1) speed (2) high-pass (3) 119911-peak (4) 119909119911-ratio and (5) speed versus 119911 ratio[9] Although these data filters can detect potholes only 119911-peak of data filter can obtain the precise pothole informationHowever high misjudgment of 119911-peak of data filters with thesurge of road
Nericell project used a smartphone based on WindowsMobile operation system which is equipped with G-sensorandGPS to collect and analyze accelerometer data for potholedetection [10] However the smartphone in this projectshould be equipped with the specific angle Furthermore thisproject only considered analyzing 119911-axis accelerometer datawith high misjudgment
Mednis et al proposed four pothole detection approacheswhich include (1) Z-THRESH approach (2) Z-DIFFapproach (3) STDEV-Z approach and (4)G-ZEROapproachto analyze the accelerometer data [11] The accelerometerdata in this study is obtained from Tmote sensors TexasInstruments controllers and Analog Devices G-sensors [12]However the results of Z-THRESH approach and G-ZEROapproach would be influenced by peak value to generatemore false-positives The results of Z-DIFF approach andSTDEV-Z approach are dependent on frequency and timingTherefore the design and comparisons of these approachesfor mobile device require to be investigated
23 Summary In summary due to the requirement of bigcomputation power for image recognition method too manyresources are allocated for this method to be an efficiencymobile device Therefore mobile sensing method is moresuitable to detect potholes for mobile device However pre-vious pothole detection approaches based on mobile sensingonly considered one threshold to detect pothole and highfalse-positives are obtained from these approaches Conse-quently this study considers Mednisrsquos approaches [11] andproposes a real-time pothole detection method to improvethe accuracy of pothole detection method
3 Real-Time Pothole Detection Method
The proposed real-time pothole detection method based onmobile sensing includes three steps (1) accelerometer datanormalization (2) pothole detection approaches and (3)pothole location determination
31 Problem Definition Some shortcomings are in previouspothole detection methods as follows (1) mobile deviceshould be equipped with the specific angle (2) high false-positives may be generated with considering only one thresh-old for pothole detection (3) the precise pothole location hasnot been investigated
Therefore this study proposes a real-time pothole detec-tion method based on mobile sensing to collect and normal-ize the accelerometer data from mobile device for free angleestablishment Furthermore a pothole detection algorithm isproposed to consider several thresholds and combine severalpothole detection approaches for pothole detection accuracyimprovement Finally the space interpolation method isadopted to determine pothole location for leaving shortcom-ings
32 Accelerometer Data Normalization For solving the lim-itation of the specific angle in previous pothole detectionapproaches this study uses Euler angle formulas to nor-malize the three-axis accelerometer data The Euler anglesdescribe the vector set in 3-dimensional Euclidean spacethree parameters and represent a sequence of three elementalrotations For example Figure 1 shows that the vector set ofaccelerometer data is defined as 1199091015840 1199101015840 1199111015840The 119909101584011991010158401199111015840 systemrotates about the 1199091015840-axis by angle 120572 The 1199101015840-axis is now atangle 120572 with respect to the 119910-axis and the 1199111015840-axis is nowat angle 120572 with respect to the 119911-axis In accordance with
Mathematical Problems in Engineering 3
z
z998400
y
y998400
120572
x = x998400
Figure 1 A case study of Euler angles (the 119909101584011991010158401199111015840 system rotatesabout the 1199091015840-axis by angle 120572)
Euler angle formulas the vector set 119909 119910 119911 can be calculatedby adopting the values of vector set 1199091015840 1199101015840 1199111015840 and angle 120572(shown in formulas (1)) Furthermore the vector of each axiscan be calculated by using Euler angle formulas when thesystem rotates about the 1199101015840-axis by angle 120573 and 1199111015840-axis byangle 120574 (shown in formulas (2))Therefore the vector of eachaxis with 0 degree angle is referred to as baseline in this studyIn runtime stage the vector set 119909 119910 119911 can be calculatedby adopting the vector set of baseline and rotation angle foraccelerometer data normalization
[119909 119910 119911] = [119909101584011991010158401199111015840][
[
1 0 0
0 cos120572 minus sin1205720 sin120572 cos120572
]
]
119909 = 1199091015840
119910 = 1199101015840times (cos120572) + 1199111015840 times (sin120572)
119911 = 1199101015840times (minus sin120572) + 1199111015840 times (cos120572)
(1)
[119909 119910 119911] = [119909101584011991010158401199111015840][
[
cos120573 0 sin1205730 1 0
minus sin120573 0 cos120573]
]
119909 = 1199091015840times (cos120573) + 1199111015840 times (minus sin120573)
119910 = 1199101015840
119911 = 1199091015840times (sin120573) + 1199111015840 times (cos120573)
[119909 119910 119911] = [119909101584011991010158401199111015840][
[
cos 120574 minus sin 120574 0sin 120574 cos 120574 0
0 0 1
]
]
119909 = 1199091015840times (cos 120574) + 1199101015840 times (sin 120574)
119910 = 1199091015840times (minus sin 120574) + 1199101015840 times (cos 120574)
119911 = 1199111015840
(2)
33 Pothole Detection Approaches This study considers theprevious four pothole detection approaches and proposes apothole detection algorithm to combine these approachesfor pothole detection improvement The notations of theseapproaches are defined and summarized in Notations
331 The First Pothole Detection Approach Z-THRESH TheZ-THRESH approach considers the minimum value of 119911-axis accelerometer data as the threshold to detect potholeThe value of 119911-axis accelerometer data is aboutminus980065ms2when the G-sensor is laid horizontally Moreover the valueof 119911-axis accelerometer data is lower than minus980065ms2when the G-sensor is dropped off Therefore the 119911-axisaccelerometer data drops off quickly when the car entersa pothole Then 119911-axis accelerometer data increases whenthe car leaves a pothole Therefore this study considers thelowest value of 119911-axis accelerometer data through a pothole inexperimental runs Furthermore the maximum value of theminimum value of 119911-axis accelerometer data in each run isselected as the threshold 120579
1which is suitable to detect pothole
for each experimental run (shown in formula (3)) In runtimestage the value of119891
1(119892119886119894119895) is 1 when the value of 119892
119886119894119895is lower
than 1205791for pothole detection (shown in formula (4))
The value of threshold is
1205791= max119886=11le119894le119899119894isin119873
min119890119894le119895le119897119894 119895isin119873
119892119886119894119895 (3)
Detection function is
1198911(119892119886119894119895) =
1 if 119892119886119894119895le 1205791
0 others
where 119886 = 1 1 le 119894 le 119899 119894 isin 119873 119895 isin 119873
(4)
332 The Second Pothole Detection Approach Z-DIFF TheZ-DIFF approach considers the maximum difference of twoconsecutive 119911-axis accelerometer records as the thresholdto detect pothole Due to much decreasing and increasingof 119911-axis accelerometer data through a pothole the velocityof variation of 119911-axis accelerometer data between time 119905
119894119895minus1
and time 119905119894119895
is calculated and used to detect potholeTherefore this study retrieves the largest value of velocity ofvariation of 119911-axis accelerometer data through a pothole inexperimental runs Furthermore the minimum value of themaximum value of variation velocity in each run is selectedas the threshold 120579
2which is suitable to detect pothole for
each experimental run (shown in formula (5)) In runtimestage the value of 119891
2(119892119886119894119895) is 1 when the value of |119892
119886119894119895minus
119892119886119894119895minus1
|(119905119894119895minus 119905119894119895minus1) is larger than 120579
2for pothole detection
(shown in formula (6)) However the limitation of thisapproach is difficult to determine the time difference between119905119894119895minus1
and 119905119894119895 and the accuracy of this approach is influenced
by this time differenceThe value of threshold is
1205792= min119886=11le119894le119899119894isin119873
max119890119894le119895le119897119894 119895isin119873
10038161003816100381610038161003816119892119886119894119895minus 119892119886119894119895minus1
10038161003816100381610038161003816
119905119894119895minus 119905119894119895minus1
(5)
4 Mathematical Problems in Engineering
Detection function is
1198912(119892119886119894119895) =
1 if10038161003816100381610038161003816119892119886119894119895minus 119892119886119894119895minus1
10038161003816100381610038161003816
119905119894119895minus 119905119894119895minus1
ge 1205792
0 others
where 119886 = 1 1 le 119894 le 119899 119894 isin 119873 119895 ge 1 119895 isin 119873
(6)
333 The Third Pothole Detection Approach STDEV(Z)The STDEV(Z) approach considers the maximum standarddeviation of 119911-axis accelerometer data as the threshold todetect pothole Due to the perturbation motion of 119911-axisaccelerometer data through a pothole the standard deviationof 119911-axis accelerometer data during 119870 records is calculatedand used to detect potholeTherefore this study gets themax-imum value of standard deviation of 119911-axis accelerometerdata through a pothole in experimental runs Furthermorethe minimum value of the maximum value of standarddeviation in each run is selected as the threshold 120579
3which is
suitable to detect pothole for each experimental run (shownin formula (7)) In runtime stage the value of 119891
3(119892119886119894119895) is 1
when the value of radicsum119895119896=119895minus119870+1
(119892119886119894119896minus 120583119894119895)2119870 is larger than
1205793for pothole detection (shown in formula (8)) However
the limitation of this approach is difficult to determine thevalue of119870which means time period and the accuracy of thisapproach is influenced by this time period
The value of threshold is
1205793= min119886=11le119894le119899119894isin119873
max119890119894le119895le119897119894 119895isin119873
radicsum119895
119896=119895minus119870+1(119892119886119894119896minus 120583119894119895)
2
119870
where 120583119894119895=
sum119895
119896=119895minus119870+1119892119886119894119896
119870
(7)
Detection function is
1198913(119892119886119894119895) =
1 if radicsum119895
119896=119895minus119870+1(119892119886119894119896minus 120583119894119895)
2
119870
ge 1205793
0 others
where 119886 = 1 1 le 119894 le 119899 119894 isin 119873 119895 ge 119870
119895 isin 119873 120583119894119895=
sum119895
119896=119895minus119870+1119892119886119894119896
119870
(8)
