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A comparative study on fault detection

methods of rail vehicle suspension

systems based on accelerationmeasurementsXiukun Wei

a, Limin Jia

a& Hai Liu

b

aState Key Lab of Rail Traffic Control and Safety, Beijing Jiaotong

University, Beijing, 100044, People's Republic of Chinab

School of Traffic and Transportation, Beijing Jiaotong University,

Beijing, 100044, People's Republic of China

Version of record first published: 18 Feb 2013.

To cite this article: Xiukun Wei , Limin Jia & Hai Liu (2013): A comparative study on fault detection

methods of rail vehicle suspension systems based on acceleration measurements, Vehicle System

Dynamics: International Journal of Vehicle Mechanics and Mobility, 51:5, 700-720

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Vehicle System Dynamics, 2013

Vol. 51, No. 5, 700720, http://dx.doi.org/10.1080/00423114.2013.767464

A comparative study on fault detection methods of rail vehicle

suspension systems based on acceleration measurements

Xiukun Weia*, Limin Jiaa and Hai Liub

aState Key Lab of Rail Traffic Control and Safety, Beijing Jiaotong University, Beijing 100044,Peoples Republic of China; bSchool of Traffic and Transportation, Beijing Jiaotong University,

Beijing 100044, Peoples Republic of China

(Received 10 July 2012; final version received 13 January 2013 )

Reliability of the railway vehicle suspension system is of critical importance to the safety of thevehicle. On-line health condition monitoring for the suspension system of rail vehicles offers a numberof benefits such as preventing further deterioration of vehicle performance, enhancing vehicle safety,increasing operational reliability and availability, and reducing maintenance costs. It is desirable totimely detect the fault and monitor the performance degradation of vehicle suspension systems. Inthis paper, a comparative study on fault detection methods of urban rail vehicle suspension systems isconsidered.A novel sensor configuration is proposed where the underlying vehicle system is equippedwith only acceleration sensors in the four corners of the carbody, the leading and trailing bogie,respectively. A mathematical model is developed for the considered vehicle suspension system. Both

model-based and data-driven approaches are studied for the suspension fault detection problem. Therobust observer, the Kalman filter combined with the generalised likelihood ratio test method, thedynamical principle components analysis and the canonical variate analysis approaches are appliedto the fault detection problem. The simulation is carried out by means of the professional multi-body simulation tool, SIMPACK. In addition, the advantages and disadvantages of these methodsare compared. The simulation results show that the data-driven methods outperform the model-basedmethods.

Keywords: rail vehicle suspension system; fault detection; model based; data driven

1. Introduction

With the rapid development of the urban railway traffic and transportation all over the world,

the safety and reliability issues of the urban railway system have been receiving more attention

than ever before. In many big cities, such as London, Paris, Beijing, Shanghai and Tokyo, the

subway is one of the most important means of transportation. However, the subway system

is often thronged with people. Especially, during the traffic peak periods when people go

to work in the morning and back home in the afternoon, it is often overloaded. Therefore,

it is necessary to ensure the reliability of the subway system, including the urban railway

vehicles. In the mean time, due to the large amount of traffic flow, it is significantly important

to ensure the availability and punctuality of rail services. To avoid unplanned delay of the

trains, short time broken of one line or even the whole subway system and to minimise the

*Corresponding author. Emails: [email protected]; [email protected]; [email protected]

2013 Taylor & Francis

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Vehicle System Dynamics 701

overall system downtime, advanced condition monitoring techniques are desired to monitor

the health condition of the system.

Reliability of the railway vehicle suspension system is of critical importance to the safety

of the vehicle. The suspension system is to support the carbody and bogie, to isolate the

forces generated by the track unevenness at the wheels and to control the altitude of the

carbody with respect to the track surface for providing ride comfort. In the case of the urban

railway, the performance of some components, such as the springs and the dampers, degrades

significantly after one or two years. Many of the components are replaced in five years due to

the performance degradation or component faults. Therefore, it is necessary to timely detect

the fault and monitor the performance degradation of vehicle suspension systems.

On-line fault detection and health condition monitoring for the suspension system of rail

vehicles offer a number of benefits to railway operations. Detecting component faults at their

early stages prevents further deterioration in vehicle performance and enhances vehicle safety.

Timely maintenance or replacement of the faulty components leads to increased operational

reliability and availability. The need for scheduled maintenance and associated costs can besignificantly reduced since maintenance in the future may be carried out on demand (condition

based rather than calendar based).

Considering the significance, the fault detection issue of the rail vehicle suspension systems

has attracted some attention in the recent years [17] and the references therein. In [8], the

fault detection issue of the railway vehicle lateral suspension system is considered, where a

Kalman filter-based method has been proposed for detecting and isolating faults in the railway

vehicle suspension system in the light of the derived vehicle dynamic model. The method is

computationally efficient and responds rapidly to the abrupt fault; thus, it is suitable for using

on-line to detect and isolate the abrupt or hard faults which usually need immediate attention.

However, the paper assumes that the vehicle parameters are known precisely andthe simulationis carried out by using a linear model. In [4], a newly developed Rao-Blackwellised particle

filter-based method is used for the parameter estimation of the railway vehicle suspension

system. Computer simulations are carried out to assess and compare the performance of the

parameter estimation with different sensor configurations as well as the robustness with respect

to the uncertainty in the statistics of the random track inputs. The proposed method is quite

attractive. Nevertheless, the computation burden of the proposed algorithm cannot be afforded

by the current available monitoring hardware. In [5,9], the interaction multi-model (IMM)

approach is applied to the vehicle suspension fault detection problem. The IMM approach

demonstrates some effective performance for the spring faults, the damper faults and also the

acceleration metre faults. However, when the IMM method is applied, the models needed are

increasing very drastically when more components in the suspension system are considered.

