Industrial Processes Fault Detection and Localization

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INDU STRIA L PROCESSES FAUL T DETE CTIO N AND LOCA LIZAT ION I A. RauIt*, D. Jaume** and M. Verge** * .-\tI''I'\{I - (~l'fhif''.

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Abstrac t. On industr ial process es, classic al fault detectio n systems are based on variabl es monitor ing around predefin ed set points. In this paper, a fault is actually consider ed as a change in relation ship between related variabl es; on- line identif ication is used to observe model paramet ers and thus detect faults. Th ese simple consi deration s are the backgrou nd of the methodo logy which has been developp ed and tested on an actual industr ial pilot unit. Keywor ds . Identifi cation; closed loop systems ; decision theory; multiva riable control systems .

INTRODUCT I ON

of inputs . These variabl es are Signific ant of the state of operatio n of the system and are the basic element s give n to the operato r who supervi ses the process evolutio n. Basical ly a process is said to be in a normal state of operatio n if its observe d variable s are in the neighbo rhood of a predefin ed set point.

During the past few years much interes t has been arisen by the fault detectio n problem . Aeronau tical and military systems for which security is a p revailin g factor had general ly solved their fault detectio n problem by hardwar e redunda ncy-dup lication o r t r ip l ication of equipme nts . The cost facto r of such solution s and the increasi ng availab ility of on- line computi ng faci l ities have brought up the question of a softwar e solution to the f au lt detectio n problem . An abundan t litterat ure has then appeare d and theoret ical solution s have been propose d [ 1] relying on system modelin g.

Actuall y, the represe ntative variable s of a process are linked by causal relation ships and we will define a state of fault or failure as a change in these relation ships. Various levels of deterio ration can be defined

On industr ial process es, the moti v ation for fault detectio n systems has just been recently appearin g. As for aeronau tical systems security has been one of the concern s mainly in nuclear and chemica l i ndustry . However , the increasi ng complex ity and automat i on of industr ial systems have also arisen severa l quest i ons linked to the fault detectio n prob l em [ 2] . Higher complex ity , automat ic control , gre ater d i sponib ility, lower cost of mainten ance , such are the present demands for industr ial sys tems . Fault detectio n is a necessa ry conditio n to satisfy the above apparen t incomp atibiliti es. I n the p resent paper, a formula tion of fault detection p r ob l ems and classic al approac hes will first be g i ve n , then a methodo logy based on on-line identifi cation and hypothe s i s testing on identifi ed paramet ers will be given a theoret ical backgro und. The l ocal ization prob l em is present ed, then the p r act i ca l imp l ementat ion is approach ed and actual r esults on a pilot unit are present ed.

FAULT AND FAILURE DETECTION - GENERAL ANALYSIS

- unsteady faults - steady faults

(random structu ral changes )

(perman ent structu ral changes )

- catastro phic faults catastr ophies) .

(structu ral changes creatin g

Faults appear often in that order and progres sive deteri o ration may lead to catastro phy especia l ly when an automat ic control compens ates for it. Faults can also be separate d in two c l asses : evolving faults mainly due to aging whose future can be prognos ed and catalep tic ones whose occurence is purely random. The classic al procedu re on industr ial process es consist s in the observa tion of a certain number of interes ting variabl es. Whether the observa tion is perform ed by a human operato r or by a compute r the decision for failure is taken on the basis of the operatin g point belongin g to the neighbo rhood of a predefin ed set point . Going back to our definiti on of a fault or fai lure as being a change in the process structu re the methodo logy which is presente d in the followin g paragrap h relies on variatio ns of on- line iden tified paramet ers of the process .

Before any methodo logical analysi s , a general backgro und of the problem will be given as well as some definiti ons .

As a conclus ion , a process detectio n system shou ld include the followin g hierarc hical steps.

A process is charact erized by a certain number of state variab l es, of observa tions or outputs , and

' Thi s wor k has b e en p e rfo rmed u nder contrac t with CGEE-AL STHOM and support of ANVAR.

1789

A. Rault, D. Jaume and M. Verge

1790 Step

A priori knowledge of the normal state

Step 2

Observation of the process

where the model parameter vector is obtained through a classical on-line identification procedure [4].

Step

Fault detection

The identification algorithm is the following

Step 4

Fault localization.

