Using conditional diffusion models for data-driven ground motion identification of structural dynamic systems under uncertainty

Diffusion models have shown promise for scientific inference, but their use in structural health monitoring has largely remained on forward or simulation-oriented tasks. Ground motion identification, i.e. , inferring the unknown ground excitation acting on structural dynamic systems from sparse and potentially corrupted sensor measurements, remains challenging because the solution is non-unique and the observations are incomplete. To address this inverse problem, this study proposes InvSHMDiff, a conditional diffusion framework that learns the conditional distribution of ground excitation given incomplete multi-channel accelerometer responses. The architecture couples a Vision Transformer sensor encoder with a U-Net denoiser, trained with a v -parameterized objective. Numerical experiments on a benchmark cable-stayed bridge model demonstrate that InvSHMDiff recovers both the amplitude and phase of the ground excitation under substantial sensor masking, and compare it against a finite-element-based Tikhonov inverse and four learned baselines under measurement noise. InvSHMDiff boasts strong performance compared to competing baselines across every scenario and is the most accurate under colored noise and degrades the least under finite element model mismatch. Tests on 76 recorded strong-motion records and on a fine-tuned nonlinear transfer indicate that the model remains robust within the evaluated regimes, showing the smallest accuracy loss toward large-amplitude ground motions and the lowest peak-acceleration, Arias-intensity, and response-spectrum errors among the compared methods, each below 11%. In addition, the stochastic generative process yields empirical ensemble bands as relative uncertainty indicators. By propagating the generated excitation ensemble through a forward solver, the model can also be used as a virtual-sensing network, yielding full-field structural response estimates. The results support conditional diffusion as a useful inverse-modeling tool for sparse SHM measurements.