In [10,11], the authors proposed a novel approach which exploits the dynamical interactions

between different vehicle modes caused by component failures in the system. In [12,13], a

fault detection approach for the light rail vehicle suspension systems based on the Kalman

filter is derived. In [6], a distributed observer is introduced for the fault detection of a light

rail vehicle suspension system.

The current reported approaches for the suspension system are mainly model-based meth-

ods. It is true that there is a great potential for the improvement in the performance of condition

monitoring if the a prior knowledge or information captured by the models is fully used. How-

ever, in many cases, the parameters of the vehicle suspension system are not available. In

the mean time, due to nonlinearities of the components and the complexity of the suspen-sion system, a precise model cannot be obtained. Due to the limitations of the model-based

fault detection approaches, there is an increasing interest in using the multivariate statistical

approaches to monitor system health conditions [1416]. Generally, there are less application

limitations for data-driven approaches. These approaches can be generalised into different

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plants conveniently if abundant dynamical data are available. As to the knowledge of the

authors, there is no report in the literature which solves the fault detection problem for rail

vehicle suspension systems based on data-driven methods.

This paper presents a comparative study on fault detection methods of urban rail vehicle

suspension systems. A novel sensor configuration is proposed where the underlying vehicle

system is equipped with only acceleration sensors in the four corners of the carbody, the

leading and trailing bogies, which provide the measured signals for the condition monitoring

of the vehicle suspension system. A mathematical model is developed for the considered

vehicle suspension system. Both model-based and data-driven approaches are studied for the

suspension fault detection problem. The robust observer, the Kalman filter combined with

the generalised likelihood ratio test (GLRT) method, the dynamical principle components

analysis (DPCA) and the canonical variate analysis (CVA) approaches are applied to the fault

detection problem, respectively. The considered faults are the vertical damper faults and the

vertical spring faults of both primary and secondary suspensions. A subway vehicle served

in Lines 1 and 8 in GuangZhou metro, China, manufactured by the CSR Zhuzhou ElectricLocomotive Co. is adopted as an example for this study. The simulation is carried out by

means of the multi-body simulation software, SIMPACK. The advantages and disadvantages

of these methods are compared.

This paper is organised as follows. The urban rail vehicle suspension system, its dynamics

and the sensor configuration for the data collection are introduced in Section 2. In Section 3,

the model-based fault detection methods, the robust observer and the GLRT method are briefly

reviewed. After that, the data-driven approaches, DPCA and CVA, are presented. SIMPACK-

MATLAB co-simulation results are presented in Section 4. Finally, some conclusions are

given in Section 5.

2. The rail vehicle suspension system modelling and sensor configuration

In this section, the traditional dynamical model of the rail vehicle suspension is brieflyreviewed

before the new model under the new sensor configuration is derived.

2.1. The vertical vehicle suspension system

The vertical suspension system considered in this paper is shown in Figure 1. Standard dynamic

equations for three degree-of-freedom (DOF) (bounce, pitch and roll) are presented for both

carbody and bogies and can be found in many references. They are briefly listed.

For the carbody, the three DOF equations are described as

Mz + 4C2 z 2C2 z1 2C2 z2 + 4K2z 2K2z1 2K2z2 = 0, (1)

J + 4C2l2 2C2lz1 + 2C2lz2 + 4K2l

2 2K2lz1 + 2K2lz2 = 0, (2)

J + 4C2b2 2C2b

21 2C2b22 + (4K2b

2 + 2K) (2K2b2

+ K)1 (2K2b2 + K)2 = 0, (3)

where z,z1 and z2 denote the vertical displacement of the carbody, the leading bogie and the

trailing bogie, respectively. denotes the pitch angle of the centre of gravity(c.g.). denotes

the roll angle of the c.g. for the masses. The parameters of the vertical vehicle suspension

system are given in Table 1.

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Figure 1. The vertical suspension system of the rail vehicle.

Table 1. The parameters of the vehicle suspension system.

Description Unit

M Carbody mass kg

MB Bogie mass kg

J Carbody pitch inertia kg m2

J Carbody roll inertia kg m2

JB Bogie pitch inertia kg m2

JB Bogie roll inertia kg m2

lb Half of the distance between two wheelsets in a bogie mwb Half of the distance between two air spring in lateral m

lc Half of the carbody length m

wc Half of the carbody width m

K2 Spring constants of air spring kN/m

K1 Spring constants of primary spring kN/m

C2 Damping constants of secondary damper kNs/m

C1 Damping constants of primary damper kNs/m

K Spring constants of the anti-roll spring kN/m

For the leading bogie, the three DOF equations are described as

MB z1 2C2 z 2C2l + (4C1 + 2C2)z1 C1d1r C1d1l C1d2r C1d2l

2K2z 2K2l + (4K1 + 2K2)z1 K1d1r K1zd1l K1d2r K1d2l = 0, (4)

JB 1 + 4C1l21 1 C1l1d1r C1l1d1l + C1l1d2r + C1l1d2l + 4K1l

21 1 K1l1d1r

K1l1d1l + K1l1d2r + K1l1d2l = 0, (5)

JB1 2C2b2 + (2C2b

2 + 4C1b21)1 + C1b1d1r C1b1d1l + C1b1d2r C1b1d2l

(2K2b2 + K) + (2K2b

2 + 4K1b21 + K)1 + K1b1d1r K1b1d1l

+ K1b1d2r K1b1d2l = 0, (6)

where d1r denotes the vertical displacement of the right wheel in the leading wheelset. d2ldenotes the vertical displacement of the left wheel in the trailing wheelset. The meaning of

other symbols is defined in a similar way. To simplify the considered problem, this paper

assumes that the vertical displacements of the wheel are equal to the unevenness of the track.

