Development of hidden semi-Markov models for diagnosis of multiphase batch operation

This paper deals with automatic on-line detection and diagnosis of fault patterns in multiphase batch processes. A novel and flexible approach based on the combination of hidden segmental semi-Markov models (HSMM) and multiway principal component analysis (MPCA) is proposed. In all batch operations, process variables may have correlations with each other, and MPCA is used to handle cross-correlation among process variables. In multiphase batch processes, the effect of external factors on process variables is phase-specific and the duration of each phase varies from batch to batch. HSMM is used to model the multiphase batch operation by representing each phase with a macro-state whose duration is determined by a phase-specific probability distribution of a number of micro-states. The output of each micro-state corresponds to the values of the monitored variables at a specific point in time. Given this structure, MPCA-HSMM parameters are trained by the batch operation data and recursive Viterbi algorithm is used to find out the optimum state sequence from each batch. Probability values of the optimum state sequence are collected to construct the probabilistic model which is used to compute the corresponding control limit for the specified operating condition. One MPCA-HSMM model is to be built for each type of previously known operating condition—normal and fault events. The power and advantages of the proposed method are successfully demonstrated in a simulated fed-batch penicillin cultivation process. MPCA-HSMM correctly identifies the type of fault from the batch operation data.