Physics-informed semi-supervised LSTM autoencoder framework for force-agnostic structural health monitoring

Abstract This study presents a physics-informed Long Short Term Memory (LSTM) autoencoder framework for input force-agnostic structural health monitoring (SHM), enabling accurate damage identification from sparse, noisy measurements. Traditional model-based SHM approaches offer interpretability and enforce physical laws, while data-driven methods provide flexibility and scalability, yet both face limitations: the former is sensitive to material and modelling uncertainties and often mandates boundary and force information, while the latter relies on extensive labelled datasets and may lack physical consistency. The proposed framework integrates governing physics directly into the LSTM autoencoder and embeds state-space observer principles, enhancing robustness to unknown, time-varying excitations and ensuring stable temporal predictions. A LSTM-based encoder is employed to map the measured accelerations to displacement and health-index estimates, while a physics-based decoder enforces the output-injected state-space dynamics as a training constraint. A semi-supervised training strategy leverages a small, non-exhaustive labelled dataset to guide optimization, improving convergence, stability, and generalization under limited-data conditions. Numerical simulations on a 10-DOF shear building and experimental validations on a four-storey bench-scale frame demonstrate that the framework operates effectively with output-only measurements, detecting, localizing, and quantifying structural damage with sufficient accuracy while maintaining consistency with physical laws. The proposed framework consistently outperforms a force-informed PINN and purely data-driven baselines, remaining reliable under measurement noise, limited training data, and reduced sensor coverage, and the estimated stiffness changes on the bench-scale frame agree with independently measured modal-frequency shifts under both single and multiple brace-removal damage scenarios. It is recognized that the proposed framework offers a computationally efficient and physically consistent route to reliable, input-robust, output-only damage identification. Moreover, this can effectively combine the rigour and interpretability of model-based methods with the adaptability of data-driven approaches within the SHM framework.