A Novel Semiparametric Hidden Markov Model for Process Failure Mode Identification

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.