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704 X. Wei et al.

In a similar way, the model of the trailing bogie can be derived as follows:

MB z2 2C2 z + 2C2l + (4C1 + 2C2)z2 C1d3r C1d3l C1d4r C1d4l

2K2z + 2K2l + (4K1 + 2K2)z2 K1d3r K1d3l K1d4r K1d4l = 0, (7)

JB 2 + 4C1l21 2 C1l1d3r C1l1d3l + C1l1d4r + C1l1d4l + 4K1l

21 2

K1l1d3r K1l1d3l + K1l1d4r + K1l1d4l = 0, (8)

Jb2 2C2b2 + (2C2b

2 + 4C1)b212 + C1b1d3r C1b1d3l + C1b1d4r C1b1d4l

(2K2b2 + K) + (2K2b

2 + 4K1b21 + K)K)

+ (2K2b2 + 4K1b

21 + K)d4r K1b1d4l = 0. (9)

The state-space description of the vertical suspension model can be derived as

x = Ax+ Bdd, (10)

y = Cx+ Ddd, (11)

where

x = [z z z1 1 1 z1 1 1 z2 2 2 z2 2 2]T,

d = [d1r d1l d2r d2l d1r d1l d2r d2l d3r d3l d4r d4l d3r d3l d4r d4l ]T,

y = [z z1 1 1 z2 2 2]T,

where matrixes A,Bd, C and Dd are derived from the previous differential equations. d is thevertical track variation velocity and displacement due to track vertical irregularities.

2.2. The dynamical suspension model under the new sensor configuration

In the developed model (10) and (11), the vertical displacement, pitch angle displacement and

roll angle displacement of the cardody and the bogie are selected as the system outputs. This

means that the displacement sensor and angle displacement sensors are required to measure

these signals for the purpose of fault detection. However, displacement sensor and angle dis-

placement sensors have some problems in reliability, maintenance and installation. Compared

with these sensors, acceleration sensors have the merits such as cheapness and reliability. Inaddition, it does not need to be maintained for a long time period. Acceleration sensors are

widely used in the health condition monitoring of railway systems.Considering all the reasons

stated above, a novel sensor configuration is proposed as shown in Figure 1. The vehicle sus-

pension system is only equipped with acceleration sensors in the four corners of the carbody,

the leading and trailing bogies. Carbody sensors are equipped in the four corners on the floor-

board, and the bogie sensors are equipped in the four corners on the upside of the bogie. The

acceleration signal can be transformed to displacement signal by applying double integral to

the acceleration signal, that is,

z = a dtdt, (12)where a is the acceleration value and z is the displacement.

Remark 2.1 In principle, the displacement signal can be obtained by double integrating

directly the acceleration signal. However, in reality, the output of acceleration sensors always

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Figure 2. Relationship among the displacement of the four points.

Figure 3. The pitch motion.

contains the direct current (DC) component. The DC component must be filtered by a high-pass

filter. The numerical integral algorithm is also critical to achieve a high accuracy.

In the following, the new output equation under the new sensor configuration framework is

derived. The problem needs to be solved is mainly how to build the relation matrix between the

outputs in Equation (11) and the new outputs, the displacements at the corners of the carbody,

the leading bogie and the trailing bogie.

Here, the relationship between the four vertical displacements {zfl,zfr,zrl,zrr} of the four

carbody floor corners and the carbody displacements, the roll angle and the pitch angle {z, , }

is derived. A simplified carbody floor is depicted in Figure 2. Define two variables zf and zr,which are the vertical displacement of the middle point of the front edge and the middle point

of the right edge, respectively, then one obtains

z + zfr = zf + zr. (13)

The displacement zf can be replaced by the following equation:

zf = z + lc sin() z + lc, (14)

which is trivially obtained by using the pitch motion of the carbody floor depicted in Figure 3.

Similarly, we have the following equation:

zr z wc, (15)

which is derived by using the roll motion of the carbody floor depicted in Figure 4.

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Figure 4. The roll motion.

In terms of Equations (13)(15), one obtains

zfr z + lc wc. (16)

Following the same procedure, one obtains

zfl z + lc + wc, (17)

zrl z lc + wc, (18)

zrr z lc wc. (19)

The transformation matrix between {zfl,zfr,zrl,zrr} and {z, , } is built, which is

zflzfrzrl

zrr

=

1 lc wc1 lc wc1 lc wc

1 lc wc

z

. (20)

The relation matrix between the four corner displacements of the leading bogie and the

trailing bogie and their three DOF variables can be derived in a similar way. The following

transformation matrix is obtained:

T =

1 lc wc 0 0 0 0 0 0

1 lc wc 0 0 0 0 0 0

1 lc wc 0 0 0 0 0 0

1 lc wc 0 0 0 0 0 0

0 0 0 1 lb wb 0 0 0

0 0 0 1 lb wb 0 0 00 0 0 1 lb wb 0 0 0

0 0 0 1 lb wb 0 0 0

0 0 0 0 0 0 1 lb wb0 0 0 0 0 0 1 lb wb0 0 0 0 0 0 1 lb wb0 0 0 0 0 0 1 lb wb

,

one yields

y = Ty, (21)

where

y = [zfl zfr zrl zrr z1_fl z1_fr z1_rl z1_rr z2_fl z2_fr z2_rl z2_rr]T

is the output under the new sensor configuration. {z1_fl,z1_fr,z1_rl,z1_rr} represent the four ver-

tical displacements of the leading bogie corners, respectively. {z2_fl,z2_fr,z2_rl,z2_rr} represent

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the four vertical displacements of the trailing bogie corners. Then, the state-space description

under the new measurement sensor configuration can be obtained

x = Ax+ Bdd, (22)

y = Ty,

= TCx+ TDdd,

= Cx + Ddd, (23)

where C = TC and Dd = TDd.

