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Model-Free Actuator Fault Detection Using a Spectral Estimation Approach: The Case of the DAMADICS Benchmark Problem
IFAC
Copyright 0 IFAC Fault Detection, Supervision and Safety of Technical Processes, Washington, D.C., USA, 2003
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Publications www.elsevier.comllocatelifac
MODEL-FREE ACTUATOR FAULT DETECTION USING A SPECTRAL ESTIMATION APPROACH: THE CASE OF THE DAMADICS BENCHMARK PROBLEM
F. Previdi • and T. Pariaini·· • Dept. of Engineering University of Bergamo, 14044 Dalmine (BG), Italy •• Dept. of Electrical, Electronic and Comp1Jter Engineering DEEI-University of7H.....te, 941~7 7He6te, Italy Abstract: Thi'l paper prc.'Ient.'I the application to the DAMADICS benchmark fault detection problem of a model-frec fault detoction tochniquc b8!led on the use of a spocifie spectral analysis tool, namely, the Squared Coherency Jilunctioru (SCFs). The detection of the fault is achieved by on-line monitoring the estimate of the squared cohereney funetion, whieh is seDB.itive to the occurrence of nonlinear effects in the plant dynamics. The alarm threshold are determined by using off-line estimates of the confidence intervals of the SCF c.'Itimation. Results on data from the simulation model of the DAMADICS benchmark (which i'l developed to approximate the industrial process in a sugar factory located in Lublin, Poland) are outlined. Copyright @ 2003 /FAC Keywords: Actuator faults, Spectral estimation, Modcl-free fault detoction
FD problem from the control-board operator's point of view. The basic idca ill to monitor on-line the me8!lUfements of the control system variables without the need for defining explicit dependence laws among them. By analysis of the mca.'1ured variables the operator can docide about the operating mode of the plant and raise alarm.'!. In thi'l context, sometimes the problem can be 8."1similated to a pattem-rocognition problem (sec, for ill.'Itance, (Guglielmi et al., 1995) and the references cited ·therein).
1. INTRODUCTION Monitoring complex indUlltrial plant.'I for the purpo.'IC of automated fault detection is a t8!lk of fundamental importance in many arca.'I of control engineering. Therefore, since the early '70s, a lot of approachc.'I to fault diagnosi'l (FD) have bcen developed that may be roughly el3.'I.'lified 3.'1 (i) modcl-b8.'Iod FD approaches and (ii) modelfree FD approaches. In thi'l work, we foOlL'I on a model-froc technique (for overvicws on modelb8.'lCd method'!, we refer the reader, for instance, to the book.'1 (GertIer, 1998; Patton et al. , 1989) , and to the references cited therein}.
In the e8.'IC of thi'l paper, the u.'IC of a Squared Coherency Jilunction (SCF) for model-free FD is investigated and some prcliminary result.'! about the application to the Damadies benchmark arc given. Wc 8.'I!Iume that the fault free dynamic behavior of the plant i'! linear. This situation is quite common in industrial procCII.'1C8 where the nominal bchavior of the plant can be regarded 8..'1 a linear one due to the prc.'lCDoc of the regulation system. One of the main (and undesired) effects of the oceurrence of a fault i'! ju.'It the deviation from the nominal healthy mode of operation. So, the effect of a fault oceurring on the plant
In general, model-frec method'! do not require the model of a plant to generate fault signals. Specifically, they mainly consist in addrCII.'!ing the
* Corresponding
author: Thomas Parisini (email: parisiniOunita.it) . The &uthon adtDowledge funding support under the EC RI'N contract (RTN-1999-00392) DAMADICS. Thanks are expr.aed to the management and eta.ff of the Lublin sugar factory, Cultrownia LubJin SA, Poland for their collaboration and provision of manpower and IOCceoII to their sugar plant.
855
Vapour model
_I
. .. . .. . . . . ....ct.::C5~~ . .. .. %
P61_04 kPa
11
·e · :
r8
%
%
~
1 1 1 1
~
, .j. ...... . . .... . . ....•.•• • + ...
:Temperature model
1 ___I
Fig. 1. The evaporation IItation. Heaters and the first evaporation soction. i.'I simply a/l.'Iumed to be a nonJinear dynamieal perturbation to the above linear onc. Then, FD can be achieved by dc.'Iigning a fault detector senllitive to the ari.'Iing of nonlinear components in the plant dynamics. Such a detector i.'I ba.'lCd on the computation of SCFs ll.'Iing mca.'Iurement signals from the plant, without rcsorting neither to a model of the plant, nor to a modcJ of the fault dynamic.'I. In fact, it ill well known that the SCF could be effectively used as a nonparamctric tool for identification of nonlinear componentll in system dynamics (lIee (Habcr, 1985».
cv
...
In the next section, we give a brief dC.'lcription of the DAMADICS FD benchmark in the framework of the con.'Iidered indlL'Itrial procc.'IIl. In Section 3, the SCF-based methodology for FD ill presented, wherea.'I, in Section 4, extensive lIimulation results on the detection of some fault.'I in the DAMADICS benchmark are reported, showing the effectiveness of the proposed FD technique. 2. THE DAMADICS BENCHMARK In thi.c; section, a brief description of the actuator that will be investigated in the paper i.'I given. The plant under concern i.'I the sugar factory Cukrownia Lublin S.A loeated in Lublin (Poland) and the procC!l.'Iunder invc.'Itigation i.'I sehematically shown in Fig. 1. We con.crider the evaporation procC!l.'I where the main ta.'Ik is to thicken the beet juice coming from thc clcaning and filtering stages, at thc minimum heat-energy con.'Iumption. Thc firllt three scction.'I work with natural juice circulation and the la.'It two work with juice circulation forced by pump.'I. Wc foclL'I on the firRt section, con.'1i.'1ting of onc evaporator and containing an important actuator, located on the inflow of thin juice and controlling its level in the first stage of evaporation Iltation.
f~
--~ VI
V
V3
Vl
Fig. 2. A control valve-pneumatie IIcrvomotorpositioner device. • Control valve driven by a servomotor, which ill UIled to prevent, to allow and/or to limit the flow of fluid'l . • Spring-and-diaphragm pneumatic senJomotor; thi.'1 i.'1 a comprC!l.'Iible fluid powered device where the fluid act.'1 upon the flexible diaphragm thlL'I providing linear motion of the Ilervomotor stem. • Positioner; thi.'I device is lL'Ied to cJiminate control-valve litem mis.'l-position.'1 due to external or internal sources such a.'1 friction or hydrodynamic forces.
