On-Line Identification and Fault Detection on Industrial Processes†

Copyright © IFAC Identification and System Parameter Estimation 1982 . Washington D.C .. USA 1982

ON -LINE IDENTIFICATION AND FAULT DETECTION ON INDUSTRIAL PROCESSESt A. Rault*, D. Jaume** and M. Verge** *A DER SA-GERBIOS, 2 avenue du l er Ma!; 911 20 Palaiseau, France **Laboratoir. d'Automatique, Conservat oire Nationa l des A rts & Metiers, 2 1 rue Pin el, 75013 Paris, France

Abstract_ On industrial processes , classical fault detection systems are based on variables monitoring around predefined set points_ However, if one considers that a fault is actually a change in relationship between some variables, it seems natural to use on line identification and thus observe model parameters to detect faults_ These simple considerations are the background of the methodology which has been developed and tested on actual industrial pilot units _

FAULT AND FAILURE DETECTIONGENERAL BACKGROUND

INTRODUCTION During the past few years much interest has been arisen by the fault detection problem _ Aeronautical and military systems for which security is a prevailing factor had generally solved their fault detection problem by hardware redundancy-duplication or triplication of equipments_ The cost factor of such solutions and the increasing availability of on line computing facilities have brought up the question of a software solution to the fault detection problem_ An abundant litterature has then appeared and theoretical solutions have been proposed [1] relying on system modeling_

Before any methodological analysis, a gene ral background of the p r oblem will be given as well as some definitions_ A process is characte ri zed by a certain number of state var i ables (whose know l edge permits t he predic t ion of the process behavior in the immediate f uture) of observations or outputs and o f inputs _ These varia bles a r e s i gnificant o f the state of operat i on of the system and are the basic elements given to the ope r ato r who supervises the process evolution _ So, basical l y a process is said to be in a normal state of operation if its observed variables are in the neighborhood of a predefined set point _

On industrial processes the motivation for fault detection systems has recently been appearing_ Similarly to aeronautical systems security has been one of the concerns mainly in nuclear and chemical industry_ However the increasing complexity and automation of industrial systems has also arisen several questions linked to the fault detection problem [2]_ Higher complexity, automatic control , greater disponibility, lower cost of maintenance, such are the present demands for industrial systems_ Fault detection is a necessary condition to satisfy the above apparent incompatibilities_

Actually, the significant variables of a process are linked by causal relation~hips and we will define a state of fault and/or failure as a change in these r elationships _ Various levels of deterioration can be defined - unsteady faults (random structural changes) ; - steady faults (permanent structural changes) ;

In the present paper, a formulation o f fault detection problems and classical approaches will first be given , then a methodology based on on-line identification and hypothesis testing on identified parameters will be given a theoretical background; in a third part implementation problems will be approached and actual results on pilot units presented_

- catastrophic faults (structural changes creating catastrophies)_ Faults appear often in that order and progressive deterioration may lead to catastrophy espescially when an automatic control compensates for it _ Faults can also be separated in two classes: evolving faults

t This work has been performed under contr~stwith CGEE- ALSTHOM and support of ANVAR _ 1299

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A. Rault, D. Jaume and M. Ve r ge

mainly due to aging whose future can be pro gnosed and calaleptic ones whose occurrence is purely random . Starting on these premices one can define how a fault supervisory system should be organized. Table 1 gives the sucessive steps of such a system , it is self explanatory. It should however be noted that the five first steps are applicable to all kinds of faults while the last two ones concern only evolving faults. Keeping in mind this frame which emphasizes the necessary steps , a brief review of possible methodologies will now be presented . The classical procedure on industrial processes consists in the observation of a certain number of interesting variables . \·Ihether the observation is performed by a human operator of by a computer , the decision for failure is taken on the basis of the operating point belonging to a neighborhood of a predefined set point . The two dangers of such a procedure are : first , not all the points of the defined neighborhood are coherent with the process structure; second , excessive de tections induce a modification of the domain by the operator and thus progressively the security domain may follow an evolving fault . Recognizing the existence of relationships between variables , several methods have been developed based on a model either static or dynamic. Refering to Table 1 , step (I) is synthetized into one or several models , step (I) consists in variables observation a~d prediction using the above models , step (l) is basically performed by the comparison of the actual behavior to the predicted one . The following steps are variously approached in the existing litterature. Steps (2) and (1) are mainly performed using Kalma~ filte ring and sequential hypothesis testing [3] [ 4] or a by a simple observer technique [ 5]. These methods rely strongly on the initial model of the process and the validity of its identification ; in particular they suppose no bias errors on the identified parameters. As most industrial processes are closed- loop, unbiased identification is difficult and appears as a major difficulty for practical implementation of these methods . Going back to our definition of a fault or failure as being a change in the process structure,the methodology which is presented in the following paragraph relies on variations of on line identified parameters of the process . Step (~) , observation of the process is Eer formed by on-line identification , step (l) makes use 0: sequentialhypothesis testing and it will be shown that step (I) can be solved by filtering . In the next paragraph a theore tical background is given; the analysis is performed under a certain number of hypotheses which are valid for open - loop proces ses . The closed loop analysis is mathemati-

cally untractable with the presently available tools; however , the practical implemen tation on a closed loop pilot unit is pre sented in part "Implementation - Practical example " .

