ieee transactions of vehicular technology, vol. , no. ,...

IEEE TRANSACTIONS OF VEHICULAR TECHNOLOGY, VOL. , NO. , 1

Sensor fault detection and isolation using a supportvector machine for vehicle suspension systems

Kicheol Jeong, Seibum B. Choi, Member, IEEE and Hyungjeen Choi

Abstract—In this paper, a means of generating residuals basedon a fault isolation observer (FIO) and evaluating them using asupport vector machine (SVM) is proposed. The proposed FIOgenerates the isolated residual signals and they shows robustperformance regardless of unknown road surface conditions. ThisFIO is designed using a linear time-invariant quarter-car model.While quarter-car models have the form of a bilinear system,in this study the authors convert this bilinear model to a linearmodel with model uncertainty based on the assumption that thecontrol input is limited. Therefore, the proposed FIO can be usedregardless of the type of damper or controller. Furthermore, theSVM based residual evaluator without empirically set thresholdsis used to evaluate the generated residuals. The proposed faultdiagnosis algorithm is expected to reduce the effort required inthe design procedure and it can also detect a small amount ofsensor fault that cannot be detected by traditional limit-checkingmethod. The proposed fault diagnosis algorithm is verified usinglow cost production accelerometers and a quarter-car test rig.Consequently, the fault diagnosis algorithm proposed in thispaper can detect the faults of a sprung mass accelerometer andan unsprung mass accelerometer independently, and this algo-rithm can reduce the effort required in designing the diagnosisalgorithm greatly.

Index Terms—fault detection and isolation, support vectormachine, eigenstructure assignment, vehicle suspension, sensorfault diagnosis

I. INTRODUCTION

THE suspension system of modern vehicles is an essentialcomponent to guarantee the ride quality, stability and

handling performance of the vehicle. In terms of the controlmethod, the vehicle suspension system can be classified as pas-sive, semi-active, or active suspension. The passive suspension,which does not utilize any control input, is generally used inthe automotive industry. However, this type of suspension can-not satisfy the desired ride quality and handling performancesince these two characteristics have a trade-off relationship.To overcome this limitation, semi-active and active suspensionsystems are increasingly used in the automotive industry. Ac-tive suspension achieves control objectives using an additionalactuator such as a motor. Although this type of suspensioncan provide high performance, it is not widely used due toexcessive energy consumption, load increase, and packagingissues. In contrast, majority of automotive manufacturers adoptsemi-active suspensions that adjust the damping characteristicsof the suspension to solve packaging and energy issues. Since

K. Jeong and S. B. Choi are with the Korea Advanced Institute of Scienceand Technology, Daejeon 34141, South Korea (e-mail: [email protected];[email protected]). H. Choi is with the Korea Automotive Technology In-stitute, 303 Pungse-ro, Pungse-myeon, Dongnam-gu, Cheonan-si, Chungnam31214, South Korea (e-mail: [email protected]).

the semi-active suspension is widely adopted in the automotiveindustry, many researchers have conducted studies to enhancethe performance of semi-active suspension systems [1]–[10].These control algorithms improve the ride quality and stabilityof the vehicle. However, if a fault occurs on the control sys-tem components, it impacts vehicle performance and stabilitynegatively. In particular, since the vehicle suspension controlsystem consists of many sensors and actuators, there is ahigh probability that the system will collapse due to faults.Therefore, in order to improve the performance and stabilityof the vehicle, a fault diagnosis algorithm as well as a controlalgorithm is required. In recent years, the electronization ofautomobiles is a trend in the global automobile industry, andvarious sensors are embedded in the vehicle. For this reason,all vehicle manufacturers have implemented fault diagnosisalgorithms for vehicle sensor systems.Today, most automotive manufacturers adopt the limit-checking method [11] which determines sensor faults based onpredetermined sensor signal thresholds. However, this methodhas poor fault detection performance since the sensor signalthreshold is set high to ensure robustness of the fault diagnosisalgorithm.Therefore, a model-based fault diagnosis method [11]–[16]using a physical model of a system has recently been studiedto design a robust and sensitive fault diagnosis algorithm. Amodel-based fault diagnosis algorithm consists of a residualgenerator that generates a fault-sensitive residual and a residualevaluator that evaluates the residual signal.Recently, model-based fault diagnosis algorithms for auto-motive suspension systems have been extensively studied. Inparticular, many studies have been conducted using a quarter-car model which is mainly used for the design of a suspensioncontrol algorithm. In general, quarter car suspension systemincludes both the nonlinear characteristics of the damper andunknown road input. Therefore, when designing a suspensionfault diagnosis algorithm, it is important to ensure robustnessagainst unknown road input and nonlinearity of the damper.Recently, various methods have been proposed to achievethese design objectives. Chamseddine [17] used a quarter-car model based sliding mode observer to diagnose sensorfaults in the vehicle suspension system. Although the faultdiagnosis algorithm is robust to disturbance, an additionalsensor such as a displacement sensor is used instead of thesensor configuration commonly used in commercial vehicles[18]. Bornor [19] and Varrier [20] used the parity spaceapproach, a well-known model-based fault diagnosis method.However, the residual generator constructed by the parityspace approach cannot guarantee robustness against modeling


