Plant-wide Monitoring of Processes Under Closed-loop

Control

Sergio Valle-Cervantes

Dr. S. J. Qin: Advisor

Chemical Engineering Department

University of Texas at Austin

Outline

• Introduction• Objective• Selection of the number of principal components• Extracting fault subspaces for fault identification of a

polyester film process• Multi-block analysis with application to decentralized

process monitoring• Extension to the MBPCA analysis with fault

directions and wavelets.• Conclusions

Introduction

• Faults in industry– Among others, bad products, insecure conditions, damage to

the equipment.

– In summary, lost of millions of dollars just because faults are not detected and identified on time

– Just in the U.S.A. petrochemical industries an annual loss of $20 billions in 1995 has been estimated because of poor monitoring and control of such abnormal situations

• Actually:– Chemical process highly automated

– The quantity of data captured by the information system is amazing

Introduction

• What can we do?– Use this huge quantity of data to monitoring, control

and optimize the process– Actually, the modern computer systems are able to

analyze that information, something in the past was not possible

• Therefore, efficient methods to on time fault detection and identification has been one of the main targets in industry to the afore mentioned.

Objectives

• Obtain novel methods for process monitoring, fault detection and identification using PCA.– Use PCA and PLS models to identify the main factors that

affect the process– Determine the number of principal factors necessary to

describe the process but not noise.– Provide industry with new ways to improve the process

operations.– Develop new monitoring tools to increase process efficiency,

thereby reducing costs and off-specification products.– Develop plant-wide monitoring strategy under closed-loop

control, including sensor fault detection, loop performance monitoring and disturbance detection.

Selection of the number of PC’s

• One of the main difficulties in PCA: selection of the # of PC’s.

• Most of the methods use monotonically increasing or decreasing indices.

• The decision to choose the # of PC’s is very subjective.• A method based on the variance of the reconstruction

error to select the # of PC’s.• The method demonstrates a minimum over the # of PC’s.• Ten other methods are compared with the proposed

method.• Data sets: incinerator, boiler, and a batch reactor

simulation.

Fewer or more PC’s?

• Key issue in PCA # of PC’s

• If fewer PC’s than required:– A poor model will be obtained

– An incomplete representation of the process

• If more PC’s than necessary:– The model will be overparameterized

– Noise will be included

Methods to choose the # of PC’s

• Two approaches to obtain the # of PCs:– Knowledge of the measurement error

– Use of statistical and empirical methods• Akaike information criterion (AIC)

• Minimum description length (MDL)

• Imbedded error function (IEF)

• Cumulative percent variance (CPV)

• Scree test on residual percent variance (RPV)

• Average eigenvalue (AE)

• Parallel analysis (PA)

• Autocorrelation (AC)

• Cross validation based in Rratio

• Variance of the reconstruction error (VRE)

PCA notation

1 2

sample vector of sensors

raw data matrix,

residual matrix

1The covariance matrix

11

diag1

m

m

T T T

T

TT

T

m

i

m

N

N

N

x

X

X TP X TP TP T T P P

X TP

S X X P P P P

T T T T

1 var

1For variance scaled , is the correlation matrix

Projecting on the PCS ( ) and RS ( )

ˆ

Since and are orthogonal

ˆ 0

and

ˆ

The task: cho

Ti i i

p r

Tp

T Tr

p r

T

N

S S

S

S

S S

t t t

X S R

x

x PP x

x PP x I PP x

x x

x x x

ˆose such that contains mostly information

and contains noise

l x

x

AIC, MDL, and IEF

• AIC and MDL: popular in signal processing.

• IEF in factor analysis.• Common attributes:

– Work only with covariance-based PCA

– Variance of measurement noise in each variable are assumed to be identical

– A minimum over the number of PC’s.