Fig. 3 shows a more detailed overview of the servomotor as well as its physical layout; the effects (forcc.'1) of the other two component.'1 arc emphasized (the meaning of the symbol'I i.'l straightforward and i.'l not prcscnted for the sake of brevity) . A rather detailed dynamic modcJ of the above evaporation procc.'1s (and of the actuator a.'1 wcJl) ha.'l becn developed · and validated in the context of the DAMADICS rcscarch training network. In this paper, the analysis is foclL'>Cd on those faults whose primary nature i.'l abrupt. The main goal is to check the effectiveness of the algorithm
A.'I shown in Fig. 2, the actuator ill made of threc main component.'I (Bartys et al., 2(02):
856
at the time tJ. Suppose that the fault modifies the lIystem dynamics, introducing nonlinear dynamics ob"enJable in the "1I"tem output. If so, wc have t hat: - if t < tJ, then "!I/(J)
= I, Vf
E :F
- if if t ;::: t J , then ":1I(J) < 1 , in a subllet of :F where :F i'l the set of frequencies where the SCF can be defined. In qualitative termll, the meaning of the above expressions is the following: prior to the oecurrenee i'l identically of a fault (i.e, at t < t f), the SCF equal to onc, wherca.'I, after the occurrence of a i'l ICSII than onc for some fault at time t J, frequency.
":11
":11
Fig. 3. The pneumatic servomotor and its physical layout.
In the DAMADICS benchmark, the con.'1idered system hR.'I not perfectly Iinca.r dynamies even in fault-free conditioIl.'1. However, the proposcd method could be lL'Ied aL'IO in the more general C8.'Ie when the plant h8.'I nonlinear dynamies, even if this could result in potential non-detectability of a fault. In general, the oecurrence of a fault will result in a change in the SCF from the nominal fault-free value, which is different from one. So, the detection algorithm will be ro-designed to react to changes in the nominal fault-free c.'Itimate of the SCF.
in detecting the faults occurring on such a dovice. So, 8.'1 a prelimina.ry t8.'1k we analysc la.rge amplitude fault.'1. We do not consider incipient faults or faults with small or medium amplitude. Moreover, as we propOlle the UIIC of a model-free technique, the problem of fault L
3. A FAULT DETECTION ALGORITHM BASED ON SPECTRAL ESTIMATION
A.'1 mentioned before, the proposed FD methodology i'l devoted to the detection of nonlincar faulty event.'I. On the other hand, 8.'1 the SCF is not sensitive to changes in the linca.r part of the input-output map of the plant, it follows that the detection of linear fault.'1 has to be done by using a different method (several well-established techniques devoted to the detection of linear faults are available in the literature (Gertler, 1998)) .
3.1 Basic theoretical framework The method. lL'Ied in thi'l paper i'l derived from the one prCIICnted in (Previdi et al., 2(01) . The method i~ b8.'1cd on the .,quared cohcrcncv function (SCF) (see, for instance (Stoica et al., 1997),(Jenkin.'1 et al., 1968)), which i'l defined as 2
"E'1
<,
(f) _
IrE'1(JW - rEE(J)r'1'1(J)
3.2 Algorithm for fault detr.ction In thi'l scction, the ba.'Iic algorithm i'l dc.'lCribed. The algorithm is b8.'Ied on three main steps. The first onc i'l an off-line step, performed on faultfree data: it i-i related to the tuning of the parameters to obtain an estimate of the SCF lL'lCfuI for FD purpOIlCll. The second and the third onc.'I are on-line steps, devoted to the final characterization of the alarm thrc.
where '7 are two real scalar stationary procc.'IIICS, r EE denotes the spectrum of r'1'1 denotc.'I the spectrum of '7 and rE'! i'l the cross-spectrum between
<,
The SCF ha.'1 a b8.'1ic property that inspired the FD scheme lL'Ied in thi'l work: given a linea.r system with input u(t), output y(t) and frequency respon.'1e G(j2rr I), in the abl!cnce of disturbancc.'I, the following hold'l
Step 1.
2 IG(j2rr fWr:" (J) ""I/(J) = r""(J)IG(j2rrf)12r,,,,(J) = 1,
Al; is well known, spectral estimates are affected
by bi8.'1 errors and have poor variance propertic.'1. To this aim, 8ffloothing techniques a.re often lL'ICd. Unfortunately, the smoothed cstimates a.re lL'Iually strongly dependent on the specific window lL'Ied and on it.'1 width. In (Previdi et al., 2001) a minimum-bia.. method for the estimation of the
forallf E R Now, con.'Iider a SISO (Single Input Single Output) linear system, in a disturbance-free setting, which is the subject of a po..'I.'Iible fault, oecurring
857
Remark 2. The time instant t.t ha.'I been defined
SCF hall been developed. The method alloWll the choice of a smoothing window family w!, among a finite set and then the estimate of the optimal window width Mo that guarantcc.'I minimum bias in the SCF estimate. The bias is c.'Itimated wring a IICCOnd order approximation which preservo the basic theoretical properties of the bias of the SCF (Lohnberg, 1978). This step must be performed off-line on fault-free input-output data.
in Step 2 only because wc need a finite batch of data to perform the initial estimate of the SCF.
Remark 3. Obviously, when dcaIing with long running measurements, the current estimate K~lI.t(f) can be performed without lL'ling all the available data, but only thORe included in a user-defined sliding window.
Step 2.