E(n) .W.e(n) ~(n+l)

=

~(n)

(4)

-

The proposed method is used :

A is a scalar called relaxation factor 0 < A < 1, W is a weighting matrix which will be neglected for ease of presentation in the following, E(n) is the prediction error

Step 1 : knowledge of the "normal" identified parameters

Step

is performed by the on line identification

Step 3

a sequential test on the parameters variance is E'mployed

E(n)

Step 4

= aT.e(n) - s

-M-

k ~

Process Model it will be assumed that the process observations are linearly dependent on the parameters. This assumption will ease the on-line identification procedure and various structures will be shown to satisfy (next chapter) the hypothesis. The process model is then given by

~~.<:.(n)

A

2

11.<:.(n)11 So (6)

becomes :

~(n+l)

=

~

(n)

In a normal state of operation the process which is indexed 0 is denoted by equation (I) taking into account observation noise b(n) :

(n) = aT.e(n) -0 -

(I)

+ ben)

In a faulty state of operation, the process satisfies equation (2)

o

T (n) = aT e(n) + 6a (n) . .<:.(n) + ben) --{)

( 2)

~(n), ~(n)

be denoted

= ~ (n) - ~ (n)

from equation (6), it is easily shown that it satisfied the following difference equation.

~(n+l)

= [I-cj> ]

~(n)

+ cj>

~(n)

+kb(n).<:.(n)

(7)

Starting from equation (7) one can easily write the covariance difference equation denoting :

[~E r~(n) ~T(n)] where E[.] is the mathematical expectation and making some fairly strong assumptions which are valid in the open loop case with noise on the observation

E [ben) . .<:.(n)] where 5(n) is a scalar observation, ~ is a N vector of parameters called the structure vector, e(n) is a N vector of past inputs or state variables called the information vector.

a (n) + k s (n) e (n) [ I - cj> ] -M 0-

Let the error between the identified parameter vector ~(n) and the normal state of operation

vector

It is not the purpose of this paper to go through the on-line identification algorithm, therefore it is given directly without justification; proofs can be found in [3].

s (n) =

(6)

For further analysis the following notation is introduced :

On-line identification

s

(5)

the localization is completed using the properties of the identified parameter variations.

In this paragraph, the main results of on-line identification are presented in the case of fault occurence. It has been proved [9 ] that within a frame of assumptions, the variation of the covariance matrix due to a structural change is independant of the measurement noise. So, it is interesting to use a sequential hypothesis testing on the covariance matrix of the identified parameters.

o

(n)

The difference equation of the identified parameter vector is expressed as follows

PROPOSED METHODOLOGY ON-LINE IDENTIFICATION HYPOTHESIS TESTING

s

0

E [b 2(n)]

=.Q..

E [.<:.(n) .

2

os

E

6~(n)]

[6~(n) . 6~(n)J=

0

r

Let us now consider the case when some fault has occuredi therefore r is different from zero. Defining L as the covariance matrix of the parameter v~ctor in stead state, and 6[ = [ - [ the variation due to the faults, the followingO covariance equation is obtained : [9]

6[+ = (1-cj»

. 6[(I-cj»

+

cj>.

r.

cj>

(8)

Several remarks should be made by discussion of equation (8).

where ~(n) is a vector of structure variation indicating that a change in the input output relationship has occurred or is occurring. The structure variation vector can be of different nature depending on the fault.

1 - The variation of the covariance matrix is independant of the observation noise. Indeed equation (8) is a difference equation which is forced by a term function of the process structure variations

The identification model indexed equation (3) :

2 - The rate of covergence of the parameters covariance matrix due to variations in the process structure is exponential [5] and function of the information matrix cj>.

M

satisfies

(3)

(n.

Industrial Processes Fault Detection and Localization In the particular case , when the information is of a "white noise" type, (8) takes t h e following form :

Starting from this basic formulation a sequen tia l test on the variance is established. Its deriva -

tion does not present any difficulty and t he r e for e is not inclued in the paper. The test read s

A

with A

179 1

(9)

N

This expression shows the direct proportionality of the identified parameters covariance matrix to the structure variations. In this paragraph, it has been shown that a process structural variation induces a variation of the identified parameters covariance matrix. Moreover, in a stationnary environment, this variation is

independent of the noise level, but depends on the information.

n I i=l

(vT. ~(1)

I i=l

(NT (. '" (. ~1).Q.~1))

HO < 2 in

'" (.

