Monitoring of batch processes through state-space models



The development of a state-space framework for monitoring batch processes that can complement the existing multivariate monitoring methods is presented. A subspace identification method will be used to extract the dynamic and batch-to-batch trends of the process and quality variables from historical operation data in the form of a “lifted” state-space stochastic model. A simple monitoring procedure can be formed around the state and residuals of the model using appropriate scalar statistical metrics. The proposed state-space monitoring framework complements the existing multivariate methods like the multi-way PCA method, in that it allows us to build a more complete statistical representation of batch operations and use it with incoming measurements for early detection of not only large, abrupt changes but also subtle changes. In particular, it is shown to be effective for detecting changes in the batch-to-batch correlation structure, slow drifts, and mean shifts. Such information can be useful in adapting the prediction model for batch-to-batch control. The framework allows for the use of on-line process measurements and/or off-line quality measurements. When both types of measurements are used in model building, one can also use the model to predict the quality variables based on incoming on-line measurements and quality measurements of previous batches. © 2004 American Institute of Chemical Engineers AIChE J, 50: 1198–1210, 2004