Model-Based Diagnosis for a Gas-Liquid Separation Unit

Copyright e IFAC Fault Detection, Supervision and Safety for Technical Processes, Kingston Upon Hull, UK, 1997

MODEL-BASED DIAGNOSIS FOR A GAS-LIQUID SEPARATION UNIT

E. Denolin", D. Vrancic"", M. Kinnaert", D. Juricic"" and J. Petrovcic""

" Department o/Control Engineering. Universite fibre de Bruxelles. Avenue Franklin D. Roosevelt. 50. B-J050. Brussels. Belgium "" Department o/Computer Automation and Control. J. Ste/an Institute Jamo va 39. SI-JOOJ . Ljubljana. Slovenia

Abstract: The design of a diagnostic system based on mathematical models of the plant components is performed for a gas-liquid separation unit. This design includes first modelling of the process by using physical laws governing its behaviour. Hardware redundancy and simple nonlinear observers are used to synthesise a residual generator with 7 outputs. The generalized likelihood ratio (GLR) test allows one to evaluate the residuals. Tuning of the design parameters is discussed, and a reinitialization procedure is proposed in order to distinguish between temporary and permanent changes in the mean of the residuals. Simulations are used to illustrate the choice of the design parameters. Copyright© 1998 IFAC Keywords: Chemical process, fault detection and isolation, GLR test, observers.

redundancy relations and nonlinear observers. The residuals are evaluated either by comparison to simple thresholds, or by the generalized likelihood ratio test (GLR) (Basseville and Nikiforov, 1993), depending on their signal to noise ratio in the presence of faults . The main contribution of the paper is to show how methods for residual generation and evaluation can be combined to deduce a maximum of information for fault isolation in a specific application.

I. INTRODUCTION A model based diagnosis system for a gas-liquid separation unit is presented in this paper. Actuator, sensor and component faults are considered. This diagnosis is performed on the closed-loop system. It consists of three steps: residual generation, residual evaluation and decision . The residual generator is a filter that takes the actuator commands and the sensor outputs as inputs, and generates output signals called residuals . The latter are nominally equal to zero in the absence of fault , when the effect of initial conditions has vanished. Some of them become distinguishably different from zero upon the occurrence of a specific fault. This phenomenon is detected by the residual evaluation module. Finally, from the pattern of zero and non zero residuals, the decision part of the diagnosis system isolates the fault(s ), i.e. determines its (their) location(s). This last part is not presented in this text, but in an associated paper (Vanden Daele et aL 1997).

The text is organised as follows . The separation unit and its model are presented in section 2. The residual generation and evaluation modules are described respectively in section 3 and 4.

2. PROCESS DESCRIPTION AND MODELLING

2.1

Process description

The unit for separation of gas from liquid (Vrancic et a\., 1995) makes part of a semi-industrial installation which consists of the two main parts. The first part serves for reduction of NO, in effluent gasses. The second one refers to the technological waste water treatment by means of neutralisation with CO 2

The model of the plant is obtained from physical laws . The unknown parameters are identified from experimental data. This leads to a nonlinear dynamic model. The latter is used to design the residual generator which is made of nonlinear hardware

229

contained in flue gasses produced by the first part. The role of the separation unit is actually to capture flue gasses under low pressure from the effluent channels by means of water flow, and then to supply them under high enough pressure to the neutralisation reactor.

2. 4

The separation unit is shown in Fig. 1.

The following notations are used in the model:

The flue gasses coming from the effluent channels are "pooled" by the water flow into the water circulation pipe through the injector 11, The water flow is generated by the pump PI (water ring). The speed of the pump is kept constant. The pump feeds the mixture of water and gas into the separator RI where gas is separated from water. Hence the accumulated gas in RI forms a sort of "gas cushion" with increased internal pressure. Owing to this pressure, flue gas is blown out from RI into the neutralisation unit. On the other side, the "cushion" forces water to circulate back to the reservoir R2. The quantity of water in the circuit is constant.

