Machine learning assisted state prediction of misspecified linear dynamical system via modal reduction

TL;DR

This paper presents a data-driven framework using Gaussian Process Latent Force Models and neural networks to estimate and correct model form errors in high-dimensional structural dynamical systems, enhancing digital twin fidelity.

Contribution

It introduces a novel combination of Bayesian filtering, modal reduction, and neural networks for real-time model correction across different FE discretizations.

Findings

Significantly reduces displacement and rotation prediction errors.

Effective across multiple model form error scenarios.

Maintains accuracy under unseen excitations.

Abstract

Accurate prediction of structural dynamics is imperative for preserving digital twin fidelity throughout operational lifetimes. Parametric models with fixed nominal parameters often omit critical physical effects due to simplifications in geometry, material behavior, damping, or boundary conditions, resulting in model form errors (MFEs) that impair predictive accuracy. This work introduces a comprehensive framework for MFE estimation and correction in high-dimensional finite element (FE) based structural dynamical systems. The Gaussian Process Latent Force Model (GPLFM) represents discrepancies non-parametrically in the reduced modal domain, allowing a flexible data-driven characterization of unmodeled dynamics. A linear Bayesian filtering approach jointly estimates system states and discrepancies, incorporating epistemic and aleatoric uncertainties. To ensure computational tractability, the FE system is projected onto a reduced modal basis, and a mesh-invariant neural network maps modal states to discrepancy estimates, permitting model rectification across different FE discretizations without retraining. Validation is undertaken across five MFE scenarios-including incorrect beam theory, damping misspecification, misspecified boundary condition, unmodeled material nonlinearity, and local damage demonstrating the surrogate model's substantial reduction of displacement and rotation prediction errors under unseen excitations. The proposed methodology offers a potential means to uphold digital twin accuracy amid inherent modeling uncertainties.