A priori knowledge of the normal state of operation (7

I process observation I

(~)

,g. I Fault detection

(l)

(~)

I

I

.!],

Fault characterization unsteady steady

~

I

Diagnosis Fault or failure classification (~)

- sensors - actuators - process

-.!.J. (§)

Prognosis Previsional evo lu tion {} Post-failure analysis

Cl)

Maintenance Wrocess reconfiguration

Table 1 - Fault analysis and superv i sory system

PROPOSED METHODOLOGY - ON -LINE IDENTIFICATION - HYPOTHESIS TESTING In this paragraph , first the on-line identi fication characteristics are analysed in the case of fault occurence . It is shown within a frame of assumptions that the variation o f the covariance matrix due to a random struc tural change is independent of the environ ment measurement noise. Then a classical sequential hypothesis testing procedure on the covariance matrix of the identified pa rameters is given. 1. On - line identification

It is not the prupose of this paper to go through the on-line identification algorithm , therefore the algorithm used is given directly without justification; proofs are given in [6] 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 va rious structures will be shown to s~tisfy

1301

On-Line Identifica ti on and Fa ult De t ec ti on on I n d ust ri al Proce s ses

~T

(next chapter) the hypothesis . e (n) ~

The process model is then given by

- A

(n+1)

So (n)

where s(n) is a scalar observation , ~ is a vector of N parameters called the struc ture vector , e(n) is a vector of N past inputs or state variables called the infor mation vector.

+

A

e (n)

Let the error between the identified parame ter vector ~1(n) and the normal state of

v(n) = a

-

~(n)

-M

be denoted

-0

v(n)

e (n) eT (n) b (n) e (n) + A2 f1a (n) + A 2 11 e (n) 11 --{) 11~(n)11

- slow monotonous variations of the drift type representing aging phenomena and evolving failures; - random variat i ons representing uncer tain relat i onships due to a bad model characterization .

k

k e(n)

2

T

~

(n)

Starting from equat i on (7) one can easily wr ite the covariance difference equation us i ng the following notation with E [.] as the mathematical expectation

L+ = E [ v(n+ 1) v -

On - line identification procedure . The model indexed M satisfies equation

(7)

For further analysis the following notation is introduced

lie (n)11

- step variations representing sudden failures ;

v(n)

From equation (6) , it

(n) - a

is easily shown that v(n) satisfies the following difference equation

(2)

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

(6)

eT (n) e (n)

.':'.(n+1 )

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

~(n)

----=~--­

operation vector In a normal state of operation the process which is indexed 0 is denoted by equation (1) taking into account observation noise b(n)

T

1

eT (n) e (n)

s(n) = aT e(n)

sO(n) = ~ e(n) + ~(n) ~(n) + b(n)

(n)

T

(n+1) ]

Making some fairly strong assumptions which are valid in the open loop case with noise on the observation

(3)

E[ b (n) . e (n)] sM(n) = aT(n) e(n) -M

(3)

-

E[b

where the model parameter vector is obtained through a classical on - line identification procedure [ 7]. The identification algorithm is the following ~(n+1)

~(n)

-

A

E (n)

W e (n)

(4)

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

0< A < 1

0

(n)

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

= as

(n)]

T

0

E [ e(n) f1a (n)] -

+

L

A

-M -

0

2

-0

The variance equation is then written as follows :

eT(n) We(n) -

£(n) = aT e(n) - s

2

=

(I -
L

(1 -
T

+



r



2 + k as



(8)

Equation (8) shows that the parameter erro r covariance satisfies a difference equation whose convergence depends on the info r mation matrix . It is forced by two inputs : the observation noise variance 0 2 and the pro cess parameter variance r s

(5) Let us first examine the normal state of operation , then the structur e va r iation i s null and r 0 ; the on-li ne identification process reaches a steady state and thus L+ = L .