.Q.~ 1))

P

M

1-P 1-P

>

2 In

HI

where

Q

P

+ i.In

(de t

+ i.In

(det

F

M

:

det Il

I~)

det I1

F

I~)

-1 -1 = Io - L1

It has the graphical interpretation shown on figure 1.

Although this theorical analysis has been performed in an academic context (open loop, "white noise" information matrix), it is a basically a justification to the chosen procedure : -

I n practice, industrial processes are generally in closed loop and identified parameters are biased. Therefore it is necessary to inject some ~tra information in order to identify.

on-li ne identification

- parameter covariance computation -

Exitation signals

sequential hypothesis testing of the covariance matrix .

Let now consider the following single input, single

output system

(figure 2).

Sequential hypothesis testing

The identification procedure sees the f ollowing transfer function between the observed input and

The classical sequential probability ratio test (SPRT) [ 6 ] will be used, two hypotheses being tested :

output.

~ U (p )

HO

l+H.R H +

HI

s

So the smaller is

the process has a fault.

H + F

~-R b +H.6

the process is in a normal state of operation

F, the bette r is the identifi -

cation. Let

P

be the "probability of missing"

a fault

i-e de~iding that the process is in normal state as it is failing and P be the "propability of

But 8 and b are noises, so , if a good identification is lo3ked for, extra signals e are

false alarm" i-e decidiKg that the process is faulty while it is in a normal state .

needed; however this is usually damageabte to the controlled output.

Under hypothesis HO' the parameter vector has a distribution f(a /HO) , while under HI it has a distribution ~(~/Hl)'

~

A procedure to avoid extra signals is t o create "implicit signals " as follows : if

\ e (n)

u(n-l)\ < eO + e

If normality is assumed, the probability density

1

wt , then u(n)

u (n-l)

wt, then u(n)

e (n)

sin

functions are written : if

\e (n) - u (n- l) \ > e

o

+ e

1

sin

f(a /H.) -M

1

with

i

With this method, the process inputs ar e composed of consecutive steps. It is important to note that when the process is perturbed, the non linea-

0 ,1

rity is not efficient, and the regulation has full authority.

f(~/Hl)

The likelihood ratio

f (~/HO)

In order to minimise P

defined which test 1-P

e1

=

M

is defined.

and P , two values are

constitu~e the thresholds for the

~o

P

M

1-P

F

Thus the sequential test performed at each sampling period is expressed as follows after taking the logarithm : Ln

£ (n)

Ln

Coupling between identification and detection It has been shown that a fault induces a variation of the identified parameters from their nominal values. When the fault disappears, the identified parameters should come back to their values. Actually, they do not because the process being in a closed loop configuration and the level of information being weak the identification proce-

dure is biased. The way out of this dead end is to keep in memory the nominal values of the parameters and re initiate the identification procedure on these values as

soon as a fault has been detected. This procedure is illustrated on figure 3.

A. Rault, D. Jaume and M. Verge

1792

Several advantages of this procedure can be listed - Parameters identified values are kept in a close neighborhood which prevents any numerical divergence.

IMPLEMENTATION RESULTS In the previous paragraphs, theoretical justifications have been given for the chosen procedure.

Beside s , it has been applied on several laboratory pilot units. Results on a mixing process are

- A fault is detected at its o rigin and during all its time lapse.

presented. I - Mixing process figur e 4

- The bias effect due to the clcsed loop situation is taken care of.

FAULT LOCALIZATION This step is very important on industrial processes,

but it is not an easy step in the context of the proposed method. The first idea consists in r ecognizing which parameter has been the most perturbed. However, generally all the parameters h ave been modified .

The upper tanks are supplied with water by input flows Q and Q . The lower tank is supplied 2 I through mixing valves vI ' v and v3 . In the 2 neighborhood of a set po1nt , the system state equation is given on figure 4. On line identification provides at each sample (T; 15 sec) 9 parameters f ij and gij (zeros are not identified). The structural vec:tor is formed of these 9 coefficients. The sequential test makes use of vector

variance to detect a fault occurence.

A large number of experiments have been performed,

one of them is presented.

