State and Parameter Estimation of Multi-rate Processes with Variable Measurement Delays

Abstract

Measurements in the process industry can arrive with fast or slow sampling rates. Fast measurements such as flowrate and temperature are sampled frequently and are obtained instantly after sampling. The slow measurements, which are usually related with chemical quality variables such as product composition, are sampled infrequently and have some delay due to the laboratory analysis. Moreover, sample collection for laboratory analysis may extend over a significant time interval, and the slow measurements are actually functions of all the states during the sampling period. Our objective is to develop a multirate state and parameter estimation method for this situation. In state estimation, the objective is to fuse the two kinds of measurements to provide a more accurate estimation of the system’s states. We propose two methods to solve the problem, the exact Bayesian approach and the augmented state approach. In the exact Bayesian approach, the algorithm is developed by implementing Bayes’ rule. In the augmented state approach, the system is reformulated by augmenting the current state with past information required for fusing the slow measurements and then apply general state estimation procedures. For system identification, the parameters are estimated along with the time delays using a particle filter (PF) under the framework of the expectation maximization (EM) algorithm. The performance of the proposed methods for both state and parameter estimation are demonstrated though simulation and experimental studies and by comparison with methods that only use the fast measurements. Finally, the proposed state and parameter estimation methods are applied to the FWKO vessel to demonstrate their effectiveness and applicability.