A sliding-window approach for latent restoring force modeling

TL;DR

This paper introduces a sliding-window method that enables nonparametric identification of nonlinear restoring forces in multidimensional systems with limited measurements, using periodic excitation and linear regression.

Contribution

It proposes a novel framework that relaxes sensing requirements and reconstructs latent states and forces without complex optimization, improving scalability and robustness.

Findings

High accuracy in synthetic data validation

Reliable parameter recovery under noise

Effective partial sensing in experimental data

Abstract

Restoring force surface (RFS) methods offer an attractive nonparametric framework for identifying nonlinear restoring forces directly from data, but their reliance on complete kinematic measurements at each degree of freedom limits scalability to multidimensional systems. The aim of this paper is to overcome these measurement limitations by proposing an identification framework with relaxed sensing requirements that exploits periodic multisine excitation. Starting from an initial linear model, a sliding-window feedback approach reconstructs latent states and nonlinear restoring forces nonparametrically, enabling identification of the nonlinear component through linear-in-parameters regression instead of highly non-convex optimization. Validation on synthetic and experimental datasets demonstrates high simulation accuracy and reliable recovery of physical parameters under partial sensing and noisy conditions.