uncertainties. Alternatively, Kim [21] proposed a method ofdiagnosing a sprung mass accelerometer based on a full-carmodel, this method cannot diagnose a fault of unsprung massaccelerometer and it is difficult to find roll dynamics propertiesused in this paper.In model-based fault diagnosis schemes, the residuals gen-erated by a fault detection algorithm are not zero becauseof model uncertainties, disturbances, and sensor noise thatare not considered. Therefore, the design of rational residualevaluation algorithm is essential to the design of fault diag-nosis algorithm. However, in most of the previous studies,residual evaluation is performed using a fixed threshold de-fined empirically. Although Kim [21] proposed an adaptivethreshold method, the form of the adaptive threshold was alsodetermined empirically. In addition, little research has beencarried out to diagnose fault of vehicle suspension systemusing the sensor configuration of most vehicle produced today.In order to overcome these limitations, this paper proposes arobust quarter-car model based suspension sensor fault diagno-sis algorithm for unknown road input and damping coefficientchanges. The quarter-car model of the semi-active suspensionis represented as a bilinear system [22] in which there iscoupling of the unmeasured state and the control input. In thispaper, this bilinear model is converted into a linear model withunknown parametric uncertainty to design a fault detection andisolation (FDI) algorithm using the eigenstructure assignmentmethod. The proposed FDI algorithm can generate residualsusing only the sensors built into the vehicle, regardless of thetype of controller or damper. In addition, this paper also usesthe support vector machine (SVM) [23]–[26], a widely usedmachine learning technique, to evaluate residual signals. Inthis paper, the feature required for the SVM learning process iscreated by model-based fault diagnosis technique. This methodallows an accurate residual evaluation while reducing the effortfor threshold tuning to evaluate residuals.This paper is organized as follows. In section II, faults inthe sprung mass accelerometer and the unsprung mass ac-celerometer are represented by a state space linear model.In this section, sensor faults are converted to pseudo-actuatorfaults. In section III, FDI algorithm consisting of a faultisolation observer (FIO) based residual generator and SVMbased residual evaluator is presented. The eigenvalues of theproposed FIO are assigned considering the performance indexof the fault diagnosis algorithm in a specific frequency region.In addition, the residuals generated by FIO based residualgenerator are evaluated using SVM. Section IV presents exper-imental verification using a quarter car test rig. In conclusion,this paper shows that the proposed FDI algorithm providesrobust performance under various road inputs.

II. MODELING FAULTS OF THE VEHICLE SUSPENSION

In this section, faults in the sprung mass accelerometer andunsprung mass accelerometer are demonstrated by the quarter-car model. To apply the eigenstructure assignment method,which is a linear fault diagnosis technique, this bilinear systemis transformed into a linear system containing bounded modeluncertainty. This conversion is performed under the reasonable

TABLE IQUARTER-CAR MODEL PROPERTIES

Symbol Quantity Valuems Sprung mass 374.03 kgmu Unsprung mass 52.25 kgks Spring coefficient 22080 N/mkt Tire vertical stiffness 248193 N/m

cnDamper nominal dampingcoefficient 1562 Ns/m

cu Control input 0≤ cu ≤6096.77 N/m

assumption that the damping coefficient is limited. In addition,in order to design a diagnostic observer, faults in a sprungmass accelerometer and an unsprung mass accelerometer aretransformed into a pseudo-actuator faults.

A. Quarter-car suspension model

A quarter-car suspension model has been widely used forsuspension control studies due to the simplicity and accuracyof the model. The governing equations of a quarter-car sus-pension model such as that in Fig. 1 are as follows:

Fig. 1. Quarter-car model of a vehicle suspension.

mszs = −ks(zs − zu)− (cn + cu)(zs − zu) (1)

muzu = −ks(zu−zr)−(cn+cu)(zu− zr)−kt(zu−zr) (2)

where ms is a sprung mass, mu is an unsprung mass, ks is aspring coefficient, cn is a nominal damping coefficient, cu is acontrol input, zs and zu are displacement of sprung mass andunsprung mass and zr is the road displacement. As in previousstudies, the damping effect of tires is neglected. Table I liststhe quarter-car model properties.This governing equations can be expressed as a bilinearsystem. The state-space representation of this system is givenas

x = Ax+Aux · cu + Er zry = Cx+ Cux · cu

(3)

where x =[zs − zu zs zu − zr zu

]T,

A =

0 1 0 −1

−ks/ms −cn/ms 0 cn/ms

0 0 0 1ks/mu

cn/mu −kt/mu −cn/mu

,


Au =

0 0 0 00 −1/ms 0 1/ms

0 0 0 10 1/mu 0 −1/mu

, y =[zs zu

]T,

C =

[−ks/ms −cn/ms 0 cn/ms

ks/mucn/mu −kt/mu −cn/mu

],

Cu =

[0 −1/ms 0 1/ms

0 1/mu 0 −1/mu

]and Er =

[0 0 −1 0

]T.

