In structural health monitoring, full-field responses are needed to assess the structural safety conditions, and they are usually identified from measurements taken at discrete locations. However, the full-field structural responses to the spatially correlated and distributed load are neither identified nor investigated. To fill up this research gap, a Bayesian system identification approach is developed for full-field response virtual sensing considering load spatial correlation. The prior probability distribution of the distributed loads is assumed to follow a zero-mean joint Gaussian function with a non-diagonal covariance matrix, in which the spatial correlation of loads is characterized by an exponentially decaying function. The most probable load and system hyperparameters are iteratively estimated by maximizing the posterior probability. Subsequently, the identified loads are used to reconstruct the full-field structural responses via finite element analysis. The developed technique is applied to a numerical shear frame, a numerical simply supported beam, and an infield long-span sea-crossing cable-stayed bridge. The results demonstrate that the structural responses, noise levels, and load covariance are correctly identified with high computational efficiency. Moreover, the accuracy of the reconstructed responses is improved by considering the spatial correlation of the loads.
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