4. RESULTS
Thi'l step is performed on-line, lL'Iing the data measured on the plant for t = 0, . .. ,ton, where ton i'l the time iD.'Itant when the FD algorithm must start (Bartys et al., 2OO2). During this time interval the algorithm computes:
The data lL'ICd in this section have been generated using the software simulator available in the Simulink library for the DAMADICS project. The simulator parameters have been tuned by using experimental data from the real proCCII.'I, i.e. the actuator 3 in the Lublin Sugar Factory. All the variables UllCd in this section are defined in (Bartys et al., 2002).
(I) a first lault-fre£ estimate of the SCF using the window family w!,- computed during Step 1. The rcsult is an estimate K!II(f) of the SCF, ba.'Ied on the data available in
[O,tun)i
The analysis is foelL'Ied on those faults whORe primary nature is abrupt. The following fault secnariO!l have been coD.'Iidered:
(2) the upper and lower alarm thfUholds to be lL'Ied in the FD stage. ThCIIC are calculated according to the following procedure: for each t E [t.t, ton), whore t.e is a WlCr-defined time instant in [0, ton), compute the 100(1 - a)% confidence inte~va1 [k;;lI. t ,.. (f), k;!"lI.t ,.. (f») for the estimate K!lI. t (f} obtained using the data in [0, t) . Then define: Upper Alarm Th'fl'.3holtf.
A+(J)
=
sup tE[t.. ,t_l
(I) Control valve faults • /1 - valve clogging: blocking servomotor rod displacement. • 12 - valve plug or lICat sedimentation: calLm by sodimentation of solid particles. • h - medium evaporation or critcal flow: the flow i.'I a mixture of fluid and steam. (2) Pneumatic servomotor faults • le - twisted servomotor rod: permanent bending of the servomotor rod. • ho - IICrvomotor diaphragm perforation: caused by fatigue of diaphragm material. • fn - servomotor spring fault: C&lL'Ied by fatigue of spring material. (3) Positioner • /12 - E1ectropneumatic tran.'Idueer fault: due to changcs in the c1eetropneumatic tran.'!duccr characteri.'Ities. • h. - Electropneumatic transducer pressure 1ICD.'Ior fault: due to prc.'I!Iurc tran.'!ducer electronies part failure. • !I5 - Positioner feedback fault: cau.'lCd by fault of the spring. (4) General faults/External faults • f11 - Unexpected prc.'I.'lUre change acros.'I the valve: caused by media pump station failure. • ite - Fully or partly opened byp8.'I.'I valve: CalL'Ied by an operator. • !ID - Flow rate sensor fault: C&lL'Ied by electronics or wiring failure.
k;!"lI. t ... (f) "If E F
Lower Alarm Thrcsholtf.
A-(f) -
inf
k-
- tE[t•••t-1 "lI. t ...
(f)
"If
E
F
where F is the set of froquencics where the c.'Itimate L'I available. Summarizing, the rcsults of this second step are a fault-free estimate of the SCF K!lI.t_ (f), done with the data up to ton, and the alarm thresholds A - (J) and A+(f}. Step 3. Thi'l is the main part of the FD algorithm. For each t E [to.. , tl.""), where tl•.". i'l the time horizon of the data coming from the plant, the current cstimate K~II.t(f} L'I computed, using the data in [0, tl. Then, if K~II.t(J} ~ A+(J) or if K!II,t(f) :::; A- (f) for any f E F, an alarm is generated. Remark 1. During Step 1 a crucial operation must he done, the choice of the two variablcs to be lL'lCd to compute the SCF cstimate and the alarm thrcshold. This choice must be "physically driven" , such 8.'1 to say, depending on the fault we are trying to deteet, wc must WIC in the algorithm tha;e measurements which are affected in some way by the fault occurrence.
The value of the rod diBplacement X and the medium flow F, generated by simulatioD.'I including mca'lurement nOL'IC, have been lL'Ied for the
858
detection of all the considered fault.'l except 117: in thi'l ca.'le, the pressure on the control valve inlet PI and the pressure ~thc control valve outlet P2 have boon lL'lcd. This ch~ have been driven by the physies of the system and they arc not unique. For in.'ltanoo, detection of h could be achieved by lL'ling al'lO the fluid temperature TI.
...
The preliminary off-line step of the algorithm ha.'l provided the window to be I18Cd for the estimation, a Papouli'l window with width Mu = 4 (Papoulis, 1973). It ha.'l been verified in practioo that this window is very effective in the estimate of SCF (sec for in.'ltanee (Previdi et al., 2001», providing minimum bias estimatc.'l, at lca.'lt in comparison with other widely lL'lCd windows. The length of the time interval noocssary to get faultfree estimates ha.'l boon decided by trial and error. The minimum requirement i'l that the data set should be large enough to obtain an c.'!timate of SCF, i.e. in general not lc.'l.'l than 256 samples.
OA
DO
.... ..,
... Normalized Frequency 1Hz)
(a)
All the expcriment.'l are performed with sampling time Ts = lH. The time sequence for all the trials is the following: tNt = 2568 is the time instant from which start.'l the preliminary on-line pha.'le for the calculation of the alarm threshold; (2) ton = 500.~ i'l the time instant at which the algorithm i'l ready to go; (3) t Ir",.,. = 900.~ i'l the time instant at which the fault occurs; (4) t,.ur = 1800,~ i'! the time instant at which the experiment stop.'l:
(1)
... Normalized Frequency 1Hz)
(b)
In the DAMADICS benchmark t",. i'l 300" and there i.'l not t.t. This difference is due to the intrinsic features of this algorithm: since it i'l ba.'led on spectral estimatc.'!, at lea.'lt 256 samplc.'! are nooded to obtain a first significative SCF estimate. Then, about 250" i'l the time interval nooc.'l.'!ary to obtain a stable estimate of the alarm thrc.'lhold.
Fig. 4. Detootion of the fault 111 with a = 95%. (a) SCF estimate with the alarm thresholds before the fault. (b) SCF estimate with the alarm thrc.'!hold'! after the fault.
