Nonlinear Moment Matching for the Simulation-Free Reduction of Structural Systems

TL;DR

This paper extends moment matching techniques to nonlinear structural systems, offering a simulation-free reduction method that simplifies model reduction while maintaining accuracy, demonstrated through numerical examples.

Contribution

It introduces a novel nonlinear moment matching reduction scheme for second-order models that does not require time-domain simulations.

Findings

The method effectively reduces nonlinear models without simulations.

Numerical examples confirm the efficiency and accuracy of the approach.

The approach extends linear moment matching concepts to nonlinear systems.

Abstract

This paper transfers the concept of moment matching to nonlinear structural systems and further provides a simulation-free reduction scheme for such nonlinear second-order models. After first presenting the steady-state interpretation of linear moment matching, we then extend this reduction concept to the nonlinear second-order case based on Astolfi [2010]. Then, similar simplifications as in Cruz Varona et al. [2019] are proposed to achieve a simulation-free nonlinear moment matching algorithm. A discussion on the simplifications and their limitations is presented, as well as a numerical example which illustrates the efficiency of the algorithm.