Action-Aided Particle Filter for Damage Detection and Diagnosis on Hysteretic Non-Linear Structures Under Varying Environmental Conditions

Condition-based and predictive-maintenance strategies require accurate real-time damage diagnosis and prognosis. However, damage-sensitive features are often affected by variations in environmental and operating conditions, which may mask or distort the effects of structural degradation. This study addresses this issue by combining feature normalisation through an autoencoder (AE) with model-based particle filtering for online state estimation, damage detection, and localisation. The proposed framework is applied to a vibrating n-degree-of-freedom system comprising a nonlinear stiffness component governed by Bouc–Wen hysteretic behaviour and subjected to varying temperature conditions. An AE trained exclusively on healthy-state data is used to compensate for temperature-induced feature drifts while preserving damage-related information. Building on a conventional Sequential Importance Resampling particle filter (SIR PF), an Action-aided Particle Filter (A-SIR PF) is introduced by augmenting the standard likelihood-based particle weights with a physics-inspired action term. Based on the principle of stationary action, this additional contribution penalises high-action trajectories and favours temporally coherent and physically plausible state evolutions. Two degradation scenarios are investigated, both affecting a single spring of the system: a step stiffness degradation and a progressive degradation evolving linearly over time. The A-SIR PF and the traditinal SIR PF are compared under identical random seeds, noise conditions, and resampling policies in terms of state-estimation accuracy, and damage detection and localisation capabilities. The results show that the A-SIR PF outperforms the conventional SIR PF while retaining a comparable computational cost. These findings demonstrate that incorporating domain-informed path regularisation into particle-filter weighting can improve structural health monitoring performance under realistic, nonlinear, and non-stationary operating conditions.