A variational Bayesian approach to identification of switched ARX models

In the identification of switched Auto-Regressive eXogenous (SARX) models, the number of local models is often assumed to be known a priori. However, in many industrial applications the prior process knowledge or the available information about the plant operation might not be sufficient to determine the number of local models. In such cases, the optimal number of local models needs to be inferred from collected operational data. The switching mechanism of the process is also often unknown. Therefore, classical SARX identification methods assuming a piecewise affine system fail to accurately identify randomly switched models. Furthermore, classical identification methods result in single-point estimates of unknown parameters, thereby ignoring the parameter uncertainty. The main objective of this work is to formulate and solve the problem of SARX model identification under the variational Bayesian framework through which the aforementioned challenging issues can be addressed. As a full Bayesian system identification approach, the proposed method not only provides a posterior distribution over model parameters to reveal the level of uncertainty of the estimated values, but also determines the optimal number of local models automatically. Since the identification pair identity at each sampling instant can be inferred from the data set, the switching mechanism will not influence the identification results. The effectiveness of the proposed Bayesian approach is demonstrated through a simulation case study.