Plant-wide Monitoring of Processes Under Closed-loop Control
description
Transcript of Plant-wide Monitoring of Processes Under Closed-loop Control
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