In Fig. 4 a typical example of the effect on the SCF of the occurrence of a fault. In fault-rroo condition.'l the current SCF estimate i.'! completely in.'lide the alarm threshold'l. An alarm is generated when thc SCF cr09.'ICS, in any point, onc of the alarm thrc.'lhold'l. The algorithm has been tested using different values for the significativity a of the confidence interval c.'ltimatc.'l. Specifically, the valuc.'1 a = 90%,95%,99% ha.'! been used. It i.'! expeeted that, a.'! a incrca.'1es, the fal'le alarm rate should deerea.'le while, on the contrary, inerca.'ling the con.'lervativencss of the algorithm, the detection time tdt should incrca.'1e. In Tablc.'l 1, 2, 3 results from detection test using different alarm thresholds are shown. In all the tablc.'l, tdt indicates the detection time, i.e. the time elap.'lCd before the fault
859
fault fault fault fault fault fault fault fault fault fault fault fault
1 2 7 8 10 11
12 14 15 17 18 19
Variables used
tdl (s)
rld
rid
X,F X,F X,F X,F X,F X,F X,F X ,F X,F
405 693 324 261 243 144 657 261 135 15 162 252
0 0 0 0 0 0 0 0 0 0 0 0
0.55 0.23 0.60 0.71 0.73 0.84 0.27 0.71 0.85 0.98 0.82 0.72
Pl, fIz
X,F X,F Table 1. Relmlt.'l for a
= 99%.
i'l detooted; rId indicatc.'l the false detootion rate, i.e. how long the alarm stays switched on before the fault occurred; rtd indicatc.'1 the true detection rate, i.e. how long the alarm stays switched on after the fault occurred. All thc.'!e values have boon defined following the Damadies benchmark definitions.
t.u CB) rld X,F 153 0.02 X,F 171 0.02 X,F 153 0.02 X,F 153 0.02 X ,F 0.02 234 10 X,F 0.02 X,F 0.02 306 X,F 153 0.02 0.02 X ,F 72 9 0 f\,PJ X,F 0.02 63 0.02 X ,F 63 Table 2. ResultR for er = 95iJi:,.
Variable8 u.d
fault fault fault fault fault fault fault fault fault fault fault fault
1 2 7 8 10 11 12 14 15 17 18 19
fault fault fault fault fault fault fault fault fault fault fault fault
1 2
Variabl. u.d
X,F X,F X,F X,F X,F X,F X,F X,F X,F
7 8 10 11 12 14 15 17 18 19
t"I CB) 72
63 72
18 135 9 81 18 54 9 36 54
PI , PJ
contrary, the lower ill the UIIcd value for er, the higher is the faille deteetion rate, i.e. a falllC alarm ill switched.
rl" 0.83 0.81 0.83
Future work will be focUllcd on detoction of IImall amplitude and/or incipient faults and, finally, on isolation.
O.SS 0.74 0.99 0.66 0.81 0.92 0.99 0.93 0.78
A last remark eonecrD.'I the signal URCd to excite the system, i.c. the control variable CV which i.'I sinUllOidai. We muat put in evidenee that such a signal is not the bCllt for spectral CIItimation baRed methods and it can have limited the power of the prCllODt method. This ill confirmed by the rCllults for fault f17 where signals not strictly depending on CV arc uacd: the deteetion is very fa.'It and no false alarms arc generated for any value of the dCllign parametcrs.
rid rld 0.22 0.92 0.22 0.93 0.22 0.92 0.22 · 0.89 0.22 0.79 0.22 0.99 0.22 0.85 0.22 0.89 0.22 0.94 0 0.99 0.22 0.96 0.22 0.94
6. REFERENCES
X,F X,F Table 3. RcsultR for er = 90%.
!1 , , , , L : : 0_
«It
_
_
....
1
,.t4IOt.o_
, , : : 11: ' : ' 1 2DO
..
_
_
,..
!1 : , : ~M 0_
4IICt
_
_
':aDO
MOO
,..
..
','1
'_,DMOI""_
Time 1-1 Fig. 5. Detection Decision signal for different valuCII of er in fault fu, .
Finally, in Fig. 5 the time plot of the Detection Dcci.'Iion lIigna! is IIhown for onc of the eOllllidered fault.'!. Similar plot.'! can be obtained from all the other fault tClltR.
5. CONCLUSIONS In thill work, faults who.'IC primary nature i.'! abrupt have been analyzcd. The propo.'!Od algorithm provides effective fault detection, at leaa;t in the ca.'!e of large abrupt faultR. In particular, for any value of the dCllign parameters, the algorithm prCllcnts a high true detection rate. In general, it ha.'! been obllerved that the detection of a fault i.'! the fa.'!ter when low valuCII of er arc UIIed. On the
860
Bartys, M. and M. Syfert, "DAMADICS benchmark definition" . J. J. Gertler, Fault Detection and Diagnosis in Engineering Systems. New York:Marccl Dckker, 1998. GugUclmi, G., T. Parisini and G. Rossi (1995). Fault diagnosis and neural networks: a power plant application. Keynote Paper, IFAC Control Engineering Practice 3,601-620. Haber, R. (1985). Nonlincarity tCllt.'I for dynamic procCII.'ICII. In: Proc. of the IFAC Identification and System Parameter Estimation. York, UK. pp. 409-413. Jenkins,G. M. and D.G. Watt.'I, Spectral Analysis and Its Applications. San Franci.'ICO:HoldenDay, 1968. Lohnberg, P., "Improved approximation of bias in Rquared coherency CIItimatCII for weakly smooth spectra ," IEEE 7ransactions on Acoustic, Speech, and Signal Processing, vol. ASSP-26, pp. 172-174,1978. Papouli.'I, A., "Mflumum-Bia.'! Windows for HighResolution Spectral Estimates ," IEEE 7hm.,actions on Information Theory, vol. IT19, No. I, pp. 9-12, 1973. R.J Patton, P.M. Frank and R.N. Clark Ed.'!., Fault Diagnosis in Dynamic Systems, Theorv and Applications, Prentice Hall, Englewood Cliffs, N.1, 1989. Previdi, F. and T . PariRini, "Model-free fault dotection: a spectral CIItimation approach ba.'lCd on coherency funetioD.'! ," Int. Journal of Contro4 vol. 74, No. 11, pp.ll07-1117, 2001. Stoica, P. and R. MOIICR, Introduction to Spectral Anal~. Englewood CliffiI, NJ:Prenticc Hall, 1997.
