A perspective on parsimonious hybrid models for online use: Augmenting fundamental models with ARIMA disturbances

Abstract

Hybrid models (HMs) combine fundamental model (FM) equations with empirical components. These models can lead to improved predictions because they reduce process/model mismatch and can account for phenomena that are not considered in the FM equations. This article reviews HM approaches that have been used for modelling of chemical processes, paying particular attention to HMs that are suitable for online process monitoring. Recent HM studies focus on development of HMs with a relatively small number of parameters that require estimation, which makes them less prone to overfitting when available data is limited. We propose a new approach to the development of parsimonious HMs that combines nonlinear dynamic material and energy balance equations with empirical stochastic disturbances. These stochastic disturbances are inspired by autoregressive integrated moving average (ARIMA) disturbances used in linear time-series models. In addition, we propose an updated Laplace approximation maximum likelihood estimation (LAMLE) algorithm that is effective for estimating parameters in the resulting stochastic differential equations. A continuous stirred tank reactor (CSTR) case study is used to illustrate the methodology. The case study reveals that improved parameter estimates are obtained when an empirical disturbance parameter is included in the model along with the fundamental CSTR parameters. In future, it will be important to test whether use of parsimonious HMs will lead to more-reliable model predictions and state estimates than online predictions resulting from the corresponding FMs.