Sparse Bayesian learning with model reduction for probabilistic structural damage detection with limited measurements

A new variant of damage detection algorithm is proposed based on Sparse Bayesian Learning (SBL) and model reduction for probabilistic structural damage detection. By exploring recent developments in SBL, we aim to produce reliable damage identification even for high-dimensional model parameter spaces for higher-resolution damage localization. By introducing the system modal parameters, the matching of model and experimental modes and solving the nonlinear eigenvalue problem of a structural model are not required. However, one inherent difficulty is that, because only a small number of degrees of freedom (DOFs) can be measured in practice due to limited instrumentation and unmeasurable rotational DOFs, the computation of the system mode shapes has a minimum chance of success. The proposed algorithm extends the applicability of SBL-based damage detection to cases with limited measurements by exploiting model reduction techniques to avoid computation of the system mode shapes for the full model. To effectively incorporate the model reduction procedure, a two-stage SBL-based damage detection algorithm is proposed, in which the first stage updates the reduced system modal properties employing the modal data, and the second stage learns the stiffness parameters and their associated hyper-parameters to produce model sparseness of stiffness losses. The performance of the proposed algorithm is investigated through a series of numerical and experimental studies involving two beam structures and a longspan cable-stayed bridge. Both modeling errors and measurement noises are considered in these studies. The results show that, despite limited measured DOFs in conjunction with modeling error and measurement noise, the proposed algorithm based on SBL and model reduction can successfully locate and quantify the damage along with their posterior uncertainties, which give a sense of identification confidence.