Bayesian Filtering of "Smearing Effect" -- Fault Isolation in Chemical Process Monitoring Jia Lin Liu Center for Energy and Environmental Research National

Bayesian Filtering of "Smearing Effect" --Fault Isolation in

Chemical Process Monitoring

Jia Lin LiuCenter for Energy and Environmental ResearchNational Tsing Hua University, Hsinchu, Taiwan

David Shan Hill WongDepartment of Chemical Engineering

National Tsing Hua University, Hsinchu, Taiwan

Shujie LiuDepartment of Control Science and Engineering

Hua Zhong University of Science and Technology, Wuhan, China

NCTS-IS Workshop26th October, 2012

CONTENT

Fault Isolation Relative Contribution and Smearing Effect Reconstructive Based Contribution Bayesian Decision Applications Conclusions

NCTS-IS WORKSHOP2012.10.26

2

MONITORING, DIAGNOSIS AND ISOLATION

The possibility of using multivariate statistical analysis to monitor manufacturing processes have been extensively researched.

For example, PCA have been widely practiced to project sensor data in high dimension to a latent structure. Hotelling T2 or Q statistics can be used to monitor whether the process is in control.

If a faulty signal appears, it is desirable to diagnosis the root cause of the fault.

Efficient diagnosis is facilitated by isolation of major contributing variables NCTS-IS WORKSHOP

2012.10.263

-6 -4 -2 0 2 4 6-6

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X1

99% Confidence Limit

PC1PC2

SUPERVISED APPROACH (1/2)

Fault Signatures1 Projecting each known event data onto the PC and residual subspaces, the fault

signatures of the two subspaces can be obtained. The detected faults are decomposed into two subspaces and inner product with each fault signature are calculated.

Fuzzy Logic Knowledge-based Expert Systems2

Generating fuzzy rules from different operational-mode data, the new data were classified into the known groups according the fuzzy rules.

Modified Fault Tree Analysis (FTA)3

Match the trend patterns of the candidates with the standard fault propagation trends to identify the root causes.

Possibilistic c-means4

Separate the known event data into groups, and to classify new data into groups according to the membership values.

SUPERVISED APPROACH (2/2)

Bayesian Classification5 Cluster data into the denser regions, and faults were identified according to the

posterior probabilities. Support Vector Machine (SVM)6

Building decision boundaries between two groups of data from different operating modes, the new fault was tested for each SVM.

Pattern-matching Approach7, 8

Several PCA models were built using known event datasets. The statistical distances and angles of the new data were measured with each group.

Fault Subspace Extraction9

Each fault subspace was extracted from each known event dataset. The detected fault can be identified by minimizing the reconstructed statistics.

An event set must be available. A new fault may lead to incorrect diagnosis.

UNSUPERVISED APPROACH -- DISCRIMINATION BASED Pairwise Fisher Discriminant Analysis10

The pairwise FDA was then applied to the normal data and each class of faulty data to find fault directions that were used to generate contribution plots for isolating faulty variables.

Dissimilarities Between Normal and Abnormal Groups11

The dissimilarities between normal and abnormal cluster centers and covariances are measured. The faulty variables of new faults can be isolated using the maximal values of the dissimilarities.

This type of approach is based on a restrictive assumption that the faulty data can be formed into groups.

Sufficient data of the faulty group must be accumulated to correctly isolate the faulty variables.

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)

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)

SampleNCTS-IS WORKSHOP

2012.10.267

PROPAGATION OF SIGNALS DUE TO CONTROL ACTION

CAF

LT

FTFC

TTTC

QFTF

QCTCF

T

h

QCTC

LC

FC FT

CAQ

CAF

LT

FTFC

TTTC

QFTF

QCTCF

T

h

QCTC

LC

FC FT

CAQ

LC

FC FT

CAQ

0 2 4 6 8 10 12 14 16 18 20 22 24400

401

402

403

404

405

406

T (

K)

Hour

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15

16

17

QC (

L/m

in)

Hour

0 2 4 6 8 10 12 14 16 18 20 22 24342

343

344

345

346

347

TC (

K)

Hour

0 2 4 6 8 10 12 14 16 18 20 22 2436

38

40

42

CA (

mol

/m3)

Hour

1. Adding a bias of 1 K to the measurement of the reactor temperature after the eighth hour.

2. The coolant flow rate was increasing for compensating this abnormality.

4. The actual reactor temperature was lower than its set point; therefore, the reactant concentration would be higher than the normal operating data due to the lower reaction rate.