Copyright 0 IFAC Fault Detection, Supervision and Safety of Technical Processes, Washington, D.C., USA, 2003
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0
t>
Publications www.elsevier.comllocatelifac
MODEL-FREE ACTUATOR FAULT DETECTION USING A SPECTRAL ESTIMATION APPROACH: THE CASE OF THE DAMADICS BENCHMARK PROBLEM
F. Previdi • and T. Pariaini·· • Dept. of Engineering University of Bergamo, 14044 Dalmine (BG), Italy •• Dept. of Electrical, Electronic and Comp1Jter Engineering DEEI-University of7H.....te, 941~7 7He6te, Italy Abstract: Thi'l paper prc.'Ient.'I the application to the DAMADICS benchmark fault detection problem of a model-frec fault detoction tochniquc b8!led on the use of a spocifie spectral analysis tool, namely, the Squared Coherency Jilunctioru (SCFs). The detection of the fault is achieved by on-line monitoring the estimate of the squared cohereney funetion, whieh is seDB.itive to the occurrence of nonlinear effects in the plant dynamics. The alarm threshold are determined by using off-line estimates of the confidence intervals of the SCF c.'Itimation. Results on data from the simulation model of the DAMADICS benchmark (which i'l developed to approximate the industrial process in a sugar factory located in Lublin, Poland) are outlined. Copyright @ 2003 /FAC Keywords: Actuator faults, Spectral estimation, Modcl-free fault detoction
FD problem from the control-board operator's point of view. The basic idca ill to monitor on-line the me8!lUfements of the control system variables without the need for defining explicit dependence laws among them. By analysis of the mca.'1ured variables the operator can docide about the operating mode of the plant and raise alarm.'!. In thi'l context, sometimes the problem can be 8."1similated to a pattem-rocognition problem (sec, for ill.'Itance, (Guglielmi et al., 1995) and the references cited ·therein).
1. INTRODUCTION Monitoring complex indUlltrial plant.'I for the purpo.'IC of automated fault detection is a t8!lk of fundamental importance in many arca.'I of control engineering. Therefore, since the early '70s, a lot of approachc.'I to fault diagnosi'l (FD) have bcen developed that may be roughly el3.'I.'lified 3.'1 (i) modcl-b8.'Iod FD approaches and (ii) modelfree FD approaches. In thi'l work, we foOlL'I on a model-froc technique (for overvicws on modelb8.'lCd method'!, we refer the reader, for instance, to the book.'1 (GertIer, 1998; Patton et al. , 1989) , and to the references cited therein}.
In the e8.'IC of thi'l paper, the u.'IC of a Squared Coherency Jilunction (SCF) for model-free FD is investigated and some prcliminary result.'! about the application to the Damadies benchmark arc given. Wc 8.'I!Iume that the fault free dynamic behavior of the plant i'! linear. This situation is quite common in industrial procCII.'1C8 where the nominal bchavior of the plant can be regarded 8..'1 a linear one due to the prc.'lCDoc of the regulation system. One of the main (and undesired) effects of the oceurrence of a fault i'! ju.'It the deviation from the nominal healthy mode of operation. So, the effect of a fault oceurring on the plant
In general, model-frec method'! do not require the model of a plant to generate fault signals. Specifically, they mainly consist in addrCII.'!ing the
* Corresponding
author: Thomas Parisini (email: parisiniOunita.it) . The &uthon adtDowledge funding support under the EC RI'N contract (RTN-1999-00392) DAMADICS. Thanks are expr.aed to the management and eta.ff of the Lublin sugar factory, Cultrownia LubJin SA, Poland for their collaboration and provision of manpower and IOCceoII to their sugar plant.
855
Vapour model
_I
. .. . .. . . . . ....ct.::C5~~ . .. .. %
P61_04 kPa
11
·e · :
r8
%
%
~
1 1 1 1
~
, .j. ...... . . .... . . ....•.•• • + ...
:Temperature model
1 ___I
Fig. 1. The evaporation IItation. Heaters and the first evaporation soction. i.'I simply a/l.'Iumed to be a nonJinear dynamieal perturbation to the above linear onc. Then, FD can be achieved by dc.'Iigning a fault detector senllitive to the ari.'Iing of nonlinear components in the plant dynamics. Such a detector i.'I ba.'lCd on the computation of SCFs ll.'Iing mca.'Iurement signals from the plant, without rcsorting neither to a model of the plant, nor to a modcJ of the fault dynamic.'I. In fact, it ill well known that the SCF could be effectively used as a nonparamctric tool for identification of nonlinear componentll in system dynamics (lIee (Habcr, 1985».
cv
...
In the next section, we give a brief dC.'lcription of the DAMADICS FD benchmark in the framework of the con.'Iidered indlL'Itrial procc.'IIl. In Section 3, the SCF-based methodology for FD ill presented, wherea.'I, in Section 4, extensive lIimulation results on the detection of some fault.'I in the DAMADICS benchmark are reported, showing the effectiveness of the proposed FD technique. 2. THE DAMADICS BENCHMARK In thi.c; section, a brief description of the actuator that will be investigated in the paper i.'I given. The plant under concern i.'I the sugar factory Cukrownia Lublin S.A loeated in Lublin (Poland) and the procC!l.'Iunder invc.'Itigation i.'I sehematically shown in Fig. 1. We con.crider the evaporation procC!l.'I where the main ta.'Ik is to thicken the beet juice coming from thc clcaning and filtering stages, at thc minimum heat-energy con.'Iumption. Thc firllt three scction.'I work with natural juice circulation and the la.'It two work with juice circulation forced by pump.'I. Wc foclL'I on the firRt section, con.'1i.'1ting of onc evaporator and containing an important actuator, located on the inflow of thin juice and controlling its level in the first stage of evaporation Iltation.
f~
--~ VI
V
V3
Vl
Fig. 2. A control valve-pneumatie IIcrvomotorpositioner device. • Control valve driven by a servomotor, which ill UIled to prevent, to allow and/or to limit the flow of fluid'l . • Spring-and-diaphragm pneumatic senJomotor; thi.'1 i.'1 a comprC!l.'Iible fluid powered device where the fluid act.'1 upon the flexible diaphragm thlL'I providing linear motion of the Ilervomotor stem. • Positioner; thi.'I device is lL'Ied to cJiminate control-valve litem mis.'l-position.'1 due to external or internal sources such a.'1 friction or hydrodynamic forces.
