Reduced order dynamical models for complex dynamics in manufacturing and natural systems using machine learning

Abstract

Dynamical analysis of manufacturing and natural systems provides critical information about production of manufactured and natural resources, respectively. Current dynamic models for full industrial process plants exist as highly accurate first-principle relationships. However, their integration is computationally intensive and provides no simplified understanding of the underlying mechanisms driving the overall dynamics. Similarly, for natural systems, most dynamical models are first principle based, with high data requirements and low state accuracy. Consequently, lower-order models that may sacrifice accuracy for simplicity and ease of training can prove useful. Yet, there have been few attempts at finding low-order models of chemical manufacturing processes and natural systems, with work focusing on modeling individual mechanisms. We seek to fill this research gap by using a machine learning (ML) approach, SINDy, validated on a soybean-diesel process plant and watershed system. This ML method combines sparse, grey-box modeling with additional nonlinear optimization to identify governing dynamics as ODEs. We find a linear ODE model for the process plant that gives an accurate relation between input and output and selected internal molar flow rates reflective of underlying linear stoichiometric mechanisms and an internal mass balance. For the natural system, we modify the SINDy approach to include the effect of past dynamics on training the model, which gives a nonlinear model for streamflow dynamics. This improves dynamical transitions, but falls short of accurate state estimation. We conclude that the proposed ML approach works well for non-chaotic systems with minimal hysteresis, but is limited when this condition is not met.