Batch processes play an important role in the production of low-volume, high-value products such as polymers, pharmaceuticals, and biochemicals. Multiway Principal Components Analysis (MPCA), one of the multivariate projection methods, has been widely used for monitoring batch processes. One major problem in the on-line application of MPCA is that the input data matrix for MPCA is not complete until the end of the batch operation, and thus the unmeasured portion of the matrix (called the "future observations") has to be predicted. In this paper we propose a new method for predicting the future observations of the batch that is currently being operated (called the "new batch"). The proposed method, unlike the existing prediction methods, makes extensive use of the past batch trajectories. The past batch trajectory which is deemed the most similar to the new batch is selected from the batch library and used as the basis for predicting the unknown part of the new batch. A case study on an industrial PVC batch process has been conducted. The results show that the proposed method results in more accurate prediction and has the capability of detecting process abnormalities earlier than the existing methods.
Key Words: Batch Process, Monitoring, Principal Component Analysis.
By HYUN-WOO CHO and KWANG-JAE KIM, Pohang University of Science and Technology, Pohang, Kyungbuk, 790-784, Korea
Continuous monitoring of process variables is an essential part in ensuring high quality product. The aim of monitoring is the early detection of process malfunctions, which leads to a quality cost reduction and operational safety enhancement. Recently, process monitoring based on multivariate statistical techniques such as principal component analysis (PCA) and projection to latent structures (PLS) has been successfully applied in both continuous (Kresta et al. (1991) and MacGregor et al. (1994)) and batch processes (Kosanovich et al. (1996) and Nomikos and MacGregor (1995a)).
Batch processes play an important role in the production of high-value-added products. A batch process has predetermined starting and stopping points, and raw materials are introduced into the process in predefined amounts using a specific sequence (Morris and Watson (1997)). The manufacture of a typical batch involves charging ingredients to the vessel, processing them under controlled conditions, and discharging the completed product. A batch operation is considered successful if one follows a prescribed recipe and keeps the process variables' trajectories with minimal batch-to-batch variation, resulting in a uniform high-quality product. Unfortunately, the typical characteristics of a batch process (e.g. finite duration, nonlinear behavior, and insufficient on-line sensors) make its on-line monitoring difficult and challenging.
Wold et al. (1987) first proposed the use of multiway PCA (MPCA) in batch process monitoring. Dong and McAvoy (1996) employed a nonlinear PCA model to take into consideration the nonlinearity of a batch process. Kosanovich et al. (1996) utilized MPCA to monitor and identify the major sources of batch-to-batch variability in a commercial batch reactor. For a fed-batch fermentation process, Lennox et al. (2000) developed a monitoring system based on MPCA in order to detect and isolate process abnormalities. Albert and Kinley (2001) utilized MPCA to develop a multivariate statistical process control (MSPC) system for industrial tylosin biosynthesis batch process.
One major problem arises when a new batch is monitored on-line; namely, the data matrix is not complete until the end of the batch operation. At each sampling time during the batch operation, the data matrix has the measurements only up to that time point, and the rest (called "future observations") are unknown. Since a "full" data matrix is required to utilize MPCA on-line for monitoring a batch process, the future observations of all the process variables should be predicted just to make the data matrix full. Monitoring performance in MPCA, especially the detection time of abnormal events, is directly dependent on the accuracy of the predicted future observations. Three approaches have been proposed for predicting the future observations in MPCA (Nomikos and MacGregor (1995b)). However, the existing methods have been criticized for not being sensitive enough to process changes and thus yielding unreliable results (Lennox et al. (2000)). Thus, a more accurate prediction method is essential in improving the monitoring performance of a batch process.
In this paper we propose a new prediction method for predicting future observations of a batch process. The proposed method, unlike those developed in Nomikos and MacGregor (1995b), makes an extensive use of the past batch trajectories. The past batch data, called the batch library, is utilized as a set of reference trajectories. The new batch is compared with those in the batch library at each sampling time. (Throughout this paper, the "new batch" refers to the batch that is currently being monitored.) The past batch trajectory that is deemed the most similar to the new batch is selected from the library and used as the basis for predicting the future observations of the new batch. The concept of "variable importance" is employed as a weighting factor in selecting the most similar batch.
This paper is organized as follows. First, the MPCA method is outlined along with a brief explanation of PCA. Then the existing methods for predicting future observations are reviewed and the proposed method is presented. Next, a case study on a PVC batch process is described to demonstrate the proposed method. Finally, the performance of the proposed method is discussed, and concluding remarks are given.
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