Variables: Uj, command signal of the valve Vi , i=I ,2 ; vi ' position of the valve Vi, i= 1,2 ; PI, relative air pressure in tank RI; hj , water level in tank Ri, i=I,2 ; CPI, air flow from tank RI ; CP2, water flow from tank

the air flow transmitter and in the water flow transmitter respectively.

Process model

R2• Constants: Sj, section area of tank Ri, i=I ,2 ; PO, atmospheric pressure; hRj , height of tank Ri, i= 1,2 ; rj , open-close flow ratio of valve Vi, i=I ,2 ; k j , flow coefficient of valve Vi, i=I ,2 ; CP w, known constant water flow through the pump P I; Vj MAX ' maximum open position of valve Vi ; Vi MAX ' maximum opening speed of Vi ;

P.

kw

PT,

I

t

!

I f---r-'=--1

11

2m

. ~.1 ..

LJ',

= Pwalerg ·

Different components are described by the following set of equations:

., ~.-

.1'¥Jlif] 1... ........11

•

Valve positions:

.'-." ':- R,

.:.~.L~--·

u=u+f I I Ui ,i=I ,2

ii,

Working conditions and control

•

Both gas pressure and water level in the separator RI are controlled at the set point PI = 05 bar and hi = 1.4 m with two single PI controllers. The actuators are respectively the valves V I and V2' No reference change is considered in this work, so that the system remains in steady state in the absence of fault. 2.3

•

Faults

in the pressure transmitter;

Ih"

transmitter for tank Ri, i= 1.2;

•

{"""

= it0,·,/1,\ , .

if V;


otherwise

Flows through the valves <1>1 = K, (VI ).jp; where K I(VI ) = klr l"' -'

(I )

<1>2 =K2 (V2 )~PI +k. (h l -hR2 ) ,

(2)

Air flux through the injector:

State equations (4)

(5)

lp, ' fault

(6)

fault in the water level

I
otherwise

i[v,>v,

(3 )

Three kinds of faults are considered: actuator, component and transmitter faults. All the faults will be represented by additive terms in the model used for plant simulation and for the design of the residual generator. The so-called failure mode signals characterize the appearance of faults in those terms. They take form of step-like signals appearing at random time instants. The considered faults and their notations are as follows : lu, ' fault in valve Vi, i=I ,2; CPIR j, leak in tank Ri, i=I ,2; c, partially clogged injector;

if u, > Vi J!·tr if ii, <0 ' v'

r'w

Vi = 0

Figure 1.: Gas-liquid separation unit

2.2

Vi MIN = maximum closing speed of Vi ;

in

230

•

Measurement equations:

him = hi + nhl +

By analysing the equations of the model, together with the expression for the different residuals, and by taking into account the use of PI controllers to regulate him

kz .. = kz + nh2 + Ih2 '

fh'

Plm = PI +n pl + f p' '

and Plm' one can deduce the effects of faults on the

=<1>, + n"., + f ."

residuals at the steady state. They are summarized by means of the incidence matrix shown in Table I . Entry «I» in the ith row and the jth column of the table indicates that residual rj is sensitive to the jth fault whilst entry «0» denotes insensitivity (Patton, 1994). A physical justification for some of the entries of this table can be found in (Denolin et aI., 1996).

<1>, ••

where n hi' n h2 ,n pi' nCl>1 and n
Table 1.: Incidence matrix

3. RESIDUAL GENERATION .fl/I -

rl r2 r3 r4

In this section we will derive seven residuals. They are not designed in order to exhibit individually particular predefined sensitivity properties, like in the so-called extended fundamental problem of residual generation (Massoumnia et aI., 1989), but follow from rather natural considerations regarding the process.

rs r6 r7

Since 5 measurements are available and the separation unit is a process with 3 state variables, we obviously have hardware redundancy. Hence, one can derive in a straightforward manner the following residuals from equations (1) and (2): r l = Cl> 'M

- K, (u,

)..r;;:: ,

r. = ct>,.. - (fJ - a PI .. ) The last residuals considered in this paper are the observation errors of the following state observers:

dh dt

1 YI (him - hi) +-(<1> ... - <1>' m) A

=

dh, dt

51

-

1

A

C

f PI ;.-..

