Data Fusion for Full-Range Response Reconstruction via Diffusion Models

Accurately capturing the full-range response of structures is crucial in structural health monitoring (SHM) for ensuring safety and operational integrity. However, limited sensor deployment due to cost, accessibility, or scale often hinders comprehensive monitoring. This paper presents a generative data fusion framework utilizing diffusion models, to reconstruct the full-range structural response from sparse and heterogeneous sensor measurements. We incorporate Diffusion Posterior Sampling (DPS) into the reconstruction framework, using sensor measurements as probabilistic constraints to guide the sampling process. Three forward models are designed: Direct Observation Mapping (DOM), Channel-based Observation Mapping (COM), and Neural Network Forward Model (NNFM), enabling flexible adaptation to different sensor placement conditions and reconstruction targets. The proposed framework is validated on a steel plate shear wall exhibiting nonlinear responses. By simultaneously sampling 100 realizations and averaging them as the ensemble prediction result, the three forward models achieve Weighted Mean Absolute Percentage Errors of 1.62% (DOM), 3.27% (COM), and 3.49% (NNFM). Sensitivity analyses further demonstrate robust performance under varying hyperparameters, sensor configurations, and noise levels. The proposed framework shows new possibilities for probabilistic modeling and decision-making in SHM by harnessing the capabilities of diffusion models, offering a novel data fusion approach for full-range monitoring of structures.