Fault Detection for Lateral and Vertical Vehicle Dynamics

ELSEVIER

Copyright © IFAC Mechatronic Systems, Sydney, Australia. 2004

IFAC PUBLICATIONS www.elsevier.comflocatelifac

FAULT DETECTION FOR LATERAL AND VERTICAL VEHICLE DYNAMICS

R. Iscrmann, D. Fischcr. M. Blirner, J. Schmitt

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Abstract: Model based IIlethods have beell developed for sensor and process f~ lult delectlon and diagllosis of all acti\'e hydraulic suspellsion system. Dynamic mathematical nlodels are used for describing the lateral \'ehiele beha\lor and vertical behavior of :111 ;Icli\e sllspension ill re;ll-time . Based on parameter estimation ,lIld parity equations S\, llIptoms for fault delection are generaled . This is follo\led by fault diagnosis \I'i lh fuzz\' logic . Results are presented for measurements \11th a vehicle and a suspension lest rig. The fault detection method is intended to be used for lI1ec\t:ltronic suspeusiOilS. driver assist;lllCC . ,lIld \'chicle control systems. C0l'vrighl ,f , ]()/)-! fr.·j(' KCy\lords: Fault Delcction. ParilY Equation s. Parameter Estimation. Vehicle Dynamics. Ac ti\e Vehicle Suspension

INTRODUCTION IVleclwtrollie S\SleIllS for \ehicles h;l\ e recei\ed increased illlpol1anee for improving ;IIIIOll1otl\e safety ;lIld co III fort. Thcse systems are designed to aid the driver by pre\ellting IInstable or unpredict,lble vehicle beh;l\ior and to stabili7.e the \ehicle's horizontal alld \'Crticallllotlon . Acl\,lIIced lIleehatronic \'Chielc s\stellls include a \:Iriet, of aetu;ltors and sensors. The mechatronic inlegratlon of these actHators. the involved sensors :md electronic control unit s IllCrC;ISe the system ' s performance. dri\ing range. and safCty. Ho\\e\'er. these benefits ,ne paralleled by an increase of the comple:\lty of the system As a result. hllllt detection ,md di;lgnosis becomes 1I10re illlPOrt:lI1t (lsen11al1ll 2()()()) This cOlllribtltion describcs ,I model-based falllt detection approach for \ehicle horizontal und Ycrt ica I d\'llamics.

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Fig . I: Fau lt detectioll and diagnosis of the lateral behaviour based on signal and process models. ,irtual "altle is calcul.lted to enable a reconfiguration . The entire scheme is shO\\I1 in Fig. 1.

2. F AUL T DETECTION FOR LATERAL VEHICLE D'{NAl\lICS

2.1

The de\eloped partty equations are based 011 analytic models of the lateral \chicle dynamics. sce e.g. lsermanll ('I al. 2()()~. Four different models calculate each sensor signal "ith different inputs lIsing analytical redund;llIcics. compare T;lble 1 The outputs of the t\lehe resulting IlIodels S,,,,,,/.,(I) arc compared with the measured sensor Signal s,"cu.<.,(1) yielding the output residuals 1',(/)

Tlte input signals for the presented fault detection alld diagnosis system are oblained by the standard sensors of the ESP-Systcm (Eh'llrtJlllc-,\laiJility/'mgrilll/): Thc stecring "hcel angle b~,. the ABS\\heel speeds I'". the lateral acceleration I). and the y,lII rate Ij/. The scnsors and also t lie lateral driving beltavlOr arc mOllitored applylllg signal and modelb,lscd methods . In case of a l;lUlt\ scnsor signal a

549

(1)

Residuals r, ... r" arc related to the yaw rate. r, ... rR to the lateral acceleration, and r9... r,: to the steering IV heel angle models.

Parameter a enters proportional into the weighting of onc fault imd is chosen e:-.:perimentally (St6lzl 2000). Eq. (·n yields directly to the following statements: • if the ASS wheel speed signal information Vi come close to each other. it follows 1I' Fl. ~ l"fon ~ II'IIL ~ H'RJi ~

•

1

if l 'n .. V IR. and " HR approaching each other. and I'HI. is diverging from the common value. follows lI' FL

~

lI 'FR

~

~ I. and II' RI. ~ ()

lI 'ru!

Two ne,,' residuals arc defined :

j

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~r .~

-

~ V ( , + ~J' V,\

'"-",

- v."

(5)

bp'

...

.1'., = 'P'"

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For instance. a faull of the front left wheel speed sensor yields residual rl :< < D.

