Online batch/fed-batch process performance monitoring, quality prediction, and variable-contribution analysis for diagnosis

An integrated online multivariate statistical process monitoring (MSPM), quality prediction, and fault diagnosis framework is developed for batch processes. Batch data from I batches, with J process variables measured at K time points generate a three-way array of size I x K x J. Unfolding this three-way array into a two-way matrix of size IK x J by preserving the variable direction is advantageous for developing online MSPM methods because it does not require estimation of future portions of new batches. Two different multiway partial least squares (MPLS) models are developed. The first model (MPLSV) is developed between the data matrix (IK x J) and the local batch time (or an indicator variable) for online MSPM. The second model (MPLSB) is developed between the rearranged data matrix in the batch direction (I x KJ) and the final quality matrix for online prediction of end-of-batch quality. The problem of discontinuity in process variable measurements due to operation switching (or moving to a different phase) that causes problems in alignment and modeling is addressed. Control limits on variable contribution plots are used to improve fault diagnosis capabilities of the MSPM framework. Case studies from a simulated fed-batch penicillin fermentation illustrate the implementation of the methodology.