For sake of simplification, let us consider the

identification algorithm in the deterministi c case b(n) ; 0 . When the process is in normal state , equation (7) gives v(n+l ) ;

~(n)

( 1-<1»

In the particular case where



is a constant

matrix , we have :

( I-
v(n) ;

The fault consists of a valve stuck at a level (figur e 5). 10% above the nominal value, between time 3600 and 5800 s.

When a failure appears , the vector ~(n) + ~ , and ~(n) becomes ~(n) + ~

becomes

~(n)

The regulator tries to keep levels at their set points, but the QI flow computed by the computer is not provided to the tank. Figure 5 shows input and output variables and identified parameters evolution. It is important to note that : first, the relative variation of the inputs or outputs are inferior to those of certain parameters; second,

some parameters are insensitive. On figure

5, the effect of coupling identification and detecI f the failure t .ime appearance is chosen as initial

tion is shown as well as the test result; note

time

that a false alarm is detected.

-~

~(O)

On figure 6 are given the test and diagnosis results.

Thus ~(n)

[ 1- (I -
;

~

(l0) Let us note that the diagnosis result is not

The coupling between identification and detection,

perfect, however the fault localization is correct

creates sawtooth type of signals for the parameters concerned by the fault. The natural idea is to sign each fault by computing a vector whose components are the sum of ~(n) between two SPRT decisions.

in the sense that is always tank I.

attribute~

it to

CONCLUSION ~(n)

A methodology for fault detection and localization has been established. It is based on on-line identification and sequential hypothesis testing.

with N state" P

if the SPRT decision is "normal

and N ; N I under fl'.'ult . p .

if the SPRT decision is ·process

It relies on the fact that a fault has been defined as a change in the structural relationship of the

In the general case, is not constant; denoting by i the value of (i ) , equation (10) becomes

~(n) z

[1 - (1-<1>0)

(I-I)·· · ( I- n _I )]

(<1>0+<1>1+"'+ n_l) ~

.

~

neglecting higher o r der

terms.

Thus the signature vector has the following approximate expression. S(N )

-

P

The assumed variations of the process relationships 6a can thus be reestimated as follows.

O

l:

[ i;1

.

l: j;O

<1>.

J ]

I t has been shown theoretically that on- line identification was the appropriate tool and that a fault occurence creates a change in the parameter covariance matrix.

Coupling of the identification and testing procedures is a way of solving the closed loop on- line identificati on bias problems. This original idea generates sawtooth type signals whose analysis gives a solution to the on-line localization problem. Implementation of this methodology has been performed on laboratory pilot units. It has been proved that the method is industrially viable because of the following properties : - ea se of implementation;

-1

i-I

Np ~;

process.

. S(N) -

-

computation time and memory very limited;

1793

Industrial Processes Fault Detecti on and Lo ca lization -

robustness to the tuning associatied to the basic tools;

- universal characte r due to the applicability to state representation and impulse response representation.

REFERENCES [1 J

Willsky, A. (1976). A survey of design methods for failur e detection in dynamic systems. Automati ca , 12 , 602- 611.

[2J

Himmelblau, D.M. (1978). Fault detection and diagnosis in chemical and petrochemical processes. Elsevier Scientific Publishing.

[ 3J

Richalet, J., Rault, A. , Testud , J.L. , Papon, J. (1978) . Model predictive heuristic cont rol : applications to industrial proces sing. Automatica, 14, 413-428.

[4J

Richalet , J ., Rault, A., Pouliquen, R. (1971) . Identification des processus par la methode du mode l e. Gordon & Breach.

[5J

Abu el Ata, S. (1982 ) . Asymtotic behavior of an adaptive estimation algorithm with application to M-dependent data . IEEE T. on Automatic Control , AC-27, 6, 1255-1 257.

[ 6J

Wald, A. (1947). Sequential analysis. John Wiley.

[7J

Verge, M. (1983). Detection de defauts sur processus industriels : methodologie. These doc teur -ingenieur .

[ 8J

Jaume, D. (1983) . De tection de defauts sur processus industriels : mise en oeuvre . These dccteur- ingenieur.

[ 9J

Rault, A., Jaume, D. , Verge , M. (198 2) . On-line identification and detection on indus trial processes. 6th Symposium on identification I FAC Washington.

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