Nonlinear Model Order Reduction of Dynamical Systems in Process Engineering: Review and Comparison

TL;DR

This paper reviews and compares various nonlinear model order reduction methods for dynamical systems in process engineering, highlighting their characteristics, extensions, and performance in a case study on an air separation process.

Contribution

It provides a comprehensive review, extends manifold-Galerkin methods to systems with inputs, and compares eight reduction techniques on a real-world chemical process model.

Findings

Manifold-Galerkin methods lack input consideration, which is addressed by extensions.

Different methods exhibit unique strengths and weaknesses in accuracy and computational efficiency.

The case study demonstrates practical applicability and comparative performance of the methods.

Abstract

Computationally cheap yet accurate dynamical models are a key requirement for real-time capable nonlinear optimization and model-based control. When given a computationally expensive high-order prediction model, a reduction to a lower-order simplified model can enable such real-time applications. Herein, we review nonlinear model order reduction methods and provide a comparison of method characteristics. Additionally, we discuss both general-purpose methods and tailored approaches for chemical process systems and we identify similarities and differences between these methods. As machine learning manifold-Galerkin approaches currently do not account for inputs in the construction of the reduced state subspace, we extend these methods to dynamical systems with inputs. In a comparative case study, we apply eight established model order reduction methods to an air separation process model: POD-Galerkin, nonlinear-POD-Galerkin, manifold-Galerkin, dynamic mode decomposition, Koopman theory, manifold learning with latent predictor, compartment modeling, and model aggregation. Herein, we do not investigate hyperreduction, i.e., reduction of floating point operations. Based on our findings, we discuss strengths and weaknesses of the model order reduction methods.