In the real world, the nominal damping coefficient cn of avehicle suspension has high nonlinear and hysteresis charac-teristics. In addition, according to (3), the control input iscombined with a state variable, which is unknown. Further-more, the damping control command and the actual dampingcontrol input are not the same due to physical limitationssuch as the actuator bandwidth. These system characteris-tics make designing fault diagnosis algorithms and analyzingfault diagnosis performance difficult. Although bilinear faultdiagnosis algorithms have been studied [27], it is difficultto obtain robustness against damping coefficient uncertaintyin such fault diagnosis algorithms. Therefore, in this paper,this bilinear system is transformed into a linear system withbounded parametric uncertainty. This transformation is basedon a reasonable assumption that the damping coefficient ofvehicle suspension is limited. According to Table I, the overalldamping coefficient cu+cn is bounded between cmax (1562.00Ns/m) and cmin (7658.77 Ns/m). Consequently, the bilinearsystem (3) can be represented as

x = Ax+ Eud+ Er zry = Cx+ Fud

(4)

where A =

0 1 0 −1

−ks/ms −c0/ms 0 c0/ms

0 0 0 1ks/mu

c0/mu −kt/mu −c0/mu

,

C =

[−ks/ms −c0/ms 0 c0/ms

ks/muc0/mu −kt/mu −c0/mu

],

Eu =[

0 −cd/ms 0 cd/mu

]T,

Fu =[−cd/ms

cd/mu

]T, d = ∆Gx, |∆| ≤ 1,

G =[

0 1 0 −1].

where c0 = (cmax + cmin)/2 and cd = (cmax − cmin)/2.Note that this linear system has bounded uncertainty since ∆and system state x are bounded. Consequently, it is possibleto apply linear fault diagnosis techniques to the transformedsystem. It is noteworthy that this converted model can be usedregardless of the type of damper controller and the hysteresischaracteristics of the damper. The proposed linear model canbe obtained under the assumption that cmax and cmin areknown variables.

B. Pseudo-actuator fault modeling

According to the quarter-car model obtained in the abovesubsection, the fault model of the vehicle suspension can berepresented as

x = Ax+ Eud+ Er zr + Ef f

y = Cx+ Fud+ Ff f(5)

where f =[fs fu

]T, fs is the fault of the sprung

mass accelerometer and fu is the fault of the unsprung massaccelerometer.Note that f is an unknown fault vector that represents allpossible types of sensor faults and should be zero on a healthysystem. It is assumed that Ef is zero, since the actuator faultsare not considered in this paper. In (5), Ff is modelled byan identity matrix. In accordance with [28]–[30], the sensorfault model can be represented by the pseudo-actuator model,without loss of generality, such as

x = Ax+ Eud+ Er zr + EfsFs + EfuFuy = Cx+ Fud

(6)

where Fs =[fs −fs

]T, Fu =

[fu −fu

]T, Efs =[

js Ajs], Efu =

[ju Aju

], js,u is the solution to

Ffs,fu = Cjs,u. Note that the derivative of the sensor faultsignal is not important, and therefore it is considered anotherdisturbances. In conclusion, the final form of the fault modelof vehicle suspension is represented as

x = Ax+ Eaugdaug + Effy = Cx+ Faugdaug

(7)

where Eaug = [ Eu Er js ju ], Ef = [ Ajs Aju ],Faug = [ Fd 0 0 0 ], daug =

[d zr fs fu

]T, f =[

−fs −fu]T

.

III. FAULT DETECTION AND ISOLATION ALGORITHM

In this section, the proposed model-based FDI algorithm isdesigned. Generally, the model-based FDI algorithm consistsof a residual generator that generates a residual signal indica-tive of a fault and a residual evaluator that determines whethera fault occurs based on the residual. First, the FIO basedon the quarter-car model, developed in the previous section,is designed using the eigenstructure assignment method. TheFIO generates a residual signal that indicates the fault of thesprung mass accelerometer and the unsprung mass accelerom-eter, respectively. Next, the SVM based residual evaluator isproposed. This residual evaluator can reduce the time andeffort required for traditional threshold tuning. In conclusion,the proposed FDI algorithm is implemented as shown in Fig.2.

Fig. 2. Schematic description of the FDI algorithm.


A. Fault isolation observer based residual generator design

In this subsection, a fault isolation observer is designed togenerate residuals for each sensor fault. The form of the faultisolation observer proposed in this paper is given as

˙x = Ax− L(y − Cx)r = V (y − Cx)

(8)

where x is the estimated state, L is the observer gain, r is theresidual vector, and V is the post filter. Assume that the errorstate is defined as e = x− x. The error dynamics is then givenas

e = (A+ LC)e+ Eff + (Eaug + LFaug)daugr = V Ce+ V Faugdaug

(9)

According to (7) and (8), the transfer matrix from the faultvector f to the residual vector r is given as

Grf (s) = V C(sI − (A+ LC))−1Ef (10)

The purpose of the fault isolation observer is to diagonalizethe transfer matrix. Therefore, if one fault occurs, only oneresidual signals is affected. In order to design such a faultisolation observer, the eigenstructure assignment methodis used in this paper. Using the eigenstructure assignmentmethod, the observer gain L and the post filter V are obtainedby the following theorem [31], [32].