1

0

h,

fh,

.fib,

Jib,

0

0

1

0

1

0

1

0

1

0 0

0 0

0 0 0

1

0 0

0 1

0 1

0 0

0 0

0 1 1

0 1

0 0 1

0 0

0

0

0

0

0

0

0

0

0

0

0

0 1

1

0

0

0

1

1

0 1

0

0

0

0

1

1

0 0

0 1

To analyse the sensitivity of the residuals to different faults, simulations were performed. Two situations were considered separately: the case of abrupt faults, which can be simulated by step-like failure modes, and slow faults, which are simulated by ramp-like signals. The motivation for studying both cases is that they lead to residuals with significantly different patterns. Indeed, step-like failure modes induce abrupt residual changes which can have a non-monotonous behaviour, i.e. they tend to zero after a few seconds or tens of seconds. The latter phenomenon is associated to zero entries in the incidence matrix. On the other hand, slowly acting faults, of which the time constants are typically much larger than the process time constants, lead to slowly drifting (monotonous) residuals. It is obvious that different strategies and tools are needed for their evaluation. Due to the lack of space, only abrupt faults are considered here. The reader is referred to (Denolin et aI., 1996) for the study of slowly acting faults .

Since the system is expected to remain in steady state as long as no fault occurs, ct>z = ct>. and ct>1 = fJ - a p, hold if the system is healthy. One may then derive the next two residuals:

_I

1R2

f1/2 - /RI

- - = y ,(h,m -h, )+-(<1>' m -<1> ... )

dp,

Tt = 13 (P I", -

-

-

-

52

-

Table 2 shows the residual patterns obtained for single step-like faults, with magnitude 5% of the nominal conditions, at time t = 200s. One can distinguish two types of residuals : those for which the signal to noise ratio is large, which can be evaluated by comparison to a simple threshold, and those for which this ratio is small, which will be processed by a generalized likelihood ratio (GLR) test.

I PI) + 51 (hRI -him) (Po (<1>air -<1>lm) A

+ (Po + Plm)(<1> .. - <1>2m»

The above observers are straightforward extensions of Luenberger observers for linear systems up to output injection. Indeed, in the second terms of the right hand side of the observer equations, all the quantities are available through measurements. Hence it suffices to choose YI. Yz and Y3 according to the desired observer dynamics .

Notice that the sensitivity of the last three residuals in Table 2, namely rs ' r6 and 1'7 ' strongly depends on the observer time constant, which is set to 20 seconds in the simulations. The larger the time constant is. the larger is the sensitivity, but the residuals react slower.

231

Table 2.. : Residual patterns resulting from abrupt faults

1: = 5%

1:", = 5%

fill I =5%

f /ll, =5 %

c =5%

[J

0

0

0

0

"I

rI

1'2

0

CD

0

0

0

.~

0

negligible transient response

.... .... . .... -

r3 IV W IV

1'4

r5

negligible transient response

..~

"

. , . ,,-,,- .. .- .

~

'"

" , ---:0

..

..

..

..

.~

0

0

0

~

0

0

r7

0

0

J:h, =5%

CEJ

0

0

..

.~ ... .. .... .. ",

0

negligible transient response

~

~

0

0

I]]

0

0

.~

0

~

...•~

.u:.d

"

.~

"

'.

"

- - . . .. .. 0

[IJ ,

..

0

"

"

..

0>

0

-

n:J ----

----

----

negligible transient response

.~ - - - - --- - - --- -

-

- - --

... -;---::- ..

o.

0

.~

0

.~

..

1IJ "

0

..

0

"

.~

0

-

... ...... .

I

0

. .... ..

"

0

0

f I =5%

.o:J ",

w

~

~ -

0

f I =5%

"

. ~

negligible transient response

r6

J:hi =5%

..

negligible trans ient response

:',

f PI =5%

--

':

"

~

0

"

"

..

. c.cJ ~ ,.

--

-

..

~

. .

