Structural Health Monitoring (SHM) systems for large-scale civil infrastructure often suffer from data loss and sensing sparsity, which severely limits the reliability of digital twin applications. This research introduces a robust framework for the probabilistic reconstruction of structural dynamic responses utilizing score-based generative diffusion models. The proposed methodology consists of three key components: (i) an offline prior training stage, where a score-based generative model learns the underlying probability distribution of structural dynamic responses using a denoising score matching objective; (ii) spatiotemporal response decomposition, which leverages the Markovian property of dynamic systems to decompose the score of long-duration responses into a series of localized scores over short, manageable segments, ensuring computational scalability; and (iii) an online inference stage formulated as a Bayesian inverse problem, where a reverse-time stochastic differential equation is solved by a predictor-corrector scheme under the constraint of available sparse observations. In the final stage, the learned prior score is dynamically guided by sparse, noisy measurements through a training-free likelihood score approximation to sample the posterior distribution of the full-field structural responses. The efficacy of the proposed approach is demonstrated through two engineering case studies: a rail-sleeper–ballasted system and a real-world long-span cable-stayed bridge. In both examples, the framework successfully reconstructs the complete acceleration field from a subset of available sensors and highly sparse temporal observations, achieving higher reconstruction accuracy and stronger robustness than traditional methods, while additionally providing quantified uncertainty.
Zeng et al. (Mon,) studied this question.