(340g) White-Box Machine Learning Approaches to Identify Governing Equations for Dynamics in Complex Manufacturing Systems and Their Comparison: A Study on Distillation Column

Modelling and predicting dynamics of a manufacturing system is a critical component for designing these systems to achieve production goals. Recently, data-driven approaches have been used to identify equations governing dynamics of physical systems such as fluid flow. However, the applicability of ML approach on correctly identifying governing mechanisms for dynamics of complex engineered systems has not been tested. There is also a need to capture both interpretability and simplicity of equations obtained from a data-driven approach similar to the first principles approach.

In this work, we address this question of testing the efficacy of ML methods to extract governing equations for manufacturing systems. We focus on distillation column which is a ubiquitous unit operation in manufacturing and demonstrates complex dynamics captured as a combination of heuristics and fundamental physical laws. We tested the methods of Sparse Identification of Non-Linear Dynamics (SINDy) and Symbolic Regression (SymReg) because of their ability to produce white-box models with terms that can be used for the physical interpretation of dynamics on data generated from mechanistic models for distillation column dynamics. We also compare these two algorithms on their efficiencies.

One promising result was reduction of number of equations for dynamic simulation from 1000s in ASPEN to only 13 – one for each state variable. For SINDy, prediction accuracy was high on the test data within the perturbation range, however, outside perturbation range equations did not perform well. In terms of physical law, few terms were interpretable as related to Fick’s law of diffusion and Henry’s law.

Compared to SINDy approach, preliminary results show that SymReg generated less complex results but still with high predictive power and forces us to look at the physical relations in a new way. Additionally, for SymReg Prediction accuracy was high on the test data within the perturbation range as well as outside perturbation range equations performed well.

However, in both SINDy and SymReg, we could not achieve a conclusive answer on physical governing laws and conclude that ML algorithms will have good predictive power for system dynamics, however, identifying new physical laws would need a hybrid heuristic approach.