DEN-HMM: Deep emission network based hidden Markov model with time-evolving multivariate observations

A Hidden Markov Model (HMM) is a popular statistical modeling technique for system health state estimation, monitoring, and prognosis. However, most existing HMMs adopt some simple parametric probability distribution as the distribution of observations for a given state, and thus, cannot capture the intricate dependency of observations on state and possibly other covariates such as time. To address this, we propose a Deep Emission Network-based Hidden Markov Model (DEN-HMM) to capture the complex evolution of multivariate observations with respect to state and time. We also address the challenging issue of state nondiscrimination in DEN-HMM. To overcome this, we propose a regularized loss function that can prevent certain non-discriminative trivial solutions and enhance the state discriminative capabilities of DEN-HMM. The study further demonstrates extensive numerical studies to show the effectiveness of the proposed DEN-HMM, including a case study on steady-state estimation in ultrasonic cavitation-based dispersion processes.