334 The Fourth Pothole Detection Approach G-ZERO TheG-ZERO approach considers all three-axis accelerometerdata and selects a lower bound and upper bound to detectpothole for accuracy improvement When a car passesthrough a pothole all values of three-axis accelerometer dataare near to zero Therefore this study considers the largestvalue of three-axis accelerometer data through a pothole asa candidate of lower bound and the lowest value of three-axis accelerometer data through a pothole as a candidate ofupper bound Then the minimum value of the maximumvalue of three-axis accelerometer data in each run is selected
as the lower bound 12057941 and the maximum value of the
minimum value of three-axis accelerometer data in each runis selected as the upper bound 120579
42(shown in formulas (9)
and (10)) In runtime stage the value of 1198914(119892119886119894119895) is 1 when
the value of 119892119886119894119895
is larger than 12057941
and is lower than 12057942
forpothole detection (shown in formula (11))
The value of lower bound is
12057941= min119886isin1231le119894le119899119894isin119873
max119890119894le119895le119897119894 119895isin119873
119892119886119894119895 (9)
The value of upper bound is
12057942= max119886isin1231le119894le119899119894isin119873
min119890119894le119895le119897119894 119895isin119873
119892119886119894119895 (10)
Detection function is
1198914(119892119886119894119895) =
1 if 12057941le 119892119886119894119895le 12057942
0 others
where 119886 = 1 2 3 1 le 119894 le 119899 119894 isin 119873 119895 isin 119873
(11)
335 The Fifth Pothole Detection Approach ProposedApproach This subsection proposes a pothole detectionapproach which combines and improves the Z-THRESHand G-ZERO approaches to detect pothole Furthermorethe Z-DIFF and STDEV(Z) approaches are limited inaccordance with time differences and time periods sothese two approaches are not adopted The pseudocode ofthe proposed pothole detection approach is presented inAlgorithm 1The input parameters of this proposed approachare three-axis accelerometer data and the value of output is 1when the proposed pothole detection approach supposes thecar passed through a pothole In the proposed approach theparameter check method is used to record whether the valueof 1198911(119892119886119894119895) or 119891
4(119892119886119894119895) is 1 When one of Z-THRESH and
G-ZERO approaches supposes that the car passed througha pothole the timestamp 119905
119894119895is recorded and compared
with the parameter check time The value of output is 1 if119905119894119895-119888ℎ119890119888119896 119905119894119898119890 is smaller than 120576 seconds which means a
pothole is detected Furthermore the parameter check timecan be trained and learned by historical data from eachpractical run
34 Pothole Location Determination For pothole locationdetermination this study uses the space interpolationmethod to obtain precise pothole location Figure 2 showsthat two locations (ie 119871
1and 119871
2) and timestamps (ie 119905
1
and 1199052) obtained from GPS module are adopted in the space
interpolation method to determine the pothole location Thefunction 119889(119871
1 1198712) is defined as the distance between location
1198711and location 119871
2 Therefore the pothole location 119871
119901can be
determined by using
119889 (1198711 119871119901) =
119889 (1198711 1198712) times (1199052minus 1199051)
(1199053minus 1199051)
119889 (1198712 119871119901) =
119889 (1198711 1198712) times (1199053minus 1199052)
(1199053minus 1199051)
(12)
Mathematical Problems in Engineering 5
Input 119892119886119894119895
where 119886 = 1 2 3 1 le 119894 le 119899 119894 isin 119873 119895 isin 119873OutputThe value of output is 1 when the proposed pothole detection approach
supposes the car passed through a potholeSet check method = 0set check time = 0while (119895 isin 119873)
if (119905119894119895-check time) gt 120576 sec thencheck method = 0check time = 0
end ifif 1198911(1198921119894119895) = 1 then
if check method = 0 thencheck method = 1check time = 119905
119894119895
else if check method = 4 thenreturn 1
elsecheck time = 119905
119894119895
end ifend ifif 1198914(119892119886119894119895) = 1 then
if check method = 0 thencheck method = 4check time = 119905
119894119895
else if check method = 1 thenreturn 1
elsecheck time = 119905
119894119895
end ifend if
end while
Algorithm 1 The pseudocode of the proposed pothole detection approach
d(L1 L2) times (t2 minus t1)
(t3 minus t1)
d(L1 L2) times (t3 minus t2)
(t3 minus t1)
GPS locationL1 at time t1
GPS location L2 at time t3at time t2
Pothole location Lp
Figure 2 The space interpolation method for pothole locationdetermination
4 Experimental Results
This section discusses the analyses of experimental resultsfor accelerometer data normalization pothole detectionapproaches and pothole location determination
41 The Analyses of Accelerometer Data Normalization Forthe analyses of accelerometer data normalization this studygives two case studies which include (1) the mobile devicewith 0 degree angle as baseline (shown in Figure 3) and (2) themobile device with minus15 degree angle (ie the value of 120572 is minus15in Figure 1) (shown in Figure 4)Then the 119905-test and119865-test are
Figure 3 A case study of the mobile device with 0 degree angle asbaseline
used to verify the difference between the 119911-axis accelerometerdata of baseline in Case 1 and the 119911-axis accelerometer dataafter accelerometer data normalization in Case 2
This study uses two-tailed 119905-test to determine significanceof the difference between the mean of 119911-axis accelerometerdata of baseline in Case 1 (120583
1= minus98489) and the mean of 119911-
axis accelerometer data after accelerometer data normaliza-tion in Case 2 (120583
2= minus98476) The sample sizes of Case 1
and Case 2 are 60 Furthermore this study also uses 119865-test to
6 Mathematical Problems in Engineering
15∘
Figure 4 A case study of the mobile device with minus15 degree angle
determine significance of the difference between the varianceof 119911-axis accelerometer data of baseline in Case 1 (120590
1
2=
0000077) and the variance of 119911-axis accelerometer data afteraccelerometer data normalization in Case 2 (120590
2
2= 0000085)
Table 1 shows the 119905-test and 119865-test for the population meansand variances of samples in Case 1 and Case 2 Experimentalresults indicate that the null hypothesis (H0 120583
1= 1205832) in 119905-
test is accepted and another null hypothesis (H0 1205901= 1205902) in
119865-test is also accepted Therefore using Euler angle formulasto normalize the accelerometer data from mobile device issuitable for free angle establishment
42 The Accuracy of Pothole Detection Approach For theanalyses of accuracy of pothole detection approach thisstudy selects a pothole (length 58 cm weight 51 cm anddepth 6 cm) as a case study (shown in Figure 5) and 10runs in experiment environment The mean frequency ofaccelerometer data detection in G-sensor in mobile device is124 countssecondThe 119896-fold cross-validation [13] is used toverify the accuracy of pothole detection approach In exper-iments training and testing are performed 10 times (ie 119896 =10) In iteration 119894 the accelerometer data in 119894th run therapyis selected as the test corpus and the accelerometer datain other runs is collectively used to train the thresholds foreach approach Table 2 shows the comparisons ofZ-THRESHapproach Z-DIFF approach STDEV(Z) approach G-ZEROapproach and the proposed approach The results showthat the proposed approach can precisely detect potholeswithout false-positives and the accuracy of the proposedapproach is 100 Furthermore this study also implementedand compared common machine learning methods whichinclude ANN SVM and decision tree (DT) (shown inTable 3) Although these machine learning methods candetect potholes several false-positives are generated by them
43 The Error of Pothole Location Determination For theanalyses of error of pothole location determination thisstudy uses the accelerometer data and location informationfrom 10 runs in Section 42 to verify the space interpolationmethod The results show that the error of pothole locationdetermination is reduced from 1747 meters to 1174 metersafter using the space interpolation method Therefore thespace interpolation method is suitable to determinate theprecise pothole location
6 cm
51 cm
58 cm
Figure 5 A case study of a pothole in University Road HsinchuTaiwan
Table 1 The test results for accelerometer data with normalization
The value of 119911-axis accelerometer datamean (standard deviation)
The 0 degree angle(baseline) minus98489 (0000077)
The minus15 degree angle afternormalization minus98476 (0000085)
Table 2 The false positive of each pothole detection approach
Detectionmethod 119885-THRESH 119885-DIFF STDEV(119885) 119866-ZERO Proposed
methodFalse-positive 49 40 274 8 0
Table 3 The comparisons of different machine learning methods
Detection method ANN SVM DTFalse-positive 1626 255 282
5 Conclusions and Future Work
This study proposes a real-time pothole detection methodbased on the mobile sensing techniques This method usesEuler angle computation to normalize the accelerometer dataobtained from mobile device with free angle establishmentMoreover a pothole detection approach is proposed tobe combined with Z-THRESH and G-ZERO approachesfor reducing the false-positives of pothole detection Fur-thermore the spatial interpolation method is adopted toobtain precisely the location of pothole In experimentsthe results show that the proposed approach can preciselydetect potholes without false-positives and the accuracy ofthe proposed approach is 100Therefore the proposed real-time pothole detection approach can be used to improve thesafety of traffic for ITS
However the limitation of this study is sample size In thefuture more practical results will be retrieved and analyzedto deploy the proposed method everywhere Furthermoredue to the limited battery capacity of mobile device the issueabout saving of computation power can be investigated Agreen pothole detection approach is needed to reduce thefrequency of accelerometer data detectionwith high accuracyof pothole detection
Mathematical Problems in Engineering 7
Notations
119892119886119894119895
The acceleration of the 119886th axle of the 119895threcord in the 119894th run
119905119894119895 The timestamp of the 119895th record in the 119894th
run119899 The number of runs119890119894 The 119890
119894th entering pothole record in the 119894th
run119897119894 The 119897
119894th leaving pothole record in the 119894th
run119886 The coordinate axis of G-sensor in mobile
device (eg the value of 119886 is 1 whichmeans 119885-axis)
119891119898(sdot) The output of the119898th pothole detection
approach (eg the value of 1198911(sdot) is 1 when
the first pothole detection approachsupposes that the car passed through apothole)
119870 The third pothole detection approachrequires119870 records to calculate thestandard deviation
120579119898 The value of threshold for the119898th
approach12057941 The value of lower bound for the fourth
pothole detection approach12057942 The value of upper bound for the fourth
pothole detection approach
