Latent variable modeling and state estimation of non-stationary processes driven by monotonic trends

Abstract

In certain non-stationary processes, the non-stationary dynamics is caused by degradation or wearing of certain process components. Such dynamics can be characterized by a latent monotonic signal. Meanwhile, there also exist stationary dynamics characterizing the regular process variables. It hence becomes pertinent to distinguish these two sets of latent variables for the monitoring of the process from both the stationary and non-stationary aspects. In this regard, we propose a methodology to achieve such a goal by modeling the latent monotonic trend as a closed skew-normal random walk model. The other stationary relations are characterized by a state-space model with Gaussian noises. The problem is solved as a simultaneous state and parameter estimation problem using the expectation–maximization algorithm. As a result of the closed skew-normal random walk model for the monotonic trend, the state estimation problem becomes a skew-normal filtering and smoothing problem. The effectiveness of the proposed method is verified through a numerical simulation, and the algorithm is applied to solve a Hot Lime Softener fouling predictive monitoring problem.