3. The excess of the coolant flow rate induced the coolant exit temperature to be lower than its normal operating values.

1

2

3

4


8

UNSUPERVISED APPROACH, CONTRIBUTION BASED

Contribution plots The most popular tool for identifying which variables are pushing the statistics out of

their control limits. It is well known that this approach suffers from the smearing effect. Reconstruction-based Contribution (RBC)12

The RBC differs from traditional contributions by a scaling factor that also appears in the corresponding control limits. Therefore, The RBC approach still suffers the smearing effect when implementing the control limits on the RBC.

Branch and Bound (BAB) method13

The time-consuming task of continuously optimizing the nonlinear integer programming problem for every sampling data is needed.

Contribution of the Reduced Statistics14

Repeatedly insert a variable with the maximal reduction of the statistics into the faulty variable set until the reconstructed statistics under the control limits. Since the selected faulty variables do not equally contribute to the faults, contribution plots of the reduced statistics are used to find the faulty variables with the most contributions.

ISOLATION BY CONTRIBUTION

Isolation is the procedure of identifying the variables contributing to a fault signal detected by multivariate analysis

This is normally by relative contribution in engineering literature


10

T T T1

1m

S X X PΛP PΛP

×N MRX

T T ˆ X XPP XPP X E

TT TQ x x x x xPP x

2 1 T T 1 TT xPΛ P x tΛ t

2 2Q Q T T

2 TQ Qi i i

i

c , ,Q c xCξ C PP

0 52 1 T 2.T Ti i i

i

c , ,T c xDξ D PΛ P

2 2i i i

i

c , Q T , c xΦξ Φ C D

is a column vector in which the ith element is one and the others are zero.

iξ

CONTROL LIMITS OF CONTRIBUTIONSBOX 1954


11

2T T TQi i i ic x Cξ x Cξ ξ Cx

2Q Q Q,i i ig h

22 TT

2T T1

i ii iQ Qi i

i i i i

trtrg ,h

tr tr

SCξ ξ CSCξ ξ C

SCξ ξ C SCξ ξ C

2T 0 5 T 0 5 T 0 5T . . .i i i ic x D ξ x D ξ ξ D x

2T T T,i i ig h

20 5 T 0 5

T 0 5 0 5

0 5 T 0 5

. .i iT . .

i i i. .i i

trg

tr

SD ξ ξ Dξ D SD ξ

SD ξ ξ D

1Tih

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T2

Sample

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cT 1

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cT 2

INCONSISTENT DIAGNOSIS (1/2)

Signaling of the overall process may be caused by signaling of individual variables Signaling of overall process may not induce signals of individual variables Signaling of individual variables do not guarantee signaling of the overall limit


12

00000000000

INCONSISTENT DIAGNOSIS (2/2)


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Sample

0

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cT 1

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cT 2

SMEARING EFFECT (1/2)