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The research is supported by the National Science Councilof Taiwan under Grants nos NSC 102-2622-H-009-001-CC3 NSC102-2410-H146-002-MY2 NSC 102-2410-H-009-052-MY3 and MOST 103-2622-H-009-001-CC3
References
[1] Ministry of Justice National Compensation Statistics andStatistics of Justice 2012 httpwwwmojgovtwctaspxItem=36988ampCtNode=11625ampmp=095
[2] E Miluzzo N D Lane K Fodor et al ldquoSensing meets mobilesocial networks The design implementation and evaluationof the CenceMe applicationrdquo in Proceedings of the 6th ACMConference on Embedded Networked Sensor Systems (SenSysrsquo08) pp 337ndash350 Raleigh Calif USA November 2008
[3] C-C Lo C-H Chen D-Y Cheng and H-Y Kung ldquoUbiqui-tous healthcare service system with context-awareness capabil-ity design and implementationrdquo Expert Systems with Applica-tions vol 38 no 4 pp 4416ndash4436 2011
[4] C I Wu H Y Kung C H Chen and L C Kuo ldquoAn intelligentslope disaster prediction andmonitoring system based onWSNand ANPrdquo Expert Systems with Applications vol 41 no 10 pp4554ndash4562 2014
[5] C-H Chen H-C Chang C-Y Su C-C Lo and H-F LinldquoTraffic speed estimation based on normal location updatesand call arrivals from cellular networksrdquo Simulation ModellingPractice andTheory vol 35 no 1 pp 26ndash33 2013
[6] X Yu and E Salari ldquoPavement pothole detection and severitymeasurement using laser imagingrdquo in Proceedings of the IEEEInternational Conference on ElectroInformation Technology(EIT rsquo11) pp 1ndash5 Mankato Minn USA May 2011
[7] J Lin and Y Liu ldquoPotholes detection based on SVM in thepavement distress imagerdquo in Proceedings of the 9th InternationalSymposium on Distributed Computing and Applications to Busi-ness Engineering and Science (DCABES rsquo10) pp 544ndash547 HongKong August 2010
[8] K de Zoysa C Keppitiyagama G P Seneviratne and W WA T Shihan ldquoA public transport system based sensor networkfor road surface condition monitoringrdquo in Proceedings of theWorkshop on Networked Systems for Developing Regions KyotoJapan August 2007
[9] J Eriksson L Girod B Hull R Newton S Madden andH Balakrishnan ldquoThe pothole patrol using a mobile sensornetwork for road surface monitoringrdquo in Proceedings of the 6thInternational Conference on Mobile Systems Applications andServices (MobiSys rsquo08) pp 29ndash39 June 2008
[10] P Mohan V N Padmanabhan and R Ramjee ldquoNericellrich monitoring of road and traffic conditions using mobilesmartphonesrdquo in Proceedings of the 6th ACM Conference onEmbedded Network Sensor Systems Raleigh NC USA 2008
[11] AMednis G Strazdins R Zviedris G Kanonirs and L SelavoldquoReal time pothole detection using Android smartphones withaccelerometersrdquo in Proceedings of the International Conferenceon Distributed Computing in Sensor Systems (DCOSS rsquo11) pp 1ndash6 IEEE Barcelona Spain June 2011
[12] R Zviedris A Elsts G Strazdins A Mednis and L SelavoldquoLynxNet wild animal monitoring using sensor networksrdquo inProceedings of the 4th International Conference on Real-worldWireless Sensor Networks Colombo Sri Lanka 2010
[13] J Han and M Kamber Data mining Concepts and TechniquesMorgan Kaufmann San Francisco Calif USA 2006
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 3
z
z998400
y
y998400
120572
x = x998400
Figure 1 A case study of Euler angles (the 119909101584011991010158401199111015840 system rotatesabout the 1199091015840-axis by angle 120572)
Euler angle formulas the vector set 119909 119910 119911 can be calculatedby adopting the values of vector set 1199091015840 1199101015840 1199111015840 and angle 120572(shown in formulas (1)) Furthermore the vector of each axiscan be calculated by using Euler angle formulas when thesystem rotates about the 1199101015840-axis by angle 120573 and 1199111015840-axis byangle 120574 (shown in formulas (2))Therefore the vector of eachaxis with 0 degree angle is referred to as baseline in this studyIn runtime stage the vector set 119909 119910 119911 can be calculatedby adopting the vector set of baseline and rotation angle foraccelerometer data normalization
[119909 119910 119911] = [119909101584011991010158401199111015840][
[
1 0 0
0 cos120572 minus sin1205720 sin120572 cos120572
]
]
119909 = 1199091015840
119910 = 1199101015840times (cos120572) + 1199111015840 times (sin120572)
119911 = 1199101015840times (minus sin120572) + 1199111015840 times (cos120572)
(1)
[119909 119910 119911] = [119909101584011991010158401199111015840][
[
cos120573 0 sin1205730 1 0
minus sin120573 0 cos120573]
]
119909 = 1199091015840times (cos120573) + 1199111015840 times (minus sin120573)
119910 = 1199101015840
119911 = 1199091015840times (sin120573) + 1199111015840 times (cos120573)
[119909 119910 119911] = [119909101584011991010158401199111015840][
[
cos 120574 minus sin 120574 0sin 120574 cos 120574 0
0 0 1
]
]
119909 = 1199091015840times (cos 120574) + 1199101015840 times (sin 120574)
119910 = 1199091015840times (minus sin 120574) + 1199101015840 times (cos 120574)
119911 = 1199111015840
(2)
33 Pothole Detection Approaches This study considers theprevious four pothole detection approaches and proposes apothole detection algorithm to combine these approachesfor pothole detection improvement The notations of theseapproaches are defined and summarized in Notations
331 The First Pothole Detection Approach Z-THRESH TheZ-THRESH approach considers the minimum value of 119911-axis accelerometer data as the threshold to detect potholeThe value of 119911-axis accelerometer data is aboutminus980065ms2when the G-sensor is laid horizontally Moreover the valueof 119911-axis accelerometer data is lower than minus980065ms2when the G-sensor is dropped off Therefore the 119911-axisaccelerometer data drops off quickly when the car entersa pothole Then 119911-axis accelerometer data increases whenthe car leaves a pothole Therefore this study considers thelowest value of 119911-axis accelerometer data through a pothole inexperimental runs Furthermore the maximum value of theminimum value of 119911-axis accelerometer data in each run isselected as the threshold 120579
1which is suitable to detect pothole
for each experimental run (shown in formula (3)) In runtimestage the value of119891
1(119892119886119894119895) is 1 when the value of 119892
119886119894119895is lower
than 1205791for pothole detection (shown in formula (4))
The value of threshold is
1205791= max119886=11le119894le119899119894isin119873
min119890119894le119895le119897119894 119895isin119873
119892119886119894119895 (3)
Detection function is
1198911(119892119886119894119895) =
1 if 119892119886119894119895le 1205791
0 others
where 119886 = 1 1 le 119894 le 119899 119894 isin 119873 119895 isin 119873
(4)
332 The Second Pothole Detection Approach Z-DIFF TheZ-DIFF approach considers the maximum difference of twoconsecutive 119911-axis accelerometer records as the thresholdto detect pothole Due to much decreasing and increasingof 119911-axis accelerometer data through a pothole the velocityof variation of 119911-axis accelerometer data between time 119905
119894119895minus1
and time 119905119894119895
is calculated and used to detect potholeTherefore this study retrieves the largest value of velocity ofvariation of 119911-axis accelerometer data through a pothole inexperimental runs Furthermore the minimum value of themaximum value of variation velocity in each run is selectedas the threshold 120579
2which is suitable to detect pothole for
each experimental run (shown in formula (5)) In runtimestage the value of 119891
2(119892119886119894119895) is 1 when the value of |119892
119886119894119895minus
119892119886119894119895minus1
|(119905119894119895minus 119905119894119895minus1) is larger than 120579
2for pothole detection
(shown in formula (6)) However the limitation of thisapproach is difficult to determine the time difference between119905119894119895minus1
and 119905119894119895 and the accuracy of this approach is influenced
by this time differenceThe value of threshold is
1205792= min119886=11le119894le119899119894isin119873
max119890119894le119895le119897119894 119895isin119873
10038161003816100381610038161003816119892119886119894119895minus 119892119886119894119895minus1
10038161003816100381610038161003816
119905119894119895minus 119905119894119895minus1
(5)
4 Mathematical Problems in Engineering
Detection function is
1198912(119892119886119894119895) =
1 if10038161003816100381610038161003816119892119886119894119895minus 119892119886119894119895minus1
10038161003816100381610038161003816
119905119894119895minus 119905119894119895minus1
ge 1205792
0 others
where 119886 = 1 1 le 119894 le 119899 119894 isin 119873 119895 ge 1 119895 isin 119873
(6)
333 The Third Pothole Detection Approach STDEV(Z)The STDEV(Z) approach considers the maximum standarddeviation of 119911-axis accelerometer data as the threshold todetect pothole Due to the perturbation motion of 119911-axisaccelerometer data through a pothole the standard deviationof 119911-axis accelerometer data during 119870 records is calculatedand used to detect potholeTherefore this study gets themax-imum value of standard deviation of 119911-axis accelerometerdata through a pothole in experimental runs Furthermorethe minimum value of the maximum value of standarddeviation in each run is selected as the threshold 120579
3which is
suitable to detect pothole for each experimental run (shownin formula (7)) In runtime stage the value of 119891
3(119892119886119894119895) is 1
when the value of radicsum119895119896=119895minus119870+1
(119892119886119894119896minus 120583119894119895)2119870 is larger than
1205793for pothole detection (shown in formula (8)) However
the limitation of this approach is difficult to determine thevalue of119870which means time period and the accuracy of thisapproach is influenced by this time period
The value of threshold is
1205793= min119886=11le119894le119899119894isin119873
max119890119894le119895le119897119894 119895isin119873
radicsum119895
119896=119895minus119870+1(119892119886119894119896minus 120583119894119895)
2
119870
where 120583119894119895=
sum119895
119896=119895minus119870+1119892119886119894119896
119870
(7)
Detection function is
1198913(119892119886119894119895) =
1 if radicsum119895
119896=119895minus119870+1(119892119886119894119896minus 120583119894119895)
2
119870
ge 1205793
0 others
where 119886 = 1 1 le 119894 le 119899 119894 isin 119873 119895 ge 119870
119895 isin 119873 120583119894119895=
sum119895
119896=119895minus119870+1119892119886119894119896
119870
(8)
334 The Fourth Pothole Detection Approach G-ZERO TheG-ZERO approach considers all three-axis accelerometerdata and selects a lower bound and upper bound to detectpothole for accuracy improvement When a car passesthrough a pothole all values of three-axis accelerometer dataare near to zero Therefore this study considers the largestvalue of three-axis accelerometer data through a pothole asa candidate of lower bound and the lowest value of three-axis accelerometer data through a pothole as a candidate ofupper bound Then the minimum value of the maximumvalue of three-axis accelerometer data in each run is selected
