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Evolving Models and a Pls Similarity Factor for Monitoring Batch Processes

Jon C. Gunther and Dale E. Seborg. Chemical Engineering, UC-Santa Barbara, Santa Barbara, CA 93105

Process monitoring based on multivariate statistical process control (MSPC) can be utilized to improve process understanding, detect abnormal and faulty operating conditions, and diagnose factors that impact product quality. For many batch processes, some process variables are easily measured on-line (PVs) while a few quality variables (QVs) are measured infrequently, for example, once per day or at the end of the batch. From a monitoring perspective, it would be desirable to develop a simple model that is able to predict QV values from PV data. In one promising approach, partial least squares (PLS), a “soft sensor” model is developed by extracting the information captured in the PV data that is most relevant for the prediction of QVs. PLS models and MSPC monitoring techniques can be used to identify abnormal operation and diagnose the root cause.

For monitoring batch processes, typical applications of PLS have been concerned with QV measurements made after the batch is complete. However, in many industrial applications, the QVs are also measured off-line infrequently during the batch, but these intermediate measurements are not used in PLS modeling. These considerations provide the motivation for an evolving model approach where the intermediate PLS measurements can be used to good advantage. In this new approach, all PV data prior to the next QV measurement are used to generate a PLS model for the time period from the beginning of the batch to the next QV sampling instant. These PLS models can then be used for the early detection of abnormal conditions and prediction of endpoints for the QVs. Each PLS model is developed from normal operating conditions (NOC). The new approach has two important advantages: (i) It uses the intermediate QV measurements, and (ii) for on-line monitoring, it avoids having to “fill in” for the missing future measurements, until the end of the batch. The latter problem occurs for existing on-line monitoring methods (Nomikos and MacGregor, 1995).

Process monitoring is typically based on two metrics, Hotelling's T2 statistic and the Sum of Squared Residuals (Q statistic). However, these metrics only consider the information captured in the score and residual subspaces. There are situations where other elements of the PLS model (e.g., the loadings and weightings) can facilitate batch comparisons by calculating similarity factors. Similarity factors can be used to good advantage to analyze PV data using Principal Component Analysis (PCA) methodology (Singhal and Seborg, 2002). In the current paper, we propose a new PLS similarity factor that offers similar advantages when QV data are also of interest.

The proposed PLS monitoring techniques were evaluated using a simulated fermentation fed-batch reactor. The detailed physically-based model was developed at the Lund Institute of Technology and has been validated with pilot-plant data. A comparison of the evolving model and the online PLS approach presented by Nomikos and MacGregor was conducted. To test the fault sensitivity, fault conditions were simulated and T2 and Q metrics were generated for both approaches. Contribution plots were used to diagnose abnormal process conditions. In contrast to most previous studies, the false alarm rate (i.e., type 1 errors) was also evaluated for each method. The advantages of the new evolving model approach and the PLS similarity factors were demonstrated by improved fault detection and lower false alarm rates.

In a current investigation, these monitoring techniques are being applied to industrial data for a fed-batch bioreactor for a cell culture process.


Nomikos, P. and J. F. MacGregor (1995). Multi-way partial least squares in monitoring batch processes. Chemom. Intell. Lab. Sys. 30, 97-108.

Singhal, A. and D. E. Seborg (2002). Pattern Matching in Historical Batch Data Using PCA. IEEE Ctrl. Sys. Mag. 22, 53-63.