The discrete model of the vertical suspension system is easily derived as follows:

xk+1 = Gxk + Hddk, (24)

yk

= Cxk

+ Dddk, (25)

where G = eAT, H =T

0eA dB and T is the sampling time.

Remark 2.2 High-integrity data are very critical for the data-driven fault detection methods.

The data should contain rich enough information of the system dynamics and the fault infor-

mation when a fault occurs in the system. In this paper, only acceleration sensors are used

for the vehicle suspension fault detection systems. From the above observation, the dynamics

of rail vehicle suspension systems are contained in the 12 displacements of the carbody, the

leading and trailing bogies, which are measured by the acceleration sensors. That is to say, the

sensor configuration presented before can provide enough information for the fault detection.

3. A brief review of the fault detection methods

In this section, the model-based fault detection methods, the robust observer-based method

and the Kalman filter-based approach, and data-driven fault detection methods, the DPCA and

CVA, are briefly reviewed.

3.1. Robust fault detection observer design and MCUMSUM

The discrete model of the suspension system with faults is described by

:=

xk+1 = Gxk + Hddk + Hffk,

yk = Cxk + Dddk + Dffk,(26)

where fk Rnf is the fault vector. The robust fault detection observer design objective here is

to design an observer O, which has the following formulation:

O := xk+1 = Gxk + L(yk yk),

y = Cxk,rk = yk yk

(27)

to maximise the sensitivity of the fault to the residual rk and also maximise the robustness of

the disturbance to the residual.

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708 X. Wei et al.

Define e = xk xk, the state estimation error dynamic equations can be described by

ek+1 = Geek + Hde dk + H

fefk,

rk = Cek + Dddk + Dffk, (28)

where Ge = G LC, Hde = Hd L

Dd, Hfe = Hf L Df.

The transfer function of the state estimation error dynamic system of the observer is given by

r = Grd(z)d + Grf(z)f, (29)

where

Grd(z) = C(zI Ge)1Hde +

Dd, (30)

Grf(z) = C(zI Ge)1Hfe + Df. (31)

The fault detection observer must be robust to the disturbances (the robustness conditions)

and sensitive to the faults (the sensitivity conditions). The observer design can be transformed

into an linear matrix inequality optimisation problem as follows:

max

s.t. Grd(z)Grd(z) < 2I

Grf(z)Grf(z) > 2I

Ge is stable.

Please refer to our previous work [17] for details of the observer design. In this paper, the

well-known multivariate CUMSUM [18] is adopted for the residual rk change detection. At

each time k, we calculate statistic Qk as

Qk = (Qk1 + rk u)

1

q

Ck

ifCk > q, (32)

where u represents the mean of the residual rk and q is a predetermined statistical distance,

Ck =

(Qk1 + rk u)1(Qk1 + rk u) (33)

and is the covariance matrix of the observation data. If Ck q, the process resets Qk = 0.

The MCUMSUM starts with Q0 = 0 and triggers an alarm when Sk =

QTk

1Qk exceeds

a predetermined threshold, h, that is chosen to achieve a desired performance. The robust

observer fault detection system is shown in Figure 5.

Figure 5. Robust observer fault detection system.

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3.2. Fault detection based on the Kalman filter and GLRT

Assume that the track irregularities are white noises, then a Kalman filter is designed for the

suspension system (25) and (26) as follows:

xk+1 = (G KC)xk + Kyk,rk = yk Cxk. (34)

The no fault (H0) and fault (H1) hypotheses test are described in terms of the innovation as

follows:

H0 : k = rk, (35)

H1 : k = rk + gk(), (36)

where rk is the residual in the absence of the fault case. gk(

) is generated by the fault withmagnitude at time . gk is generated by the failure signature dynamical equation

k+1 = (G KC)k + (Hf K Df)sk , (37)

gk = Ck + Dfsk . (38)

The primary principle behind is that for each time instant k, check if there is a failure in the

past time with the generalised likelihood ratio

k(, ) =

p(kL, kL+1, . . . , k|H1, , )

p(kL, kL+1, . . . , k|H0)

=

j=kj=kL

p(j|H1, , )

p(j|H0)(39)

for all k [k L, k], where L is the sliding window length.

Taking the log of the above ratio, it follows that

k(, ) = () 1

22Sk(

), (40)

where

k() =

kj=

gTj ()R1j j, (41)

Rj = CPjC + DD, (42)

Sk() =

kj=

gTj ()R1j gj(

), (43)

where Pj is the system noise covariance.

The generalised log likelihood ratio is given by

lk = max(kL,k)

maxR

k(, ). (44)

Further explanation and detailed algorithm of GLRT can be found in [1923]. The Kalman

filter and GLRT-based fault detection system is shown in Figure 6.

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710 X. Wei et al.

Figure 6. Kalman filter and the GLRT-based fault detection system.

3.3. A brief description of PCA-based fault detection method

The standard PCA-based fault detection consists of three steps and is formulated as follows:

Data collection and pre-processing: Consider a data matrix X RNm consisting of N

samples and m sensors collected from process. Matrix X is then scaled to zero mean, and

often to unit variance. Let the scaled data be

Y =

yT1...

yTN

RNm (45)with yi R

m, i = 1, . . . ,N, denoting the ith scaled vector.

