White-box Machine learning approaches to identify governing equations for overall dynamics of manufacturing systems: A case study on distillation column

Abstract

Dynamical equations form the basis of design for manufacturing processes and control systems; however, identifying governing equations using a mechanistic approach is tedious. Recently, Machine learning (ML) has shown promise to identify the governing dynamical equations for physical systems faster. This possibility of rapid identification of governing equations provides an exciting opportunity for advancing dynamical systems modeling. However, applicability of the ML approach in identifying governing mechanisms for the dynamics of complex systems relevant to manufacturing has not been tested. We test and compare the efficacy of two white-box ML approaches (SINDy and SymReg) for predicting dynamics and structure of dynamical equations for overall dynamics in a distillation column. Results demonstrate that a combination of ML approaches should be used to identify a full range of equations. In terms of physical law, few terms were interpretable as related to Fick’s law of diffusion and Henry’s law in SINDy, whereas SymReg identified energy balance as driving dynamics.