Theorem 1: If a system (7) fulfilled assumption describedbelow,• Assumption 1: (A,C) is observable• Assumption 2: rank(C) is equal to the number of mea-

surements• Assumption 3: rank(P = CEf ) is equal to the number

of faults• Assumption 4: The system (A,Ef , C, 0) is minimum

phasethe observer gain L and post filter V are then given as

L = (EfΛ−AEf )(P )† +R(I − PP †) (11)

V = MP † + S(I − PP †) (12)

where Λ = diag(λ1, λ2), λi < 0, M = diag(m1,m2) andP † = (PTP )−1PT is the Moore-Penrose pseudoinverse ofmatrix P . In addition, R and S are arbitrary matrices.As a result, if there exist L and V , then the transfer matrixGrf is given as

Grf (s) =

[gs 00 gu

](13)

where gs = m1

s−λ1and gu = m2

s−λ2.

According to (7), the number of faults and the number ofmeasurements are equal. Thus, the matrix P is square andinvertible, and therefore (I − PP †) is a zero matrix. Thismeans that L and V are uniquely determined when Λ andM are given. It is noteworthy that since the fault isolation ob-server does not satisfy perfect fault isolation with an unknowninput decoupling (PFIUID) condition (rank

[Grd Grf

]=

rank(Grd) + rank(Grf )), the observer cannot decouple theunknown disturbance Eaug . In conclusion, the problem of

designing robust fault isolation observers is the same asdetermining Λ and M to make the observer robust againstunknown disturbances. At the same time, the fault sensitivityperformance should be considered. This paper uses the H−and H∞ performance indexes [33]–[36] to evaluate the per-formance of FIO. These performance indexes are defined as

‖Grf (s)‖− = infω∈[ω1,ω2]

σ−(Grf (jω)) (14)

‖Grd(s)‖∞ = supω∈[ω1,ω2]

σ−(Grd(jω)) (15)

where σ− is the largest singular value of Grd, σ− is the small-est singular value of Grf , and ω1 and ω2 are the minimum andmaximum frequencies of the frequency range of interest. Notethat ‖Grf (s)‖− denotes the minimum influence of the faulton the residual signal over the frequency range of interest.Similarly, ‖Grd(s)‖∞ denotes the maximum influence of thedisturbance on the residual signal over the frequency rangeof interest. Generally, these two performance indexes have atrade-off relationship. Therefore, it is impossible to design anFDI algorithm that is both robust to disturbances and sensitiveto faults. However, if the performance of the FDI algorithm isdefined as H−/H∞, then an optimized FDI algorithm usingthis performance index can be designed. In this paper, theeigenstructure Λ is set considering the performance index inthe frequency range from 0.2hz to 20hz where the drivingquality is mainly evaluated. Fig. 3 and Fig. 4 show theperformance indices of residual 1 and residual 2 obtainedby theorem 1 and the quarter-car model properties in TableI. Based on these results, the eigenstructure Λ is defined asdiag(−1,−0.35) and M is defined as an identity matrix. As aresult, the observer gain L and the post filter V of the observerbased residual generator are as follows.

L =

0.0920 0.0027−0.5368 0.10960.3697 0.10650.1289 −0.9628

(16)

V =

[−0.4632 −0.1096−0.3682 −0.1062

](17)

0.04165

0

0.0417

0

0.04175

-0.2

Residual 1 Performance Index

λ2

-0.5-0.4

λ1

0.0418

-0.6

-0.8-1 -1

Fig. 3. Performance index for residual 1.


0.0417

0

0.04171

0.04172

0

0.04173

0.04174

-0.2

Residual 2 Performance Index

λ2

-0.5

0.04175

-0.4

λ1

0.04176

-0.6

-0.8-1 -1

Fig. 4. Performance index for residual 2.

B. Residual evaluation based on SVM

Ideally, if there are no faults, the residuals from the residualgenerator have to be zero. However, in the real world there arealways unexpected model uncertainties, unknown inputs andnoise. Therefore, the residual evaluator is necessary to ensurethe robustness of the fault diagnosis algorithm. Most residualevaluations are performed using fixed thresholds. However, ittakes a lot of effort to determine the thresholds for optimalperformance. Moreover, fixed thresholds are vulnerable tomodel uncertainty and disturbance that are not considered.Although an adaptive threshold concept was proposed insome previous studies, designing adaptive thresholds is stilla difficult task.Therefore, this paper proposes a SVM based residual evalua-tion method. SVM is a kind of machine-learning algorithmoptimized for classification and requiring a small data set.Therefore, it can be concluded that SVM is an appropriatemethod to evaluate the residual signal. Fig. 5 shows the

0 1 2 3 4 5 6 7 8 9 10

Feature 1

0

2

4

6

8

10

12

14

16

18

20

Fe

atu

re 2

2-D classification

Decison Boundary

support vector

geometrical

margin

Fig. 5. Basic concept of support vector machine.

concept of the SVM classifier. In this figure, the positiveclass (blue-o) and negative class (red-x) are separated by thedecision boundary. The decision boundary can be described asa hyperplane, as follows:

f(x) = wT · x + b = 0 (18)

where x is a features of the data, w is the normal vector of thehyperplane, and b is the bias factor. To classify the dataset, thelabels are assigned as yi = 1 for a positive class and yi = −1for a negative class, where i = 1, 2, ..., N , N is the numberof data sets, and the hyperplane must satisfy the followingconstraints:

f(xi) = 1 if yi = 1f(xi) = −1 if yi = −1

(19)