=~ . ';F v""

2.3 1)

f)iagll().\·/.\·

Weighting o/AB.':.' wheel :;peed signals:

The ground velocity v can be calculated averaging the four wheel speed signals

(2) 4 v

=(j)

'r

(3 )

with (j) as rotational speed and r as dynamic tire radius . After a fault in thefroll/lefi "heel speed sensor " 1'1. . all rcsiduals except rcsidual exceed its nominal \;!Iues (sec Table I) . Hence. a di stinction between faulls in the left or right hand side of onc axle is not possible by this simple way. Therefore. the deviation of all ASS signals to each other is takcn into account to distinguish bet,,'een sensor faults of the front left or front right sensor signals or rear left or rear right sensor signals respectively. Therefore. a weighted fa c/ur l'ofer is used (Sroell . 1975). The weighted factor Yoter is based on a weighted mean calculation from four measured sensor signals. Faulty sensor si gnals arc then weighted ill dependence on the fault amplitude. After exceeding of a certain t1u·eshold. a sort masking in dependence on the fault size is used (similar to the principle of fu zzy logic) . The weights lI 'n. H' FR. H'RL ulld H'RR of each ASS \rheel speed sensor VFL . " FR . I'RL and VRR arc now calculated in the range between zero and onc according to its fault size. The more a signal distinguishes from the others. the smaller the corresponding weight

r,

lI ' ,

i

Table 2: Fault sVlllptOIll relationships, Influences of different sensor faults on the estimated symptoms ,be .;,.' ,,,, ';&\IlUpI.,...• ;. I i'ij>.,<~,,;: . . . . ,':!",.;.,.~L~.. ,,""';;" .i'i' ,. ~~~~~\ ' .. ,

..==/

=--------- - - -_:_ I+

IT

(~~.~~)'

Ic iH. FR.RLRR f.i,1

a

The twelve calculated residuals ri(t) arc then used for the fu zzy logic fault diagnosis. Table 2 shows ho\\ different sensor faults affect the symptoms. A different patlem appears for each fault. The processing of Table 2 is performed by a fuzzy logic system. For the residuals of the ya\\ rate models. the lateral acceleration models. and the steering wheel angle models three trapezoid membership functions arc applied such as " residual positive". " residual zero". and " residual negative". Two symmetric membership functions arc applied for the residuals r" and rl 4 Thc mles of the fn zzy systcm arc given "ith AND connections of the linguistic formulations. The outputs arc singletons describing the flllfilllllent of the mic in form of a possibility. The maximal value of the possibility is then further used . As a result. 14 different sensor faults and a noonal driving condition can be classified. A critical driving situation exists if no

(4)

= FL. FR.RL.RR

550

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lateral act tl. 9-&ij

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F7

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F8

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norm.1 driving situalion

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()

0

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0

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I)

0

no detl ectlOl1 ±L'. pOSitive or negative ons et of st!nsor Signal

normal driving situation and no scnsor fault is classificd. Thc automatcd fault diagnosis show cd vcry good rcsults during scvcraltcst-drives. Thc robustncss to falsc alanns is achicvcd by taking into account scnsor faults grcatcr tllan 10%. during nonnal opcration and non-critical dliYing situations. [n addition to scnsor fault diagnosis a monitoring systcm for critical driving situations mls dcvclopcd bascd on the characteristic velocJly. Borncr et al. 2()()2. ] -I

widely (Rajamani and Hedrick 1995). [n the [ollowing. model based fault detection methods arc applied to an active vehicle suspension system on a tcst rig.

3.1

Examp/e (J/OII ac tive SI/,lpellSiuII svstelll

The investigated activc suspen sion is a flll1y loaded hydraulic system . Fig. 3. It consists of a hydraulic cyl i nder. "hich is constructed as a plungcr and is connected in series to a steel spring. The damper direetly connects the body and the \\"heel mass. This asscmbly is equivalent to the Active-Body-ControlSystem of DaimlerChryslcr (e .g. Mercedes CLClass) . The plunger is connected to a motor-pumpunit. which provides a controlled hydraulic flow [rom/ to a hydraulic accumulator. The test rig demonstrates a quarter o[ a real car " 'ith suspension anns. a rcal tire and an appropriate body mass. A realistic road excitation is simulated by thc vertical movement of the base plate. Thc test rig is equipped "ith a variety of sensors. ,,·hereas the presented algorithms are based on a min imal sensor setup due to automotive requirements. The sensor setup complies scnsors for the suspcnsion dellection ZWIJ . the body accelcration i Jj . and the motor speed liJM . voltage I/ ~ I. and current i M . The applied controller is a statc space controller with pole placement dcsign.