as the lower bound 12057941 and the maximum value of the
minimum value of three-axis accelerometer data in each runis selected as the upper bound 120579
42(shown in formulas (9)
and (10)) In runtime stage the value of 1198914(119892119886119894119895) is 1 when
the value of 119892119886119894119895
is larger than 12057941
and is lower than 12057942
forpothole detection (shown in formula (11))
The value of lower bound is
12057941= min119886isin1231le119894le119899119894isin119873
max119890119894le119895le119897119894 119895isin119873
119892119886119894119895 (9)
The value of upper bound is
12057942= max119886isin1231le119894le119899119894isin119873
min119890119894le119895le119897119894 119895isin119873
119892119886119894119895 (10)
Detection function is
1198914(119892119886119894119895) =
1 if 12057941le 119892119886119894119895le 12057942
0 others
where 119886 = 1 2 3 1 le 119894 le 119899 119894 isin 119873 119895 isin 119873
(11)
335 The Fifth Pothole Detection Approach ProposedApproach This subsection proposes a pothole detectionapproach which combines and improves the Z-THRESHand G-ZERO approaches to detect pothole Furthermorethe Z-DIFF and STDEV(Z) approaches are limited inaccordance with time differences and time periods sothese two approaches are not adopted The pseudocode ofthe proposed pothole detection approach is presented inAlgorithm 1The input parameters of this proposed approachare three-axis accelerometer data and the value of output is 1when the proposed pothole detection approach supposes thecar passed through a pothole In the proposed approach theparameter check method is used to record whether the valueof 1198911(119892119886119894119895) or 119891
4(119892119886119894119895) is 1 When one of Z-THRESH and
G-ZERO approaches supposes that the car passed througha pothole the timestamp 119905
119894119895is recorded and compared
with the parameter check time The value of output is 1 if119905119894119895-119888ℎ119890119888119896 119905119894119898119890 is smaller than 120576 seconds which means a
pothole is detected Furthermore the parameter check timecan be trained and learned by historical data from eachpractical run
34 Pothole Location Determination For pothole locationdetermination this study uses the space interpolationmethod to obtain precise pothole location Figure 2 showsthat two locations (ie 119871
1and 119871
2) and timestamps (ie 119905
1
and 1199052) obtained from GPS module are adopted in the space
interpolation method to determine the pothole location Thefunction 119889(119871
1 1198712) is defined as the distance between location
1198711and location 119871
2 Therefore the pothole location 119871
119901can be
determined by using
119889 (1198711 119871119901) =
119889 (1198711 1198712) times (1199052minus 1199051)
(1199053minus 1199051)
119889 (1198712 119871119901) =
119889 (1198711 1198712) times (1199053minus 1199052)
(1199053minus 1199051)
(12)
Mathematical Problems in Engineering 5
Input 119892119886119894119895
where 119886 = 1 2 3 1 le 119894 le 119899 119894 isin 119873 119895 isin 119873OutputThe value of output is 1 when the proposed pothole detection approach
supposes the car passed through a potholeSet check method = 0set check time = 0while (119895 isin 119873)
if (119905119894119895-check time) gt 120576 sec thencheck method = 0check time = 0
end ifif 1198911(1198921119894119895) = 1 then
if check method = 0 thencheck method = 1check time = 119905
119894119895
else if check method = 4 thenreturn 1
elsecheck time = 119905
119894119895
end ifend ifif 1198914(119892119886119894119895) = 1 then
if check method = 0 thencheck method = 4check time = 119905
119894119895
else if check method = 1 thenreturn 1
elsecheck time = 119905
119894119895
end ifend if
end while
Algorithm 1 The pseudocode of the proposed pothole detection approach
d(L1 L2) times (t2 minus t1)
(t3 minus t1)
d(L1 L2) times (t3 minus t2)
(t3 minus t1)
GPS locationL1 at time t1
GPS location L2 at time t3at time t2
Pothole location Lp
Figure 2 The space interpolation method for pothole locationdetermination
4 Experimental Results
This section discusses the analyses of experimental resultsfor accelerometer data normalization pothole detectionapproaches and pothole location determination
41 The Analyses of Accelerometer Data Normalization Forthe analyses of accelerometer data normalization this studygives two case studies which include (1) the mobile devicewith 0 degree angle as baseline (shown in Figure 3) and (2) themobile device with minus15 degree angle (ie the value of 120572 is minus15in Figure 1) (shown in Figure 4)Then the 119905-test and119865-test are
Figure 3 A case study of the mobile device with 0 degree angle asbaseline
used to verify the difference between the 119911-axis accelerometerdata of baseline in Case 1 and the 119911-axis accelerometer dataafter accelerometer data normalization in Case 2
This study uses two-tailed 119905-test to determine significanceof the difference between the mean of 119911-axis accelerometerdata of baseline in Case 1 (120583
1= minus98489) and the mean of 119911-
axis accelerometer data after accelerometer data normaliza-tion in Case 2 (120583
2= minus98476) The sample sizes of Case 1
and Case 2 are 60 Furthermore this study also uses 119865-test to
6 Mathematical Problems in Engineering
15∘
Figure 4 A case study of the mobile device with minus15 degree angle
determine significance of the difference between the varianceof 119911-axis accelerometer data of baseline in Case 1 (120590
1
2=
0000077) and the variance of 119911-axis accelerometer data afteraccelerometer data normalization in Case 2 (120590
2
2= 0000085)
Table 1 shows the 119905-test and 119865-test for the population meansand variances of samples in Case 1 and Case 2 Experimentalresults indicate that the null hypothesis (H0 120583
1= 1205832) in 119905-
test is accepted and another null hypothesis (H0 1205901= 1205902) in
119865-test is also accepted Therefore using Euler angle formulasto normalize the accelerometer data from mobile device issuitable for free angle establishment
42 The Accuracy of Pothole Detection Approach For theanalyses of accuracy of pothole detection approach thisstudy selects a pothole (length 58 cm weight 51 cm anddepth 6 cm) as a case study (shown in Figure 5) and 10runs in experiment environment The mean frequency ofaccelerometer data detection in G-sensor in mobile device is124 countssecondThe 119896-fold cross-validation [13] is used toverify the accuracy of pothole detection approach In exper-iments training and testing are performed 10 times (ie 119896 =10) In iteration 119894 the accelerometer data in 119894th run therapyis selected as the test corpus and the accelerometer datain other runs is collectively used to train the thresholds foreach approach Table 2 shows the comparisons ofZ-THRESHapproach Z-DIFF approach STDEV(Z) approach G-ZEROapproach and the proposed approach The results showthat the proposed approach can precisely detect potholeswithout false-positives and the accuracy of the proposedapproach is 100 Furthermore this study also implementedand compared common machine learning methods whichinclude ANN SVM and decision tree (DT) (shown inTable 3) Although these machine learning methods candetect potholes several false-positives are generated by them
43 The Error of Pothole Location Determination For theanalyses of error of pothole location determination thisstudy uses the accelerometer data and location informationfrom 10 runs in Section 42 to verify the space interpolationmethod The results show that the error of pothole locationdetermination is reduced from 1747 meters to 1174 metersafter using the space interpolation method Therefore thespace interpolation method is suitable to determinate theprecise pothole location
6 cm
51 cm
58 cm
Figure 5 A case study of a pothole in University Road HsinchuTaiwan
Table 1 The test results for accelerometer data with normalization
The value of 119911-axis accelerometer datamean (standard deviation)
The 0 degree angle(baseline) minus98489 (0000077)
The minus15 degree angle afternormalization minus98476 (0000085)
Table 2 The false positive of each pothole detection approach
Detectionmethod 119885-THRESH 119885-DIFF STDEV(119885) 119866-ZERO Proposed
methodFalse-positive 49 40 274 8 0
Table 3 The comparisons of different machine learning methods
Detection method ANN SVM DTFalse-positive 1626 255 282
5 Conclusions and Future Work
This study proposes a real-time pothole detection methodbased on the mobile sensing techniques This method usesEuler angle computation to normalize the accelerometer dataobtained from mobile device with free angle establishmentMoreover a pothole detection approach is proposed tobe combined with Z-THRESH and G-ZERO approachesfor reducing the false-positives of pothole detection Fur-thermore the spatial interpolation method is adopted toobtain precisely the location of pothole In experimentsthe results show that the proposed approach can preciselydetect potholes without false-positives and the accuracy ofthe proposed approach is 100Therefore the proposed real-time pothole detection approach can be used to improve thesafety of traffic for ITS
However the limitation of this study is sample size In thefuture more practical results will be retrieved and analyzedto deploy the proposed method everywhere Furthermoredue to the limited battery capacity of mobile device the issueabout saving of computation power can be investigated Agreen pothole detection approach is needed to reduce thefrequency of accelerometer data detectionwith high accuracyof pothole detection
Mathematical Problems in Engineering 7
Notations
119892119886119894119895
The acceleration of the 119886th axle of the 119895threcord in the 119894th run
119905119894119895 The timestamp of the 119895th record in the 119894th
run119899 The number of runs119890119894 The 119890
119894th entering pothole record in the 119894th
run119897119894 The 119897
119894th leaving pothole record in the 119894th
run119886 The coordinate axis of G-sensor in mobile
device (eg the value of 119886 is 1 whichmeans 119885-axis)
119891119898(sdot) The output of the119898th pothole detection
approach (eg the value of 1198911(sdot) is 1 when
the first pothole detection approachsupposes that the car passed through apothole)
119870 The third pothole detection approachrequires119870 records to calculate thestandard deviation
120579119898 The value of threshold for the119898th
approach12057941 The value of lower bound for the fourth
pothole detection approach12057942 The value of upper bound for the fourth
pothole detection approach
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The research is supported by the National Science Councilof Taiwan under Grants nos NSC 102-2622-H-009-001-CC3 NSC102-2410-H146-002-MY2 NSC 102-2410-H-009-052-MY3 and MOST 103-2622-H-009-001-CC3
References
[1] Ministry of Justice National Compensation Statistics andStatistics of Justice 2012 httpwwwmojgovtwctaspxItem=36988ampCtNode=11625ampmp=095
