Hierarchical sparse Bayesian learning for structural damage detection: Theory, computation and application

Structural damage due to excessive loading or environmental degradation typically occurs in localized areas (in the absence of collapse) where it leads to local stiffness reductions. This prior information about the spatial sparseness of structural damage and the associated stiffness loss is exploited here by a hierarchical sparse Bayesian learning (SBL) framework, with the goal to reduce the ill-conditioning in the stiffness loss inversion problem for damage detection. We have previously proposed a SBL approach to establish the probability of localized stiffness reductions caused by damage by using noisy incomplete modal data from before and after possible damage. The excellent performance achieved by introducing sparseness in the damage pattern was demonstrated by using synthetic data where there are only small modeling errors. In this research, a more rigorous formulation along with a corresponding efficient and scale-invariant SBL algorithm are developed. The algorithm is first applied to synthetic data, then to real vibration response from a steel-frame test structure where there are large modeling errors. These data are from the Phase II simulated and experimental benchmark studies that were sponsored by the IASC-ASCE Task Group on Structural Health Monitoring. The results show that, even for the real data, the proposed method can reliably detect, locate and assess damage of the benchmark structure by inferring substructure stiffness losses using the identified modal parameters from the calibration and monitoring stages. The occurrence of missed and false damage alerts is effectively suppressed, and we show that the new algorithm gives a better performance than our previous SBL method in the real data case where there is significant modeling error. Several appealing features of our method are summarized at the end of the paper