These two constraints can be presented in a simple equationas follows:

yi(wT · xi + b) ≥ 1 (20)

SVM is based on the structural risk minimization principle[25]. Therefore, it is necessary to solve the optimizationproblem in order to find the optimal decision boundary havingthe maximum classification margin. The classification marginis described as the distance from the nearest dataset to thehyperplane. In the SVM theory, the nearest dataset is nameda support vector. The distance r between the support vectorx and a point on the hyperplane xh is expressed as shownbelow.

x = xh + rw

‖w‖(21)

f (xh) = 0 (22)

By substituting (21) and (22) into (18), the following equationis obtained:

f(x) = wT ·x+ b = wT ·(xh + r

w

‖w‖

)+ b = r ‖w‖ (23)

Therefore,

r =f(x)

‖w‖(24)

As a result, the problem of maximizing the distance r can beexpressed as follows.

minw,b

1

2‖w‖2 subject to (wT · x + b)y ≥ 1 (25)

To apply this theory in the real world, the noise and reliabilityof the data set should be considered. Therefore, in most SVMapplications, a slack variable is assigned to handle errors inthe data set. Consequently, the optimal decision boundary canbe obtained by the following problem:

minw,b

12 ‖w‖

2+ C

N∑i=1

ξi

subject to

{(w · xi + b)yi ≥ 1− ξi

ξi ≥ 0

(26)

In addition, using the mathematical techniques such as theLagrangian multiplier and the Karush-Kuhn-Tucker (KKT)condition [37], the optimization problem (26) can be convertedas follows [24]:

minL(w, b, ξ, α) =1

2‖w‖2

+ C

N∑i=1

ξi − αiyi(wT · x + b− 1 + ξi) (27)


Using the KKT condition to eliminate the duality gap,

∂L

∂w= 0,

∂L

∂b= 0 (28)

αi ≥ 0 for ∀i (29)

αi((wT · xj + b)yj − 1) = 0 for ∀i (30)

Therefore,

w =

N∑i=1

αiyixi,

N∑i=1

αiyi = 0 (31)

Consequently, using (31) and (27), the quadratic optimizationproblem is obtained by

maxL(α) =N∑i=1

αi − 12

N∑i=1

N∑j=1

αiαjyiyjxiTxj

subject toαi ≥ 0,N∑i=1

αiyi = 0

(32)

The above optimization problem can only be applied to clas-sification problems with a linear decision boundary. However,with kernel functions [25], a nonlinear decision boundary canbe designed while maintaining this concept. Based on thekernel function, the optimization problem (32) can be rewrittenas

maxL(α) =N∑i=1

αi − 12

N∑i=1

N∑j=1

αiαjyiyjK(xi,xj)

subject toαi ≥ 0,N∑i=1

αiyi = 0

(33)

In this paper, a residual evaluation is conducted by SVMusing different kernel functions such as linear, polynomial,Gaussian RBF. In order to reduce the effect of sensor noise,preprocessing such as low pass filtering is performed. Thefeature for SVM learning consists of the mean and varianceof a scaled residual, which is commonly used in previousmachine learning applications. In the following section, theresidual evaluation performance of SVM is verified using well-known performance measures for machine learning.

IV. EXPERIMENTAL VALIDATION

In this section, an experimental validation is conductedusing a quarter-car test rig. This section is organized asfollows. First, the performance of FIO proposed in this paperis verified using experimental results. The experimental roadinput consists of sine wave, sine sweep and rectangular wavemodes. Next, SVM learning is conducted using the sensorsignal and the residual signals obtained with the proposed FIO.Finally, the performance of the residual evaluator is measuredusing well-known machine learning performance indexes.

A. Experimental set-up

To verify the proposed FDI algorithm, a quarter-car test rigis used, which is used widely to develop suspension controlsystems in many previous studies. In this study, the frontsuspension of a Hyundai Genesis Coupe (midsize coupe) isused. In order to obtain actual states such as the suspensiondisplacement and relative velocity, a linear variable differential

TABLE IIEXPERIMENTAL SCENARIOS

Case Road input Frequency range of interest1 Sine wave Low2 Sine sweep Mid range3 Rectangular wave High

transformer (LVDT) (SLS130) is attached to the suspension.In addition, to ensure practicality of the proposed algorithm,a MANDO accelerometer, which is actually used in theHyundai Genesis Coupe, is attached to a sprung mass andan unsprung mass. The measuring range of the sprung massaccelerometer is ±2g and the measuring range of the unsprungmass accelerometer is ±50g.The experimental validation is performed under three roadsurfaces. First, a low frequency sine wave road test with anelevation of +0.02 meter to -0.02 meter was performed to eval-uate the performance of the proposed FDI algorithm in a lowfrequency range. Nest, a sine sweep road test with an elevationof -0.018 meter to +0.018 meter was performed. Finally, arectangular wave road test with an elevation of -0.02 meterto +0.02 meter was performed to evaluate the performanceof the proposed FDI algorithm in a high frequency range.The sensor faults are implemented with a data acquisition unitconsisting of Micro AutoBox, Matlab&Simulink and LenovoThinkpad. Fig. 6 shows the experimental equipment and TableII summarize the experimental scenarios to verify the faultdiagnosis performance. The physical characteristics of thequarter-car test rig are listed in Table I.

