Efficient Reduction of Interconnected Subsystem Models using Abstracted Environments

TL;DR

This paper introduces two structure-preserving model order reduction frameworks that use abstracted environments to improve computational efficiency and accuracy in interconnected subsystem models, ensuring stability and bounded errors.

Contribution

It proposes novel abstraction-based reduction methods that incorporate environmental dynamics, enhancing accuracy and reducing computational costs compared to existing approaches.

Findings

Achieved improved accuracy in a structural dynamics model

Reduced computational costs through environment abstraction

Guaranteed stability and accuracy bounds in reduced models

Abstract

We present two frameworks for structure-preserving model order reduction of interconnected subsystems, improving tractability of the reduction methods while ensuring stability and accuracy bounds of the reduced interconnected model. Instead of reducing each subsystem independently, we take a low-order abstraction of its environment into account to better capture the dynamics relevant to the external input-output behaviour of the interconnected system, thereby increasing accuracy of the reduced interconnected model. This approach significantly reduces the computational costs of reduction by abstracting instead of fully retaining the environment. The two frameworks differ in how they generate these abstracted environments: one abstracts the environment as a whole, whereas the other abstracts each individual subsystem. By relating low-level errors introduced by reduction and abstraction to the resulting high-level error on the interconnected system, we are able to translate high-level accuracy requirements (on the reduced interconnected system) to low-level specifications (on abstraction and reduction errors) using techniques from robust performance analysis. By adhering to these low-level specifications, restricting the introduced low-level errors, both frameworks automatically guarantee the accuracy and stability of the reduced interconnected system. We demonstrate the effectiveness of both frameworks by applying them to a structural dynamics model of a two-stroke wafer stage, achieving improved accuracy and/or greater reduction compared to an existing method from literature.