A Robust Infinite Gaussian Mixture Model and Its Application in Fault Detection of Nonlinear Multimode Processes

Finite Gaussian mixture model (GMM) has recently proven to be a powerful unsupervised treatment for monitoring nonlinear processes with multiple operating conditions. The performance of GMM-based monitoring method largely depends on the number of mixture densities. However, the popular penalty method, such as Bayesian information criterion (BIC) and Akaike's information criterion (AIC), usually tend to yield noisy model size estimates. Moreover, the parameter estimates in GMM are susceptible to outliers. To overcome these deficiencies, this paper proposes a new process monitoring technique based on a robust infinite Gaussian mixture model (Ro-IGMM). Specifically, a separate weight at each point is assigned to the precisions as a measure of smoothness, representing the similarities to other data points. The Chinese restaurant process is then placed on a prior to turn into infinite groupings. The informations, such as a distribution over the number of clusters, the cluster assignments, and the parameters associated with each cluster, can be given by the posterior which is obtained by a collapse Markov chain Monte Carlo (MCMC) inference. Simulation results on the benchmark Tennessee Eastman process show that Ro-IGMM-based process monitoring method is more insensitive to outliers during process modeling, compared to traditional methods working with BIC model selection.