Interval Based Fault Detection and Isolation for Vehicle-Dynamics Monitoring

Copyright @ IFAC Mechatronic Systems. Darmstadt. Germany. 2000

INTERVAL BASED FAULT DETECTION AND ISOLATION FOR VEHICLE-DYNAMICS MONITORING Pascal Bouron· Dominique Meizel·

• Heudiasyc/UTC, BP 20529 , F-60205 Compiegne

Abstract: In this paper, we expose a way for detecting component fault and model failures and isolating the cause of the fault by the use of set membership techniques in the case where a non linear model of the process is known. Set membership estimation techniques can inherently detect model failure when the estimated set becomes empty. This property is here applied for fusing parity equations generated by an analytic redundancy study. For each parity equation, one defines a symbolic indicator that individually characterizes a certain or possible failure. Defining a {cause/effect} array makes it possible to isolate the certain or possible causes of the defect. The method is developed within a pedagogical example of the kinematic model of a vehicle and experimental results are exposed. Copyright ©2000 [FAC . Keywords: Interval, Residues, Diagnosis, Fault detection, Fault Isolation.

1. INTRODUCTION

reliable data management protocol that are able to self-detect their failures.

The present study takes place in the trend of the generalisation of mechatronics in the automotive industry. All basic functions such as braking (Daib and Kiencke 1996), engine-control and more elaborated ones like trajectory management (Kiencke 1996, Ackerman 1996) are now designed as closed loop mechanisms. They have first be designed independently as optional devices aiming to improve comfort, security, or to decrease the pollution impacts. The ever increasing worldcompetition in the automotive industry have led to standardize equipment such as ABS. It is reasonable to think that this generalization should be extended to active trajectory-control and GPS based navigation within the next 5 years. Networking these equipments is another basic trend for the simple reason that it cuts down production costs (Thompson 1996). An indirect consequence of sharing these data is the possibility to control and observe higher-level functions. As safety is a mandatory requirement in the automotive industry, smart mechatronic functions must rely on

The work presented in this communication is a first step in this direction. We propose to show how its is possible to use a simple kinematic model of a vehicle to manage the redundancy between data such as accelerations, turning rates, wheels speeds and GPS position with the only assumption that their definition interval is known. Parity equations are revisited in this set-membership context with the aim of detecting sensor faults and model failures.

2. STUDIED PROCESS Consider the experimental car STRADA shown on Fig. 1. Among its sensors, consider the following ones used for monitoring its trajectory and more generally its dynamic behaviour: • 3 accelerometers ±O.lm.s-2 ),

1001

([-20m.s- 2 ,20m.s- 2 ]

,

• 1 gyro ([-100deg.s- 1 ,100deg.s- 1l ±0.5 deg .S-I), • 1 GPS antenna used in differential mode.

where v is the velocity, x and y denote the location of the vehicle characteristic point C, 8 is the orientation of the vehicle, L is the wheel base and 1/; the steering angle. This model is completed by two dynamic properties (2).

an=vw { at =dv dt

(2)

where an and at are respectively the normal and tangential accelerations. The model's parameters (here only L) and the measured variables are inaccurately known . This lack of precision is expressed in the bounded error context by stating that the quantity belongs to a known interval. In the sequel, we consider the following sensors to monitor the vehicle motion:

Figure 1. Experimental vehicle STRADA These data are measured with different sampling periods by parallel tasks on the vehicle network. Storing these measurements in circular buffers and managing them via interpolating processes makes it possible to synchronize them and even to compute a reasonable estimate of their derivatives.

• the position (xgp.,Ygp,), orientation (8gp. ) and velocity (v x , v y ) measured by the GPS in a earth centered reference frame, • the velocity of the rear wheel v (odometer), • the yaw rate w (gyrometer) , • the tangential acceleration at (accelerometer), • the normal (centripetal) acceleration an (accelerometer) and • the steering angle 1/;.

Let us consider a simplified "bicycle model" of STRADA (Fig. 2). In this two-wheels model, each wheel represents the center of an axle. Despite of its simplicity, this kinematic model has been proved pertinent for real applications like lane keeping (Jurie et al. 1993) . In the present case, we rather use it as a pedagogical support, the model being now used for the real application incorporating the description of tyre-slip angles as (Scheding et al. 1997), for instance.