[2] E Miluzzo N D Lane K Fodor et al ldquoSensing meets mobilesocial networks The design implementation and evaluationof the CenceMe applicationrdquo in Proceedings of the 6th ACMConference on Embedded Networked Sensor Systems (SenSysrsquo08) pp 337ndash350 Raleigh Calif USA November 2008
[3] C-C Lo C-H Chen D-Y Cheng and H-Y Kung ldquoUbiqui-tous healthcare service system with context-awareness capabil-ity design and implementationrdquo Expert Systems with Applica-tions vol 38 no 4 pp 4416ndash4436 2011
[4] C I Wu H Y Kung C H Chen and L C Kuo ldquoAn intelligentslope disaster prediction andmonitoring system based onWSNand ANPrdquo Expert Systems with Applications vol 41 no 10 pp4554ndash4562 2014
[5] C-H Chen H-C Chang C-Y Su C-C Lo and H-F LinldquoTraffic speed estimation based on normal location updatesand call arrivals from cellular networksrdquo Simulation ModellingPractice andTheory vol 35 no 1 pp 26ndash33 2013
[6] X Yu and E Salari ldquoPavement pothole detection and severitymeasurement using laser imagingrdquo in Proceedings of the IEEEInternational Conference on ElectroInformation Technology(EIT rsquo11) pp 1ndash5 Mankato Minn USA May 2011
[7] J Lin and Y Liu ldquoPotholes detection based on SVM in thepavement distress imagerdquo in Proceedings of the 9th InternationalSymposium on Distributed Computing and Applications to Busi-ness Engineering and Science (DCABES rsquo10) pp 544ndash547 HongKong August 2010
[8] K de Zoysa C Keppitiyagama G P Seneviratne and W WA T Shihan ldquoA public transport system based sensor networkfor road surface condition monitoringrdquo in Proceedings of theWorkshop on Networked Systems for Developing Regions KyotoJapan August 2007
[9] J Eriksson L Girod B Hull R Newton S Madden andH Balakrishnan ldquoThe pothole patrol using a mobile sensornetwork for road surface monitoringrdquo in Proceedings of the 6thInternational Conference on Mobile Systems Applications andServices (MobiSys rsquo08) pp 29ndash39 June 2008
[10] P Mohan V N Padmanabhan and R Ramjee ldquoNericellrich monitoring of road and traffic conditions using mobilesmartphonesrdquo in Proceedings of the 6th ACM Conference onEmbedded Network Sensor Systems Raleigh NC USA 2008
[11] AMednis G Strazdins R Zviedris G Kanonirs and L SelavoldquoReal time pothole detection using Android smartphones withaccelerometersrdquo in Proceedings of the International Conferenceon Distributed Computing in Sensor Systems (DCOSS rsquo11) pp 1ndash6 IEEE Barcelona Spain June 2011
[12] R Zviedris A Elsts G Strazdins A Mednis and L SelavoldquoLynxNet wild animal monitoring using sensor networksrdquo inProceedings of the 4th International Conference on Real-worldWireless Sensor Networks Colombo Sri Lanka 2010
[13] J Han and M Kamber Data mining Concepts and TechniquesMorgan Kaufmann San Francisco Calif USA 2006
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
4 Mathematical Problems in Engineering
Detection function is
1198912(119892119886119894119895) =
1 if10038161003816100381610038161003816119892119886119894119895minus 119892119886119894119895minus1
10038161003816100381610038161003816
119905119894119895minus 119905119894119895minus1
ge 1205792
0 others
where 119886 = 1 1 le 119894 le 119899 119894 isin 119873 119895 ge 1 119895 isin 119873
(6)
333 The Third Pothole Detection Approach STDEV(Z)The STDEV(Z) approach considers the maximum standarddeviation of 119911-axis accelerometer data as the threshold todetect pothole Due to the perturbation motion of 119911-axisaccelerometer data through a pothole the standard deviationof 119911-axis accelerometer data during 119870 records is calculatedand used to detect potholeTherefore this study gets themax-imum value of standard deviation of 119911-axis accelerometerdata through a pothole in experimental runs Furthermorethe minimum value of the maximum value of standarddeviation in each run is selected as the threshold 120579
3which is
suitable to detect pothole for each experimental run (shownin formula (7)) In runtime stage the value of 119891
3(119892119886119894119895) is 1
when the value of radicsum119895119896=119895minus119870+1
(119892119886119894119896minus 120583119894119895)2119870 is larger than
1205793for pothole detection (shown in formula (8)) However
the limitation of this approach is difficult to determine thevalue of119870which means time period and the accuracy of thisapproach is influenced by this time period
The value of threshold is
1205793= min119886=11le119894le119899119894isin119873
max119890119894le119895le119897119894 119895isin119873
radicsum119895
119896=119895minus119870+1(119892119886119894119896minus 120583119894119895)
2
119870
where 120583119894119895=
sum119895
119896=119895minus119870+1119892119886119894119896
119870
(7)
Detection function is
1198913(119892119886119894119895) =
1 if radicsum119895
119896=119895minus119870+1(119892119886119894119896minus 120583119894119895)
2
119870
ge 1205793
0 others
where 119886 = 1 1 le 119894 le 119899 119894 isin 119873 119895 ge 119870
119895 isin 119873 120583119894119895=
sum119895
119896=119895minus119870+1119892119886119894119896
119870
(8)
334 The Fourth Pothole Detection Approach G-ZERO TheG-ZERO approach considers all three-axis accelerometerdata and selects a lower bound and upper bound to detectpothole for accuracy improvement When a car passesthrough a pothole all values of three-axis accelerometer dataare near to zero Therefore this study considers the largestvalue of three-axis accelerometer data through a pothole asa candidate of lower bound and the lowest value of three-axis accelerometer data through a pothole as a candidate ofupper bound Then the minimum value of the maximumvalue of three-axis accelerometer data in each run is selected
as the lower bound 12057941 and the maximum value of the
minimum value of three-axis accelerometer data in each runis selected as the upper bound 120579
42(shown in formulas (9)
and (10)) In runtime stage the value of 1198914(119892119886119894119895) is 1 when
the value of 119892119886119894119895
is larger than 12057941
and is lower than 12057942
forpothole detection (shown in formula (11))
The value of lower bound is
12057941= min119886isin1231le119894le119899119894isin119873
max119890119894le119895le119897119894 119895isin119873
119892119886119894119895 (9)
The value of upper bound is
12057942= max119886isin1231le119894le119899119894isin119873
min119890119894le119895le119897119894 119895isin119873
119892119886119894119895 (10)
Detection function is
1198914(119892119886119894119895) =
1 if 12057941le 119892119886119894119895le 12057942
0 others
where 119886 = 1 2 3 1 le 119894 le 119899 119894 isin 119873 119895 isin 119873
(11)
335 The Fifth Pothole Detection Approach ProposedApproach This subsection proposes a pothole detectionapproach which combines and improves the Z-THRESHand G-ZERO approaches to detect pothole Furthermorethe Z-DIFF and STDEV(Z) approaches are limited inaccordance with time differences and time periods sothese two approaches are not adopted The pseudocode ofthe proposed pothole detection approach is presented inAlgorithm 1The input parameters of this proposed approachare three-axis accelerometer data and the value of output is 1when the proposed pothole detection approach supposes thecar passed through a pothole In the proposed approach theparameter check method is used to record whether the valueof 1198911(119892119886119894119895) or 119891
4(119892119886119894119895) is 1 When one of Z-THRESH and
G-ZERO approaches supposes that the car passed througha pothole the timestamp 119905
119894119895is recorded and compared
with the parameter check time The value of output is 1 if119905119894119895-119888ℎ119890119888119896 119905119894119898119890 is smaller than 120576 seconds which means a
pothole is detected Furthermore the parameter check timecan be trained and learned by historical data from eachpractical run
34 Pothole Location Determination For pothole locationdetermination this study uses the space interpolationmethod to obtain precise pothole location Figure 2 showsthat two locations (ie 119871
1and 119871
2) and timestamps (ie 119905
1
and 1199052) obtained from GPS module are adopted in the space
interpolation method to determine the pothole location Thefunction 119889(119871
1 1198712) is defined as the distance between location
1198711and location 119871
2 Therefore the pothole location 119871
119901can be
determined by using
119889 (1198711 119871119901) =
119889 (1198711 1198712) times (1199052minus 1199051)
(1199053minus 1199051)
119889 (1198712 119871119901) =
119889 (1198711 1198712) times (1199053minus 1199052)
(1199053minus 1199051)
(12)
Mathematical Problems in Engineering 5
Input 119892119886119894119895
where 119886 = 1 2 3 1 le 119894 le 119899 119894 isin 119873 119895 isin 119873OutputThe value of output is 1 when the proposed pothole detection approach
supposes the car passed through a potholeSet check method = 0set check time = 0while (119895 isin 119873)
if (119905119894119895-check time) gt 120576 sec thencheck method = 0check time = 0
end ifif 1198911(1198921119894119895) = 1 then
if check method = 0 thencheck method = 1check time = 119905
119894119895
else if check method = 4 thenreturn 1
elsecheck time = 119905
119894119895
end ifend ifif 1198914(119892119886119894119895) = 1 then
if check method = 0 thencheck method = 4check time = 119905
119894119895
else if check method = 1 thenreturn 1
elsecheck time = 119905
119894119895
end ifend if
end while
Algorithm 1 The pseudocode of the proposed pothole detection approach
d(L1 L2) times (t2 minus t1)
(t3 minus t1)
d(L1 L2) times (t3 minus t2)
(t3 minus t1)
GPS locationL1 at time t1
GPS location L2 at time t3at time t2
Pothole location Lp
Figure 2 The space interpolation method for pothole locationdetermination
4 Experimental Results
This section discusses the analyses of experimental resultsfor accelerometer data normalization pothole detectionapproaches and pothole location determination
41 The Analyses of Accelerometer Data Normalization Forthe analyses of accelerometer data normalization this studygives two case studies which include (1) the mobile devicewith 0 degree angle as baseline (shown in Figure 3) and (2) themobile device with minus15 degree angle (ie the value of 120572 is minus15in Figure 1) (shown in Figure 4)Then the 119905-test and119865-test are
Figure 3 A case study of the mobile device with 0 degree angle asbaseline
used to verify the difference between the 119911-axis accelerometerdata of baseline in Case 1 and the 119911-axis accelerometer dataafter accelerometer data normalization in Case 2
This study uses two-tailed 119905-test to determine significanceof the difference between the mean of 119911-axis accelerometerdata of baseline in Case 1 (120583
1= minus98489) and the mean of 119911-
axis accelerometer data after accelerometer data normaliza-tion in Case 2 (120583
2= minus98476) The sample sizes of Case 1
and Case 2 are 60 Furthermore this study also uses 119865-test to
6 Mathematical Problems in Engineering
15∘
Figure 4 A case study of the mobile device with minus15 degree angle