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A faull-tolerant scnsor system should at least be failopcrational for one sensor falllt. Thi s can bc obtaincd by applying at Icast thrcc scnsors or analytic rcdundancy \rilh process models and [ault detcetion. ISenmlllll et of. 2002 . The [alllty scnsor has to be excluded fram c.g. drivcr assistancc systems within 250 ms. Van Zilntcn et of. I ~9X. Thc decision \rhcn a scnsor has to bc cxcluded and thc systcm has to be reconfigurcd is done by the fuzzy logie fault diagllOsis system and a fault countcr. A stationary circular lest dri\c. Fig 2. shO\rs thc rcconfiguration o[ the scnsor systcm during an offsct fault in thc lateral ,Iccelcromcter or the yaw ratc scnsor. A nonlincar two-track \·chicle dynamics model is uscd to dcliver an estimatc of thc faulty scnsor. Borncr ,md Iscnnanll 200 .1 .

lIydrnu.lh AI.'ClduflIal(·r .

.\. FAULT DlAGNOS[S FOR VERT[CAL VEHICLE DYNAMIC SYSTEMS

Il yd muli, Lluc

First results on 1~lult detection mcthods for passive and scmi-acti\c suspcnsion s \rcrc published by e.g. Bu~hardt 1995. Maiiad I ~,) 7. Wcispfenning and IserInallll 19'J7. Although a variety of publications exists dealing with control strategies for activc suspensIon systems (e.g . AlIeyne and Hedrick 1995). fault detection for these systems has not been invcsti gatcd

eJl!ctro-

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Thc components of the electra-hydraulic suspension system such as hydraulic accumulator. hydraulic lines. Illotor. pump. plunger and suspension system are 1Il0deled according to Iscrm,ulIl 200.\. for details see Fischer et al. 2004. Considcring a linear spring. a nonlincar (pieccwise square root) damper with Coulomb friction. laminar hydraulic resistance. the motor as DC drive. the hydraulic accumulator as an air spring and the pump as positivc dispbcement pump. thc follO\\"ing equations are derived

----~----I

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Fig . .\ Activc suspension test rig with measured signals (el) and control scheme.

llGg. l~tcr;11 a~ c d ero l1le l e r

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•

.-l

f

liJ(I)dt

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tim" '1' 1 Fig. 2 Reeonfiguration of a sensor system during a) a fault in the lateral acceleration sensor .li b) a fault in the y,l\I rate scnsor Vi

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. .. j

(6)

Square-ROOI-Fi ller-i 11-/Il/iJrmatioll-Furm (lsenmum, 1(92) . . where the forgetting factor \\'as chosen to A. = 0.9999 and A. = 0.99 for the motor equation. The required derivatives of the suspension deflection and the motor speed were determined using state variable filters . The identification results show a fast and converging estimation for all twelve parameters (A and r la have to be known a pliori). Some concrete results arc presented in connection with the fault detection. In general. the comparison of the esti mated values with reference values indicates an accurate estimation and substantiates the correct modeling of the process. ~or fault detection. the online estimated parameters 11 arc compared to reference values S, cl and the differen ces arc used as symptoms for fault detection

(7) . m M (I)

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Falllt defectio/l schellle

The entire fault detection scheme is presented in Fig. -t . The measured signals of the process arc used to generate symptoms using signal and model-based methods. These snnptoms arc then used to classify faults of the process. In case of a detected sensor fault. the system can be reeonfigured and the physical sensor is replaced by an estimated sensor signal on basis of analyti c models. Signal b;lsed symptoms Ss arc generated \yitll low-pass and high-pass filters in order to detect obvious faults such as outliers. noise. and breakdowns. Fiseher el al. 20()-t . The generation of model based symptoms is described in the folio\\'IIIg. The fault detection scheme was applied to test rig data . For this purpose. the base plate of the " 'heel at the test rig \Y;IS excited according to a measured street profile and a speed of 15m/s. The power densi ty spectrum of the wheel movement and the wheel and body mass acceleration show all typical frequencies for a vehicle demonstrating a realistic setup.