1/

1

1

1/

1

1

1/ 2

1

AIC 2log 21

MDL 2log log1

IEF

m l Nmm l

ss l

m

ss l

m l Nmm l

ss l

m

ss l

m

jj l

dl M

dm l

dl M N

dm l

l

lNm m l

Selection Criteria in Chemometrics

• CPV: measure of the percent variance captured by the first l PCs.

• Scree test on RPV: the method looks for a “knee” point in the RPV plotted against the number of PCs.

• AE: accepts all eigenvalues above the average eigenvalue and rejects those below the average.

• PA: two models, original and uncorrelated data matrix. All the values above the intersection represent the process information and the values under the intersection are considered noise.

1

1

CPV 100 %

l

jj

m

jj

l

For covariance-based PCA:

1= trace

For correlation-based PCA:

1= trace 1

m

m

S

R

1

1

RPV 100 %

m

jj l

m

jj

l

Selection Criteria in Chemometrics

• Autocorrelation: use an autocorrelation function to separate the nosy eigenvectors from the smooth ones.

• Cross validation based on the R ratio:– R < 1 the new component

improve the prediction, then the calculation proceeds.

– R > 1 the new component does not improve the prediction then should be deleted.

• Cross validation based on PRESS:– Use PRESS alone to determine

the number of PCs.

– A minimum in PRESS(l) corresponds to the best number of PCs to choose.

1

, 1,1

ACN

i l i li

l t t

PRESS

RSS 1

lR l

l

Variance of the Reconstruction Error

• Based on the best reconstruction of the variables

• VRE index has a minimum, corresponding to the best reconstruction

• VRE is decomposed in two subspaces:– The portion in PCS has a

tendency to increase with the number of PC’s.

– The portion in the RS has a tendency to decrease.

– Result: a minimum in VRE.

*

*

2

Corrupted sensor measurement:

Reconstruction of the fault:

Reconstruction error:

Variance of the reconstruction error:

The VRE to be minimized:

i

i i i

i

Ti i

iT

i i

T Ti i i

f

f

u

x x

x x

x x

R

I PP PP

1

VREm

iT

i i i

ul

R

Examples: Batch Reactor

• Simulated batch reactor– Isothermal batch reactor– 4 first order reactions– 2% of noise– 200 samples, 5 variables

• Boiler– 630 samples, 7 variables– T, P, F, and C.

• Incinerator– 900 samples, 20 variables.– T, P, F, and C.

1 1.5 2 2.5 3 3.5 410

0

102

104

AIC

1 1.5 2 2.5 3 3.5 410

0

102

104

MDL

0 1 2 3 410

-1

100

101

VRE

cov

0 1 2 3 410

0

101

102

VRE

cor

0 1 2 3 4 50

50

100

CPV,

%

0 1 2 3 40

50

100

RPV,

%

1 2 3 4 50

2

4

AE

1 2 3 4 50

2

4

Paral

lel

1 1.5 2 2.5 3 3.5 40

1

2x 10

-3

IEF

1 2 3 4 5-1

0

1

Autoc

or.

0 1 2 3 410

2

103

PRES

S

1 2 3 4 50

0.5

1

Rrat

io

Boiler and Incineration Process

1 2 3 4 5 610

0

105

AIC

1 2 3 4 5 610

2

104

106

MDL

0 1 2 3 4 5 610

-2

100

102

VRE

cov

0 1 2 3 4 5 610

-1

100

101

VRE

cor

0 2 4 6 80

50

100

CPV,

%

0 1 2 3 4 5 60

50

100

RPV,

%

1 2 3 4 5 6 70

5

10

AE

1 2 3 4 5 6 70

5

10Pa

rallel

1 2 3 4 5 60

0.05

0.1

IEF

1 2 3 4 5 6 70.5

1

Autoc

or.