=

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A. Rault, D. Jaume and M. Verge

The steady state value of the variance LO in a normal state of operation satisfies the following equation

In order to perform on-line identification, it is necessary to introduce some information into the process; this is generally done by introducing pseudo random binary noise or similar signals whose characteristics are close to white noise with respect to the process dynamics and with an average energy level £2 as low as possible. Then the information matrix ~ tends to the following value ~ = k ~(n) ~T (n) + \ I and

k =

_~ e

Equation (9) takes a simplified expression

\

Lo

2-\

2 a s - 2 e

(10)

I

This particular result shows that the identified parameter variance depends directly on the noise to signal ratio which is a classical result in on-l ine identification . Let us now consider the case when some ,fault has occurred; therefore r is different from zero and equation (8) is again to be considered . The steady state value LO given by (9) will be introduced in equation (8) and defining /'; L = L - LO as the covariance matrix of the parameter vector variation due to faults, the following covariance equation is obtained :

(11 )

Several remarks should be made by discussion of equation (11) . 1/ The variation of the covariance matrix is independent of the observation noise. Indeed equation (11) is a difference equa tion forced by a term which is function of the process structure variations ( r) 2/ The rate of convergence of the parameters covariance matrix due to variations in the process structure is exponential [8] and function of the information matrix ~ This means that information is needed to reveal a fault. 3/ If some fault induces a stationnary covariance matrix on the process parameters the stationnary value of the identified parameters covariance matrix would reach a value satisfying the following equation

~ /'; L ~T _ ~ /'; L _ /'; L ~T + ~

r

~T

=

0 (12)

So to a typical fault would be associated a covariance matrix of the identified parame ters Ll = LO + /'; L In the particuler case when the information is of a "white noise" type , Ll takes the following simplified form a 2

L

and

1

=

\

2- \

(~- 2 e

I + \

f)

r

(13)

( 14)

This expression shows the direct proportionality of the identified parameters covariance matrix to the structure variations: indeed in the present context /'; L is independent of the state perturbations . In this paragraph it has been shown that a pLOcess structural variation induces a variation of the identified parameters covariance matrix. Moroever, in a stationnary environment, this variation is independent of the noise level but depends on the information. This theoretical analysis has been performed in a rather academic context : open-loop , "white noise " information matrix, as compared to the industrial reality : closed loop, biased identification. The theoretical background is basically a justification to the chosen procedure : - on-line identification - parameter covariance computation - sequential hypothesis testing of the covariance matrix. The practical experimentation on a pilot unit will exhibit the feasibility of this procedure which theoretically is independent of the state perturbations.

2 . Detection procedure The classical sequential probability ratio test (SPRT) [ 9 ] will be used , two hypotheses being tested : the process is in a normal state of operation the process has a fault . The basis of ~his decision procedure and the development of its formulae will be recalled rapidly as it is almost classical in decision theory. Let P be the "probability of missing " a fault ~-e deciding that the process is in normal state as it is failing and P be F the " probability of false alarm" i - e deciding that the process is faulty while it is in a normal state.

On-Line Identification and Fault Detection on Industrial Processes Under hypothesis HO' the parameter vector has a distribut~on f(a ,HO) , while under H1 it has a distri~tion f(~,H1).

~

If normality is assumed, the probability density functions are written : 1 f(aM,H O) = (27T ) N/

1 p Z y det La ex [-2"

1 (27T) N/2

f(~,H1)

v

det L1 exp[-

T

-1

~ La ~] ( 16)

1

2" ~

-1

L1

~] (17)

The likelihood ratio

~

In order to minimise P and P two values F are chosen which consti~ute the thresholds for the test : 1-P F

1

=

M

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

In '£,(n)

Starting from this basic formulation a sequential test on the variance is established. Its derivation does not present any difficulty and therefore is not included in the paper. The test reads n HO E CaT (i) Q a (i)) < 2 i=l --+1 --t-I

where

Q

It has the graphical interpretation shown on figure 1.

IMPLEMENTATION - PRACTICAL EXAMPLE In the previous paragraph, justification has been given for the chosen procedure : on-line identification, followed by hypothesis testing. On actual industrial processes several difficulties arise which are related to the on-line identification. Indeed, it is a well known result that identification of a process in a closed-loop situation and in a regulation mode will lead to a biased non stationary result. One way to improve the closedloop identification is to introduce extrasignals either in an explicit fashion or implicitly bya slight modification of the