,1 ..1

(9)

3. -I

I'ari fy equatiol1s lI'ith semi-physical models

The goal in designing parity equations is to find a set of isolating residual s that shows an unambiguous pattem of deflections for each fault. As this is not fulfilled by the models of Eqs. (G)-(X) . three fmth er models arc obtained by combining thcse equations · with each other. Ho\\ever. the resulting six models shO\\'ed insufficient accuracy for residuals due to unmodeled nonlinearilies and effects of the spring. hydraulic accuJllulator. pump. damper and the suspension transmission ratio . As a con sequence. the semi-physical approach LOLlMOT is applied . \vhich is based on a local linc;u' network. for details sce NelIes 20()O . The input s and output s of the local linear network are defined by the stmcture of the six models according to

Parallleter estimatioll

Based on measurements at the test rig the parameters of Eqs. (6)-(8) arc estimated using the Discrete-

"R (k ) - /, (:WR (k . ... k - ~) . "'1-, (k . .. k ' ~) . 'M (k. . k - 4). :B (k -

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11" (k) -

- I))

/ ;. (:\\,I1(k . .. k - ~). Cd., (k . .. k - 4). 11" (k . ... k - 2))

( I ()

The LOLl MOT nets arc trained with test ri g data and verified "'ith generalization data . The models show nns-values of the relative ClTors at an average of 15'10. Hence. the models arc used for residuals according to Fi g. 5 and Eq . (l) . The models can al so be used as analytic redundancy for sensor reconfiguration. As a signal is invariant to offsets according to

Fig . -t. Fault detection, isolation and reconfiguration concept for the active suspension .

the \'ariances of the residual s arc addition,r1ly used to distinguish bet\\een sensor offsets and gains.

552

the model equations, \\'here these variables arc strongly linked ,yith each other. This phenomenon is already known from passive and semi-active suspension systellls (Weispfenning and Isennann 1(97).

Parity Equation!

a) 1

~ I' FB

:1 0.5 - -

!l(OfTsetIOffset) .

:

.

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:t 0 L-_~.&I.I.':'-''''''~''",

b)

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'. "'-----'J'L"---..........

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0 .5

Fig. 5: Model based fault detection with parity equations. 3.5

...

I· 1

llIM

~1(Gain IO fTsct)

ZWB "

10 ____~. .t . ._.1L. . . .~,_____. . .__'

I )iag/losl.\·

:i

Fig.

T,lble .' sllo\\'s an excerpt from the fault symptom relationship for the motor speed sensor fault and the process fault c10ggillg ill the! oil lille . It summarizes the efTects of various process and sensor faults on the parameter estimations and the residuals. The total fault symptom relationship distinguishes 16 process faults as well as offset and gain faults of the five sensors. for details see Fischer C!I al. 2()().J. . The elements of Table 3 indicate whether a f,nlit influences a symptom with a positive (+). negati\e (-). positive or negative (±). or without any deflection (0). For the eyaluation of T;lble 3 a fuzzy di;lgnosis systelll is applied. for detail s see Fischer er at. 2()()·t

3. (,

fI(Gain IGain)

5

(1.

9 t [s)

7

11

13

15

Fault detection of sensor offset s (a) and gains

(b)

3.7

Enllll/7/e/ilr proceSS/allll dC! rectioll : Clogging

Clogging in the oil line ,yas generated at the test rig by partial closing of a "alve in the hydraulic line be(ween plunger and pUlllp. Fault detection of clogging in the hydraulie lines is essentially based on the estimated hydr,nliic resistanees and on the related parity equations. TIle online estimated hydranlic resistance is presented in Fig. 7<1. The estimated resist,Ulce sho\\s an increased ,,
Ue lC!ctioll alld diagllosis o(se!lIsor/CI/I/rs

For the demonstration of the correct diagnosis of all se nsor faults. offsets and gains are applied to all sensor signals. The offsets refer to G% of the total sensor range and the gain faults refer to a multiplication of the signal by J .3 . TIle results are presented in Fig. G. The results ,u(OffsetIOffset) describe the fault possibility for an offset fault in case of an existing offset fault. Those values have to be higher than the possibility for all offset fault in case of a gain fault ,u(Offset IGaill) of the same sensor for an unambiguous detection. Both. offset faults and sensor faults arc detected and unambiguously classified for all sensors with the presented approach . Only faults in the sensors for body acceleration and suspension deflection slimy reduced diagnosis sharpness. This cOllies from

~()8 , 1; (Ui -

.Clogging.. _ .. : _____:__ ~.

)~

~1

~


~ 0.4 0 -l

f-X fir I

:::::;'

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-x

to

t2

t4

t8

t6

20

22

t[sJ

Fig. 7: Fault detection of clogging in the line between plunger ;U1d pump.

