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, thus playing an important role in assessing sustainability of these systems. However, current dynamic models for these systems exist as mechanistic models, simulation of which is computationally intensive and does not provide a simplified understanding of the mechanisms driving the overall dynamics. For such systems, lower-order models can prove useful to enable sustainability analysis through coupled dynamical analysis. There have been few attempts at finding low-order models of manufacturing and natural systems, with existing work focused on model development of individual mechanism level. This work seeks to fill this current gap in the literature of developing simplified dynamical models for these systems by developing reduced-order models using a ML approach. The approach is demonstrated on an entire soybean-oil to soybean-diesel process plant and a lake system. We use a grey-box ML method with a standard nonlinear optimization approach to identify relevant models of governing dynamics as ODEs using the data simulated from mechanistic models. Results show that the method identifies a high accuracy linear ODE models for the process plant, reflective of underlying linear stoichiometric mechanisms and mass balance driving the dynamics. For the natural systems, we modify the ML approach to include the effect of past dynamics, which gives non-linear ODE. While the modified approach provides a better match to dynamics of stream flow, it falls short of completely recreating the dynamics. We conclude that the proposed ML approach work well for systems where dynamics is smooth, such as in manufacturing plant whereas does not work perfectly well in case of chaotic dynamics such as water stream flow.