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control signal [1 0 ]. This last solution has been retained. The amount of energy of these extra- signals is limited as much as possible which brings up the compromise informationidentification or in the present context information-detection. These are arguments adjustable according to the problem. It has been shown ill the previous paragraph that the fault occurence will create a change in the covariance matrix. It has just Leen reminded that Ln e closed-loop situation creates a result of the identification which is b jas i. Thes e two arguments justify the following procedure : before computation of the covariance matrix the parameters are filtere d throug h a high pass filter. Figure 3 gives a summary of the actually implemented pro~edure. As shown on this figure, characterization of the faults is performed by applying hypothesis testing to filtered identified parameters . Occurence of faults is detected by the variance test while a permanent failure will show on a parameter mean value test. The whole procedure has been implemented on a laboratory pilot unit. This laboratory pilot unit is by no means an industrial process; however, sensors , actuators, computer interfaces are industrial ones and permit an analysis of the methodology to practical problems. Figure 2 shows the part of the process which has been considered; it is modeled by a discrete second order system and observation of all the state variables enables, the choice of a model structure s(n) : ~T ~(n). In other applications, modeling with the impulse response will satisfy this general structure. Figure 4 shows the various steps of the de tection on a practical example. The reader should make a parallel between figures 3 and 4 thus see at various steps the treatment of the signals. Several remark s should be made on figure 4. The fault artificially introduced is a leak on one of the reservoir, the process being closed-loop it hardly appears on the level h2 because the water flow Q2 compensates for it. The on-line identification shows that some parameters do not change while others are strongly perturbed. The detection result shows that the reaction time to the fault appearance is very rapid (a few sampling times). Various types of faults have been analysed on this process and the procedure has given full satisfaction.

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A. Rault, D. Jaume and M. Ver ge CONCLUSION

Me reau, P., D. Guillaume , and R . K .M e ~1 r a . Fli gh t con tro l app li ca ti on o f mode l a l go rithmic cont r o l with IDCOM. I EE E Con f e r ence on Decision and Contro l, 19 78 .

[1 0 ]

Analysis of industrial processes fault supervision has been Made. A fault has been d efined as a change in the process structure , therefore on-line identification appears as an appropriate tool for struc ture variation detection. This detection is performed by a sequential test on the covariance matrix. Implementation of the overall procedure on a pilot unit has shown its actual feasibility. Thus a procedure for fault detection and characterization on industrial processes has been presented. From the theoretical point of view the classification problem has still to be looked at. The next step towards implementation is the analysis of an actual process and its decomposition into coherent subsystems which could be supervised by such a procedure.

det L,

./>

)- p

2 In

e'<" Slope

";

I n(- - -)

det I:. 0

c,c,

~

~

'0()

~-~~-----------~"

,

FIGURE 1

rh,] [b" J[q,] [h,h'J ".,= la"raIl a,,] a" 'lh , "+ 0 b" . 0

REFERENCES

[ 1]

Willsky, A. ( 1976). A survey of design methods for failure detection in dynamic systems. Automatica, Vol.12, pp. 602-611.

[2]

Himmelblau, D.H. (1978). Fault detection and diagnosis in chemical and petrochemical processes. Elsevier Scient. Publish.

[3]

Deckert, J.C., M.N. Desai, J.J. Deyst, and A. ~lillsky (1977). F8DFBW sensor failure identification using analytic redundancy. IEEE Transactions on Automatic Control, October 1977.

[4]

q, "

Mehra, R.K. (1978). Fault dete ction, diagnosis and compensation in dynamic systems. Scientific Systems Inc. ,re p o rt.

[5]

Clark, R.N. (1979). The dedicated o b server approach to instrument failure detection. IEEE Conference on Decision and Control, 1979.

[6]

Richalet, J., A. Rault, J.L. Testud, and J. Papon (1978). Model predictive heuristic control : applications to industrial processes. Automatica, Vol.14, pp. 413-428.

[7]

Richalet, J., A. Rault, and R.Po ulique n (1971). Identification des processus par la methode du mode le . Gordon & Breach .

[8]

Abu el Ata, S. Asymptotic behavior of an adaptive estimation algorithm with application to an M-dependent data. Submitted for publication to IEEE Transactions on Automatic Control, 1982 .

[9]

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

water

su pply

FIGURE PILOT

UNIT

2

DES C RIPTION

extra.slgnal

identification

unsteady fault FIGURE IMPLEMENTATION OF

steady fault

3 THE DETECTION PROCEDURE

On- Line I de nti f i cation and Fault Detection on Industrial Processes

H, (mm) 300.'+-_______- - " " - - - - -

H2

T 200.'

i-'-"-"---'-'-'"V'----..."......JV.......""""-"-'

100'Ilj-o._ _..,.,._N

Leak O.

T

\4w---~..........

Tend

Q I ( 1/ h ) Q2

of leak

k---~--~--~--~--~--~--r_--~~time

o.

800.

1.CO.

2iOO.

3200.

sec

1000

800.

Parameters from on li ne i de ntif i ca ti on

':'b,c O.

SOO.

10~0.

2100.

I

~

3200.

Parame t er s af t e r

O.

- 100.kL--+---1 f- -.-1---+.- -.-+---ZIf-- .-1'---3+Z-:-CO-l>. OO 1 00 s00

Ex i stance of fault

O.

SOO.

FIGURE

1000.

Detect i o n I

2iOO.

result

3200.

Succen5ivc ~tcrs of t he fault detection procedur~

1305