" .,

-- ----

4. RESIDUAL EVALUATION BY MEANS OF THE GLR TEST ,/.1

the least sensitive to the fault must be considered for this purpose. However, the cases where the residual reacts only temporarily should not be taken into account here, as they were associated to a zero entry in the incidence matrix. From Fig. 2 and the evaluation of the test for residual r3, corresponding to f PI =5% and

General considerations

Residuals r3 to r7 are strongly affected by measurement noise, so they cannot be evaluated by comparison to a simple threshold. The GLR test will be used for this task. Besides detecting changes in the properties of the residual, it also gives reliable estimates of the fault magnitude and the fault occurrence time.

f
fixed by looking at the test function obtained for <1>/R/=5%. 0=0.002 seems to be a reasonable choice.

At this stage, it is possible to detect residual changes even in the worst cases. However, it is not possible to tell whether the residual reacts only temporarily or remains different from zero as long as the fault affects the process. This is the subject of the next subsection.

The design of the GLR test requires knowledge of the dynamic profile of the change, namely the map between the failure mode and the residual. However, as each residual is sensitive to several faults, and as this map is different in each case, we necessarily have to make an approximation here. The simplest solution is chosen, namely to design the test assuming it has to detect changes in the mean of the residuals. The algorithm of the corresponding GLR test is presented by Basseville and Nikiforov (1993) and Denolin et al. (1996). Notice that it is theorically developed to detect changes in the mean of a sequence of independent Gaussian variables with constant variance. Although the residual samples do not exactly make such a sequence, the test yields suitable results, as is illustrated in the example considered below.

4.3

Delection of non-monOlonous residuals which decay to zero

For the residuals reacting only temporarily to the faults, an abrupt change is immediately followed by a smoother change in the opposite direction, except for fh 0 (see Table 2). Moreover, notice that time I

*"

constants characterizing the transient with which residuals drift back to zero are known. For residuals r3 and r4, they correspond to the dominant time constants of the level and pressure closed-loop respectively. The order of magnitude of the former is from a few tens of seconds to a minute, while it is only a few seconds for the pressure loop . Regarding the last three residuals, rj, r6 and r7, the time constants characterizing their transient are mainly related to the observer time constants.

When applying the GLR test, one should fix two design parameters, namely the test window M and the threshold 5. From the general point of view, the threshold depends on the noise level. It should obviously be fixed beyond the typical test output in the absence of fault, in order to avoid false alarms. Furthemore the threshold should be chosen so that it can be reached within the time interval [to, 10 +:\1] when a fault occurs. Here, 10 denotes the fault occurrence time. The choice of the test window length is probably less crucial. However, one should be aware that the larger is M, the larger is the test output at time 10 + AI . One could be tempted then to choose M rather large, but this would lead to more computational efforts.

r3 (/u2

As an illustration, the above considerations are now used to evaluate the residual rJ. ,/.2

one deduces that the threshold 0 should be

= 5% al

10=200s) .;C; ••'~----------,

Evalualion ofr;

The test horizon ,'.1 is fixed to lOOs. Notice that this value roughly corresponds to the time constant of the residual transient (see Table 2). The GLR test function can now be computed for r 3 , for each fault case. This is illustrated in Fig. 2 for fu2 = 5% and <1>/lu=5% respectively. Notice that the extension of the GLR function beyond 1=300s (= 10 + M) is meaningless, as the threshold will normally be reached before 10 + M, which should yield a reinitialization of the test. The chosen value of AI is seen to yield large enough values of the test function.

GLR test function (:\.1=100s) GLR test function (M=100s) Figure 2.: Response of the classical GLR test for detecting changes in residuals

To detect whether the change in the mean of the residual is temporary or not, we shall reinitialize the GLR test after the detection of a change in the mean and we shall apply it to a new set of data. More precisely, the residual evaluation strategy is the following. The GLR test considered in Fig. 2 is reinitialised as soon as the threshold is reached and the data to be tested are

