A Bayesian bias updating procedure for automatic adaptation of soft sensors

Abstract

Straightforward bias updating procedures for online adjustment of soft sensors (SS) are of interest for industrial processes in which quality or production variables cannot be measured online. This work proposes a Bayesian strategy for automatically updating the bias of a SS from: (i) online measurements of typical process variables and (ii) sporadic laboratory measurements of the critical variable to be estimated. The method continuously monitors the mean and standard deviation of the prediction error (i.e., the difference between the laboratory value and the SS output), and self-adapt the bias without requiring the adjustment of additional parameters. The proposal was evaluated on the basis of simulated examples of an industrial continuous process for the production of Styrene-Butadiene Rubber. The estimates are similar to those obtained with classical methods after optimizing their parameters. Moreover, the bias obtained with the Bayesian approach is preferable in the industrial practice due to its lower variability.