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Multi-Phase Analysis Framework for Handling Batch Process Data
J. Camacho, J. PicóDepartment of Systems Engineering and Control.
A. FerrerDepartment of Applied Statistics, Operations Research and Quality.
Technical University of ValenciaCno. de Vera s/n, 46022, Valencia, Spain
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Index• Introduction to Batch Processing• Model Structures• Aim of the work• Multi-Phase Framework• End-quality Prediction• Other Applications• Conclusions
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Introduction to BatchProcessing
• Repetitive nature: charge, processing anddischarge.
• Three-way data: a set of variables are measured at different sampling times during the processing of a batch, and this is repeated for a number of batches.
• The duration of the processing of a batch may be variable in some processes Aligment methods.
• After the alignment, data matrix X (I×J×K) contains the values of J variables at K sampling times in Ibatches.
Index
1. Introduction toBatch Processing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
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• Convert into two-way data and apply PCA, PLS, …
• Apply three-way methods: PARAFAC, Tucker-3,…
Model Structures
Trilinear Nature???
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
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• Convert into two-way data and apply PCA, PLS, …
• Apply three-way methods: PARAFAC, Tucker-3,…
Model StructuresIndex1. Introduction to Batch
Processing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
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• Convert into two-way data and apply PCA, PLS, …
– Unfold the three-way matrix.
– Divide in K local matrices.
– Use an adaptive approach.
• Apply three-way methods: PARAFAC, Tucker-3,…
Model StructuresIndex1. Introduction to Batch
Processing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
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• Unfold the three-way matrix.– Batch-wise unfolding
Model Structures
Thousands ofvariables!!!
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
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• Unfold the three-way matrix.– Batch-wise unfolding
Model Structures
2 variables x 116 sampling times
More thana half isnoise!!!
Dynamicsare built inthe model
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
Variables closein time are more
related
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• Unfold the three-way matrix.– Variable-wise unfolding
Model Structures
dynamics are notbuilt in the model
Constant CorrelationImposed!!!
Low number ofparameters
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
More samples/parameter
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• Unfold the three-way matrix.– Variable-wise unfolding
Model Structures
Constant Correlation Imposed!!!
V-W scores
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
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• Unfold the three-way matrix.– Batch dynamic unfolding = VW + LMVs
Model Structures
↓LMVs ≈ VW
↑LMVs ≈ BW
Adjust the amountof dynamicinformation
Dynamics are imposed to be constant
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
1 LMV
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• Divide in K matrices
Model Structures
High numberof models
LMVs locallyAdjustable
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
Moving Average
Evolving
Local
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• Context:a) A large number of possible Model Strutures, each of
them with advantages and drawbacks.b) Very different batch processes, (constant or varying
dynamics, dynamics of different order, etc…)
• NO MODELLING STRUCTURE IS THE BEST ALWAYS!!!
• WHY DON’T WE IDENTIFY THE MODEL STRUCTURE FOR THE CURRENT CASE STUDY???
Aim of the workIndex1. Introduction to Batch
Processing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
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Index• Introduction to Batch Processing• Model Structures• Aim of the work• Multi-Phase Framework• End-quality Prediction• Other Applications• Conclusions
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Multi-Phase Framework- Three-steps Analysis:
a) Multi-phase Algorithm.Camacho J, Picó J , Multi-phase principal component analysis for batch processesmodelling. Chemometrics and Intelligent Laboratory Systems. 2006; 81:127-136.
Camacho J, Picó J. Online Monitoring of Batch Processes using Multi-Phase Principal Component Analysis. Journal of Process Control. 2006;10:1021-1035.
Greedy Optimization + Pattern Recognition
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
X I
J
K
II
II
JX1
X2XK-1
XK
Multi-PhaseAlgorithm
XI
J
K
I
I
J
I
I
J
I
I
J
PCA
PCA
PCA
PCA
Parameters
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Multi-Phase Framework- Three-steps Analysis:
a) Multi-phase Algorithm.
b) Merging Algorithm:
Camacho J, Picó J , Multi-phase principal component analysis for batch processesmodelling. Chemometrics and Intelligent Laboratory Systems. 2006; 81:127-136.