Table 3: Exceq;)t from the fault symQtolll relatiollshiQ. Symptoms

Faults Clogging Offset 11J,I/ Gain l1Jl/

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Variances

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deflection and demonstrates that this fault can be classificd. Similar results could be obtained for the following process faults that could be introduced to the test rig: inner pump leakage. trapped air. ,rinding rapture. gas leakage of the hydraulic accumulator. for details sce Fischer and Isermann 200-1- .

REFERENCES Alleyne. A. und 1. K. Hedrick (1995): Non-linear Adaptive Control of Active Suspensions. IEEE Transactiulls Ull ('ulltrol Svstel1ls Techllulogy, 3 (I) .

Borner. M .. L. Andrcani, P. Albertos und R. Isermann (2002): Detection of Lateral Vehicle Driving Conditions Based on the Characteristic Velocity. IF.,,/, C Worldcungress. Barcelona. Spain. Borner. M. und R. IscflnalUl (2003) : Supervision, Fault Detection. and Sensor Fault Tolerance of Passenger Cars. 5th JF·I (' .':>:vmposilll7l Oil Fallll Detec-

-1- . CONCLUSION

The presented results arc an extract for the fault detection and diagnosis for lateral and vertical vehicle clvlulInics . It is demonstmted hO\l different sellsor and process faults arc detected using physical models or the meehatronic systems to estimate parameters and to design parity equations. The generated symptoms can be used for early fault deteetioll to prevent f~ lilures of automotive mechatronic systems. Especially the combination of parameter estimatioll and p:lrity equations turned out to be useful. This also allows the detection of intennitlent and creeping process faults. In the case of sensor raults the implied analytical redundancy of vehicle models can be used to design fault-tolerant systems with \ 'irtual sensors.

tioll, SlfJ1C'1'visjoll alld .':;af;'~y o('Tec/lIlical Processes, .,):'JF Ef'RO( 'F''-,'):)'. Washington. D.e., USA. BuBhardt. 1. (I ')')5): ,,,'e lhstl'illsfellellde Fi:,derDdJllp!er-.';vsfe/llejiir Krafifahrzellge. Dissertation.

TU Darmstadl. VDI Fortschrittsberichte, Reihe 12. Nr. 2-1-0 . VDI Verlag. Diisseldorf. Fischer. D. und R. iSerlllann (2004) : Model based process fault detection for a vehicle suspension actuator. 1" flltenw/iolla/ .<":VI7lPUSilff1l Oil .-Idvallced r 'ehic/e C'()/I/ro/, ,·1r 'E( '. Arnheim. The Netherlands . Fischer. D .. H. P. Schoner und R. Iscnnann (2004) : Model-Based Fault Detection For An Active Vellicle Suspension . F f,')'J7>1 IVorld A II/OJllofi v(' C'011~re.l'.I' . Barcelona. Iseflnalln, R. (2000) : Diagnosis methods for electronic controlled vehicles. 5th IlIlema/iollal SVl1lpO-

SYMBOLS Symbol Description motor field flux linkage '/' va\l' annle If/ '" mean pUIllP position qJ(l wheel speed, i = n . FR. RL, RR: (1) / Front Lcft/right. Rear Left /Rigllt motor torque constant 'PI I motor speed ('},I ( A plunger cross sectional area spring coefficient CH stiffness of hydwlIlic accumulator c,. . . damper coefficient tiH Coulomb force I~ · motor current ill steering system gear ratio is! .I momcnt of inertia motor length between front and rear axle III /I . 1/1,," body mass, wheel mass ,\ /0 static motor moment armature resistance Nel laminar hydraulic resistance Nh,." Illotor voltage " .11 I' longitudinal velocity characteristic velosity " ,.:h r':IJ volume constallt of pump body height Zu suspension dcflection ::/11'" plun12er position

-

="

Silllll

Unit Vs [rad] I lis

Oil

,..Je/vallced r 'ehic/e ('olltrol (,·1 r EC"20(0).

Ann Arbor. Michigan. USA. Iserlllllilll. R. (20(B) : "[echatrullic :::':vste/JIs: Jilllda/IIelllal,I·. Springer-Verlag. LOlldon . Isermann. R .. 1. Schmitt, M. Borner und D. Fischer (200-1-) : Control of vehicle dynamic systems. IF...J C Svmpos"",' (Ill A/e c/zatrollic ,':,:vstel1ls. Syndney, Australia. Isennann. R .. R. Sclmarz ulld S. Stblzl (2002) : FaultTolerant Dri\'e-by-Wire Systems. IEEE COlltrol

Nml A I Is m~

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.))JsleJIIs ,\ [agazille. 22 (5).

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