determine significance of the difference between the varianceof 119911-axis accelerometer data of baseline in Case 1 (120590
1
2=
0000077) and the variance of 119911-axis accelerometer data afteraccelerometer data normalization in Case 2 (120590
2
2= 0000085)
Table 1 shows the 119905-test and 119865-test for the population meansand variances of samples in Case 1 and Case 2 Experimentalresults indicate that the null hypothesis (H0 120583
1= 1205832) in 119905-
test is accepted and another null hypothesis (H0 1205901= 1205902) in
119865-test is also accepted Therefore using Euler angle formulasto normalize the accelerometer data from mobile device issuitable for free angle establishment
42 The Accuracy of Pothole Detection Approach For theanalyses of accuracy of pothole detection approach thisstudy selects a pothole (length 58 cm weight 51 cm anddepth 6 cm) as a case study (shown in Figure 5) and 10runs in experiment environment The mean frequency ofaccelerometer data detection in G-sensor in mobile device is124 countssecondThe 119896-fold cross-validation [13] is used toverify the accuracy of pothole detection approach In exper-iments training and testing are performed 10 times (ie 119896 =10) In iteration 119894 the accelerometer data in 119894th run therapyis selected as the test corpus and the accelerometer datain other runs is collectively used to train the thresholds foreach approach Table 2 shows the comparisons ofZ-THRESHapproach Z-DIFF approach STDEV(Z) approach G-ZEROapproach and the proposed approach The results showthat the proposed approach can precisely detect potholeswithout false-positives and the accuracy of the proposedapproach is 100 Furthermore this study also implementedand compared common machine learning methods whichinclude ANN SVM and decision tree (DT) (shown inTable 3) Although these machine learning methods candetect potholes several false-positives are generated by them
43 The Error of Pothole Location Determination For theanalyses of error of pothole location determination thisstudy uses the accelerometer data and location informationfrom 10 runs in Section 42 to verify the space interpolationmethod The results show that the error of pothole locationdetermination is reduced from 1747 meters to 1174 metersafter using the space interpolation method Therefore thespace interpolation method is suitable to determinate theprecise pothole location
6 cm
51 cm
58 cm
Figure 5 A case study of a pothole in University Road HsinchuTaiwan
Table 1 The test results for accelerometer data with normalization
The value of 119911-axis accelerometer datamean (standard deviation)
The 0 degree angle(baseline) minus98489 (0000077)
The minus15 degree angle afternormalization minus98476 (0000085)
Table 2 The false positive of each pothole detection approach
Detectionmethod 119885-THRESH 119885-DIFF STDEV(119885) 119866-ZERO Proposed
methodFalse-positive 49 40 274 8 0
Table 3 The comparisons of different machine learning methods
Detection method ANN SVM DTFalse-positive 1626 255 282
5 Conclusions and Future Work
This study proposes a real-time pothole detection methodbased on the mobile sensing techniques This method usesEuler angle computation to normalize the accelerometer dataobtained from mobile device with free angle establishmentMoreover a pothole detection approach is proposed tobe combined with Z-THRESH and G-ZERO approachesfor reducing the false-positives of pothole detection Fur-thermore the spatial interpolation method is adopted toobtain precisely the location of pothole In experimentsthe results show that the proposed approach can preciselydetect potholes without false-positives and the accuracy ofthe proposed approach is 100Therefore the proposed real-time pothole detection approach can be used to improve thesafety of traffic for ITS
However the limitation of this study is sample size In thefuture more practical results will be retrieved and analyzedto deploy the proposed method everywhere Furthermoredue to the limited battery capacity of mobile device the issueabout saving of computation power can be investigated Agreen pothole detection approach is needed to reduce thefrequency of accelerometer data detectionwith high accuracyof pothole detection
Mathematical Problems in Engineering 7
Notations
119892119886119894119895
The acceleration of the 119886th axle of the 119895threcord in the 119894th run
119905119894119895 The timestamp of the 119895th record in the 119894th
run119899 The number of runs119890119894 The 119890
119894th entering pothole record in the 119894th
run119897119894 The 119897
119894th leaving pothole record in the 119894th
run119886 The coordinate axis of G-sensor in mobile
device (eg the value of 119886 is 1 whichmeans 119885-axis)
119891119898(sdot) The output of the119898th pothole detection
approach (eg the value of 1198911(sdot) is 1 when
the first pothole detection approachsupposes that the car passed through apothole)
119870 The third pothole detection approachrequires119870 records to calculate thestandard deviation
120579119898 The value of threshold for the119898th
approach12057941 The value of lower bound for the fourth
pothole detection approach12057942 The value of upper bound for the fourth
pothole detection approach
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The research is supported by the National Science Councilof Taiwan under Grants nos NSC 102-2622-H-009-001-CC3 NSC102-2410-H146-002-MY2 NSC 102-2410-H-009-052-MY3 and MOST 103-2622-H-009-001-CC3
References
[1] Ministry of Justice National Compensation Statistics andStatistics of Justice 2012 httpwwwmojgovtwctaspxItem=36988ampCtNode=11625ampmp=095
[2] E Miluzzo N D Lane K Fodor et al ldquoSensing meets mobilesocial networks The design implementation and evaluationof the CenceMe applicationrdquo in Proceedings of the 6th ACMConference on Embedded Networked Sensor Systems (SenSysrsquo08) pp 337ndash350 Raleigh Calif USA November 2008
[3] C-C Lo C-H Chen D-Y Cheng and H-Y Kung ldquoUbiqui-tous healthcare service system with context-awareness capabil-ity design and implementationrdquo Expert Systems with Applica-tions vol 38 no 4 pp 4416ndash4436 2011
[4] C I Wu H Y Kung C H Chen and L C Kuo ldquoAn intelligentslope disaster prediction andmonitoring system based onWSNand ANPrdquo Expert Systems with Applications vol 41 no 10 pp4554ndash4562 2014
[5] C-H Chen H-C Chang C-Y Su C-C Lo and H-F LinldquoTraffic speed estimation based on normal location updatesand call arrivals from cellular networksrdquo Simulation ModellingPractice andTheory vol 35 no 1 pp 26ndash33 2013
[6] X Yu and E Salari ldquoPavement pothole detection and severitymeasurement using laser imagingrdquo in Proceedings of the IEEEInternational Conference on ElectroInformation Technology(EIT rsquo11) pp 1ndash5 Mankato Minn USA May 2011
[7] J Lin and Y Liu ldquoPotholes detection based on SVM in thepavement distress imagerdquo in Proceedings of the 9th InternationalSymposium on Distributed Computing and Applications to Busi-ness Engineering and Science (DCABES rsquo10) pp 544ndash547 HongKong August 2010
[8] K de Zoysa C Keppitiyagama G P Seneviratne and W WA T Shihan ldquoA public transport system based sensor networkfor road surface condition monitoringrdquo in Proceedings of theWorkshop on Networked Systems for Developing Regions KyotoJapan August 2007
[9] J Eriksson L Girod B Hull R Newton S Madden andH Balakrishnan ldquoThe pothole patrol using a mobile sensornetwork for road surface monitoringrdquo in Proceedings of the 6thInternational Conference on Mobile Systems Applications andServices (MobiSys rsquo08) pp 29ndash39 June 2008
[10] P Mohan V N Padmanabhan and R Ramjee ldquoNericellrich monitoring of road and traffic conditions using mobilesmartphonesrdquo in Proceedings of the 6th ACM Conference onEmbedded Network Sensor Systems Raleigh NC USA 2008
[11] AMednis G Strazdins R Zviedris G Kanonirs and L SelavoldquoReal time pothole detection using Android smartphones withaccelerometersrdquo in Proceedings of the International Conferenceon Distributed Computing in Sensor Systems (DCOSS rsquo11) pp 1ndash6 IEEE Barcelona Spain June 2011
[12] R Zviedris A Elsts G Strazdins A Mednis and L SelavoldquoLynxNet wild animal monitoring using sensor networksrdquo inProceedings of the 4th International Conference on Real-worldWireless Sensor Networks Colombo Sri Lanka 2010
[13] J Han and M Kamber Data mining Concepts and TechniquesMorgan Kaufmann San Francisco Calif USA 2006
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 5
Input 119892119886119894119895
where 119886 = 1 2 3 1 le 119894 le 119899 119894 isin 119873 119895 isin 119873OutputThe value of output is 1 when the proposed pothole detection approach
supposes the car passed through a potholeSet check method = 0set check time = 0while (119895 isin 119873)
if (119905119894119895-check time) gt 120576 sec thencheck method = 0check time = 0
end ifif 1198911(1198921119894119895) = 1 then
if check method = 0 thencheck method = 1check time = 119905
119894119895
else if check method = 4 thenreturn 1
elsecheck time = 119905
119894119895
end ifend ifif 1198914(119892119886119894119895) = 1 then
if check method = 0 thencheck method = 4check time = 119905
119894119895
else if check method = 1 thenreturn 1
elsecheck time = 119905
119894119895
end ifend if
end while
Algorithm 1 The pseudocode of the proposed pothole detection approach
d(L1 L2) times (t2 minus t1)
(t3 minus t1)
d(L1 L2) times (t3 minus t2)
(t3 minus t1)
GPS locationL1 at time t1
GPS location L2 at time t3at time t2
Pothole location Lp
Figure 2 The space interpolation method for pothole locationdetermination
4 Experimental Results
This section discusses the analyses of experimental resultsfor accelerometer data normalization pothole detectionapproaches and pothole location determination
41 The Analyses of Accelerometer Data Normalization Forthe analyses of accelerometer data normalization this studygives two case studies which include (1) the mobile devicewith 0 degree angle as baseline (shown in Figure 3) and (2) themobile device with minus15 degree angle (ie the value of 120572 is minus15in Figure 1) (shown in Figure 4)Then the 119905-test and119865-test are
Figure 3 A case study of the mobile device with 0 degree angle asbaseline
used to verify the difference between the 119911-axis accelerometerdata of baseline in Case 1 and the 119911-axis accelerometer dataafter accelerometer data normalization in Case 2
This study uses two-tailed 119905-test to determine significanceof the difference between the mean of 119911-axis accelerometerdata of baseline in Case 1 (120583
1= minus98489) and the mean of 119911-
axis accelerometer data after accelerometer data normaliza-tion in Case 2 (120583
2= minus98476) The sample sizes of Case 1
and Case 2 are 60 Furthermore this study also uses 119865-test to
6 Mathematical Problems in Engineering
15∘
Figure 4 A case study of the mobile device with minus15 degree angle
determine significance of the difference between the varianceof 119911-axis accelerometer data of baseline in Case 1 (120590
1
2=
0000077) and the variance of 119911-axis accelerometer data afteraccelerometer data normalization in Case 2 (120590
