Sparse Bayesian learning for structural damage identification

Abstract Identification of structural parameters can be cast as the process of solving an inverse problem, in which regularization may be required when the problem is ill-posed. Bayesian inference provides a probabilistic interpretation of the regularization and yields a statistically stable/bounded solution. To this end, this paper presents a hierarchical Bayesian learning methodology with sensitivity analysis for identification of structural damage which has sparse characteristics. The proposed learning framework consists of two hierarchies: (1) the classical Bayesian learning and (2) the sparse Bayesian learning. Based on the incomplete modal quantities extracted from measurements such as the acceleration time histories, the classical Bayesian learning is utilized to update a parameterized baseline model followed by the sparse Bayesian learning which can accurately identify the sparsity of damage. The Bayesian learning procedures are formulated with the sensitivity analysis of model parameters, which compensate the linear truncation errors and produce accurate identification results through iterative optimization. The performance of the proposed approach has been illustrated through two numerical examples (a 10-story shear-type building and a 33-bar truss structure) and an experimental validation (a shake-table test of an 8-story frame). Results indicate that the proposed method is robust for structural damage identification even in the presence of high measurement noise and a limited number of sensor recordings. This hierarchical Bayesian learning approach is generally more efficient than classical regularization techniques such as the Tikhonov regularization.

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