Physics informed Long Short-Term Memory neural network for dual state-parameter estimation of linear dynamical systems robust to input forces

Abstract

Structural Health Monitoring (SHM) of structures is significantly challenged by the presence of unknown input forces, e.g, external unmeasured and non-stationary excitations applied to the system such as wind or loads, which hinder accurate damage assessment and system identification. Traditional model-based approaches face inherent limitations related to model inversion, observability, and identifiability, all of which are impaired by the need for input force knowledge. Data-driven methods offer advantages in terms of scalability and automation but still depend on known inputs and often lack physical interpretability. To address these issues, an input-robust Physics-Informed Long Short-Term Memory (rPi-LSTM) framework is introduced, integrating input-robust physical modeling of system dynamics with the temporal learning capabilities of LSTM networks. The framework employs an output injection strategy to reject unknown input forces, enabling estimation of system states and spatial health parameters without requiring input force information. By preserving temporal dependencies with the LSTM network, an aspect that is often neglected in conventional physics-informed networks, the method ensures stable and accurate system estimation while complying with the system physics. Validation through numerical simulations and real laboratory-scale experiments confirms its robustness to input forces, noise, data sparsity, and varying damage scenarios, demonstrating strong potential for real-world SHM applications under uncertain conditions.