Stable Sparse Operator Inference for Nonlinear Structural Dynamics

TL;DR

This paper introduces a data-driven, stable, and sparse operator inference method for creating reduced-order models of nonlinear structural dynamics, ensuring physical stability and computational efficiency.

Contribution

It proposes a novel operator inference approach with stability constraints, sum-of-squares relaxation, and clustering-based sparsification for nonlinear structural dynamics models.

Findings

Successfully inferred stable reduced-order models from simulation data.

Achieved significant model size reduction and improved numerical conditioning.

Validated on complex 3D finite element models with promising results.

Abstract

Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications or multi-query workflows. Hence, model reduction is needed. However, the mathematical operators of these models are often not available since, as is common in industry practice, the models are constructed using commercial simulation software. In this work, we propose an operator inference-based approach aimed at inferring, from data generated by the simulation model, reduced-order models (ROMs) of structural dynamics systems with stiffness terms represented by polynomials of arbitrary degree. To ensure physically meaningful models, we impose constraints on the inference such that the model is guaranteed to exhibit stability properties. Convexity of the optimization problem associated with the inference is maintained by applying a sum-of-squares relaxation to the polynomial term. To further reduce the size of the ROM and improve numerical conditioning of the inference, we also propose a novel clustering-based sparsification of the polynomial term. We validate the proposed method on several numerical examples, including a representative 3D Finite Element Model (FEM) of a steel piston rod.