Camacho J, Picó J. Online Monitoring of Batch Processes using Multi-Phase Principal Component Analysis. Journal of Process Control. 2006;10:1021-1035.
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
MergingAlgorithm
XI
J
K
X1 X2 Xn1+1
Xk1
Xk1-1
Xk1-n1+1Xk1-n1
Xk1-n1-1 Xk1-n1
Xk1-n2+1 Xk1-n2+2 Xk1+1
Xk2
Xk2-1
Xk2-n2+1Xk2-n2
Xk2-n2-1 Xk2-n2
Xk2-n3+1 Xk2-n3+2 Xk2+1
XK
XK-1
XK-n3+1XK-n3
XK-n3-1 XK-n3
XI
J
K
I
I
J
I
I
J
I
I
J
PCA
PCA
PCA
XI
J
K
X2 Xn1+1
Xk1
Xk1-1
Xk1-n1+1
Xk1-n1
Xk1-n2+2 Xk1+1
Xk2
Xk2-1
Xk2-n2+1
Xk2-n2
Xk2-n3+1 Xk2-n3+2
XK-n3+1XK-n3
XK-n3-1 XK-n3
Tm, Criterium
XI
J
K
X1 X2 Xn1+1
Xk1
Xk1-1
Xk1-n1+1Xk1-n1
Xk1-n1-1 Xk1-n1
Xk1-n2+2
Xk2-n2+1
Xk2-n2
Xk2-n3+1 Xk2-n3+2
XK-n3+1XK-n3
XK-n3-1 XK-n3
PCA
PCA
PCA
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Multi-Phase Framework- Three-steps Analysis:
a) Multi-phase Algorithm.
b) Merging Algorithm:
c) Compromise Performance - Complexity
Camacho J, Picó J , Multi-phase principal component analysis for batch processesmodelling. Chemometrics and Intelligent Laboratory Systems. 2006; 81:127-136.
Camacho J, Picó J. Online Monitoring of Batch Processes using Multi-Phase Principal Component Analysis. Journal of Process Control. 2006;10:1021-1035.
Anova + LSD
Why merge? Greedy Optimization Sub-optimal solution
To allow obtaining sub-models with different unfolding methods
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
-
Multi-Phase Framework- Three-steps Analysis:
Anova + LSD
c) Compromise Performance - Complexity
5 LVs
3 LVs
5 LVs 15 LMVs
BW
1 LMV
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
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Multi-Phase Framework- Three-steps Analysis:
Anova + LSD
c) Compromise Performance - Complexity
2 LVs
1 LVs
VW
1 LMV
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
5 LVs
3 LVs
5 LVs 15 LMVs
BW
1 LMV
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Index• Introduction to Batch Processing• Model Structures• Aim of the work• Multi-Phase Framework• End-quality Prediction• Other Applications• Conclusions
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End-Quality Prediction- On-line prediction
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
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End-Quality Prediction- Prediction performance:
Anaerobicstage
Saccha. Cerev. Waste-water treat.
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
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End-Quality Prediction- Process understanding:
BW-PLSMPPLS = VW-PLS(Anaerobic Stage)
1 PC = 1250 parameters(5 var x 250 sam. tim.)
1 PC = 5 parameters(5 variables)
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
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Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
Other Applications• Off-line Monitoring: Batch-Wise PCA
a) The Charts of MP are more informative.
1 2 3 40
2
4
6
8
10
Phases
Q−
stat
istic
0 20 40 60 80 100600
800
1000
1200
1400
1600
1800
Sampling time
Var
8
Abnormality inbatches
#1, #2, #4 and #5.
Abnormality inbatch #3.
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Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
Other Applications• Off-line Monitoring: Batch-Wise PCA
a) The Charts of MP are more informative.
• On-line Monitoring: PCAa) MP avoids problems found in some modelling
structures:• BW models have low detection capabilities in the D-
statistic and high Overall Type I Risk in the SPE.• VW models have high OTI Risk in the D-statistic.• Local models have high OTI Risk in the SPE.
b) MP yields monitoring systems of fast response to faults.