2.2 Redundancy relations

Establishing redundancy relations in the framework of linear stationary systems is now a mature technique known as analytical redundancy theory (Brunet et al. 1990). The linear stationary case has been treated in (Bouron and Meizel 2000). We propose here to apply this theory in the non-linear and non-stationary case. Using (1) and (2) , we obtain the following independent relations between the measurements: (

v = Vx cos 8 + Vy sin8 vw = an dv = at dt tan( 1/;) w = v -- L

)

Figure 2. Two-wheeled vehicle model

2.1 Vehicle model

(3)

We use the following notations for the sensors:

ml m2 m3 m4 ms m6 m7 ms

Assuming that the wheels are rolling without slipping, one gets the following kinematic relations:

&t dt

= v cos(8)

= vsin(8) Ld8 tan 1/; = v dt

1

(1 )

1002

= Vx = Vy =v = at = an =w = tan 1/;/ L = 8gp•

(4)

At last, using analytical redundancy theory (Brunet et al. 1990) yields the following parity relations ri(t) = 0; i = a, b, c, d ml cosms

+ m2 sin ms - m3

m3 m 6 - ms ni3 - m4 m6 - m3m7

{

= ra(t) = rb(t) = rc(t) = rd(t)

To take into account the sign of the error, we note q

= p.

sign(r)

-(8x My)

(5)

r= x· y

R r ..

~<----:>

When they are provided by the manufacturer's documentations, the accuracy of the sensors is limited to the statement that the true value belongs to a bounded interval around the measurement. This justifies the set-membership approach used in this paper. Inaccuracy is stated classically by: mi E Mi


+ 6mil

3. FAULT DETECTION The parity relations are not identically zero because of the inaccuracy inherent to any sensor and to any model. When measuring a non-zero ri(t), the question consists now to distinguish between a normal and an abnormal value. A set-membership approach makes it possible to combine the analysis of the different residuals ri(t)j i = a, b, c, d to detect gross failures without the need to introduce an artificial threshold as it will be shown with a basic example:

x

• P-- : certain negative error when r < -(
4. FAULT ISOLATION To isolate the error causes, we'll rewrite the parity's equations (5) into the following redundant system:

Let a parity relation Pi : ri(t) = Yi(t) Xi(X) , with Xi E Xi and Yi E Yi. So, if ri(t) i Ri = [-(
PI: ml cosms + m2 sin ms - m3 P2: m3m6 -m5 P3: ni3 - m4 P4: m6 - m3m7 P5: m5 -m5m7 P6: m~ - mSm7

Pt+ and Pi-- characterizing certain failures, we propose now to treat the ambiguous case where the measurements Xi,mes(t) and Yi,mes(t) may be compatible or not. The width of the intersection of the admissible domain X and Y of the measurement Xi,mes(t) and Yi,mes(t) can be an indicator of this compatibility.

= rl (t) = r2(t)

= r3 (t) = r4(t)

= r5(t) = r6(t)

This system explicits the effect of the measured variables upon the re si dues {ri(t); i = 1, ... , 6}. These relations are translated into a qualitative form in the following array (Table 1) where • the 1 or -1 represents the signs of the influence from the variable to the residues {Ti(t); i = 1, ... , 6}, 0 denoting that there is no influence, • X means that there is an influence in a direction that is not a priori known. • Si is the sign of mi ( ie Si = sg(mi»).

It is considered that there is no fault when the intersection between X and Y is either X or Y, and that the fault is certain when this intersection is empty. So considering Fig.3 we can define a possibility p of component fault by:

=1-

= xrw

We deduce for each equation of parity Pi the most probable assumption between:

where mi denotes the true value and mi,mes the available measurement.

p

y

x""

Figure 3.

= [mi' mi)

= [mi,mes -

y ...,

width(X n Y) min(width(X); width(Y))

For ml = V z , m2 = Vy and ms = Ogps we consider only a single line ( the sensor 'GPS' ).

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GPS

X

0

m~

1 -1

-S6 S6

0 X X

0 0 0 0 0 0 0 0

0 0

1 -1

1 -1

0 0 0 0 0 0

m~

m4

mt m; mS

mR mt m; m:j

-53 53

0 0

0 57

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-S7

-S7

0 0 0 0

0 0

-1

1

• on w between times 800 and 900, • on an between times 1100 and 1200 and • on v between times 1800 and 2000.

0 0 0 0 0

0

-1

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1

-57

0 0

-1

-200

1

53

1

55

-53

-1

-ss

Table 1. QualItatIve mfluence of the variables to the residuals. -800

This array is used to diagnose each sensor. A defect is suspected as soon as the value of one of the indicators Pi is not O. To reduce the rate of false alarms, we only consider the cases where at least one parity relation has a certain marker P-or P++.

-'000 -1200

-'000

-800

~

-400

-200

400

Figure 4. Trajectory of the vehicle. The distances are in meters

To match the uncertain markers (P-, pO, P+) with the table 1, we use the following rules: • a 0 can be matched with all incertain markers • a X can be matched with P- ,P-- ,P++ and P+ • a 1 can be matched with p++ ,P+ and pO • a -1 can be matched with P-- ,P- and pO

----

I - ++ I m~

1

1

m mfi

0 0

1

1

X 0 0

0

+

1

1

0

0

-1

1

0

1 1

?tVYl

""""

W"'~

I

,

""""

?tVYl

""""

""'"

""""

,

Figure 5. Sensors

~_::t~~~

Table 2.

