# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1903.12303