0 1 2 3 4 5 610

2

103

104

PRES

S

1 2 3 4 5 6 70

1

2

Rrat

io

0 5 10 15 2010

2

104

106

AIC

0 5 10 15 2010

3

104

105

MDL

0 2 4 6 8

102

VRE

cov

2 4 6 8

VRE

cor

0 5 10 15 200

50

100

CPV,

%

0 5 10 15 200

50

100

RPV,

%

0 5 10 15 200

5

10

AE

0 5 10 15 200

5

10

Paral

lel

0 5 10 15 200

0.05

0.1

IEF

0 5 10 15 200

0.5

1

Autoc

or.

0 5 10 15

PRES

S

2 4 6 8 10

0.80.9

1

Rrat

io

Comparison

CPV RPV AE PA AC IEF R PRESS AIC MDL VREObjectiveness x x y y x y y y y y yUniqueness y x y y x y y y y y y

Covariance-based y y y y y y y y y y yCorrelation-based y y y y y x y y x x y

Reliability y x y y x x x y x x yComputation L L L L L L H M L L L

CPV RPV AE PA AC IEF R PRESS AIC MDL VREcov VREcor

Reactor 3 ambiguous 1 1 2 2 2 3 2 2 2 2Boiler 1 1 1 1 no solution no solution 2 1 no solution no solution 1 1

Incinerator 15 ambiguous 7 7 2 no solution 5 15 no solution no solution 2 5

Summary

• Most of the methods have monotonically decreasing or increasing indices

• The IEF, AC, AIC, and MDL worked well with the simulated example, but they failed with the real data.

• The most reliable methods are: CPV, AE, PA, PRESS, and VRE.

• Considering the effectiveness, reliability, and objectiveness, the PRESS method, and correlation based VRE method are superior to the others.

• VRE is preferred to the PRESS method in the consistency of the estimate, computational cost, and ability to include a particular disturbance or fault direction in the selection.

Extracting Fault Subspaces for Fault Identification

• As chemical processes becomes more complex:– Tightly control the process

– Detect disturbances before they affect the process quality

• Monitoring and diagnosis of chemical processes:– Asses process performance

– Improve process efficiency

– Improve product quality

• More sensors > more data.– How to analyze the data to obtain the best process

knowledge

Extracting Fault Subspaces for Fault Identification

• Extracting the information is not trivial• Extremely important for chemical processes:

– The analysis of sensor conditions– Process performance

• Fault detection and identification are essential for a good monitoring system

• Statistical process control– Based on control charts for certain quality variables

• Multivariate statistical process control– Model process correlation, detect and classify faults, control

product quality with long time delays, monitoring dynamic processes, and detect and identify upsets in multiple sensors.

Extracting Fault Subspaces for Fault Identification

• Two indices used in PCA or PLS based monitoring:– Hotelling’s statistics T2: gives a measure of the

variation within the PCA model.– Squared prediction error (SPE) of the residuals:

indicates how much each sample deviates from the PCA model.

• Often insufficient to identify the cause of the upsets. Then to identify the cause of the upsets:– Contribution plots– Sensor validity index

New Approach

• To extract process fault subspaces from historical process faults using SVD.– Historical process data are first analyzed using PCA to isolate between

normal and abnormal operations.– Process knowledge, operational and maintenance records are incorporated to

assist the isolation of abnormal operation periods.– The abnormal operation data are used to extract the fault subspaces.– The extracted fault subspaces are used to reconstruct new abnormal data that

are detected by the fault detection step.– If the new faulty data can be reconstructed by one of the extracted fault

subspaces, fault identification is completed for the new faulty data.– Otherwise, the new faulty data are from a different type of fault that has not

been recorded in the historical data.– A new fault subspace is then extracted from the data and is added to the fault

data base for future fault identification.