Decomposition of covariance matrix: The covariance matrix is formed as

0 =1

N 1

YTY. (46)

By means of singular value decomposition (SVD), the covariance matrix is decomposed as

follows:

1

N 1YTY = PPT, =

pc 0

0 res

, (47)

where pc = diag(2

1 , . . . , 2l ), res = diag(

2l+1, . . . ,

2m), with

2i , i = 1, . . . , m, is the ith

singular value of the covariance matrix, PPT = Imm and

PTpc

PTres

[Ppc Pres] =

Ill 0

0 I(ml)(ml)

.

On-line fault detection: When a new scaled measurement y Rm is available, the squared

prediction error (SPE) and Hostelings T2 indices can be computed as

T2 = yTPpc1pc P

Tpcy, (48)

SPE = yTPresPTresy. (49)

The fault detection logic is SPE Jth,SPE and T2 Jth,T2 fault-free. Otherwise faulty.

Jth,T2 and Jth,SPE are the thresholds for SPE and T2 test, respectively.

The PCA methods can be extended to take the serial correlations into account by aug-

menting each observation vector with the previous l observations and stacking the data

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matrix in the following manner:

Y(l) =

yTk yTk1 y

Tkl

yTk1 yTk2 y

Tkl1

. . . ...

yTk+ln yTk+ln1 y

Tkn

, (50)

where yTk is the m-dimensional observation vector in the training set at time instant k. This

approach of applying PCA to Equation (50) is referred to as dynamic PCA (DPCA).

The vehicle suspension system is a dynamical system and the measured outputs are cor-

related with the past measurements. Hence, DPCA rather than PCA is applied for its fault

detection.

3.4. CVA-based fault detection method for dynamic processes

The stacked past and future vectors, p and f, are represented as follows:

pklk1 = [yTk1 y

Tkl]

T, (51)

fk+l+1k = [yTk y

Tk+l1]

T, (52)

where y denotes output vectors, subscript k is the present time index for y, and l is the number

of the lag or the lead. In CVA, the stacked future and past vectors are normalised by using

df,k = 1/2

fffk+l+1k , dp,k1 =

1/2

pppklk1, (53)

where

ff = E(fk+l+1k f

k+l+1k

T) and

pp = E(p

klk1p

klk1

T) (E() denotes the expectation oper-

ator). The normalised vectors df,k and dp,k1 are defined as the scaled stacked future and past

vectors at time k, respectively. The conditional expectation of the scaled future vector takes

the following form:

E(df,k|dp,k1) =1/2

ff

fp

1/2pp

dp,k1, (54)

where E(|) denotes the expectation of under condition . The physical meaning of

fp, defined as E(fk+l+1k pklk1T

), is the well-known Hankel matrix. Thus, 1/2ff fp 1/2ppindicates the scaled Hankel matrix. The scaled Hankel matrix can be factorised by using SVD,

df,k

=1/2

ff

fp

1/2pp

dp,k1

= USVTdp,k1 UqSqVTq dp,k1, (55)

where

df,k denotes E(df,k|dp,k1) and q represents the state order. Uq and Vq consist of the first

q column vectors ofU and V, respectively, and the diagonal matrix Sq is the q q principal

submatrix ofS. Then, the past and future canonical variates at time k are given by

zk = UTq df,k = UTq 1/2ff fk+l+1k = Lqfk+l+1k ,mk = V

Tq dp,k1 = V

Tq

1/2pp

pklk1 = Jqpklk1, (56)

respectively.

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712 X. Wei et al.

Similar to the T2 and SPE indices, the following indices are used for the CVA fault detection

test in this paper

T2s = pklk1

TJqJ

Tq p

klk1, (57)

SPEs = Tk k, (58)

where k = (I JqJq)pklk1.

4. Simulations

In this section, the simulation environment and the fault generation principle are introduced

at first. After that the fault detection result for all the four detection methods is presented in

detail. The advantages and disadvantages are compared and pointed out.

4.1. Simulation environment and the suspension fault generation

To analyse and study the fault detection performance of the four methods stated in the last

section, a SIMPACK and MATLAB co-simulation environment is built. The parameters are

provided by the vehicle manufacturer to obtain the simulation data for the purpose of algorithm

validation.The multi-body simulation model is built by the construction of coordinates system,

bodies, joints, constraints, force elements, track excitations and so on. The SIMPACK vehicle

model is used to generate the acceleration signals and different faults in both primary and

secondary suspensions. The SIMPACK vehicle suspension simulation model equipped withacceleration sensors is shown on the right part of Figure 7.

In the SIMPACK simulation environment, it is not easy to generate a component fault in

the course of a simulation. One way is to build a new model, whose components are already

faulty. However, there are several different faults with different magnitudes for the underlying

suspension system. Many SIMPACK models need to be built and it is a very time-consuming

work. In order to simulate the fault components, the SIMPACK and MATLAB co-simulation

environment is built. On the MATLAB side, the data generated by the SIMPACK are acquired

and some pre-processing work is also carried out. Another important task for MATLAB is to

control SIMPACK and simulate the suspension faults with different fault magnitudes at any

time when the vehicle is running. In the following, the fault simulation method is presented.

In the light of the working principle of the damper component, the force generated by thedamper is equal to the damper coefficient times pistons velocity, which is used to prevent the

Figure 7. Co-simulation between SIMPACK and MATLAB/SIMULINK.