• Estimation of trayectories (Soft-sensors): PLSa) MP yields accurate estimations, outperforming BW,
VW, Local, Evolving and Adaptive approaches.
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Index• Introduction to Batch Processing• Model Structures• Aim of the work• Multi-Phase Framework• End-quality Prediction• Other Applications• Conclusions
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Conclusions• The Multi-phase (MP) framework, with application to off-line and
on-line monitoring, final quality prediction and estimation of trajectories of variables in batch processes, has been presented.
• The MP approach is based on the data-driven identification of the (PCA or PLS) model structure, using pattern recognition and optimization techniques. Flexibility to adjust the structure to the case: Number of sub-models, dynamics, …
• This approach has several general advantages:
– The identification of the structure of the models and the convenient use of the tools within the MP framework helps to improve the process understanding.
– The MP approach allows to obtain a compromise solution between complexity and performance.
– The MP approach yields good performance in several applications.
Index
1. Introduction to BatchProcessing.
2. Model Structures
3. Aim of the work
4. Multi-Phase Framework
5. End-qualityPrediction
6. Other applications
7. Conclusions
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Multi-Phase Analysis Framework for Handling Batch Process Data
J. Camacho, J. PicóDepartment of Systems Engineering and Control.
A. FerrerDepartment of Applied Statistics, Operations Research and Quality.
Technical University of ValenciaCno. de Vera s/n, 46022, Valencia, Spain
-
Index
1. Introduction to BatchProcessing.
2. Aim of the work
3. Multi-Phase Algorithm
4. Merging Algorithm
5. Multi-Phase Framework
6. On-line Monitoring
7. End-qualityPrediction
8. Conclusions
On-line Monitoring- Monitoring Charts: D-statistic and SPE
Batch under NOC
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Index
1. Introduction to BatchProcessing.
2. Aim of the work
3. Multi-Phase Algorithm
4. Merging Algorithm
5. Multi-Phase Framework
6. On-line Monitoring
7. End-qualityPrediction
8. Conclusions
On-line Monitoring- Monitoring Charts: D-statistic and SPE
Abnormal Batch
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Index
1. Introduction to BatchProcessing.
2. Aim of the work
3. Multi-Phase Algorithm
4. Merging Algorithm
5. Multi-Phase Framework
6. On-line Monitoring
7. End-qualityPrediction
8. Conclusions
On-line Monitoring- Case Studies:
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Index
1. Introduction to BatchProcessing.
2. Aim of the work
3. Multi-Phase Algorithm
4. Merging Algorithm
5. Multi-Phase Framework
6. On-line Monitoring
7. End-qualityPrediction
8. Conclusions
On-line Monitoring- Preliminary Study: Saccharomyces Cerevisiae Cultivation.
Overall Type I Risk computed from the NOC test set,Imposed significance level 1%
nf number of faults
Conclusion: The structure of the model is importantin the on-line monitoring.
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Index
1. Introduction to BatchProcessing.
2. Aim of the work
3. Multi-Phase Algorithm
4. Merging Algorithm
5. Multi-Phase Framework
6. On-line Monitoring
7. End-qualityPrediction
8. Conclusions
On-line Monitoring
Conclusion: The structure of the model is importantin the on-line monitoring.
Solutions:
a) To readjust the control limits of the monitoringcharts using a left-one-out approach.
b) To identify the covenient model structure Multi-Phase Framework
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Index
1. Introduction to BatchProcessing.
2. Aim of the work
3. Multi-Phase Algorithm
4. Merging Algorithm
5. Multi-Phase Framework
6. On-line Monitoring
7. End-qualityPrediction
8. Conclusions
On-line Monitoring- Nylon 6’6 Polymerization:
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Index
1. Introduction to BatchProcessing.
2. Aim of the work
3. Multi-Phase Algorithm
4. Merging Algorithm
5. Multi-Phase Framework
6. On-line Monitoring
7. End-qualityPrediction
8. Conclusions
On-line Monitoring- Saccharomyces Cerevisiae Cultivation:
- Waste-water Treatment:
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