Fig. 3 shows a more detailed overview of the servomotor as well as its physical layout; the effects (forcc.'1) of the other two component.'1 arc emphasized (the meaning of the symbol'I i.'l straightforward and i.'l not prcscnted for the sake of brevity) . A rather detailed dynamic modcJ of the above evaporation procc.'1s (and of the actuator a.'1 wcJl) ha.'l becn developed · and validated in the context of the DAMADICS rcscarch training network. In this paper, the analysis is foclL'>Cd on those faults whose primary nature i.'l abrupt. The main goal is to check the effectiveness of the algorithm
A.'I shown in Fig. 2, the actuator ill made of threc main component.'I (Bartys et al., 2(02):
856
at the time tJ. Suppose that the fault modifies the lIystem dynamics, introducing nonlinear dynamics ob"enJable in the "1I"tem output. If so, wc have t hat: - if t < tJ, then "!I/(J)
= I, Vf
E :F
- if if t ;::: t J , then ":1I(J) < 1 , in a subllet of :F where :F i'l the set of frequencies where the SCF can be defined. In qualitative termll, the meaning of the above expressions is the following: prior to the oecurrenee i'l identically of a fault (i.e, at t < t f), the SCF equal to onc, wherca.'I, after the occurrence of a i'l ICSII than onc for some fault at time t J, frequency.
":11
":11
Fig. 3. The pneumatic servomotor and its physical layout.
In the DAMADICS benchmark, the con.'1idered system hR.'I not perfectly Iinca.r dynamies even in fault-free conditioIl.'1. However, the proposcd method could be lL'Ied aL'IO in the more general C8.'Ie when the plant h8.'I nonlinear dynamies, even if this could result in potential non-detectability of a fault. In general, the oecurrence of a fault will result in a change in the SCF from the nominal fault-free value, which is different from one. So, the detection algorithm will be ro-designed to react to changes in the nominal fault-free c.'Itimate of the SCF.
in detecting the faults occurring on such a dovice. So, 8.'1 a prelimina.ry t8.'1k we analysc la.rge amplitude fault.'1. We do not consider incipient faults or faults with small or medium amplitude. Moreover, as we propOlle the UIIC of a model-free technique, the problem of fault L
3. A FAULT DETECTION ALGORITHM BASED ON SPECTRAL ESTIMATION
A.'1 mentioned before, the proposed FD methodology i'l devoted to the detection of nonlincar faulty event.'I. On the other hand, 8.'1 the SCF is not sensitive to changes in the linca.r part of the input-output map of the plant, it follows that the detection of linear fault.'1 has to be done by using a different method (several well-established techniques devoted to the detection of linear faults are available in the literature (Gertler, 1998)) .
3.1 Basic theoretical framework The method. lL'Ied in thi'l paper i'l derived from the one prCIICnted in (Previdi et al., 2(01) . The method i~ b8.'1cd on the .,quared cohcrcncv function (SCF) (see, for instance (Stoica et al., 1997),(Jenkin.'1 et al., 1968)), which i'l defined as 2
"E'1
<,
(f) _
IrE'1(JW - rEE(J)r'1'1(J)
3.2 Algorithm for fault detr.ction In thi'l scction, the ba.'Iic algorithm i'l dc.'lCribed. The algorithm is b8.'Ied on three main steps. The first onc i'l an off-line step, performed on faultfree data: it i-i related to the tuning of the parameters to obtain an estimate of the SCF lL'lCfuI for FD purpOIlCll. The second and the third onc.'I are on-line steps, devoted to the final characterization of the alarm thrc.
where '7 are two real scalar stationary procc.'IIICS, r EE denotes the spectrum of r'1'1 denotc.'I the spectrum of '7 and rE'! i'l the cross-spectrum between
<,
The SCF ha.'1 a b8.'1ic property that inspired the FD scheme lL'Ied in thi'l work: given a linea.r system with input u(t), output y(t) and frequency respon.'1e G(j2rr I), in the abl!cnce of disturbancc.'I, the following hold'l
Step 1.
2 IG(j2rr fWr:" (J) ""I/(J) = r""(J)IG(j2rrf)12r,,,,(J) = 1,
Al; is well known, spectral estimates are affected
by bi8.'1 errors and have poor variance propertic.'1. To this aim, 8ffloothing techniques a.re often lL'ICd. Unfortunately, the smoothed cstimates a.re lL'Iually strongly dependent on the specific window lL'Ied and on it.'1 width. In (Previdi et al., 2001) a minimum-bia.. method for the estimation of the
forallf E R Now, con.'Iider a SISO (Single Input Single Output) linear system, in a disturbance-free setting, which is the subject of a po..'I.'Iible fault, oecurring
857
Remark 2. The time instant t.t ha.'I been defined
SCF hall been developed. The method alloWll the choice of a smoothing window family w!, among a finite set and then the estimate of the optimal window width Mo that guarantcc.'I minimum bias in the SCF estimate. The bias is c.'Itimated wring a IICCOnd order approximation which preservo the basic theoretical properties of the bias of the SCF (Lohnberg, 1978). This step must be performed off-line on fault-free input-output data.
in Step 2 only because wc need a finite batch of data to perform the initial estimate of the SCF.
Remark 3. Obviously, when dcaIing with long running measurements, the current estimate K~lI.t(f) can be performed without lL'ling all the available data, but only thORe included in a user-defined sliding window.
Step 2.
4. RESULTS
Thi'l step is performed on-line, lL'Iing the data measured on the plant for t = 0, . .. ,ton, where ton i'l the time iD.'Itant when the FD algorithm must start (Bartys et al., 2OO2). During this time interval the algorithm computes:
The data lL'ICd in this section have been generated using the software simulator available in the Simulink library for the DAMADICS project. The simulator parameters have been tuned by using experimental data from the real proCCII.'I, i.e. the actuator 3 in the Lublin Sugar Factory. All the variables UllCd in this section are defined in (Bartys et al., 2002).