Detection and Identification of Process Faults

• The purpose of fault detection and identification is to improve the safety and reliability of the automated system

• PCA

• Detection indices:– SPE

– Hotelling’s T2

cov1

T

m

X X

X

1 1 2 2

min ,

T T Tk k

k m n

X t p t p t p E

T T Ti i i i k k iQ e e x I P P x

2 1 1T T Ti i i i iT t t x P P x

Contribution Plots

• Monitoring and Diagnosis Based on SPE

• Monitoring and Diagnosis Based on T2

22 2

2

2

When a fault occurs in a process

SPE

samples residual vector

loadings matrix from the PCA model using normal

data

samples raw data previously auto-scaled

t

T

m l

m

x I PP x

x

P

x

2

1

hreshold obtained from the normal process

Contributions to SPE from each variable

SPE

Although these plots will not uniquely diagnose the cause, they

will provide insight into possible causes an

m

ii

x

d thereby narrow

the search.

2

2 1 1

1

2 22

1 1 1

The statisticas can be calculated as

eigenvalues diagonal matrix for the eigenvector

retained in the model

For fault detection

/ /

T T T

M M l

ik k i ik k ik k i

T

T

l

T p x p x

t t x P P x

1

22

1

2

The contribution to the variable is

/

If is large comparing to others, the variable is heavily

affected by the fault, which indicates a potential cause of the

fault.

l

i

th

l

k ik k ii

thk

k

T p x

T k

Fault Subspace Extraction

2

*

*

*

1 2

1 2

Detection

|| ||

Directions extraction from faulty data

If

Then

For observations under fault

Applying SVD on the

i

k k i k

k i k

k i k

i

T

i p

Ti i p

SPE

p F

2x

x x f

x x f

x f

x f

X x x x

X f f f

residual matrixT Ti i i i

i i

X U D V

U

2 2

Reconstruction

ˆ

Identification

|| ||

Fault identification index

0 1

j j j

j j j j j

j j

Tj j j

j j

j

j

j

SPE

SPE

SPE

x x f

x x f x U f

f U x

x I U U x

x x

x

x

Polyester Film Process

• Different grades of products are processed in the same equipment.

• A typical fault: sudden oscillation of some temperature loops which swings in 10 degrees, then stop after a while.

• Hundred of sensors used in the process, including temperature, thickness, tension, etc., with a gauge.

• Grade changes for different products are frequent, approximately once a day.

• Changes in set points are made more frequently, and if it is needed the operators change the set points manually.

• Currently:– SPE always exceeds limits; contribution

plots indicate multiple suspects and no limits; multiple grades with only one model clusters for different grades.

Data Analysis: clusters

• 308 variables– Process variables– Set points– Output variables– Monitoring variables

• Process and monitoring variables were used in this analysis, 103 variables.

• Four clusters– Red cluster: normal– Blue, green, and black

clusters: faulty.

Data Analysis: PCs

5 10 15 20 25 30

VRE

cor

70 75 80 85 9090

92

94

96

98

100

CPV,

%

20 25 30 35 400.8

0.9

1

1.1

1.2

AE

10 15 20 25 30

1

1.2

1.4

1.6

1.8

Paral

lel

• Determining the number of PC’s.

• Four methods– Average eigenvalue

– Parallel analysis

– Cumulative percent variance

– Variance of the reconstruction error.

• Fifteen PC’s were used to build the model.

Data Analysis: Contribution Plots

• The variables that are contributing to the out of control situation in this window of 250 samples are, mainly variable 28 and in a minor proportion variables 25 and 32

• In particular for sample 71:– Highest contribution:

variable 28– Smaller contribution:

variables 25, 32, and 93

50 100 150 200 250

500

1000

1500

SPE

Samples50 100 150 200 250

25

30

35

40

45

50

Variable with highest contribution

Samples

Varia

bles

20 40 60 80 100

50

100

150

200

250

300

Samp

le 71

Variables

Contribution to SPE

0 100 200 300-20

0

20

40

60

Varia

ble 28

Samples

Data (b), projection (g), reconstruction (r)

Fault Direction Extraction

• The fault directions are modeled from abnormal data.

• These directions are used to identify the true type of faults.

• Subplot(5,2,1)– Highest direction variable 28

• Subplot(5,2,2)– Highest direction variable 25

• Subplot(5,2,3)– 32, 30, 29, 28, and 25

• Subplot(5,2,4)– 34 and 40

SPE deflation

• The fault directions are extracted from the faulty SPE until it is under the limit defined by the PCA model.