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movement of the piston. When the damper is faulty, for instance, the coefficient has a 25%

reduction, a smaller force is generated by the damper and the reduced force is proportional

to the product of the pistons velocity and the reduced damper coefficient. A virtual force is

generated in the light of the fault scenarios and acts on the position where the damper is fixed.

As shown in Figure 7, for instance, sensors are equipped at the position of a secondary damper

to measure its moving velocity. Assume that the damper coefficient is reduced to half of its

normal value at the 15th second (controlled by MATLAB), then an external force (the fault

signal in Figure 7) is exerted on the piston to reduce the resistance generated by the damper.

The direction of the virtual force is opposite to the force generated by the damper and the

value of force is equal to the fault magnitude times the pistons velocity. In a similar way,

spring faults and other components faults can also be simulated.

4.2. Performance assessment by simulation experiments

The fault detection results for the railway vehicle suspension system are shown in this section.

The track irregularity used in the simulations is the fifth-grade track irregularity spectrum of

the US railway lines. The proposed sensor configuration and the fault detection result do not

depend on the special track irregularity. All vertical suspension component faults are fully

studied, but only some typical faults detection results are demonstrated here. The typical

faults considered are two primary suspension spring coefficient reduction scenarios and two

secondary suspension damper coefficient reduction scenarios listed in Table 2. The considered

spring or damper coefficient reduction of 25% and 75% represents a fault at its early stage

and a severe fault, respectively.

Remark 4.1 For urban railway suspension systems, the performance of the dampers andsprings degrades significantly after one year or two years. This can be indicated by the damper

and spring coefficients. When the damper has leakage problem, the damper coefficient also

changes. These slow change faults can be described by the small fault, and the condition

monitoring device can provide useful information for component maintenance. For abrupt

and server fault case, fault detection device should send an alarm to the driver after the fault

occurs and an emergency braking is needed to guarantee the safety of the train. Fault detection

can be used to detect small faults to provide maintenance decision on the one hand. On the

other hand, it can also be applied to guarantee the safety of the train when severe faults come

forth.

The threshold for the fault detection alarm depends on the system disturbances (track irreg-

ularities), the residual generation algorithm and the residual evaluation method as well. In the

simulations, the threshold is trivially taken as a constant which is larger than the maximal value

of the residual evaluation function output when no faults occur in the system in the course

of a long enough simulation. For practical application, the threshold determination should

Table 2. Fault scenarios used in the simulation.

Scenario Fault Fault pattern Faulty time (s)

Fault 0 No fault

Fault 1 C2 25% reduction 15

Fault 2 C2 75% reduction 15Fault 3 K1 25% reduction 15

Fault 4 K1 75% reduction 15

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714 X. Wei et al.

make a tradeoff between sensitivity to faults and robustness to uncertainties such as the track

irregularities and model uncertainties. Different thresholds can be chosen for different track

segments to improve the fault detection performance.

In all the figures, the red solid line indicates the threshold. The blue dashed-dotted line

represents the result of no fault case. The suspension component losing 25% of its value is

indicated by the green dashed line. For the last scenario, 75% reduction of the components

coefficient is represented by the black dotted line. In all the simulations, the vehicle velocity

is set to 80 km/h and the sampling time for fault detection is 0.1 s. All the faults of different

scenarios are introduced into the suspension system at 15 s after the SIMPACK-MATLAB

co-simulation starts. The detailed simulation results are presented below.

Robust observer-based method:A robustobserver is designed based on the former work [17].

The parameters used for the observer synthesis are the same as those used for building the

SIMPACK vehicle dynamicalmodel. The residual generatedby the robust observeris evaluated

by the MCUMSUM algorithm. The results are shown in Figures 8 and 9. It can be seen clearly

from Figure 8 that the algorithm detects the 75% reduction fault of the secondary suspensiondamper coefficient after 7 s when it occurs. The Sk value is larger than the predefined threshold

in most of the time after the fault occurs. This fault is clearly detected by the robust observer

method. On the other hand, the 25% reduction fault of the damper coefficient is not detected

clearly by the robust observer and at only several time instants, the Sk value is above the

predefined threshold. It is hardly concluded whether a fault occurs or not. For the early stage

secondary suspension damper fault, the robust observer-based approach is not very effective.

The fault detection result for the primary spring fault scenario is shown in Figure 9. Similar to

the damper fault case, the severe fault (75% coefficient reduction) is clearly detected around 7 s

after it emerges. Nevertheless, the small fault (25% coefficient reduction) is not successfully

detected. There are only several time instants where the Sk is larger than the threshold. Thealarm is not persistent and it is hardly determined that a fault has come forth already.

0 10 20 30 40 50 60 70 80 900

10

20

30

40

50

60

70

Sk

Time(s)

Simulation results for secondary suspension damper faults

threshold

no fault

C2

25% reduction

C2

75% reduction

Figure 8. Robust observer and MCUMSUM algorithm for C2 fault.

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0 10 20 30 40 50 60 70 80 900

10

20

30

40

50

60

70

80

90

Sk

Time(s)

Simulation results for primary suspension spring faults

threshold

no fault

K1

25% reduction

K1

75% reduction

Figure 9. Robust observer and MCUMSUM algorithm for K1 fault.

Remark 4.2 The model used for the fault detection does not include the coupling between

roll and lateral motion of the car body and bogie. This causes some model uncertainties. A

more precise model is helpful to improve the performance for detecting small fault.

