Adaptive Physics-Informed System Modeling with Control for Nonlinear Structural System Estimation

TL;DR

This paper introduces an adaptive physics-informed modeling framework that combines Kalman filtering and proximal gradient optimization to accurately estimate nonlinear structural dynamics in real-time, even under noisy conditions.

Contribution

It presents a novel integration of physics-informed control with adaptive parameter updating, ensuring convergence to optimal solutions for nonlinear system estimation.

Findings

Successfully predicts 19 consecutive time series segments with minimal error

Demonstrates superior noise robustness and online identification capabilities

Validates effectiveness through simulations and experimental tests

Abstract

Accurately capturing the nonlinear dynamic behavior of structures remains a significant challenge in mechanics and engineering. Traditional physics-based models and data-driven approaches often struggle to simultaneously ensure model interpretability, noise robustness, and estimation optimality. To address this issue, this paper proposes an Adaptive Physics-Informed System Modeling with Control (APSMC) framework. By integrating Kalman filter-based state estimation with physics-constrained proximal gradient optimization, the framework adaptively updates time-varying state-space model parameters while processing real-time input-output data under white noise disturbances. Theoretically, this process is equivalent to real-time tracking of the Jacobian matrix of a nonlinear dynamical system. Within this framework, we leverage the theoretical foundation of stochastic subspace identification to demonstrate that, as observational data accumulates, the APSMC algorithm yields state-space model estimates that converge to the theoretically optimal solution. The effectiveness of the proposed framework is validated through numerical simulations of a Duffing oscillator and the seismic response of a frame structure, as well as experimental tests on a scaled bridge model. Experimental results show that, under noisy conditions, APSMC successfully predicts 19 consecutive 10-second time series using only a single initial 10-second segment for model updating, achieving a minimum normalized mean square error (NMSE) of 0.398%. These findings demonstrate that the APSMC framework not only offers superior online identification and denoising performance but also provides a reliable foundation for downstream applications such as structural health monitoring, real-time control, adaptive filtering, and system identification.