• Nine fault directions are necessary to deflate the SPE under the threshold.

• Observe how the first peek in the original SPE is deflated immediately after the first direction is extracted (second plot). And the residual peek in the second plot is deflated after subtracting the next direction (third plot).

20 40 60 80 100 120

50010001500

SPE for the original faulty data

20 40 60 80 100 120

100200300

SPE after the 1 th fault direction

20 40 60 80 100 12050

100

150

SPE after the 2 th fault direction

20 40 60 80 100 120406080

100120140

SPE after the 3 th fault direction

20 40 60 80 100 120

50

100SPE after the 4 th fault direction

20 40 60 80 100 120

4060

80

SPE after the 5 th fault direction

20 40 60 80 100 120

4060

80SPE after the 6 th fault direction

20 40 60 80 100 120

406080

SPE after the 7 th fault direction

20 40 60 80 100 120

3040506070

SPE after the 8 th fault direction

20 40 60 80 100 120

3040506070

SPE after the 9 th fault direction

Fault Identification

• First subplot:– The SPE for a window of 125

samples in the testing data.

• Second subplot:– The reconstructed SPE on the

testing data after extracting the fault directions. The fault is partially identified.

• Third subplot:– The fault identification index

shows a tendency to increase after sample 80, that is because no fault was identified there. The fault has been identified in the first part, between sample 20 and 80.

20 40 60 80 100 120200400600800

10001200

SPE (original test data/reconstructed data) and Fault Identification Index

SPE

20 40 60 80 100 120

100

150

200

250

SPE

20 40 60 80 100 120

0.1

0.2

0.3

0.4

0.5

samples

FII

Summary

• With the extraction of fault directions from historical data, it is possible to identify process faults for the out-of-control situation.

• These directions are “signatures” that characterize certain types of faults.

• It is viable to use them to identify similar faults in the future.• This technique requires only historical faulty data to model the

fault directions and normal data to build a PCA process model.• In the case that a new type of faults is identified, the new fault

subspace is extracted and stored for future fault identification.• In this way the number of fault subspaces can grow as more

faults are encountered.

Multi-block Analysis

• Large processes

• Hundred of variables (difficult to detect and identify faults)

• Divide the plant in sections or blocks

• Using multi-block algorithms localize the faulty section or block.

• Basic idea: divide the descriptor variable (X) into several blocks in the PCA case, to obtain local information (block scores) and global information (super scores) simultaneously from data.

• Use the regular PCA to calculate block scores and loadings based on the scores.

• The use of multi-block analysis methods for process monitoring and diagnosis can be directly obtained from regrouping contributions of regular PCA model.

Regular Algorithms

• Regular PCA algorithm • Regular PLS algorithm

1 2

1Scale with 0,B

bm

X X X X

1Set , and 1i X X

Choose a start and iterate until convergence of

/

i i

T Ti ii ii

ii i

t t

p X t X t

t X p

1Residual deflation:

