Multi-Phase Analysis Framework for Handling Batch Process...

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• Introduction to Batch Processing• Model Structures• Aim of the work• Multi-Phase Framework• End-quality Prediction• Other Applications• Conclusions

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

• 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




7. Conclusions



Model StructuresIndex1. Introduction to Batch

Processing.

2. Model Structures

3. Aim of the work




7. Conclusions


– Unfold the three-way matrix.

– Divide in K local matrices.

– Use an adaptive approach.


Model StructuresIndex1. Introduction to Batch

Processing.

2. Model Structures

3. Aim of the work




7. Conclusions

• Unfold the three-way matrix.– Batch-wise unfolding

Model Structures

Thousands ofvariables!!!

Index


2. Model Structures

3. Aim of the work




7. Conclusions

• 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


2. Model Structures

3. Aim of the work




7. Conclusions

Variables closein time are more

related

• Unfold the three-way matrix.– Variable-wise unfolding

Model Structures

dynamics are notbuilt in the model

Constant CorrelationImposed!!!

Low number ofparameters

Index


2. Model Structures

3. Aim of the work




7. Conclusions

More samples/parameter

• Unfold the three-way matrix.– Variable-wise unfolding

Model Structures

Constant Correlation Imposed!!!

V-W scores

Index


2. Model Structures

3. Aim of the work




7. Conclusions

• 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


2. Model Structures

3. Aim of the work




7. Conclusions

1 LMV

• Divide in K matrices

Model Structures

High numberof models

LMVs locallyAdjustable

Index


2. Model Structures

3. Aim of the work




7. Conclusions

Moving Average

Evolving

Local

• 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




7. Conclusions

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


2. Model Structures

3. Aim of the work




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


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.


Index


2. Model Structures

3. Aim of the work




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


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.


Anova + LSD

Why merge? Greedy Optimization Sub-optimal solution

To allow obtaining sub-models with different unfolding methods

Index


2. Model Structures

3. Aim of the work




7. Conclusions


Anova + LSD


5 LVs

3 LVs

5 LVs 15 LMVs

BW

1 LMV

Index


2. Model Structures

3. Aim of the work




7. Conclusions


Anova + LSD


2 LVs

1 LVs

VW

1 LMV

Index


2. Model Structures

3. Aim of the work




7. Conclusions

5 LVs

3 LVs

5 LVs 15 LMVs

BW

1 LMV

End-Quality Prediction- On-line prediction

Index


2. Model Structures

3. Aim of the work




7. Conclusions

End-Quality Prediction- Prediction performance:

Anaerobicstage

Saccha. Cerev. Waste-water treat.

Index


2. Model Structures

3. Aim of the work




7. Conclusions

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


2. Model Structures

3. Aim of the work




7. Conclusions

Index


2. Model Structures

3. Aim of the work




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.

Index


2. Model Structures

3. Aim of the work




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.

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


2. Model Structures

3. Aim of the work




7. Conclusions

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


2. Aim of the work

3. Multi-Phase Algorithm

4. Merging Algorithm


6. On-line Monitoring


8. Conclusions

On-line Monitoring- Monitoring Charts: D-statistic and SPE

Batch under NOC

Index


2. Aim of the work






8. Conclusions

On-line Monitoring- Monitoring Charts: D-statistic and SPE

Abnormal Batch

Index


2. Aim of the work






8. Conclusions

On-line Monitoring- Case Studies:

Index


2. Aim of the work






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.

Index


2. Aim of the work






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

Index


2. Aim of the work






8. Conclusions

On-line Monitoring- Nylon 6’6 Polymerization:

Index


2. Aim of the work






8. Conclusions

On-line Monitoring- Saccharomyces Cerevisiae Cultivation:

- Waste-water Treatment:

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