Bayesian Identification of Hidden Markov Models and Their Use for Condition-Based Monitoring

In this paper, we propose a Bayesian estimation scheme for hidden Markov model (HMM) parameters, as well as a method for monitoring systems whose degradation processes are modeled using HMMs identified using this novel estimation approach. The Bayesian estimation naturally yields information about model parametric uncertainties via posterior distributions of HMM parameters emanating from the estimation procedure. Numerous simulations implementing the newly proposed method for estimation of HMM parameters were conducted demonstrating its capability to identify several types of HMMs, including the commonly encountered ergodic and homogeneous HMM, as well as less commonly studied nonergodic or/and nonhomogeneous HMM. In addition, a novel condition monitoring scheme based on uncertain HMMs of the degradation process is proposed and demonstrated on a large dataset obtained from a semiconductor-manufacturing facility. A small portion of the data was used to build operating mode specific HMMs of machine degradation via the newly proposed Bayesian estimation, while the remainder of the data was used for condition monitoring based on the uncertain degradation HMMs yielded by the novel Bayesian estimation method. Comparison with a traditional sensory signature-based statistical monitoring method showed that the newly proposed approach significantly outperforms the traditional method in terms of its detection capabilities and false alarm ratios.