Fig. 6. Overall experimental scheme.

B. Experimental results

1) Case 1 - Sine wave test: Fig. 7 shows the results of thesine wave test. In this test scenario, a +0.5m/s2 fault signalis added to the sprung mass accelerometer at four secondsand this fault signal is also added to the unsprung massaccelerometer at 17 seconds. To emphasize the performance ofthe model-based fault diagnosis algorithms, this paper did notconsider fault signals such as signal loss that can be detectedby traditional limit checking methods. According to the testresults, it is verified that residual 1 responds only to a faultin the sprung mass accelerometer. Likewise, the other residualresponds only to a fault of the unsprung mass accelerometer.


0 10 20 30 40 50 60

time[s]

-5

0

5

10

accele

ration[m

/s2]

(a)

as

au

0 10 20 30 40 50 60

time[s]

0

0.5

1

1.5

2

|resid

ual|

(b)

r1

r2

as fault occurs

au fault occurs

Fig. 7. Sine wave test results for fault detection and isolation: (a) Raw sensorsignal of sprung mass accelerometer (as) and unsprung mass accelerometer(au) (b) Absolute value of residual 1 (r1) and residual 2 (r2).

This phenomenon appears prominently between four and 17seconds in Fig. 7. In accordance with this experimental results,it is confirmed that the observer gain (16) and the post filter(17) obtained using theorem 1 make the fault transfer matrixa diagonal matrix, as in (13). The experimental results showthat there is a slight response delay in the residual signal sincethe signal preprocessing process such as low pass filtering.

0 2 4 6 8 10 12 14 16 18

time[s]

-40

-20

0

20

40

accele

ration[m

/s2]

(a)

as

au

0 2 4 6 8 10 12 14 16 18

time[s]

0

0.5

1

1.5

|resid

ual|

(b)

r1

r2

as fault occurs

au fault occurs

Fig. 8. Sine sweep test results for fault detection and isolation: (a) Raw sensorsignal of sprung mass accelerometer (as) and unsprung mass accelerometer(au) (b) Absolute value of residual 1 (r1) and residual 2 (r2).

2) Case 2 - Sine sweep test: Fig. 8 shows the results of thesine sweep test. In this test scenario, a +0.5m/s2 fault signalis added to the sprung mass accelerometer at two secondsand this fault signal is also added to the unsprung massaccelerometer at seven seconds. Unlike the sine wave test incase 1, the signal range of the unsprung mass accelerometeris as large as ±30m/s2. The experimental results show thatresidual 1 responds only to a fault of the sprung massaccelerometer and residual 2 responds only to a fault of theunsprung mass accelerometer. Fig. 8 shows that the residual 2tends to increase finely between 0 and 7 seconds. This is dueto the initial sensor bias in the unsprung mass accelerometer.This sensor bias is converted to a bias of residual 2.

0 2 4 6 8 10 12 14 16 18

time[s]

-30

-20

-10

0

10

20

30

accele

ration[m

/s2]

(a)

as

au

0 2 4 6 8 10 12 14 16 18

time[s]

0

0.5

1

1.5

2

|resid

ual|

(b)

r1

r2

as fault occurs

au fault occurs

Fig. 9. Rectangular wave test results for fault detection and isolation: (a)Raw sensor signal of sprung mass accelerometer (as) and unsprung massaccelerometer (au) (b) Absolute value of residual 1 (r1) and residual 2 (r2).

3) Case 3 - Rectangular wave test: Fig. 9 shows the resultsof the rectangular wave test. In this test scenario, a +0.5m/s2

fault signal is added to the sprung mass accelerometer atthree seconds and this fault signal is also added to theunsprung mass accelerometer at nine seconds. In accordancewith the experimental results, it is verified that FIO has robustperformance against high frequency road input. As in case 2,residual 2 showed a slight increase between 0 and 9 secondsdue to the initial sensor bias. This experimental results showthat the disturbance effect on the residual is attenuated ascompared with the low frequency road surface test such as case1. This is because the fault transfer matrix (13) is in the formof a first order low pass filter. In addition, the preprocessingof the residual signal also reduces the effect of high frequencydisturbance.

C. Residual evaluation result

In this paper, the authors propose to evaluate the residualsignal obtained by FIO using the SVM classifier. This section


presents and discusses the residual evaluation results obtainedusing various SVM classifiers with different kernel functions.The data set for learning the SVM classifier is obtained byvarious experiments using quarter-car test equipment. Sensorsignals and residual signals obtained from various experimentswere classified as faulty data and healthy data respectively andused for learning. In this paper, 189003 data sets were usedand the standard deviation and mean value of each data setwere chosen as the features to be used for SVM learning.In order to verify the performance of the SVM based residualevaluation, five-cross validation and the F0.5-Measure areused. Generally, the fault diagnosis algorithm used in vehiclesystems should be designed to minimize false alarms wherefaults are detected in the absence of actual faults. Therefore,it is reasonable to use the F0.5-Measure, which emphasizesprecision rather than recall, to evaluate the performance of thefault diagnosis algorithm. In this paper, various types of SVMclassifiers are constructed using Matlab & Simulink quadraticprogramming solver.Table III and Table IV show the classification results using