To complete the test design, a suitable threshold must be determined. The situation where the test function is 233

updated. The new data vector consists of the residual to +2T , which samples, except the samples from are skipped. T is the dominant time constant of the residual transient, which is 60s in our example and is the estimated fault occurrence time. In this way, the new vector to be tested is quasi step-like, if the residual remains different from zero as long as the fault affects the system, and a second abrupt change will be detected through the GLR test. If the residual reacts only temporarily, no second change is detected. One can draw a definite conclusion concerning this feature at time + 2T + M . Notice that the second GLR test can typically be performed with the same parameters as the first one. The result of this second test allows one to isolate the fault thanks to a decision system based on the incidence matrix of Table 1.

to

and isolate abrupt faults . Several rules of thumb and design considerations have been provided for the GLR test, on the basis of our application. We believe that this work illustrates the flexibility offered by the combination of different residual generation and evaluation methods for the design of a diagnosis system.

to

to

Further studies must be performed for the actuator faults. Indeed, the latter were simulated by adding a constant signal to the controller output. In general, this is probably not the most realistic way for simulating valve faults, since these are typically of friction type. Such faults affect the dynamical behaviour of the process. A more realistic model for valve friction should be investigated and a strategy including oscillation analysis (c.f. Hagglund, 1994) should probably be developed.

to

This strategy is now illustrated for two fault cases : fU2 = 5% and IRI=5%. The first and the second column of Fig. 3 show the residual and the resulting GLR test function for each situation. The threshold 0 is indicated by the dotted line. As previously, the fault occurs at to = 2005 . It is detected a few seconds later

ACKNOWLEDGMENT The support of the European Commission in the framework of the Copernicus project CIPA-CT94-0237 is gratefully acknowledged. REFERENCES

for fu2 and around 2805 later for lRl' Fault isolation will then be performed on the basis of Table I at time + 2 T + M =4205. At that time instant, one can clearly distinguish between temporary and non temporary changes in the mean of the residual as is illustrated in Fig. 3.

Basseville M. and LV. Nikiforov (1993). Detection of abrupt Changes, Theory and ApplicatiOns. Englewood Cliffs, NJ, Prentice-Hall.

to

Denolin E., D. Vrancic, M. Kinnaert, D. Juricic and 1. Petrovcic (1996). Model-based diagnosis for a gas-liquid separation unit. Internal report. Copernicus project CT94-0237. Hagglund T. (1994). Automatic Supervision of Control Valves, Preprint 0/ SAFEPROCESS '94, Espoo, Finland, Vol. 2, pp. 439-444 .

.,

,' ''''.o~--:,,,, :c--::,,,,: :--= ,.,----:.=,,, --::,.,::---:!..

rJ (/,,2=5% at to=200s)

Massoumnia M., G.c. Verghese and A.S . Willsky (1989). Failure Detection an Identification. IEEE Trans. Automatic Control, AC-34, pp. 316-321.

r] ('Rl=5% at to=200s)

.,,'

>,~------------~

I

'r

Patton R.J. (1994). Robust model based Fault Diagnosis: the State of the Art. Preprint of SAFEPROCESS '94, Espoo, Finland, Vol. 1, pp. 1-24.

,,,I

I

'1

I

'1,,

......

... co

Peng Y., A. Youssouf, P. Arte and M. Kinnaert (1996). A complete Procedure for Residual Generation and evaluation with Application to Heat Exchanger. To appear in IEEE Trans. Control Technology and Applications.

'0

GLR testfitnction (M=IOOs) GLR test/unction M=IOOs) Figure 3.. Response o/the GLR test/or detecting the temporary changes in residuals This strategy holds for most of the faults , except for the level transmitter fault. In this case, the residual goes back to zero only after a few minutes, during which the residual amplitude remains constant. This phenomenon can be detected and used to isolate faults in the level transmitter for h, (Denolin et al., 1996).

Vanden Daele R., Y. Peng and M. Kinnaert (1997). Fault diagnosis using belief functions . Proceedings of SAFEPROCESS '97. Vrancic D., D. Juricic and J. Petrovcic (1995) . Semiindustrial benchmark problem: measurement and mathematical modelling of a process for separation of gas from liquid . Internal report. Copemicus Project CT94-0237 .

5. CONCLUSIONS A model based diagnosis system for a gas-liquid sepration unit was presented. Seven residuals were generated and evaluated in parallel in order to detect 234