GLRT based on the Kalman filter method: Figures 10 and 11 demonstrate the fault detection

results by using GLRT based on the Kalman filter method for the secondary suspension damper

fault and the primary spring fault, respectively. For the damper fault scenario, both the early

stage fault (25% coefficient reduction) and the severe fault case (75% coefficient reduction) are

detected successfully. For the 75% coefficient reduction fault case, the first alarm is triggered

out at around 10 s after the fault occurs. It takes more than 17 s to trigger the first alarm for the

early stage fault (25% coefficient reduction). For the primary suspension spring fault, it can be

seen clearly that the severe fault is detected successfully 15 s after it comes forth. Nevertheless,

for the early stage fault, the alarm is triggered out only at very limited instants, even thoughthe first alarm is triggered out just 4 s after the fault emerges.

Remark 4.3 In the Kalman filter and GLRT-based fault detection method, the disturbance is

assumed to be white noise. However, in the suspension system, the disturbance is the track

irregularity and it is not totally white. The fault detection performance could be improved if

more precise system model and disturbance model are used.

DPCA method: In this data-driven fault detection approach, a data set generated by the

SIMPACK without faults is used for building the statistical model. The time lag steps l in

Equation (50) is selected as 20. One hundred and twenty principle components are finally

selected to be retained in the model. Both T2 test and SPE test are applied in the simulations.It is found that the fault detection results based on the SPE test outperform the T2 test. Hence,

only the SPE test results for the two typical fault scenarios are presented in the following.

The fault detection results for the secondary suspension damper faults and the primary

suspension spring faults are shown in Figures 12 and 13, respectively. It can be seen clearly

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716 X. Wei et al.

0 10 20 30 40 500

0.5

1

1.5

2

2.5x 10

4 Simulation results for secondary suspension damper faults

Time(s)

l k

threshold

no fault

C2 25% reduction

C2 75% reduction

Figure 10. Kalman filter and GLRT algorithm for C2 fault.

0 10 20 30 40 500

0.5

1

1.5

2

2.5

3

3.5x 10

4 Simulation results for primary suspension spring faults

Time(s)

l k

threshold

no faultK1 25% reduction

K1 75% reduction

Figure 11. Kalman filter and the GLRT algorithm for the K1 fault.

that for the severe fault cases (C2 75% reduction and K1 75% reduction), the SPE test values aremuch higher than the predefined thresholds. For the early stage faults (C2 25% reduction and

K1 25% reduction), they are also successfully detected. Nevertheless, the SPE test values are

very close to the predefined threshold. The response of the DPCA-based method to the faults

is much faster than the robust observer- and Kalman filter-based approaches stated before.

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10 15 20 25 30 35 40 450

0.1

0.2

0.3

0.4

0.5

0.6

0.7

SPE

Time(s)


threshold

no fault

C2

25% reduction

C2

75% reduction

Figure 12. DPCA and SPE for the C2 fault.

10 15 20 25 30 35 40 450

0.1

0.2

0.3

0.4

0.5

0.6

0.7

SPE

Time(s)


thresholdno fault

K1

25% reduction

K1

75% reduction

Figure 13. DPCA and SPE for the K1 fault.

CVA method: For the CVA approach, the dimension of the measured data is reduced from

12 to 6 by PCA techniques first. This avoids the problem that 1/2

ff and 1/2

pp in Equation

(53) are not real. The time lag and lead steps l in Equation (51) are selected as 20. In the

CVA model, 18 states are selected. Both T2s test and SPEs test are applied in the simulations.

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718 X. Wei et al.

10 15 20 25 30 35 4060

80

100

120

140

160

180

200

220

240

T2 s

Time(s)


threshold

no fault

C2

25% reduction

C2

75% reduction

Figure 14. CVA and T2s for C2 fault.

10 15 20 25 30 35 400

1000

2000

3000

4000

5000

6000

7000

8000

T2 s

Time(s)


threshold

no fault

K1

25% reduction

K1

75% reduction

Figure 15. CVA and T2s for the K1 fault.

Contrary to the DPCA methods, the fault detection results based on the T2s test outperformsthe SPEs test. Hence, only the T

2s test results for the two typical fault scenarios are presented

in the following.

The fault detection results are shown in Figures 14 and 15. It can be seen that the CVA

method detects all the faults successfully. Especially, for the primary suspension spring fault

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Table 3. Comparison of the fault detection methods.

Method Sensitivity Response speed Complexity Limitation

Observer Worst Slow Complex Precise model required

GLRT Bad Slowest Complex Precise model requiredPCA Good Fast Simple Fault isolation is difficult

CVA Best Fast Simple Fault isolation is difficult

cases, CVA even outperforms the DPCA method. Nevertheless, for the C2 fault cases, DPCA

is better than the CVA approach.

4.3. Comparison of the four fault detection methods

In this part, the four fault detection methods are compared in terms of the sensitivity to

faults, response speed to faults, complexity of the methods and application limitations. The

comparison results are given Table 3.

It is surprising that the data-driven approaches have better performance in all aspects.

Actually, this result is much easier to be accepted when we notice the point that the model-

based method needs a precise model to achieve a good performance. Since the rail vehicle

suspension system is very complicated and there is nonlinearity existing in the system, the

model is certainly not a precise one, while the data-driven approaches do not need the model.

However, the model-based approach also has advantages such as dealing with fault isolation

and identification problems. The model-based fault detection approach is still being developed

and better detection performance is expected from the improvement of modelling techniquesand fault detection algorithms.