~

Now, if we look the other markers, we deduce that the fault is on w = m6 and W mes > Wtrue

,

""""

""'"

mt.

+

,

?tVYl

~

For example, if we have {P1-,pi+,P3-,PJ,Ps+,pt} (with m3 > 0 , m6 < 0 and m7 > 0), because of pi+ the fault can be either m3" , or By extracting these lines, we try to match the first line of the Table 2 with the three next ones.

ms

600

_:[ 50

~ 500

~---;-v::- 2~ 1000

~3 ~~~I~lrA '"':....

+ aw.

~

If the situation represented by one step is ambiguous, one uses the previous data assuming that the cause of the defect has not changed. If it 's still ambiguous, the decision is delayed.

_::[

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~_~t

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h

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1500

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,

~ , -~

~ ~~t ~~~~'---,-~-,-

5. EXPERIMENTAL RESULTS Let us consider the data collected by STRADA during a short travel displayed on Fig. 4.

Figure 6. Residual values Fig. 6 shows the values of the different residues. Notice the effect of each fault on the residuals. For instance the failure on w (times 800-900) generates a non-zero values on residuals r2, r4 and r6 .

Four failures have been artificially added to these real measurements : • on tan 7jJ / L between times 225 and 300,

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By using the decisions of the previous steps, the diagnosis are improved (Fig. 10). Then there are only one (and the good) cause for each fault.

~3~1 ~ ~ -~~ '~ '~ '~II~ ~ ,~

400

Figure 9. I-Step Decision

On Fig. 7 we can notice that all markers are null outside the periods with fault. So, there are no false alarm. Between times 800-900, the certains markers are p:j+ and P6++ (this one only after times 830).

~I,

200

• 0 is used to represents no fault on the sensors, • -1 is used to represents a possible negative fault, • + 1 is used to represents a possible positive fault.

Figure 7. Certain markers

I,

:. .

>_~p. ~ ~ Sl'~ '~ '~ '~

2200

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• -1 represents the uncertain markers P- , • 0 represents the uncertain markers po, • 1 represents the uncertain markers P+,

Figure 10. Result

Figure 8. Uncertain makers 6. CONCLUSION

On Fig. 8 we can see the uncertain markers. One see these markers (particularly P6 ) can be non-zero even there are no errors. The uncertain marker P4+ is active between the fault on w. This help us to determinate the cause of the error.

The study presented in this communication has been revisiting the use of parity equations in a bounded error context. The present work is complementary to another one concerning an interval version of a dynamic state estimator. The method detailed here presents good diagnosis capabilities; particularly in case of small errors or drifts. Moreover, this method can be applied to imprecise model as in (Katsillis and Chantler 1999).

Fig. 9 shows the I-step decision, ie the diagnosis with only the present markers. We notice there are often several cause in respect with the markers. For instance, between time 800-900 one can see some possible errors on v, an and w.

1005

7. REFERENCES Ackerman, J . (1996). Yaw disturbance attenuation by robust decoupling of car stereing. In: Proceedings of the IFAC World Congress. San Fransisco. Bouron, P. and D. Meizel (2000) . Interval based fault detection and isolation for vehicledynamics monitoring. In: Fusion2000. Paris. Brunet, Jean, Michel Labarrere, Daniel Jaume, Andre Rault and Michel Verge (1990) . Detection et diagnostic de pannes - approche par modilisation. Hermes. Daib, A. and U. Kiencke (1996). Estimation of tyre slip during combined cornering and braking observer supported fuzzy information. In: Proceedings of the IFAC World Congress. San Fransisco. Jurie, F. , P. Rives , J. Gallice and Brame J .L. (1993) . High speed vehicle guidance based on vision. In: Proceedings of the lrst IFAC Intelligent Autonomous Vehicle Symposium (lA V'93) . Southampton, Britain. Katsillis, Georgios and Mike Chantler (1999) . Comparing two methods for diagnosis of imprecise dynamic systems. In: Proceedings of European Control Conference ECC'99. number F381. Kiencke, U. (1996) . Yaw disturbance attenuation by robust decoupling of car stereing. In: Proceedings of the IFAC World Congress. San Fransisco. Scheding, S., G. Dissanayake, E. Nebot and H. Durrant-Whyte (1997). Slip modelling and aided inertial navigation of an LHD . IEEE - International Conference on Robotics and Automation pp. 1904-1909. Thompson, M. (1996) . The thick and thin of car cabling. IEEE Spectum.

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