14

VARIABLE CONTRIBUTIONS OF CSTR EXAMPLE

CAF

LT

FTFC

TTTC

QFTF

QCTCF

T

h

QCTC

LC

FC FT

CAQ

CAF

LT

FTFC

TTTC

QFTF

QCTCF

T

h

QCTC

LC

FC FT

CAQ

LC

FC FT

CAQ

0 2 4 6 8 10 12 14 16 18 20 22 24

1

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7

8

9

Hour

Var

iabl

e 5%

10%

20%

40%

80%

T

CA

TC

QC


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RECONSTRUCTION BASED CONTRIBUTION ALCALA AND QIN AUTIOMATICA 2009


16

, ,1

mi 1 i 1 i 1 2

xx =argmin m x , x y x x m=Q,T,

‘

, , , ,mi 1 i 1 i i 1 2 1 i 1 i i 1 2RBC =m x , x x x x m x , x x x x

m=Q,T,

mm ii m

ii

cRBC =

Cm 2 2mj i ijm m m 2 mi

i j ij ii i i ii jm mii jj jj

c x Ccx x C C RBC = =x C RBC = =

C C C

2 m mii jj ij i jC C C RBC RBC

CONTROL LIMITS OF RELATIVE CONTRIBUTIONS


17

2 1T T T T1Qi i i i i i

i ,i

RBCc

x Cξ x Cξ ξ Cξ ξ Cx

2

21T T

1T T

21T T

21T T

1

1

RQ RQ RQ,i i i

i i i iRQ Qi i

i ,ii i i i

i i i iRQi

i i i i

g h

trg g

ctr

trh

tr

SCξ ξ Cξ ξ C

SCξ ξ Cξ ξ C

SCξ ξ Cξ ξ C

SCξ ξ Cξ ξ C

Q Qi iQ RQ

,i ,i

c RBC


18

2 1T T T T1Ti i i i i i

i ,i

RBCd

x Dξ x Dξ ξ Dξ ξ Dx

2

21T T

T T 1 T

1T T

21T T

21T T

1 1

1

RT RT RT,i i i

i i i iRTi i i i i

i ,i i ,ii i i i

i i i iRTi

i i i i

g h

trg

d dtr

trh

tr

SDξ ξ Dξ ξ Dξ DSDξ ξ PΛ P ξ

SDξ ξ Dξ ξ D

SDξ ξ Dξ ξ D

SDξ ξ Dξ ξ D

2T 1 T

0 52 T 1 T

1

1

Ti i

.RT,i i i

RBC

x PΛ P ξ

ξ PΛ P ξ

T Ti iT RT

,i ,i

c RBC

BAYESIAN DECISION

1

1 11

j jj

The posterior probability of class w after an observation x

P Pw wxP x =w

w wP Px

,1 2Let w w be a set of decisions classes

11P is the prior probability of class w w

11P x is the conditional probability of observation x given class w w


19

BAYESIAN FILTERING APPLIED TO FAULT ISOLATION


20

,

, , .

m mi iLet N F be two classes of decisions for variable i,normal, fault

according respective indices m T Q

m mi t i t

t

P F and P N be the posterior probabilities

of the two classes after observation was recieved.

x x

x

m mi i

t

P F and P N be the prior probabilities

of the two classes before observation was recieved.

x

m mt ti i

tht

P and P are the conditional probabilitiesF N

of observing given the i variable is

faulty or normal respectively

x x

x

CONDITIONAL PROBABILITY BASED ON RBC

For the ith variable there are two classes, in fault (Fi) or normal (Ni).


21

min max min mi

mt i z

1P =P + P P F

1 e

x

max

.mi

i m

RBC0 5z s

RBC

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

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1.0

Con

ditio

nal P

roba

bilit

ies

Ci / C

max

max

mi

m

RBC

RBC

mt i

P Fx

EVOLUTION OF POSTERIOR


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REVISIT THE CSTR EXAMPLE

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le 51%

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nfe

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t

T

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TC

QC


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FAULT 1 OF TE PROCESS

Fault 1: A/C feed ratio changes and B composition remains constant (Stream 4)

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COMPOSITION A CONTROLLER IN REACTOR FEED

The scenario of Fault 1 was that the composition of A of Stream 4 was changed from 48.5 mol% to 45.5 mol%; meanwhile, the composition of C was changed from 51 mol% to 54 mol%.

Stream 1 flow rate (x1) was increasing through opening the valve (x44) and trying to maintain the composition A in the reactor feed flow

.