5. Conclusions

In this paper, the fault detection problem of the urban railway vehicle suspension system

is studied. A novel sensor configuration is proposed where the underlying vehicle system

is equipped with only acceleration sensors in the four corners of the carbody, the leading

and trailing bogies, respectively. A mathematical model is built for the considered vehicle

suspension system. After that a comparative study on fault detection methods of urban rail

vehicle suspension systems is considered. Both model-based and data-driven approaches are

studied for the suspension fault detection problem. The robust observer, the Kalman filter

combined with the GLRT method, the DPCA and the dynamical CVA approaches are applied

to the fault detection problem, respectively. The simulation results show that the data-driven

methods outperform the model-based methods.

In this paper, the vertical suspension system is considered for our comparative study. How-

ever, the sensor configuration, modelling and the fault detection methods can be trivially

extended to the lateral suspension system. In addition, the proposed methods can also being

applied to the gyro sensor configuration framework when robust and cheap gyros are available.In this paper, only the fault detection issue for the suspension system is concerned. It

is necessary to further investigate the suspension system model, robustness and sensitivity

analysis of the fault detection methods. In addition, how to isolate these faults and estimate

the magnitude of each fault are not studied yet. This will be carried out in the future work.

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Acknowledgements

This work is partly supported by Chinese 863 program (Contract No. 2011AA110503-6), State Key Laboratory of RailTraffic Control and Safety (Contract No.RCS2010ZT003) and Ph.D. Programs Foundation of Ministry of Educationof China (Grant number: 20110009120037).

References

[1] S. Bruni, R. Goodall, T.X. Mei, and H. Tsunashima, Control and monitoring for railway vehicle dynamics, Veh.Syst. Dyn. 45 (2007), pp. 765771.

[2] R. Goodall and T. Mei, Advanced control and monitoring for railway vehicle suspensions, International Sym-posium on Speed-up and Service Technology for Railway and Maglev Systems(STECH06), Chengdu, China,2006, pp. 1016.

[3] R. Goodall1 and C. Roberts, Concepts and techniques for railway condition monitoring, IET InternationalConference on Railway Condition Monitoring, Birmingham, UK, 2006, pp. 9095.

[4] P. Li, R. Goodall, P. Weston, C.S. Ling, C. Goodman, and C. Roberts, Estimation of railway vehicle suspensionparameters for condition monitoring, Control Eng. Pract. 15 (2007), pp. 4355.

[5] Y. Hayashi, H. Tsunashima, andY. Marumo, Faultdetection of railway vehicle suspension systemsusing multiple-model approach, Mech. Syst. Transp. Log. 1 (2008), pp. 8898.

[6] X. Wei, S. Lin, and H. liu, Distributed fault detection observer for rail vehicle suspension systems, ChineseControl and Decision Conference, Taiyuan, China, 2012, pp. 34083413.

[7] X. Wei, L. Jia, and H. Liu, Fault diagnosis filter design for railway vehicle suspension systems based on LMIoptimization, Int. Interdiscip. J. accepted (2012).

[8] P. Li and R. Goodall, Model based condition monitoring for railway vehicle systems, Control 2004, Universityof Bath, 2004, ID-508.

[9] H.T. Yusuke Hayashi and Y. Marumo, Condition monitoring of railway vehicle suspension, InternationalConference on Control, Automation and Systems, Gyeonggi-do, Korea, 2010, pp. 584589.

[10] T.X. Mei and X.J. Ding, A model-less technique for the fault detection of rail vehicle suspensions , Veh. Syst.Dyn. 46 (2008), pp. 277287.

[11] T.X. Mei and X.J. Ding, Condition monitoring of rail vehicle suspensions based on changes in system dynamicinteractions, Veh. Syst. Dyn. 47 (2009), pp. 11671181.

[12] X. Wei, H. liu, and Y. Qin, Fault diagnosis of rail vehicle suspension systems by using GLRT, Chinese Controland Decision Conference, Mianyang, China, 2011, pp. 19321937.

[13] X. Wei, H. Liu, and Y. Qin, Fault isolation of rail vehicle suspension systems by using similarity measure ,International Conference on Intelligent Railway Tranportation, Beijing, China, 2011, pp. 391396.

[14] S.J. Qin, Data-driven fault detection and diagnosis for complex industrial processes, The 7th IFAC Symposiumon Fault Detection, Supervision and Safety of Technical Processes, Barcelona, Spain, 2009, pp. 11151125.

[15] S. Yin, S. Ding, A. Naik, P. Deng, and A. Haghani, On PCA-based fault diagnosis techniques, 2010 Conferenceon control and Fault Tolerant Systems, Nice, France, 2010, pp. 179184.

[16] C. Lee, S.W. Choi, and L. In-Beum, Variable reconstruction and sensor fault identification using canonicalvariate analysis, J. Process Control 16 (2006), pp. 747761.

[17] X. Wei, L. Liu, and M. Verhaegen, Fault detection and estimation for LTI systems and its application to a labrobotic manipulator, Control and Decision Conference, 2009. CCDC 09.Chinese, Guilin,2009, pp. 15951600.

[18] R.B. Crosier,Multivariate generalizations of cumulative sum quality-control schemes, Technometrics 30 (1988),

pp. 291303.[19] A.S. Willsky and H.L. Jones, A generalized likelihood ratio approach to the detection and estimation of jumps

in linear systems, IEEE Trans. Autom. Control 21 (1976), pp. 108112.[20] F. Gustafsson, Adaptive Filtering and Change Detection, Wiley, Chichester, 2000.[21] F. Guatafusson, The marginalized likelihood ratio test for detecting abrupt change, IEEE Trans.Autom. Control

41 (1996), pp. 6678.[22] H.L.V. Trees, Detection, Estimation, and Modulation Theory, Part I, John Wiley and Sons, New York, 1968.[23] R.S. Mangoubi, Robust Estimation and Failure Detection, Springer, London, 1998.

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