TABLE IIISVM CLASSIFIER PERFORMANCE OUTCOMES FOR RESIDUAL 1

Kernel function Kernel scale F0.5-MeasureLinear - 0.997Quadratic - 0.997Gaussian RBF 0.5 0.998Gaussian RBF 2 0.999

TABLE IVSVM CLASSIFIER PERFORMANCE OUTCOMES FOR RESIDUAL 2

Kernel function Kernel scale F0.5-MeasureLinear - 0.994Quadratic - 0.996Gaussian RBF 0.5 0.996Gaussian RBF 2 0.997

SVM classifiers with various kernel functions. As presentedin the tables, the SVM based residual evaluator achieveshigh accuracy. Since the initial bias is on the unsprung massaccelerometer, the classification performance for residual 2 isslightly lower than the classification performance for residual1. Overall, the SVM classifier achieved high accuracy. Inorder to investigate the effect of residuals on fault decision,SVM leaning was conducted using only sensor signals with noresiduals. From the results of SVM leaning without residuals,the SVM classifier accuracy is around 0.75. In conclusion,it is confirmed that residuals have a positive effect on SVMclassifier learning.Fig. 10 and Fig. 11 show confusion matrices of the SVMclassifiers for residual evaluation. These figures show thatas the nonlinearity of the decision boundary increases, falsepositive error tends to increase. Generally, a nonlinear deci-sion boundary exhibits higher accuracy than linear decisionboundaries, but over fitting can occur. In conclusion, the falsepositive error in Fig. 10 and Fig. 11 is due to overfitting. Asmentioned above, the fault diagnosis algorithm used in vehiclesystems should be designed to minimize false positive errors.

In accordance with Fig. 10, neither the linear nor quadraticSVM classifier exhibits false positive error.Fig. 12 and Fig. 13 show the residual evaluation results of

Fig. 10. Confusion matrix of SVM classifiers for evaluation residual 1: (a)Linear SVM (b) Quadratic SVM (c) Gaussian RBF SVM with Kernel scale= 2 (d) Gaussian RBF SVM with Kernel scale = 0.5.

Fig. 11. Confusion matrix of SVM classifiers for evaluation residual 2: (a)Linear SVM (b) Quadratic SVM (c) Gaussian RBF SVM with Kernel scale= 2 (d) Gaussian RBF SVM with Kernel scale = 0.5.

the sine wave and sine sweep experiments. Note that theseexperiments are conducted in order to verify the performanceof the SVM based residual evaluator. Therefore, the data setsof these experiments are different from the learning data.In these experiments, a +0.5m/s2 fault signal is added tothe sprung mass accelerometer at five seconds and this faultsignal is also added to the unsprung mass accelerometer at 10seconds. According to the experimental results, false alarms donot occur and error cases consist only of false negative error.This false negative error is caused by the residual responsedelay due to the preprocessing such as low pass filtering. Inconclusion, the SVM based residual evaluator presents reason-able performance for a vehicle suspension sensor system.Fig. 14 and Fig. 15 show the residual evaluation resultsfor signal loss fault. According to Fig. 14, the sprung massaccelerometer signal is lost at seven seconds and this signalis recovered at 15 seconds. In this experimental scenario, theunsprung mass accelerometer is fault free but residual 2 is


not zero due to the sensor bias. However, the fault index Fuis zero during the experimental scenario. This experimentalresult show that the SVM-based residual evaluation algorithmmakes accurate decision despite the presence of unconsideredsensor bias. Likewise, according to Fig. 15, the unsprungmass accelerometer signal is lost at seven seconds. In thisexperimental scenario, the sprung mass accelerometer is faultfree and the fault index Fs is zero during the experimentalscenario same as Fig. 14.Fig. 16 and Fig. 17 show the residual evaluation results forrandom noise fault. According to Fig. 16, the sprung massaccelerometer signal is contaminated with random noise at 12seconds. Likewise, according to Fig. 17, the unsprung massaccelerometer signal is contaminated with random noise at12 seconds. As a results of these experiments, it is concludethat the proposed fault diagnosis algorithm has robust perfor-mance for random noise fault. Consequently, the experimentalresults show that the proposed residual evaluation method hasreasonable performance against unconsidered sensor bias anduntrained type of fault.It is note worthy that the SVM classifier used in this paper doesnot learn about signal loss fault. In general, machine learningalgorithms are vulnerable to untrained data types. However,the proposed SVM classifier uses the residuals obtained bythe model-based fault diagnosis technique in the learningprocedure. This can complement the weaknesses of traditionalmachine learning algorithms and show reasonable performanceagainst untrained type of fault.

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Fig. 12. Experimental result for sine sweep test: (a) Raw sensor signal ofsprung mass accelerometer (as) and unsprung mass accelerometer (au) (b)Absolute value of residual 1 (r1) and residual 2 (r2) (c) Fault indicator forsprung mass accelerometer (Fs) and unsprung mass accelerometer (Fu).

V. CONCLUSION

In this paper, a fault diagnosis algorithm for a vehiclesuspension sensor is proposed. The proposed fault diagnosis

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Fig. 13. Experimental result for sine wave test: (a) Raw sensor signal ofsprung mass accelerometer (as) and unsprung mass accelerometer (au) (b)Absolute value of residual 1 (r1) and residual 2 (r2) (c) Fault indicator forsprung mass accelerometer (Fs) and unsprung mass accelerometer (Fu).