1

Ti ii i

i i

X X t p

1 2Scale as in regular PCA and ,BX X X X Y 0 1

1 1Set , , and 1i X X Y Y

Choose a start and iterate until convergence of

/

/

/

i i

T Ti ii i i

ii i

T Ti i i ii

Tii i i i

u t

w X u X u

t X w

q Y t t t

u Y q q q

1

1

Residual deflation: /

1

T Ti i i ii

Ti i i i

Ti i i i

i i

p X t t t

X X t p

Y Y t q

CPCA and MBPCA

• CPCA algorithm based on PCA scores • MBPCA algorithm based on PCA loadings

1 2Perform regular PCA on to obtain , , , , iX t t t

, , ,

, , ,

/T Ti ib i b i b i

b i b i b i

p X t X t

t X p

, 1 ,/T Ti i i ib i b i X I t t t t X

1Scale . Set and 1i X X X

1Regular PCA on to obtain the first loadings i i

X p

1 1, 2, ,

T T T T

i i i B i p p p p

, , ,

, , , , ,/

b i b i b i

T Tb i b i b i b i b i

t X p

p X t t t

, 1 , , ,

1 1, 1 , 1

Tb i b i b i b i

i i B i

X X t p

X X X

Monitoring and Diagnosis

• Based on SPE: • Based on T2

Model with PCA (or with PLS)X Y

21

2 22

1

BTb b

b

T

P x

2

1/ 22 2,,

1

bm

b b k bb kk

T x

p

No fault

Model with PCA (or with PLS)X Y

2 2 2ˆSPE x x x

2 2 2ˆb b b b bSPE x x x

2 2, ,, , ˆb k b kb k b kSPE x x x

22 1/ 2, ,,b k b kb k

T p x

No fault

Standard MSPC monitoring

• A standard PCA model is applied to all the variables.

• Identification of the out-of-control situation variables is difficult.

• SPE and T^2 do not agree in all the variables.

• Contribution plots does not have a confidence limit.

1100 1200 1300 1400

20

40

60

80

SPE

SPE with 95% limit based on 15 pcs model

0 50 100

5

10

15

Variables contribution to SPE

Samp

le # 1

238

1100 1200 1300 1400

50

100

150

200

250

Sample number

Value

of T

2

T2 with 95% limit based on 15 pcs model

0 50 100

1

2

3

4

Variable number

Variables contribution to T2

Samp

le # 1

238

SPE for each block

• Process data is divided in 7 blocks.

• Faulty block is located applying decentralized monitoring.

• Block 2 is where the main fault is located.

1100 1200 1300 1400

1

2

3

Bloc

k # 1

Squared Prediction Error

1100 1200 1300 1400

2040

60

Bloc

k # 2

Squared Prediction Error

1100 1200 1300 1400

2468

10

Bloc

k # 3

1100 1200 1300 1400

1

2

3

Bloc

k # 4

1100 1200 1300 1400

1

2

3

Bloc

k # 5

1100 1200 1300 1400

2

4

Bloc

k # 6

samples

1100 1200 1300 1400

12

3

Bloc

k # 7

samples

Identification of Faulty Blocks Using SPE

• In block 2 is identified the largest contribution.

• Variables 28 and 25 are mainly responsible for the out-of-control situation using contribution plots.

• Identification of the variables is clearer with CPCA than with standard MSPC monitoring.

1 2 3 4 5 6 7

2

4

6

8

10

12

14

Block

Samp

le # 1

238

Block Contributions to SPE

10 12 14 16 18 20 22 24 26 28 300

5

10

15

Samp

le # 1

238

Variables contribution to SPE in block # 2

Variables number

Identification of Faulty Blocks Using T2

• T2 also shows that the main fault is located in the second block.

• Again variables 28 and 25 are identified.

• The decentralized monitoring approach gives a much clearer indication of the faulty variables.

1 2 3 4 5 6 70

0.5

1

1.5

2

2.5

Samp

le # 1

238

Blocks

Block contribution to T2

10 12 14 16 18 20 22 24 26 28 300

1

2

3

4

Samp

le # 1

238

Variables contribution to T2 in block # 2

Variables number

Block SPE Index

• The SPE index is shown for all blocks along samples of data.

• Any significant departure from the horizontal plane is an indication of a fault.

050

100150

200250

0

2

4

6

80

10

20

30

40

50

samplesBlock

Bloc

k SPE

inde

x

Summary

• The use of multi-block PCA and PLS for decentralized monitoring and diagnosis is derived in terms of regular PCA and PLS scores and residuals.

• The decentralized monitoring method based on proper variable blocking is successfully applied to an industrial polyester film process.

• Using the subspace extraction method and decentralized monitoring PCA method, it is shown that the identification of the fault is clearer than using a whole PCA model.

