Batch process modeling by using temporal feature and Gaussian mixture model

Multi-model/multi-phase modeling algorithm has been widely used to monitor the product quality in complicated batch processes. Most multi-model/ multi-phase modeling methods hinge on the structure of a linearly separable space or a combination of different sub-spaces. However, it is impossible to accurately separate the overlapping region samples into different operating sub-spaces using unsupervised learning techniques. A Gaussian mixture model (GMM) using temporal features is proposed in the work. First, the number of sub-model is estimated by using the maximum interval process trend analysis algorithm. Then, the GMM parameters constrained with the temporal value are identified by using the expectation maximization (EM) algorithm, which minimizes confusion in overlapping regions of different Gaussian processes. A numerical example and a penicillin fermentation process demonstrate the effectiveness of the proposed algorithm.