(404d) A New Gaussian Mixture Model Based Bayesian Inferential Monitoring Framework for Complex Chemical Processes

Authors: 
Yu, J. - Presenter, McMaster University


For complex chemical processes, the operating conditions often shift due to the changes of various factors such as feedstock, product specifications, set points and manufacturing strategies. Thus the plant operating data can be significantly away from multivariate Gaussian distribution so that the conventional statistical process monitoring methods like principal component analysis (PCA) and partial least squares (PLS) fail to detect the process abnormalities with the unreliable T2 and SPE control limits. More recent effort has been reported to monitor such non-Gaussian multimode processes using multiple PCA/PLS models. However, a priori process knowledge is typically required to segment the historical operating data into multiple groups that correspond to different operating modes. In contrast, Gaussian mixture model (GMM) has not been explored for process monitoring until very recently and most of the literature study attempted to approach it in a deterministic way. That is, every monitored sample is classified into a particular Gaussian cluster instead of viewed as a random point that may comes from various modes with different posterior probabilities.

In this research, a finite Gaussian mixture model (FGMM) based Bayesian inferential framework is developed for fault detection and diagnosis of non-Gaussian processes with different operating modes. The normal process data at each individual operating mode are assumed to follow a multivariate Gaussian distribution and the operation status is treated as a random variable that can be at any of the possible modes with a prior probability. A FGMM is then built to characterize the multiple operating regions, each of which corresponds to a Gaussian component. With the estimated FGMM, a Bayesian inference strategy is used to compute the posterior probability of a monitored sample belonging to each Gaussian component. Further, the regularized Mahalanobis distance metrics are integrated across all different Gaussian modes through Bayesian inference strategy and the formed Bayesian inferential probability (BIP) index can be computed to detect abnormal process events. In addition to fault detection, a Bayesian inference based Gaussian mixture contribution (BIGMC) index is derived with posterior probabilities as weighting factors to isolate process faults and diagnose the root-cause variables. The Tennessee Eastman process (TEP) is used to demonstrate the utility of the Bayesian inferential monitoring approach and the comparison of monitoring results proves its superiority in terms of fault detection and diagnosis accuracy.