Numerical Stability of EKF-Based Software Sensors in Chemical Engineering: A Van Der Vusse Reaction Case Study

Abstract

This paper aims at exploring numerical stability properties of various software sensors used in chemical science and engineering. These are applied commonly to evaluation of variables and/or parameters of chemical systems, which cannot be measured by technical means. Practical software sensors are often grounded in the extended Kalman filtering (EKF) method applied to estimation of this and that stochastic model. Usually, a conventional chemical system consists of an It-type stochastic differential equation representing the chemical reaction's dynamics and a discrete-time equation linking the model's state to the measurement information. The focus of this research is on the numerical stability of various EKF-based software sensors in the presence of round-off errors. Our case study exploration is fulfilled on the famous Van der Vusse reaction model but used with an ill-conditioned measurement function, here. We reveal that only square-root versions of the EKF-based software sensors (grounded in numerically stable orthogonal transformations) are the methods of choice for state and/or parameter estimations of stochastic chemical systems in the presence of round-off and other disturbances.