• What we need is only good faulty data to extract the “signature” of the fault.• Future task is use recursive PCA, or recursive PLS for adaptive decentralized

monitoring.• Develop fault identification index to uniquely identify the root cause of a fault

instead of contribution plots.• Integrate multi-scale monitoring approach in the decentralized monitoring

approach for partitioning the data, to provide flexible partition and interpretation of information contained in the process data.

Multi-Block PCA and FII

• Instead of extracting the fault directions using one PCA model for the whole plant, now extract the directions only in the faulty block.

• The information required to identify a new fault is less than using the whole PCA model.

Fault Direction Extraction: Block 2

• Fault directions are extracted from the SPE until it is under the limit defined by

• Three fault directions are necessary to deflate the SPE under the threshold. In the whole PCA model it was necessary to extract 9 directions.

20 40 60 80 100 120

20

40

60

SPE for the original faulty data

20 40 60 80 100 120

5

10

15

SPE after the 1 th fault direction

20 40 60 80 100 120

0.5

1

1.5

2

2.5

SPE after the 2 th fault direction

20 40 60 80 100 120

0.5

1

1.5

SPE after the 3 th fault direction

Fault Directions

• Directions that will be used to identify the true faults in a new data set.

• Clearly it is shown that variables 19 and 16 are the variables mainly responsible for the out-of-control situation.

• The projections here are more clear that using the whole PCA model.

5 10 15 20 25

0

0.2

0.4

0.6

0.8

Direc

tion 1

5 10 15 20 25

-0.8

-0.6

-0.4

-0.2

0

Direc

tion 2

5 10 15 20 25

-0.4

-0.2

0

0.2

0.4

Direc

tion 3

Fault Identification

• First subplot– The SPE for 125 samples for the

testing data is shown.

• Second subplot– The reconstructed SPE on the

testing data after extracting the fault directions, identifies the fault.

• Third subplot– The fault identification index value

goes to zero from sample 20 to sample 90, then the fault is identified. After sample 100 a new fault arrives to the system

20 40 60 80 100 120

1020304050

SPE (original test data/reconstructed data) and Fault Identification Index

SPE

20 40 60 80 100 120

0.5

1

1.5

2

2.5

SPE(

rec)

20 40 60 80 100 120

0.2

0.4

0.6

samples

FII

Conclusions and Future Work

• The merging of MBPCA and the directions extraction has bettered the identification of the fault.

• Less quantity of information to needed to identify new faults.

• Integrate in this new approach the multi-scale monitoring approach for partitioning the data, to provide flexible partition and interpretation of information contained in the process data.

• Use dynamic PCA modeling to extract the full process model and capture the true characteristics of the process.

Related Publications

• S. Valle, W. Li, and S. J. Qin, “Selection of the Number of Principal Components: the Variance of the Reconstruction Error Criterion with a Comparison to Other Methods”. Ind. Eng. Chem. Res., 38, 4389-4401 (1999)

• W. Li, H. Yue, S. Valle, and S. J. Qin, “Recursive PCA for Adaptive Process Monitoring”, J. of Process Control., 10 (5), 471-486 (2000)

• S. Valle,S. J. Qin, and M. Piovoso, “Extracting Fault Subspaces for Fault Identification of a Polyester Film Process”. Submitted to ACC-2001

• S. J. Qin, S. Valle, and M. Piovoso, “On Unifying Multi-block Analysis with Application to Decentralized Process Monitoring”. Accepted by J. Chemometrics

Acknowledgements

• National Science Foundation (CTS-9814340)

• Texas Higher Education Coordinating Board

• DuPont through a DuPont Young Professor Grant

• Consejo Nacional de Ciencia y Tecnología (CONACyT)

• Instituto Tecnológico de Durango (ITD)

• The authors are grateful to Mr. Mike Bachmann and Mr. Nori Mandokoro at DuPont plant in Richmond, Virginia for providing the data and process knowledge for this project