A Gaussian Mixture Model Algorithm using the Temporal Information

Soft sensor is widely used in batch processes to monitor the products quality which is unmeasurable or measured with low frequency. Most multi-model/multi-phase modelling methods cannot deal with the overlapping section in different operating regimes. A GMM algorithm based on temporal information is proposed to overcome the overlapping problem in this paper. The proposed method maximizes the posterior probability by introducing a temporal penalty term. Then the parameters of GMM can be estimated with the punitive log-likelihood function using expectation maximization (EM) algorithm. Applications on a numerical simulation and a penicillin production process demonstrate the performance of the presented algorithm.