Nonlinear time-varying system response modeling via a real-time updated Runge-Kutta physics-informed neural network

Document Type

Article

Publication Date

3-15-2025

Abstract

Accurate structural response modeling advances the understanding of complex dynamic systems and enables effective structural design, control and monitoring. Due to damage, engineering structures will exhibit nonlinear and time-varying characteristics, which makes the structural response highly complex and challenging to be accurately modeled by traditional methods. This study proposes a Runge-Kutta-based real-time updated physics-informed neural network (RTU-PINN) to model structural responses of complex dynamic systems. The Recurrent Neural Network (RNN) is enhanced with Runge-Kutta method and neural Ordinary Differential Equations (neural ODEs) to model the system responses. The unknown structural parameters and nonlinear restoring force can be identified from the neural network. To capture the nonlinear and time-varying characteristics caused by structural damage or hysteretic behaviors, a Real-Time Updating (RTU) strategy is proposed to update the time-varying parameters and nonlinear restoring force with a sliding time window to minimize the discrepancy between predicted result and testing data. In addition, the proposed method can be applied to high-dimensional time-varying structures. Performance of the proposed method is examined via numerical and laboratory case studies. It is found that the RTU-PINN models the dynamic response with Relative Root Mean Square Error (RRMSE) values less than 0.001 in the target nonlinear time-varying dynamic system. Research results show that the proposed RTU-PINN method can accurately model the complex dynamic responses of the numerical and experimental structures with time-varying and nonlinear characteristics. The proposed method has the potential to address modeling uncertainties/errors and is applicable for system identification of complex systems with nonlinear and time-varying features.

Publication Source (Journal or Book title)

Engineering Applications of Artificial Intelligence

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