PROCESS PERFORMANCE MONITORING IN THE PRESENCE OF CONFOUNDING VARIATION Baibing Li, Elaine Martin and Julian Morris University of Newcastle Newcastle upon Tyne, England, UK

Techniques for Improved Operation Enhanced Profitability and Improved Customer Satisfaction Modern Process Control Systems Process Optimisation Process Monitoring for Early Warning and Fault Detection

n Mechanistic models developed from process mass and energy balances and kinetics provide the ideal form given: u process understanding exists u time is available to construct the model. n Data based models are useful alternatives when there is: u limited process understanding u process data available from a range of operating conditions. n Hybrid models combine several different approaches. Process Modelling

Industrial Semi-discrete Manufacturing Process n 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. n Thirty-six process variables are recorded every minute, whilst five quality variables are measured off-line in the quality laboratory every two hours. n A nominal process performance monitoring scheme was developed using PLS from 41 ideal batches, based on 3 recipes. n A further 6 batches, A4, A10, A29, A35, A38 and B32, that lay outside the desirable specification limits were used for model interrogation.

Industrial Semi-discrete Manufacturing Process Latent variable 1 V Latent variable 2Latent variable 3 V Latent variable 4

Industrial Semi-discrete Manufacturing Process Bivariate Scores PlotHotellings T 2 and SPE

Industrial Semi-discrete Manufacturing Process n 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. n Two solutions to this have been proposed l The multi-group approach (Hwang et al,1998) l Generic modelling (Lane et al, 1997, 2001)

Process Modelling n Traditionally two types of variables have been used in the development of a process model/process performance monitoring scheme: l Process variables (X) l Quality variables (Y) n In practice, a third class of variables exists: l Confounding variables (Z). n A confounding variable is any extraneous factor that is related to, and affects, the two sets of variables under study (X) and (Y). n 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 X X Mal-operation Global Process Variation

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

n Standard constrained optimisation techniques can be used to solve the equations in each iteration. n An algorithm has been developed that enhances the efficiency of the constrained PLS algorithm. n The other steps of the constrained PLS are as for ordinary PLS. n 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. n Any unusual variation detected from these latent variables can then be assumed to be related to abnormal process behaviour. Constrained PLS

Simulation Example n Consider a process where the confounding variation is a result of recipe changes. l Recipe A - Observations [1, 50]. l Recipe B - Observations [51, 100]. l Recipe C - Observations [101, 150]. n Measurements on three process variables and two quality variables were made over 150 time points. n Non-conforming operation occurred at time points 1, 2, 51 to 54, and 101, 102.

Simulation Example - Scatter Plot The process variables x 1 and x 2 for recipes A, B, C

Simulation Example - Bivariate Scores Ordinary PLS Constrained PLS

Simulation Example - T 2 Chart Ordinary PLS Constrained PLS

Orthogonal Signal Correction (OSC ) n Wold et al.s (1989) OSC algorithm operates by removing those wavelengths of the spectra that are unrelated to the target variables. n 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 n 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. l The OSC algorithm is based on PCA where at each iteration, that variation associated with the response variables is removed. l 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 OSC - Ordinary PLS Constrained PLS

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

Continuous Confounding Variables n In some processes there exist recipe or operating condition set- point variables that are varied continuously during production to meet changing customer requirements. n The variation caused by these continuously varying recipe variables, i.e. confounding variables, is usually not of direct interest for process monitoring. n 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 n Consider a process where the confounding variation is a result of a continuously changing variable. l The confounding variable continuously takes values in the interval [0, 1]. n Measurements on three process variables and two quality variables were made over 100 time points. n Samples 1, 2, 51 and 52 are representative of non-conforming operation. l 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 x 1 and x 2

Ordinary PLS - Three Latent Variables Hotellings T 2 Squared Prediction Error X-block comprising process and confounding variables

SPE Contribution Plot SPE contribution plot for observation 51

Ordinary PLS - Two Latent Variables X-block comprising only process variables Hotellings T 2 Squared Prediction Error

OSC based Ordinary PLS Hotellings T 2 Squared Prediction Error Two latent variables

Constrained PLS Two Latent Variables Hotellings T 2 Squared Prediction Error

Scores Contribution Plot Scores contribution plot for observation 51 Latent variable 1 Latent variable 2

Industrial Semi-discrete Manufacturing Process n Returning to the industrial semi-discrete batch manufacturing process the advantages of the constrained PLS algorithm over ordinary PLS.

Industrial Semi-discrete Manufacturing Process Bivariate Scores PlotHotellings T 2 and SPE

LV 1 versus LV 2LV 3 versus LV 4 Constrained Partial Least Squares Industrial Application

Hotellings T 2 Squared Prediction Error Constrained Partial Least Squares Industrial Application

Contribution Plot Industrial Application

Constrained PLS - Conclusions n Constrained PLS possesses the following important characteristics: l It removes that information correlated with the confounding variables. l The information excluded by constrained PLS contains only variation associated with the confounding variables. l 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 n The authors acknowledge the financial support of the EU ESPRIT PERFECT No (Performance Enhancement through Factory On-line Examination of Process Data). n They also acknowledge colleagues at BASF Ag. for stimulating the research, in particular Gerhard Krennrich and Pekka Teppola.