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Fig. 14. Experimental result for signal loss(sine sweep test): (a) Raw sensorsignal of sprung mass accelerometer (as) and unsprung mass accelerometer(au) (b) Absolute value of residual 1 (r1) and residual 2 (r2) (c) Fault indicatorfor sprung mass accelerometer (Fs) and unsprung mass accelerometer (Fu).

algorithm consists of FIO that generates a residual signaland a SVM based residual evaluator. Using the eigenstructureassignment method and H−/H∞ performance index, FIO,which is both robust against unknown disturbance and sensi-tive to sensor fault, is designed. In addition, using the residualsgenerated by FIO for SVM training, this paper combinesmodel-based fault diagnosis with machine learning based fault


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Fig. 15. Experimental result for signal loss(sine wave test): (a) Raw sensorsignal of sprung mass accelerometer (as) and unsprung mass accelerometer(au) (b) Absolute value of residual 1 (r1) and residual 2 (r2) (c) Fault indicatorfor sprung mass accelerometer (Fs) and unsprung mass accelerometer (Fu).

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Fig. 16. Experimental result for random noise fault(sine sweep test): (a)Raw sensor signal of sprung mass accelerometer (as) and unsprung massaccelerometer (au) (b) Absolute value of residual 1 (r1) and residual 2 (r2)(c) Fault indicator for sprung mass accelerometer (Fs) and unsprung massaccelerometer (Fu).

diagnosis. This paper also validates the performance of FIOand SVM based residual evaluator using a quarter-car test rigand commercial sensors. From the results, it is confirmed thatan isolated residual signal is generated by FIO regardless ofan unknown disturbance. Furthermore, it is verified that theSVM based residual evaluator has high accuracy for various

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Fig. 17. Experimental result for random noise fault(sine wave test): (a)Raw sensor signal of sprung mass accelerometer (as) and unsprung massaccelerometer (au) (b) Absolute value of residual 1 (r1) and residual 2 (r2)(c) Fault indicator for sprung mass accelerometer (Fs) and unsprung massaccelerometer (Fu).

road inputs and robust against untrained type of fault.This paper provides the following contributions. First, theproposed fault diagnosis algorithm considers a practical sus-pension sensor system. A commercial accelerometer used inpractical fields is used to verify the performance of the faultdiagnosis algorithm. In addition, using a quarter-car test rigand the commercial accelerometer, the practicality of theproposed fault diagnosis algorithm is confirmed. Next, theproposed fault diagnosis algorithm can be used in any kind ofsemi-active suspension system. Since the bilinear term coupledwith control input and unknown system state is converted tomodeling uncertainty, it is possible to adopt the proposed faultdiagnosis algorithm when the damping coefficient range ofthe vehicle suspension system is known. Finally, this paperverified that the SVM based residual evaluator can replace theheuristically tuned residual threshold. It thus becomes possibleto reduce the effort required to design fault diagnosis algo-rithms. In conclusion, the proposed fault diagnosis algorithmcan be used to detect sensor faults in vehicle suspension.

ACKNOWLEDGMENT

This work was supported by the Technology InnovationProgram (or Industrial Strategic Technology DevelopmentProgram (10084619, Development of Vehicle Shock Absorber(Damper) and Engine Mount Using MR Fluid with YieldStrength of 60kPa) funded By the Ministry of Trade, Industry& Energy (MOTIE, Korea); the BK21+ program through theNRF funded by the Ministry of Education of Korea; theNational Research Foundation of Korea(NRF) grant fundedby the Korea government(MSIP) (No. 2017R1A2B4004116)


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Kicheol Jeong received his B.S. degree in Mechan-ical Engineering from Hanyang University, Busan,South Korea, and M.S. in Mechanical Engineeringfrom the Korea Advanced Institute of Science andTechnology (KAIST), in 2015 and 2017, respec-tively. Since 2017, he is currently pursuing thePh.D. degree in Mechanical engineering at KAIST.His research interests include vehicle dynamics andcontrol, fault diagnosis and control theory.

Seibum B. Choi received B.S. degree in mechanicalengineering from Seoul National University, Korea,M.S. degree in mechanical engineering from Ko-rea Advanced Institute of Science and Technology(KAIST), Korea, and the Ph.D. degree in controlsfrom the University of California, Berkeley in 1993.Since 2006, he has been with the faculty of theMechanical Engineering department at KAIST. Hisresearch interests include fuel saving technology,vehicle dynamics and control, and application ofself-energizing mechanism.


Hyungjeen Choi recieved B.S degree in Mechani-cal Engineering and Electronics(minor) from Dong-guk University, Korea, M.S degree in Mechatronicsfrom Gwangju Instutitue of Science and Technology,Korea, and is currently pursuining PhD degree inMechanical Enginnering in Korea Advanced Insti-tute of Science and Technology (KAIST), Korea.He has joined Korea Automotive Technology In-situte(KTAECH) since 2004. He is focusing onvehicle dynamics and control, active control sys-tem, advanced driver assistnace system(ADAS), au-

tonomous vehicle control, and micro-mobility.

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