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Multivariate Statistical Process Control in Batch Process Monitoring
7e-Ol 1
Copyright © 1996 IFAC 13th Triennial World Congress, San Francisco. USA
MULTIV ARIATE STATISTICAL PROCESS CONTROL IN BATCH PROCESS MONITORING
S.Albert, E.B.Martin+, G.A.Montague, A.J.Morris
Department of Chemical and Process Engineering Department of Engineering Mathematics+ University of New casi le. Newcastle-upon-Tyne. NE1 7RU. U.K. Tel.: +44-191-2227266 Fax: +44-191-2225292 E-mail:[email protected]
Abstract: Batch processing was widely practised long before the advent of the modem chemical industry. A number of limitations have inhibited the success of batch monitoring:- the finite duration of a batch, the presence of significant nonlinearities, the lack of on-line sensors for measuring quality variables, the absence of steady-state operation, the difficulty of developing accurate mechanistic models and finally, process measurements are autocorrelated in time as well as being correlated with one another at any given time. Recent approaches to the monitoring of batch behaviour have been based on the extension of univariate statistical process control (SPC) philosophy to handle multivariate processes. These tools have been the statistical projection methods of principal components analysis (PCA) and projection to latent structures (PLS), and their extensions to batch operation, i.e. multiway PCA and PLS. In this paper, multi way PCR is applied to the monitoring of a batch polymerisation reactor and an industrial fed-batch fermentation process using two alternative approaches. These tools have been found to be an effective method for monitoring industrial processes when the data is of high dimension and ill-conditioned. Furthermore, they provide a useful modelling technique for predicting key quality variables which are either not measured on-line or else are monitored at a much slower frequency than the process variables. Keywords: Multivariate SPC, Batch Processes, On-line Monitoring
l. INTRODUCfION In general, achieving consistency and quality of production is a significant challenge to the process industries. The availability of cheap computing power has increased the potential for routine data collcction on a large number of variables. In its raw state the monitored plant data may be of limited use. However, such computer systems permit not only the monitoring of vast amount of information, but also the implementation of advanced control technology which could potentially satisfy batch optimisation objectives.
Multivariate Statistical Process Control (MSPC) techniques are receiving significant attention in response to increasing demands for enhanced process performance and product reproducibility. Batch processes are rarely operated steady-state, the general objective is to achieve a well-defined end-point, and pass through a much wider range of dynamic conditions than continuous processes, which alters the manner in which modelling and control is implemented. In order to minimise the batch-to-batch variation it is essential that the variability within the process duration is monitored in accordance with a desired state profile.
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Another restriction is the lack of on-line sensors for measuring quality variables. However, the most easily measured and frequently available information is collected on the process parameters which are, theoretically, only indicators of process behaviour. Through inferential estimation, quality prediction may be monitored based on the monitored process variables. MacGregor and Nomikos (1992) extended the multivariate SPC methods of PCA and PLS to batch processes, multiway PCA and multiway PLS. This approach allows on-line monitoring of a batch process to be undertaken, once a model has been developed from nominal or good batch operation, using the projection based approaches of PCA and PLS, (Nomikos and MacGregor, 1994, 1995). This paper shows that multivariate statistical projection techniques are not only valuable for performance monitoring and fault detection but also for the inferential prediction of the profiles of certain key variables throughout the batch duration. The advantage of such information is that, potentially, if the batch appears to moving away from it'> 'nominal' trajectory' then corrective action may be implemented. The results of a new approach using principal components regression is presented in the paper for defining batch trajectories. Its application is demonstrated on two industrial applications, the monitoring of a batch polymerisation reactor and an industrial fed-batch fermentation process.
