A Latent Restoring Force Approach to Nonlinear System Identification

TL;DR

This paper introduces a Bayesian filtering method that models nonlinear restoring forces as Gaussian processes, enabling effective identification of nonlinear dynamics in systems through state-space inference, demonstrated on simulations and experimental data.

Contribution

It presents a novel latent restoring force approach using Gaussian processes and Bayesian filtering for nonlinear system identification, offering an alternative to traditional restoring force surface methods.

Findings

Effective in simulated nonlinear systems

Successfully applied to experimental benchmark data

Provides accurate internal state and nonlinear force estimation

Abstract

Identification of nonlinear dynamic systems remains a significant challenge across engineering. This work suggests an approach based on Bayesian filtering to extract and identify the contribution of an unknown nonlinear term in the system which can be seen as an alternative viewpoint on restoring force surface type approaches. To achieve this identification, the contribution which is the nonlinear restoring force is modelled, initially, as a Gaussian process in time. That Gaussian process is converted into a state-space model and combined with the linear dynamic component of the system. Then, by inference of the filtering and smoothing distributions, the internal states of the system and the nonlinear restoring force can be extracted. In possession of these states a nonlinear model can be constructed. The approach is demonstrated to be effective in both a simulated case study and on an experimental benchmark dataset.