process performance monitoring in the presence of confounding variation baibing li, elaine martin...

Centre for Process Analytics and Control Technology (CPACT)University of Newcastle, UK

PROCESS PERFORMANCE MONITORING IN THE PRESENCE

OF CONFOUNDING VARIATION

Baibing Li, Elaine Martin and Julian MorrisUniversity of Newcastle

Newcastle upon Tyne, England, UK


Techniques for Improved Operation

Enhanced Profitabilityand

Improved CustomerSatisfaction Modern Process

ControlSystems

Process Optimisation

Process Monitoring for Early Warning

andFault Detection


Mechanistic models developed from process mass and energy balances and kinetics provide the ideal form given:

process understanding exists time is available to construct the model.

Data based models are useful alternatives when there is:

limited process understanding process data available from a range of operating conditions.

Hybrid models combine several different approaches.

Process Modelling


Industrial Semi-discrete Manufacturing Process

Consider a situation where a variety of products (recipes) are produced, some of which are only manufactured in small quantities to meet the requirements of specialist markets.

Thirty-six process variables are recorded every minute, whilst five quality variables are measured off-line in the quality laboratory every two hours.

A nominal process performance monitoring scheme was developed using PLS from 41 ‘ideal’ batches, based on 3 recipes.

A further 6 batches, A4, A10, A29, A35, A38 and B32, that lay outside the desirable specification limits were used for model interrogation.



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By applying ordinary PLS, the variability between recipes dominates the model and hence masks the variability within a specific recipe that is of primary interest.

Two solutions to this have been proposed

The multi-group approach (Hwang et al,1998)

Generic modelling (Lane et al, 1997, 2001)


Process Modelling

Traditionally two types of variables have been used in the development of a process model/process performance monitoring scheme:

Process variables (X) Quality variables (Y)

In practice, a third class of variables exists:

Confounding variables (Z).

A confounding variable is any extraneous factor that is related to, and affects, the two sets of variables under study (X) and (Y).

It can result in a distortion of the true relationship between the two sets of variables, that is of primary interest.


Confidence ellipse including confounding

variation

Trajectory of confounding

variable Confidence ellipse excluding confounding variation

X

X X X X XX

Mal-operation

Global Process Variation


To exclude the nuisance source of variability, a necessary condition is that the derived latent variables, , and , are not correlated with the confounding variables:

and for .

The idea of constrained PLS is to apply the constraints given by equation to ordinary PLS.

0tZ hT 0uZ h

T Ah ,,1

ht hu

2T minarg hhh twEtt

2T minarg hhh uqFuu

2T minargT

hhh twEt0tZ

2T minargT

hhh uqFu0uZ

Constrained PLS


Standard constrained optimisation techniques can be used to solve the equations in each iteration.

An algorithm has been developed that enhances the efficiency of the constrained PLS algorithm.

The other steps of the constrained PLS are as for ordinary PLS.

The resulting latent variables can then be used for process monitoring with the knowledge that they are not confounded with the nuisance source of variability.

Any unusual variation detected from these latent variables can then be assumed to be related to abnormal process behaviour.

Constrained PLS


Simulation Example

Consider a process where the confounding variation is a result of recipe changes.

Recipe A - Observations [1, 50]. Recipe B - Observations [51, 100]. Recipe C - Observations [101, 150].

Measurements on three process variables and two quality variables were made over 150 time points.

Non-conforming operation occurred at time points 1, 2, 51 to 54, and 101, 102.


Simulation Example - Scatter Plot

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The process variables x1 and x2 for recipes A, B, C


Simulation Example - Bivariate Scores

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Simulation Example - T2 Chart

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Orthogonal Signal Correction (OSC)

Wold et al.’s (1989) OSC algorithm operates by removing those wavelengths of the spectra that are unrelated to the target variables.

It achieves this by ensuring that the wavelengths that are removed are mathematically orthogonal to the target variables or as close to the orthogonal as possible

Although OSC and the PLS filter have similar bilinear structures, the objective and methodology of OSC in terms of extracting the systematic part, T, differs to that of the constrained approach.

The OSC algorithm is based on PCA where at each iteration, that variation associated with the response variables is removed.

The filter in constrained PLS is based on the PLS algorithm. The process signal, X, is related to the confounding information, Z, through PLS.


Simulation Example - Comparison with OSC

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OSC - Ordinary PLS Constrained PLS


Simulation Example - Comparison with OSC

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Continuous Confounding Variables

In some processes there exist ‘recipe’ or ‘operating condition set-point’ variables that are varied continuously during production to meet changing customer requirements.

The variation caused by these continuously varying recipe variables, i.e. confounding variables, is usually not of direct interest for process monitoring.

In this situation the effect of the confounding variables should be removed so that the detection of more subtle process changes and malfunctions is not masked.


Continuous Confounding Variable

Consider a process where the confounding variation is a result of a continuously changing variable.

The confounding variable continuously takes values in the interval

[0, 1].

Measurements on three process variables and two quality variables were made over 100 time points.

Samples 1, 2, 51 and 52 are representative of non-conforming operation.

Non-conforming operation was generated by adding a disturbance term to process variables one and two but not to process variable three


Continuous Confounding Variable

Scatter plot of the process variables x1 and x2

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Ordinary PLS - Three Latent Variables

Hotelling’s T2Squared Prediction Error

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SPE Contribution Plot

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Ordinary PLS - Two Latent Variables

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Scores Contribution Plot

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Returning to the industrial semi-discrete batch manufacturing process the advantages of the constrained PLS algorithm over ordinary PLS.



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Constrained Partial Least Squares

Industrial Application


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Constrained PLS - Conclusions

Constrained PLS possesses the following important characteristics:

It removes that information correlated with the confounding variables.

The information excluded by constrained PLS contains only variation associated with the confounding variables.

The derived constrained PLS latent variables achieve optimality in terms of extracting as much of the available information as possible contained in the process and quality data.


Acknowledgements

The authors acknowledge the financial support of the EU ESPRIT PERFECT No. 28870 (Performance Enhancement through Factory On-line Examination of Process Data).

They also acknowledge colleagues at BASF Ag. for stimulating the research, in particular Gerhard Krennrich and Pekka Teppola.

process performance monitoring in the presence of confounding variation baibing li, elaine martin...

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