0 200 400 600 8000.0

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x 1

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Sample


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FAULT 7 OF TE PROCESS

Fault 7: C header pressure loss – reduced availability (Stream 4)

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ROOT CAUSES OF FAULT 7

Since the C header pressure loss could be compensated by increasing the open position of the feed flow valve of Stream 4 (x45), the process would be gradually settled down by the controllers.

Comparing the symptoms of Fault 1 and Fault 7, since the scenario of Fault 7 did not change any compositions in the streams, the diagnosis of Fault 7 was relatively easier than that of Fault 1.

0 200 400 600 80055

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x 45

Sample


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FAULT EVOLUTION OF FAULT 7

Since the condenser cooling water flow rate (x52) almost kept in a constant range, the temperature of the reactor outlet passed through the condenser would be inversely proportional to the flow rate of the output, i.e., the reactor pressure. Therefore, the separator temperature (x11) inversely varied with the reactor pressure. The function of the separator was to separate produces G and H from the reactor outlet. In addition, the vapor pressure of component G was higher than that of component H; therefore, composition G in the purge (x35) was more sensitive with the separator temperature.

160 200 240 280 320 360

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90%

0 40 80 120 160 200 240 280 320 36075

78

81

84

x 11

Sample

0 40 80 120 160 200 240 280 320 3604

5

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x 35

Sample

0 40 80 120 160 200 240 280 320 36020

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x 52

Sample


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Composition E Controllers in Product Flow

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90%

The variation of Stream 4 flow rate (x4) resulted in the variation of composition C in the reactor; therefore, composition E in the Product flow (x38) would be varied as well. The controllers of x38 was trying to maintain the set point that induced the variations of x50, x19 and x18.

29

INDUSTRIAL APPLICATION C

ooli

ng T

ower

Tc, 1

1st Stage 2nd Stage 3rd Stage 4th Stage

1st Intercooler 2nd Intercooler 3rd Intercooler

Cooling Water

Air

Compressed Air

Fa

Pin, 1

Tin, 1

Pout, 1

Tout, 1

Pin, 2

Tin, 2

Pout, 2

Tout, 2

Pout, 3

Tout, 3

Pout, 4

Tout, 4

Pin, 3

Tin, 3

Pin, 4

Tin, 4

Fc ,Tc

Tc, 2 Tc, 3

The compression process used a four-stage centrifugal compressor that was equipped with an intercooler between stages to cool down the compressed air.


30

FAULT DETECTION AND ISOLATION

31

0 1 2 3 4 50

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bine

d In

dex

Day

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Day

Var

iabl

e 0

1

2

4

Bay

esia

n I

nfe

ren

ce

Plo

tR

BC

Im

ple

men

tin

g C

on

tro

l L

imit

1st AE

2nd AE

3rd AE

0 1 2 3 4 5

2

4

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Day

Var

iabl

e 51%

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90%

FIRST ABNORMAL EVENT

0 1 2 3 4 5

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Va

ria

ble 51%

60%

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80%

90%

The measurements of Tout,1 were compared with the averages of the training and test data, from which the sensor drift can be observed. Calibration of the sensor was requested by the field operators after they were informed about this abnormality.

-10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5

Test Data

Measurements Averages

Pin

, 1

Day

Training Data


32

SECOND ABNORMAL EVENT

0 1 2 3 4 5

2

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Day

Va

ria

ble 51%

60%

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90%

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Measurements Averages

To

ut,

2

Day

Training Data Test Data

0 1 2 3 4 5

0.8

0.9

1.0 1st Stage 2nd Stage 3rd Stage 4th Stage

Com

pres

sion

Effi

cien

cy

Day

The left figure shows that it was difficult to convince the operators that the measurements of the sensors were questionable, since the two temperature averages were close. However, they were convinced after the comparison of the compression efficiencies for all stages was displayed, as the right figure shows. The second stage efficiency dramatically surged around day 1.5, and then highly fluctuated; meanwhile the other stages’ efficiencies were maintained in stable ranges. NCTS-IS WORKSHOP

2012.10.2633

THIRD ABNORMAL EVENT

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The cooling water flow rate suddenly dropped at day 3.4, bounced back to a lower flow rate, and then dropped again around day 3.5. Since the intercoolers were arranged in a series, the decreases of the cooling water flow rate apparently did not affect the function of the first intercooler; contrarily, the performances of the second and third intercoolers deteriorated due to the insufficient cooling water.