2
2= 0000085)
Table 1 shows the 119905-test and 119865-test for the population meansand variances of samples in Case 1 and Case 2 Experimentalresults indicate that the null hypothesis (H0 120583
1= 1205832) in 119905-
test is accepted and another null hypothesis (H0 1205901= 1205902) in
119865-test is also accepted Therefore using Euler angle formulasto normalize the accelerometer data from mobile device issuitable for free angle establishment
42 The Accuracy of Pothole Detection Approach For theanalyses of accuracy of pothole detection approach thisstudy selects a pothole (length 58 cm weight 51 cm anddepth 6 cm) as a case study (shown in Figure 5) and 10runs in experiment environment The mean frequency ofaccelerometer data detection in G-sensor in mobile device is124 countssecondThe 119896-fold cross-validation [13] is used toverify the accuracy of pothole detection approach In exper-iments training and testing are performed 10 times (ie 119896 =10) In iteration 119894 the accelerometer data in 119894th run therapyis selected as the test corpus and the accelerometer datain other runs is collectively used to train the thresholds foreach approach Table 2 shows the comparisons ofZ-THRESHapproach Z-DIFF approach STDEV(Z) approach G-ZEROapproach and the proposed approach The results showthat the proposed approach can precisely detect potholeswithout false-positives and the accuracy of the proposedapproach is 100 Furthermore this study also implementedand compared common machine learning methods whichinclude ANN SVM and decision tree (DT) (shown inTable 3) Although these machine learning methods candetect potholes several false-positives are generated by them
43 The Error of Pothole Location Determination For theanalyses of error of pothole location determination thisstudy uses the accelerometer data and location informationfrom 10 runs in Section 42 to verify the space interpolationmethod The results show that the error of pothole locationdetermination is reduced from 1747 meters to 1174 metersafter using the space interpolation method Therefore thespace interpolation method is suitable to determinate theprecise pothole location
6 cm
51 cm
58 cm
Figure 5 A case study of a pothole in University Road HsinchuTaiwan
Table 1 The test results for accelerometer data with normalization
The value of 119911-axis accelerometer datamean (standard deviation)
The 0 degree angle(baseline) minus98489 (0000077)
The minus15 degree angle afternormalization minus98476 (0000085)
Table 2 The false positive of each pothole detection approach
Detectionmethod 119885-THRESH 119885-DIFF STDEV(119885) 119866-ZERO Proposed
methodFalse-positive 49 40 274 8 0
Table 3 The comparisons of different machine learning methods
Detection method ANN SVM DTFalse-positive 1626 255 282
5 Conclusions and Future Work
This study proposes a real-time pothole detection methodbased on the mobile sensing techniques This method usesEuler angle computation to normalize the accelerometer dataobtained from mobile device with free angle establishmentMoreover a pothole detection approach is proposed tobe combined with Z-THRESH and G-ZERO approachesfor reducing the false-positives of pothole detection Fur-thermore the spatial interpolation method is adopted toobtain precisely the location of pothole In experimentsthe results show that the proposed approach can preciselydetect potholes without false-positives and the accuracy ofthe proposed approach is 100Therefore the proposed real-time pothole detection approach can be used to improve thesafety of traffic for ITS
However the limitation of this study is sample size In thefuture more practical results will be retrieved and analyzedto deploy the proposed method everywhere Furthermoredue to the limited battery capacity of mobile device the issueabout saving of computation power can be investigated Agreen pothole detection approach is needed to reduce thefrequency of accelerometer data detectionwith high accuracyof pothole detection
Mathematical Problems in Engineering 7
Notations
119892119886119894119895
The acceleration of the 119886th axle of the 119895threcord in the 119894th run
119905119894119895 The timestamp of the 119895th record in the 119894th
run119899 The number of runs119890119894 The 119890
119894th entering pothole record in the 119894th
run119897119894 The 119897
119894th leaving pothole record in the 119894th
run119886 The coordinate axis of G-sensor in mobile
device (eg the value of 119886 is 1 whichmeans 119885-axis)
119891119898(sdot) The output of the119898th pothole detection
approach (eg the value of 1198911(sdot) is 1 when
the first pothole detection approachsupposes that the car passed through apothole)
119870 The third pothole detection approachrequires119870 records to calculate thestandard deviation
120579119898 The value of threshold for the119898th
approach12057941 The value of lower bound for the fourth
pothole detection approach12057942 The value of upper bound for the fourth
pothole detection approach
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The research is supported by the National Science Councilof Taiwan under Grants nos NSC 102-2622-H-009-001-CC3 NSC102-2410-H146-002-MY2 NSC 102-2410-H-009-052-MY3 and MOST 103-2622-H-009-001-CC3
References
[1] Ministry of Justice National Compensation Statistics andStatistics of Justice 2012 httpwwwmojgovtwctaspxItem=36988ampCtNode=11625ampmp=095
[2] E Miluzzo N D Lane K Fodor et al ldquoSensing meets mobilesocial networks The design implementation and evaluationof the CenceMe applicationrdquo in Proceedings of the 6th ACMConference on Embedded Networked Sensor Systems (SenSysrsquo08) pp 337ndash350 Raleigh Calif USA November 2008
[3] C-C Lo C-H Chen D-Y Cheng and H-Y Kung ldquoUbiqui-tous healthcare service system with context-awareness capabil-ity design and implementationrdquo Expert Systems with Applica-tions vol 38 no 4 pp 4416ndash4436 2011
[4] C I Wu H Y Kung C H Chen and L C Kuo ldquoAn intelligentslope disaster prediction andmonitoring system based onWSNand ANPrdquo Expert Systems with Applications vol 41 no 10 pp4554ndash4562 2014
[5] C-H Chen H-C Chang C-Y Su C-C Lo and H-F LinldquoTraffic speed estimation based on normal location updatesand call arrivals from cellular networksrdquo Simulation ModellingPractice andTheory vol 35 no 1 pp 26ndash33 2013
[6] X Yu and E Salari ldquoPavement pothole detection and severitymeasurement using laser imagingrdquo in Proceedings of the IEEEInternational Conference on ElectroInformation Technology(EIT rsquo11) pp 1ndash5 Mankato Minn USA May 2011
[7] J Lin and Y Liu ldquoPotholes detection based on SVM in thepavement distress imagerdquo in Proceedings of the 9th InternationalSymposium on Distributed Computing and Applications to Busi-ness Engineering and Science (DCABES rsquo10) pp 544ndash547 HongKong August 2010
[8] K de Zoysa C Keppitiyagama G P Seneviratne and W WA T Shihan ldquoA public transport system based sensor networkfor road surface condition monitoringrdquo in Proceedings of theWorkshop on Networked Systems for Developing Regions KyotoJapan August 2007
[9] J Eriksson L Girod B Hull R Newton S Madden andH Balakrishnan ldquoThe pothole patrol using a mobile sensornetwork for road surface monitoringrdquo in Proceedings of the 6thInternational Conference on Mobile Systems Applications andServices (MobiSys rsquo08) pp 29ndash39 June 2008
[10] P Mohan V N Padmanabhan and R Ramjee ldquoNericellrich monitoring of road and traffic conditions using mobilesmartphonesrdquo in Proceedings of the 6th ACM Conference onEmbedded Network Sensor Systems Raleigh NC USA 2008
[11] AMednis G Strazdins R Zviedris G Kanonirs and L SelavoldquoReal time pothole detection using Android smartphones withaccelerometersrdquo in Proceedings of the International Conferenceon Distributed Computing in Sensor Systems (DCOSS rsquo11) pp 1ndash6 IEEE Barcelona Spain June 2011
[12] R Zviedris A Elsts G Strazdins A Mednis and L SelavoldquoLynxNet wild animal monitoring using sensor networksrdquo inProceedings of the 4th International Conference on Real-worldWireless Sensor Networks Colombo Sri Lanka 2010
[13] J Han and M Kamber Data mining Concepts and TechniquesMorgan Kaufmann San Francisco Calif USA 2006
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
6 Mathematical Problems in Engineering
15∘
Figure 4 A case study of the mobile device with minus15 degree angle
determine significance of the difference between the varianceof 119911-axis accelerometer data of baseline in Case 1 (120590
1
2=
0000077) and the variance of 119911-axis accelerometer data afteraccelerometer data normalization in Case 2 (120590
2
2= 0000085)
Table 1 shows the 119905-test and 119865-test for the population meansand variances of samples in Case 1 and Case 2 Experimentalresults indicate that the null hypothesis (H0 120583
1= 1205832) in 119905-
test is accepted and another null hypothesis (H0 1205901= 1205902) in
119865-test is also accepted Therefore using Euler angle formulasto normalize the accelerometer data from mobile device issuitable for free angle establishment
42 The Accuracy of Pothole Detection Approach For theanalyses of accuracy of pothole detection approach thisstudy selects a pothole (length 58 cm weight 51 cm anddepth 6 cm) as a case study (shown in Figure 5) and 10runs in experiment environment The mean frequency ofaccelerometer data detection in G-sensor in mobile device is124 countssecondThe 119896-fold cross-validation [13] is used toverify the accuracy of pothole detection approach In exper-iments training and testing are performed 10 times (ie 119896 =10) In iteration 119894 the accelerometer data in 119894th run therapyis selected as the test corpus and the accelerometer datain other runs is collectively used to train the thresholds foreach approach Table 2 shows the comparisons ofZ-THRESHapproach Z-DIFF approach STDEV(Z) approach G-ZEROapproach and the proposed approach The results showthat the proposed approach can precisely detect potholeswithout false-positives and the accuracy of the proposedapproach is 100 Furthermore this study also implementedand compared common machine learning methods whichinclude ANN SVM and decision tree (DT) (shown inTable 3) Although these machine learning methods candetect potholes several false-positives are generated by them
43 The Error of Pothole Location Determination For theanalyses of error of pothole location determination thisstudy uses the accelerometer data and location informationfrom 10 runs in Section 42 to verify the space interpolationmethod The results show that the error of pothole locationdetermination is reduced from 1747 meters to 1174 metersafter using the space interpolation method Therefore thespace interpolation method is suitable to determinate theprecise pothole location
6 cm
51 cm
58 cm
Figure 5 A case study of a pothole in University Road HsinchuTaiwan
Table 1 The test results for accelerometer data with normalization
The value of 119911-axis accelerometer datamean (standard deviation)
The 0 degree angle(baseline) minus98489 (0000077)