(I) a first lault-fre£ estimate of the SCF using the window family w!,- computed during Step 1. The rcsult is an estimate K!II(f) of the SCF, ba.'Ied on the data available in
[O,tun)i
The analysis is foelL'Ied on those faults whORe primary nature is abrupt. The following fault secnariO!l have been coD.'Iidered:
(2) the upper and lower alarm thfUholds to be lL'Ied in the FD stage. ThCIIC are calculated according to the following procedure: for each t E [t.t, ton), whore t.e is a WlCr-defined time instant in [0, ton), compute the 100(1 - a)% confidence inte~va1 [k;;lI. t ,.. (f), k;!"lI.t ,.. (f») for the estimate K!lI. t (f} obtained using the data in [0, t) . Then define: Upper Alarm Th'fl'.3holtf.
A+(J)
=
sup tE[t.. ,t_l
(I) Control valve faults • /1 - valve clogging: blocking servomotor rod displacement. • 12 - valve plug or lICat sedimentation: calLm by sodimentation of solid particles. • h - medium evaporation or critcal flow: the flow i.'I a mixture of fluid and steam. (2) Pneumatic servomotor faults • le - twisted servomotor rod: permanent bending of the servomotor rod. • ho - IICrvomotor diaphragm perforation: caused by fatigue of diaphragm material. • fn - servomotor spring fault: C&lL'Ied by fatigue of spring material. (3) Positioner • /12 - E1ectropneumatic tran.'Idueer fault: due to changcs in the c1eetropneumatic tran.'!duccr characteri.'Ities. • h. - Electropneumatic transducer pressure 1ICD.'Ior fault: due to prc.'I!Iurc tran.'!ducer electronies part failure. • !I5 - Positioner feedback fault: cau.'lCd by fault of the spring. (4) General faults/External faults • f11 - Unexpected prc.'I.'lUre change acros.'I the valve: caused by media pump station failure. • ite - Fully or partly opened byp8.'I.'I valve: CalL'Ied by an operator. • !ID - Flow rate sensor fault: C&lL'Ied by electronics or wiring failure.
k;!"lI. t ... (f) "If E F
Lower Alarm Thrcsholtf.
A-(f) -
inf
k-
- tE[t•••t-1 "lI. t ...
(f)
"If
E
F
where F is the set of froquencics where the c.'Itimate L'I available. Summarizing, the rcsults of this second step are a fault-free estimate of the SCF K!lI.t_ (f), done with the data up to ton, and the alarm thresholds A - (J) and A+(f}. Step 3. Thi'l is the main part of the FD algorithm. For each t E [to.. , tl.""), where tl•.". i'l the time horizon of the data coming from the plant, the current cstimate K~II.t(f} L'I computed, using the data in [0, tl. Then, if K~II.t(J} ~ A+(J) or if K!II,t(f) :::; A- (f) for any f E F, an alarm is generated. Remark 1. During Step 1 a crucial operation must he done, the choice of the two variablcs to be lL'lCd to compute the SCF cstimate and the alarm thrcshold. This choice must be "physically driven" , such 8.'1 to say, depending on the fault we are trying to deteet, wc must WIC in the algorithm tha;e measurements which are affected in some way by the fault occurrence.
The value of the rod diBplacement X and the medium flow F, generated by simulatioD.'I including mca'lurement nOL'IC, have been lL'Ied for the
858
detection of all the considered fault.'l except 117: in thi'l ca.'le, the pressure on the control valve inlet PI and the pressure ~thc control valve outlet P2 have boon lL'lcd. This ch~ have been driven by the physies of the system and they arc not unique. For in.'ltanoo, detection of h could be achieved by lL'ling al'lO the fluid temperature TI.
...
The preliminary off-line step of the algorithm ha.'l provided the window to be I18Cd for the estimation, a Papouli'l window with width Mu = 4 (Papoulis, 1973). It ha.'l been verified in practioo that this window is very effective in the estimate of SCF (sec for in.'ltanee (Previdi et al., 2001», providing minimum bias estimatc.'l, at lca.'lt in comparison with other widely lL'lCd windows. The length of the time interval noocssary to get faultfree estimates ha.'l boon decided by trial and error. The minimum requirement i'l that the data set should be large enough to obtain an c.'!timate of SCF, i.e. in general not lc.'l.'l than 256 samples.
OA
DO
.... ..,
... Normalized Frequency 1Hz)
(a)
All the expcriment.'l are performed with sampling time Ts = lH. The time sequence for all the trials is the following: tNt = 2568 is the time instant from which start.'l the preliminary on-line pha.'le for the calculation of the alarm threshold; (2) ton = 500.~ i'l the time instant at which the algorithm i'l ready to go; (3) t Ir",.,. = 900.~ i'l the time instant at which the fault occurs; (4) t,.ur = 1800,~ i'! the time instant at which the experiment stop.'l:
(1)
... Normalized Frequency 1Hz)
(b)
In the DAMADICS benchmark t",. i'l 300" and there i.'l not t.t. This difference is due to the intrinsic features of this algorithm: since it i'l ba.'led on spectral estimatc.'!, at lea.'lt 256 samplc.'! are nooded to obtain a first significative SCF estimate. Then, about 250" i'l the time interval nooc.'l.'!ary to obtain a stable estimate of the alarm thrc.'lhold.
Fig. 4. Detootion of the fault 111 with a = 95%. (a) SCF estimate with the alarm thresholds before the fault. (b) SCF estimate with the alarm thrc.'!hold'! after the fault.
