A Novel Semiparametric Hidden Markov Model for Process Failure Mode Identification

Abstract

The emitting distributions of a hidden Markov model (HMM) are normally constructed using the cross moments of the process variables. Similar to the mean of a univariate probability distribution, the cross moment is the most fundamental statistic of a multivariate probability distribution, which is not capable of capturing the high-order statistical features of process data. To alleviate this limitation, the high-order equivalence of the cross moment demonstrated in this paper, as the complete dependence structure, is used to construct the emitting distribution for HMM. The complete dependence structure among the process variables is modeled in a Gaussian copula. A semiparametric data transformation is also proposed to ensure the necessary conditions for using a Gaussian copula are met. The final emitting distribution is constructed as a finite mixture of the copula models. The proposed HMM is tested on two industrial studies for performance validation. Note to Practitioners —Gaussian mixture model HMM (GMM-HMM) is an efficient and easy-to-implement tool for mode identification of dynamic industrial processes. These virtues of GMM-HMM mainly come from the use of Gaussian emitting distribution, which allows closed-form derivatives to be computed for the expectation and maximization (EM) estimation of mode parameters. The main novelty of the proposed copula mixture model HMM (SPCMM-HMM) is twofold; its emitting distribution also belongs to the exponential family, thus enabling efficient estimation of parameters through an exact EM procedure; meanwhile, it is also capable of characterizing complex dependence structures among process variables. However, the proposed SPCMM-HMM has more model parameters compared with the GMM-HMM. It excels in situations where the operation of the process system being monitored is highly integrated (with complex process variable interactions) and abundance of training data samples is available. In this paper, the interactions between process variables in both case studies are complex due to the implementation of multiple closed control loops, and a large amount of training data samples can be easily generated from simulation. The performance of the SPCMM-HMM is shown to be consistently better than that of the GMM-HMM under such settings, which are fairly common in modern industrial processes. Nonetheless, if the process system being considered is only designed for a simple operation or there is a scarcity of training data samples, the GMM-HMM is still the preferred method as it is less prone to overfitting.