2. STATISTICAL PROCESS CONTROL (SPC) OF MULTIV ARIATE PROCESSES SPC should be seen as an objective statistical analysis of process variation and its causes which provides a conceptually different, but complementary technique to automatic feedback control. Traditional SPC charts ignore interactions between variables which are poorly understood, complex and highly non-linear. Assumption of normality, compression of relevant process information into means and standard deviations are a further drawback. These limitations can be addressed through multivariate projection techniques such as Principal Component Analysis, (PCA), Pearson (1901) and Projection to Latent Structures, (PLS) Joreskog and Wold (1981). Batch data differs from continuous data in that the problem is now three dimensional, the added dimension being that of time. In addition to the possible correlation amongst variables they are also autocorrelatcd in time. The data reduction technique of principal components analysis can be used to project the process information (X)
onto a lower dimensional space which summarises the variables and their time history during previous successful batches, i.e. multiway PCA. A simple way to view multiway PCA is to consider opening out the three dimensional matrix into a two-dimensional array, by placing each 2-D block consecutively and performing a standard PCA (MacGregor et al., 1994). There are three possible ways of unfolding this matrix. MacGregor and Nomikos support the approach illustrated in Figure 1 which regards each batch as an independent representation of the process and each process variable as a different variable at each instant in time. Variables are highly correlated when they represent the time trajectories of the original process variables and therefore a considerable reduction in dimension can be achieved when performing multi-way PCA. The loadings matrix (P) summarises the information in the data with respect both to variables and their time variation, the scores (t) represent a summary of the overall performance of one batch. Multi-way PCA utilises not just the magnitude of the deviation of a variable from its mean trajectory, but the correlation structure between variables. Indeed, it is the correlation structure which can be particularly important in the detection of faults. An alternative way of unfolding the 3D matrix (Figure 2) results in a different form of analysis and interpretation of the problem; time-variations of several batches are compressed into scalar variables. Here each batch is reduced to a time history of scores rather than one score. MulLi-way PCA has been shown to be successful in analysing batch operations in terms of data compression, modelling, building process performance monitoring, fault detection and classification. Nomikos and MacGregor (1995) demonstrated the on-line application of the MPCA model for monitoring purposes using nominal operating data. This nominal model allows the construction of muItivariate control charts with control limits defined using modifications to Hotelling's T2 statistic. The limitations of the approach described is that the information concerning batch behaviour is generally only available at the end of a batch - too late for corrective action to be taken. For successful on-line monitoring, the behaviour of the batch is required to be known throughout its trajectory but in practice information is only available up to time point, t, on the batch. Four ways have been proposed in the literature (MacGregor et ai, 1994) to predict the behaviour between time point t and the end of the batch (i) zero deviations method, (ii) current deviations method, (iii) projection method and (iv) multi model method.
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Copyright © 1996 IFAC 13th Triennial World Congress, San Francisco. USA
MULTIV ARIATE STATISTICAL PROCESS CONTROL IN BATCH PROCESS MONITORING
S.Albert, E.B.Martin+, G.A.Montague, A.J.Morris
Department of Chemical and Process Engineering Department of Engineering Mathematics+ University of New casi le. Newcastle-upon-Tyne. NE1 7RU. U.K. Tel.: +44-191-2227266 Fax: +44-191-2225292 E-mail:[email protected]
Abstract: Batch processing was widely practised long before the advent of the modem chemical industry. A number of limitations have inhibited the success of batch monitoring:- the finite duration of a batch, the presence of significant nonlinearities, the lack of on-line sensors for measuring quality variables, the absence of steady-state operation, the difficulty of developing accurate mechanistic models and finally, process measurements are autocorrelated in time as well as being correlated with one another at any given time. Recent approaches to the monitoring of batch behaviour have been based on the extension of univariate statistical process control (SPC) philosophy to handle multivariate processes. These tools have been the statistical projection methods of principal components analysis (PCA) and projection to latent structures (PLS), and their extensions to batch operation, i.e. multiway PCA and PLS. In this paper, multi way PCR is applied to the monitoring of a batch polymerisation reactor and an industrial fed-batch fermentation process using two alternative approaches. These tools have been found to be an effective method for monitoring industrial processes when the data is of high dimension and ill-conditioned. Furthermore, they provide a useful modelling technique for predicting key quality variables which are either not measured on-line or else are monitored at a much slower frequency than the process variables. Keywords: Multivariate SPC, Batch Processes, On-line Monitoring
l. INTRODUCfION In general, achieving consistency and quality of production is a significant challenge to the process industries. The availability of cheap computing power has increased the potential for routine data collcction on a large number of variables. In its raw state the monitored plant data may be of limited use. However, such computer systems permit not only the monitoring of vast amount of information, but also the implementation of advanced control technology which could potentially satisfy batch optimisation objectives.
