Offline and Online Parameter Learning for Switching Multirate Processes With Varying Delays and Integrated Measurements

It is difficult to measure properties of certain key/quality variables at a fast rate due to technical constraints or economical considerations. Such variables are measured infrequently through laboratory analysis with a considerable delay. Also, sample collection for laboratory analysis may be extended over a significant time interval. In this article, the objective is to solve the parameter estimation problem along with real-time output prediction for switching multirate sampled processes with unknown varying delays and unknown varying sampling intervals. First, under the framework of the expectation–maximization (EM) algorithm, offline parameter estimation problem of dual-rate switching augmented regression models is handled. The delays, sampling intervals, and operating modes are considered as the hidden variables modeled by a nonparametric-distribution-based approach. In addition, as the fast-rate prediction of the slow-rate sampled variables is often used for process control applications, a recursive EM algorithm is used to predict the fast-rate outputs in real time. The efficacy of the proposed algorithms is shown through an experimental study on a laboratory hybrid tank system. The results show a satisfactory fast-rate prediction of the slow-rate sampled variables, and the significance of considering different sampling intervals is highlighted. Also, estimates of the occurrence probabilities of each possible delay, sampling interval, and mode are obtained without being limited by the assumption of a prior distribution.