Noise-aware Structural Health Monitoring: Integrating a Deep Modal Denoiser with Surrogate-induced HMC for Robust Bayesian Updating

This study proposes a novel two-stage, noise-aware Bayesian framework for structural health monitoring (SHM) to bridge the gap between noisy modal measurements and computationally intensive posterior inference. First, a deep modal denoiser was trained solely on undamaged-structure modal data to map noisy frequency measurements to their clean counterparts while preserving damage-sensitive features. Next, a Random Network Surrogate–Hamiltonian Monte Carlo (RNS–HMC) sampler, utilizing a shallow random-network surrogate of the Hamiltonian, was employed to make Bayesian finite-element model updating computationally efficient. This integrated pipeline overcomes the common HMC assumption of cleaned or low-noise data by merging principled denoising with surrogate-enhanced sampling, yielding accurate and reliable posterior estimates despite noise, at a remarkably reduced computational cost. Key methodological novelties include an encoder–decoder deep denoiser trained only on undamaged modal data to prevent corrupting damage indicators, alongside an RNS–HMC workflow that uses a rapid random-network surrogate to accelerate sampling while maintaining validity. Numerical tests on a 3-DOF mass–spring system, a 47-bar planar truss, and a 25-element spatial truss show accurate estimates of the imposed damage ratios with minimal errors, reasonable posterior dispersion, and greatly reduced computational time, with chain convergence occurring at least nine times faster. Hence, the proposed approach advances SHM by offering a practical, scalable path to perform noise-resilient Bayesian updating while preserving sensitivity to damage and making repeated or near-real-time probabilistic inference computationally feasible.