3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0

3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.03.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0

3.0 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 4.0

Day

Flo

w R

ate

Cooling Water

3rd Stage 4th Stage

Out

let

Tem

pera

ture

2nd Intercooler 3rd Intercooler

Out

let

Tem

pera

ture

Day

3rd Stage 4th Stage

Inle

t T

empe

ratu

re


34

CONCLUSIONS

Bayesian inference-based fault isolation is derived

Smearing effect of traditional contributions and RBC is eliminated.

Predefined known event datasets are not necessary.

Fault propagation due to the process controllers can be traced.

Multiple sensor faults can be identified.


35

REFERENCES

S. Yoon, J.F. MacGregor, Fault diagnosis with multivariate statistical models part I: using steady state fault signatures, J Proc. Cont. 11 (2001) 387-400.

E. Musulin, I. Yélamos, L. Puigjaner, Integration of principal component analysis and fuzzy logic systems for comprehensive process fault detection and diagnosis, Ind. Eng. Chem. Res. 45 (2006) 1739-1750.

Y.S. Oh, K.J. Mo, E.S. Yoon Fault diagnosis based on weighted symptom tree and pattern matching, Ind. Eng. Chem. Res. 36 (1997) 2672-2678.

K.P. Detroja, R.D. Gudi, S.C. Patwardhan, A possibilistic clustering approach to novel fault detection and isolation, J. Proc. Cont. 16 (2006) 1055-1073.

J. Liu, Process monitoring using Bayesian classification on PCA subspace, Ind. Eng. Chem. Res. 43 (2004) 7815-7825.


36

REFERENCES, CONT.

6. Y.H. Chu, S.J. Qin, C. Han, Fault detection and operation mode identification based on pattern classification with variable selection, Ind. Eng. Chem. Res. 43 (2004) 1701-1710.

7. A. Raich, A. Çinar, Statistical process monitoring and disturbance diagnosis in multivariable continuous processes, AIChE J. 42 (1996) 995-1009.

8. M.C. Johannesmeyer, A. Singhal, D.E. Seborg, Pattern matching in historical data, AIChE J. 48 (2002) 2022-2038.

9. R. Dunia, S.J. Qin, Subspace approach to multidimensional fault identification and reconstruction, AIChE J. 44 (1998) 1813-1831.

10. Q.P. He, S.J. Qin, J. Wang, A new fault diagnosis method using fault directions in Fisher discriminant analysis, AIChE J. 51 (2005) 555-571.

11. J. Liu, D.S. Chen, Fault detection and identification using modified Bayesian classification on PCA subspace, Ind. Eng. Chem. Res. 48 (2009) 3059-3077.


37

REFERENCES, CONT.

12. C.F. Alcala, S.J. Qin, Reconstruction-based contribution for process monitoring, Automatica 45 (2009) 1593-1600.

13. V. Kariwala, P.E. Odiowei, Y. Cao, T. Chen, A branch and bound method for isolation of faulty variables through missing variable analysis, J. Proc. Cont. 20 (2010) 1198-1206.

14. J. Liu, Fault diagnosis using contribution plots without smearing effect on non-faulty variables, J. Proc. Cont. (2012) http://dx.doi.org/10.1016/j.jprocont.2012.06.016


38

http://dx.doi.org/10.1016/j.jprocont.2012.06.016

Thank you for your attentions ！Questions?


39

Documents

Bayesian Filtering of "Smearing Effect" -- Fault Isolation in Chemical Process Monitoring Jia Lin Liu Center for Energy and Environmental Research National