Multivariate Statistical Process Control (MSPC) techniques are receiving significant attention in response to increasing demands for enhanced process performance and product reproducibility. Batch processes are rarely operated steady-state, the general objective is to achieve a well-defined end-point, and pass through a much wider range of dynamic conditions than continuous processes, which alters the manner in which modelling and control is implemented. In order to minimise the batch-to-batch variation it is essential that the variability within the process duration is monitored in accordance with a desired state profile.
6708
Another restriction is the lack of on-line sensors for measuring quality variables. However, the most easily measured and frequently available information is collected on the process parameters which are, theoretically, only indicators of process behaviour. Through inferential estimation, quality prediction may be monitored based on the monitored process variables. MacGregor and Nomikos (1992) extended the multivariate SPC methods of PCA and PLS to batch processes, multiway PCA and multiway PLS. This approach allows on-line monitoring of a batch process to be undertaken, once a model has been developed from nominal or good batch operation, using the projection based approaches of PCA and PLS, (Nomikos and MacGregor, 1994, 1995). This paper shows that multivariate statistical projection techniques are not only valuable for performance monitoring and fault detection but also for the inferential prediction of the profiles of certain key variables throughout the batch duration. The advantage of such information is that, potentially, if the batch appears to moving away from it'> 'nominal' trajectory' then corrective action may be implemented. The results of a new approach using principal components regression is presented in the paper for defining batch trajectories. Its application is demonstrated on two industrial applications, the monitoring of a batch polymerisation reactor and an industrial fed-batch fermentation process.
2. STATISTICAL PROCESS CONTROL (SPC) OF MULTIV ARIATE PROCESSES SPC should be seen as an objective statistical analysis of process variation and its causes which provides a conceptually different, but complementary technique to automatic feedback control. Traditional SPC charts ignore interactions between variables which are poorly understood, complex and highly non-linear. Assumption of normality, compression of relevant process information into means and standard deviations are a further drawback. These limitations can be addressed through multivariate projection techniques such as Principal Component Analysis, (PCA), Pearson (1901) and Projection to Latent Structures, (PLS) Joreskog and Wold (1981). Batch data differs from continuous data in that the problem is now three dimensional, the added dimension being that of time. In addition to the possible correlation amongst variables they are also autocorrelatcd in time. The data reduction technique of principal components analysis can be used to project the process information (X)
onto a lower dimensional space which summarises the variables and their time history during previous successful batches, i.e. multiway PCA. A simple way to view multiway PCA is to consider opening out the three dimensional matrix into a two-dimensional array, by placing each 2-D block consecutively and performing a standard PCA (MacGregor et al., 1994). There are three possible ways of unfolding this matrix. MacGregor and Nomikos support the approach illustrated in Figure 1 which regards each batch as an independent representation of the process and each process variable as a different variable at each instant in time. Variables are highly correlated when they represent the time trajectories of the original process variables and therefore a considerable reduction in dimension can be achieved when performing multi-way PCA. The loadings matrix (P) summarises the information in the data with respect both to variables and their time variation, the scores (t) represent a summary of the overall performance of one batch. Multi-way PCA utilises not just the magnitude of the deviation of a variable from its mean trajectory, but the correlation structure between variables. Indeed, it is the correlation structure which can be particularly important in the detection of faults. An alternative way of unfolding the 3D matrix (Figure 2) results in a different form of analysis and interpretation of the problem; time-variations of several batches are compressed into scalar variables. Here each batch is reduced to a time history of scores rather than one score. MulLi-way PCA has been shown to be successful in analysing batch operations in terms of data compression, modelling, building process performance monitoring, fault detection and classification. Nomikos and MacGregor (1995) demonstrated the on-line application of the MPCA model for monitoring purposes using nominal operating data. This nominal model allows the construction of muItivariate control charts with control limits defined using modifications to Hotelling's T2 statistic. The limitations of the approach described is that the information concerning batch behaviour is generally only available at the end of a batch - too late for corrective action to be taken. For successful on-line monitoring, the behaviour of the batch is required to be known throughout its trajectory but in practice information is only available up to time point, t, on the batch. Four ways have been proposed in the literature (MacGregor et ai, 1994) to predict the behaviour between time point t and the end of the batch (i) zero deviations method, (ii) current deviations method, (iii) projection method and (iv) multi model method.
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