Latent variable modeling and state estimation of non-stationary processes driven by monotonic trends. (December 2021) - Chiplunkar, Ranjith; Huang, Biao
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. Highlights: Separation of the stationary and non-stationary sources of a deteriorating process. The non-stationary source is modeled as a monotonic random walk model. The monotonic latent variable is modeled as a closed skew-normal random walk model. The proposed model leads to a simultaneous state and parameter estimation problem. The problem is solved using the expectation-maximization (EM) algorithm. Analytical derivation of the smoothing equations for a CSN state-space model. Application of the proposed method on an industrial hot lime softener process.