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

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.