Modeling and Bayesian inference for processes characterized by abrupt variations

Abstract

Abrupt variations are often observed in the datasets of chemical processes but they have not been well studied in the literature. This paper proposes a method of modeling and estimating systems characterized by abrupt (impulsive) changes. Abrupt changes may be due to multiple reasons such as disturbances, capacity change, etc. All these cases result in signals that appear to have sudden jumps. But mixed with these jumps are the other dynamic variations characterizing the regular dynamics of the process. For effective modeling, it is important to capture both the jumps and the regular dynamic variations. This paper proposes to model such behavior through a dynamic latent variable (LV) model. The resulting model has two types of LVs characterizing the abrupt and the regular variations. These two behaviors are modeled using a Cauchy and a Gaussian dynamic model respectively. The inference of the LVs and model parameters is done in the variational Bayesian framework.