The minus15 degree angle afternormalization minus98476 (0000085)
Table 2 The false positive of each pothole detection approach
Detectionmethod 119885-THRESH 119885-DIFF STDEV(119885) 119866-ZERO Proposed
methodFalse-positive 49 40 274 8 0
Table 3 The comparisons of different machine learning methods
Detection method ANN SVM DTFalse-positive 1626 255 282
5 Conclusions and Future Work
This study proposes a real-time pothole detection methodbased on the mobile sensing techniques This method usesEuler angle computation to normalize the accelerometer dataobtained from mobile device with free angle establishmentMoreover a pothole detection approach is proposed tobe combined with Z-THRESH and G-ZERO approachesfor reducing the false-positives of pothole detection Fur-thermore the spatial interpolation method is adopted toobtain precisely the location of pothole In experimentsthe results show that the proposed approach can preciselydetect potholes without false-positives and the accuracy ofthe proposed approach is 100Therefore the proposed real-time pothole detection approach can be used to improve thesafety of traffic for ITS
However the limitation of this study is sample size In thefuture more practical results will be retrieved and analyzedto deploy the proposed method everywhere Furthermoredue to the limited battery capacity of mobile device the issueabout saving of computation power can be investigated Agreen pothole detection approach is needed to reduce thefrequency of accelerometer data detectionwith high accuracyof pothole detection
Mathematical Problems in Engineering 7
Notations
119892119886119894119895
The acceleration of the 119886th axle of the 119895threcord in the 119894th run
119905119894119895 The timestamp of the 119895th record in the 119894th
run119899 The number of runs119890119894 The 119890
119894th entering pothole record in the 119894th
run119897119894 The 119897
119894th leaving pothole record in the 119894th
run119886 The coordinate axis of G-sensor in mobile
device (eg the value of 119886 is 1 whichmeans 119885-axis)
119891119898(sdot) The output of the119898th pothole detection
approach (eg the value of 1198911(sdot) is 1 when
the first pothole detection approachsupposes that the car passed through apothole)
119870 The third pothole detection approachrequires119870 records to calculate thestandard deviation
120579119898 The value of threshold for the119898th
approach12057941 The value of lower bound for the fourth
pothole detection approach12057942 The value of upper bound for the fourth
pothole detection approach
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The research is supported by the National Science Councilof Taiwan under Grants nos NSC 102-2622-H-009-001-CC3 NSC102-2410-H146-002-MY2 NSC 102-2410-H-009-052-MY3 and MOST 103-2622-H-009-001-CC3
References
[1] Ministry of Justice National Compensation Statistics andStatistics of Justice 2012 httpwwwmojgovtwctaspxItem=36988ampCtNode=11625ampmp=095
[2] E Miluzzo N D Lane K Fodor et al ldquoSensing meets mobilesocial networks The design implementation and evaluationof the CenceMe applicationrdquo in Proceedings of the 6th ACMConference on Embedded Networked Sensor Systems (SenSysrsquo08) pp 337ndash350 Raleigh Calif USA November 2008
[3] C-C Lo C-H Chen D-Y Cheng and H-Y Kung ldquoUbiqui-tous healthcare service system with context-awareness capabil-ity design and implementationrdquo Expert Systems with Applica-tions vol 38 no 4 pp 4416ndash4436 2011
[4] C I Wu H Y Kung C H Chen and L C Kuo ldquoAn intelligentslope disaster prediction andmonitoring system based onWSNand ANPrdquo Expert Systems with Applications vol 41 no 10 pp4554ndash4562 2014
[5] C-H Chen H-C Chang C-Y Su C-C Lo and H-F LinldquoTraffic speed estimation based on normal location updatesand call arrivals from cellular networksrdquo Simulation ModellingPractice andTheory vol 35 no 1 pp 26ndash33 2013
[6] X Yu and E Salari ldquoPavement pothole detection and severitymeasurement using laser imagingrdquo in Proceedings of the IEEEInternational Conference on ElectroInformation Technology(EIT rsquo11) pp 1ndash5 Mankato Minn USA May 2011
[7] J Lin and Y Liu ldquoPotholes detection based on SVM in thepavement distress imagerdquo in Proceedings of the 9th InternationalSymposium on Distributed Computing and Applications to Busi-ness Engineering and Science (DCABES rsquo10) pp 544ndash547 HongKong August 2010
[8] K de Zoysa C Keppitiyagama G P Seneviratne and W WA T Shihan ldquoA public transport system based sensor networkfor road surface condition monitoringrdquo in Proceedings of theWorkshop on Networked Systems for Developing Regions KyotoJapan August 2007
[9] J Eriksson L Girod B Hull R Newton S Madden andH Balakrishnan ldquoThe pothole patrol using a mobile sensornetwork for road surface monitoringrdquo in Proceedings of the 6thInternational Conference on Mobile Systems Applications andServices (MobiSys rsquo08) pp 29ndash39 June 2008
[10] P Mohan V N Padmanabhan and R Ramjee ldquoNericellrich monitoring of road and traffic conditions using mobilesmartphonesrdquo in Proceedings of the 6th ACM Conference onEmbedded Network Sensor Systems Raleigh NC USA 2008
[11] AMednis G Strazdins R Zviedris G Kanonirs and L SelavoldquoReal time pothole detection using Android smartphones withaccelerometersrdquo in Proceedings of the International Conferenceon Distributed Computing in Sensor Systems (DCOSS rsquo11) pp 1ndash6 IEEE Barcelona Spain June 2011
[12] R Zviedris A Elsts G Strazdins A Mednis and L SelavoldquoLynxNet wild animal monitoring using sensor networksrdquo inProceedings of the 4th International Conference on Real-worldWireless Sensor Networks Colombo Sri Lanka 2010
[13] J Han and M Kamber Data mining Concepts and TechniquesMorgan Kaufmann San Francisco Calif USA 2006
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Mathematical Problems in Engineering 7
Notations
119892119886119894119895
The acceleration of the 119886th axle of the 119895threcord in the 119894th run
119905119894119895 The timestamp of the 119895th record in the 119894th
run119899 The number of runs119890119894 The 119890
119894th entering pothole record in the 119894th
run119897119894 The 119897
119894th leaving pothole record in the 119894th
run119886 The coordinate axis of G-sensor in mobile
device (eg the value of 119886 is 1 whichmeans 119885-axis)
119891119898(sdot) The output of the119898th pothole detection
approach (eg the value of 1198911(sdot) is 1 when
the first pothole detection approachsupposes that the car passed through apothole)
119870 The third pothole detection approachrequires119870 records to calculate thestandard deviation
120579119898 The value of threshold for the119898th
approach12057941 The value of lower bound for the fourth
pothole detection approach12057942 The value of upper bound for the fourth
pothole detection approach
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
Acknowledgment
The research is supported by the National Science Councilof Taiwan under Grants nos NSC 102-2622-H-009-001-CC3 NSC102-2410-H146-002-MY2 NSC 102-2410-H-009-052-MY3 and MOST 103-2622-H-009-001-CC3
References
[1] Ministry of Justice National Compensation Statistics andStatistics of Justice 2012 httpwwwmojgovtwctaspxItem=36988ampCtNode=11625ampmp=095
[2] E Miluzzo N D Lane K Fodor et al ldquoSensing meets mobilesocial networks The design implementation and evaluationof the CenceMe applicationrdquo in Proceedings of the 6th ACMConference on Embedded Networked Sensor Systems (SenSysrsquo08) pp 337ndash350 Raleigh Calif USA November 2008
[3] C-C Lo C-H Chen D-Y Cheng and H-Y Kung ldquoUbiqui-tous healthcare service system with context-awareness capabil-ity design and implementationrdquo Expert Systems with Applica-tions vol 38 no 4 pp 4416ndash4436 2011
[4] C I Wu H Y Kung C H Chen and L C Kuo ldquoAn intelligentslope disaster prediction andmonitoring system based onWSNand ANPrdquo Expert Systems with Applications vol 41 no 10 pp4554ndash4562 2014
[5] C-H Chen H-C Chang C-Y Su C-C Lo and H-F LinldquoTraffic speed estimation based on normal location updatesand call arrivals from cellular networksrdquo Simulation ModellingPractice andTheory vol 35 no 1 pp 26ndash33 2013
[6] X Yu and E Salari ldquoPavement pothole detection and severitymeasurement using laser imagingrdquo in Proceedings of the IEEEInternational Conference on ElectroInformation Technology(EIT rsquo11) pp 1ndash5 Mankato Minn USA May 2011
[7] J Lin and Y Liu ldquoPotholes detection based on SVM in thepavement distress imagerdquo in Proceedings of the 9th InternationalSymposium on Distributed Computing and Applications to Busi-ness Engineering and Science (DCABES rsquo10) pp 544ndash547 HongKong August 2010
[8] K de Zoysa C Keppitiyagama G P Seneviratne and W WA T Shihan ldquoA public transport system based sensor networkfor road surface condition monitoringrdquo in Proceedings of theWorkshop on Networked Systems for Developing Regions KyotoJapan August 2007
[9] J Eriksson L Girod B Hull R Newton S Madden andH Balakrishnan ldquoThe pothole patrol using a mobile sensornetwork for road surface monitoringrdquo in Proceedings of the 6thInternational Conference on Mobile Systems Applications andServices (MobiSys rsquo08) pp 29ndash39 June 2008
[10] P Mohan V N Padmanabhan and R Ramjee ldquoNericellrich monitoring of road and traffic conditions using mobilesmartphonesrdquo in Proceedings of the 6th ACM Conference onEmbedded Network Sensor Systems Raleigh NC USA 2008
[11] AMednis G Strazdins R Zviedris G Kanonirs and L SelavoldquoReal time pothole detection using Android smartphones withaccelerometersrdquo in Proceedings of the International Conferenceon Distributed Computing in Sensor Systems (DCOSS rsquo11) pp 1ndash6 IEEE Barcelona Spain June 2011
[12] R Zviedris A Elsts G Strazdins A Mednis and L SelavoldquoLynxNet wild animal monitoring using sensor networksrdquo inProceedings of the 4th International Conference on Real-worldWireless Sensor Networks Colombo Sri Lanka 2010
[13] J Han and M Kamber Data mining Concepts and TechniquesMorgan Kaufmann San Francisco Calif USA 2006
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of
Submit your manuscripts athttpwwwhindawicom
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical Problems in Engineering
Hindawi Publishing Corporationhttpwwwhindawicom
Differential EquationsInternational Journal of
Volume 2014
Applied MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Mathematical PhysicsAdvances in
Complex AnalysisJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
OptimizationJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Operations ResearchAdvances in
Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Function Spaces
Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
International Journal of Mathematics and Mathematical Sciences
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Algebra
Discrete Dynamics in Nature and Society
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Decision SciencesAdvances in
Discrete MathematicsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Stochastic AnalysisInternational Journal of