In Fig. 4 a typical example of the effect on the SCF of the occurrence of a fault. In fault-rroo condition.'l the current SCF estimate i.'! completely in.'lide the alarm threshold'l. An alarm is generated when thc SCF cr09.'ICS, in any point, onc of the alarm thrc.'lhold'l. The algorithm has been tested using different values for the significativity a of the confidence interval c.'ltimatc.'l. Specifically, the valuc.'1 a = 90%,95%,99% ha.'! been used. It i.'! expeeted that, a.'! a incrca.'1es, the fal'le alarm rate should deerea.'le while, on the contrary, inerca.'ling the con.'lervativencss of the algorithm, the detection time tdt should incrca.'1e. In Tablc.'l 1, 2, 3 results from detection test using different alarm thresholds are shown. In all the tablc.'l, tdt indicates the detection time, i.e. the time elap.'lCd before the fault
859
fault fault fault fault fault fault fault fault fault fault fault fault
1 2 7 8 10 11
12 14 15 17 18 19
Variables used
tdl (s)
rld
rid
X,F X,F X,F X,F X,F X,F X,F X ,F X,F
405 693 324 261 243 144 657 261 135 15 162 252
0 0 0 0 0 0 0 0 0 0 0 0
0.55 0.23 0.60 0.71 0.73 0.84 0.27 0.71 0.85 0.98 0.82 0.72
Pl, fIz
X,F X,F Table 1. Relmlt.'l for a
= 99%.
i'l detooted; rId indicatc.'l the false detootion rate, i.e. how long the alarm stays switched on before the fault occurred; rtd indicatc.'1 the true detection rate, i.e. how long the alarm stays switched on after the fault occurred. All thc.'!e values have boon defined following the Damadies benchmark definitions.
t.u CB) rld X,F 153 0.02 X,F 171 0.02 X,F 153 0.02 X,F 153 0.02 X ,F 0.02 234 10 X,F 0.02 X,F 0.02 306 X,F 153 0.02 0.02 X ,F 72 9 0 f\,PJ X,F 0.02 63 0.02 X ,F 63 Table 2. ResultR for er = 95iJi:,.
Variable8 u.d
fault fault fault fault fault fault fault fault fault fault fault fault
1 2 7 8 10 11 12 14 15 17 18 19
fault fault fault fault fault fault fault fault fault fault fault fault
1 2
Variabl. u.d
X,F X,F X,F X,F X,F X,F X,F X,F X,F
7 8 10 11 12 14 15 17 18 19
t"I CB) 72
63 72
18 135 9 81 18 54 9 36 54
PI , PJ
contrary, the lower ill the UIIcd value for er, the higher is the faille deteetion rate, i.e. a falllC alarm ill switched.
rl" 0.83 0.81 0.83
Future work will be focUllcd on detoction of IImall amplitude and/or incipient faults and, finally, on isolation.
O.SS 0.74 0.99 0.66 0.81 0.92 0.99 0.93 0.78
A last remark eonecrD.'I the signal URCd to excite the system, i.c. the control variable CV which i.'I sinUllOidai. We muat put in evidenee that such a signal is not the bCllt for spectral CIItimation baRed methods and it can have limited the power of the prCllODt method. This ill confirmed by the rCllults for fault f17 where signals not strictly depending on CV arc uacd: the deteetion is very fa.'It and no false alarms arc generated for any value of the dCllign parametcrs.
rid rld 0.22 0.92 0.22 0.93 0.22 0.92 0.22 · 0.89 0.22 0.79 0.22 0.99 0.22 0.85 0.22 0.89 0.22 0.94 0 0.99 0.22 0.96 0.22 0.94
6. REFERENCES
X,F X,F Table 3. RcsultR for er = 90%.
!1 , , , , L : : 0_
«It
_
_
....
1
,.t4IOt.o_
, , : : 11: ' : ' 1 2DO
..
_
_
,..
!1 : , : ~M 0_
4IICt
_
_
':aDO
MOO
,..
..
','1
'_,DMOI""_
Time 1-1 Fig. 5. Detection Decision signal for different valuCII of er in fault fu, .
Finally, in Fig. 5 the time plot of the Detection Dcci.'Iion lIigna! is IIhown for onc of the eOllllidered fault.'!. Similar plot.'! can be obtained from all the other fault tClltR.
5. CONCLUSIONS In thill work, faults who.'IC primary nature i.'! abrupt have been analyzcd. The propo.'!Od algorithm provides effective fault detection, at leaa;t in the ca.'!e of large abrupt faultR. In particular, for any value of the dCllign parameters, the algorithm prCllcnts a high true detection rate. In general, it ha.'! been obllerved that the detection of a fault i.'! the fa.'!ter when low valuCII of er arc UIIed. On the
860
Bartys, M. and M. Syfert, "DAMADICS benchmark definition" . J. J. Gertler, Fault Detection and Diagnosis in Engineering Systems. New York:Marccl Dckker, 1998. GugUclmi, G., T. Parisini and G. Rossi (1995). Fault diagnosis and neural networks: a power plant application. Keynote Paper, IFAC Control Engineering Practice 3,601-620. Haber, R. (1985). Nonlincarity tCllt.'I for dynamic procCII.'ICII. In: Proc. of the IFAC Identification and System Parameter Estimation. York, UK. pp. 409-413. Jenkins,G. M. and D.G. Watt.'I, Spectral Analysis and Its Applications. San Franci.'ICO:HoldenDay, 1968. Lohnberg, P., "Improved approximation of bias in Rquared coherency CIItimatCII for weakly smooth spectra ," IEEE 7ransactions on Acoustic, Speech, and Signal Processing, vol. ASSP-26, pp. 172-174,1978. Papouli.'I, A., "Mflumum-Bia.'! Windows for HighResolution Spectral Estimates ," IEEE 7hm.,actions on Information Theory, vol. IT19, No. I, pp. 9-12, 1973. R.J Patton, P.M. Frank and R.N. Clark Ed.'!., Fault Diagnosis in Dynamic Systems, Theorv and Applications, Prentice Hall, Englewood Cliffs, N.1, 1989. Previdi, F. and T . PariRini, "Model-free fault dotection: a spectral CIItimation approach ba.'lCd on coherency funetioD.'! ," Int. Journal of Contro4 vol. 74, No. 11, pp.ll07-1117, 2001. Stoica, P. and R. MOIICR, Introduction to Spectral Anal~. Englewood CliffiI, NJ:Prenticc Hall, 1997.