PROCESS PERFORMANCE MONITORING IN THE PRESENCE OF CONFOUNDING VARIATION

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PROCESS PERFORMANCE MONITORING IN THE PRESENCE
OF CONFOUNDING VARIATION
Baibing Li, Elaine Martin and Julian
Morris University of Newcastle Newcastle upon
Tyne, England, UK
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Techniques for Improved Operation
Enhanced Profitability and Improved
Customer Satisfaction
Modern Process Control Systems
Process Monitoring for Early Warning and Fault
Detection
Process Optimisation
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Process Modelling

• 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.

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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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Industrial Semi-discrete Manufacturing Process
Latent variable 1 V Latent variable 2
Latent variable 3 V Latent variable 4
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Industrial Semi-discrete Manufacturing Process
Bivariate Scores Plot
Hotellings T2 and SPE
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Industrial Semi-discrete Manufacturing Process

• 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)

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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.

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Global Process Variation
Confidence ellipse including confounding
variation
Mal-operation
X
X
X
X
X
X
X
Trajectory of confounding variable
Confidence ellipse excluding confounding variation
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Constrained PLS

• 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.

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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.

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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.

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Simulation Example - Scatter Plot
The process variables x1 and x2 for recipes A, B,
C
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Simulation Example - Bivariate Scores
Ordinary PLS
Constrained PLS
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Simulation Example - T2 Chart
Ordinary PLS
Constrained PLS
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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.

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Simulation Example - Comparison with OSC
Constrained PLS
OSC - Ordinary PLS
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Simulation Example - Comparison with OSC
Constrained PLS
OSC - Ordinary PLS
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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.

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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

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Continuous Confounding Variable
Scatter plot of the process variables x1 and x2
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Ordinary PLS - Three Latent Variables
Hotellings T2
Squared Prediction Error
X-block comprising process and confounding
variables
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SPE Contribution Plot
SPE contribution plot for observation 51
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Ordinary PLS - Two Latent Variables
Squared Prediction Error
Hotellings T2
X-block comprising only process variables
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OSC based Ordinary PLS
Hotellings T2
Squared Prediction Error
Two latent variables
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Constrained PLS
Squared Prediction Error
Hotellings T2
Two Latent Variables
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Scores Contribution Plot
Latent variable 1
Latent variable 2
Scores contribution plot for observation 51
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Industrial Semi-discrete Manufacturing Process

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

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Industrial Semi-discrete Manufacturing Process
Bivariate Scores Plot
Hotellings T2 and SPE
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Industrial Application
Constrained Partial Least Squares
LV 1 versus LV 2
LV 3 versus LV 4
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Industrial Application
Constrained Partial Least Squares
Hotellings T2
Squared Prediction Error
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Industrial Application
Contribution Plot
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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.

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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.