Research On Structural Damage Identification Based On Sparse Bayesian Learning And Gibbs Sampling

For civil structures, structural damage due to excessive loading or environmental degradation typically occurs in localized areas, which will lead to the change of structural stiffness, as well as the change of structural modal parameters(natural frequency, mode shape). As the core problem of structural health monitoring, structural damage identification has the vital significance to protect the safety of civil engineering structure, especially the major infrastructures.The main contributions of the paper are as follows:The study develops a hierarchical Bayesian learning model aimed to alleviate the ill-conditioning and ill-posedness in inverse problems under the background of Structural Health Monitoring. In the Bayesian model, we consider the uncertainty of the structural model explicitly and incorporate the prior information that structural damage typically occurs in localized areas in the absence of collapse.For Bayesian inference, we first undertake a study on sparse Bayesian learning based fast algorithm for damage identification. Posterior probability model of structural stiffness parameters can be inferred by Bayesian updating and learning, which includes the information of the most plausible value of structural stiffness as well as its associated posterior uncertainty, which can be utilized to estimate the probability of a prescribed damage fraction for any substructure to describe the structural damage more precisely.Then we introduce Gibbs Sampling to provide a fuller treatment of the model posterior uncertainty and to avoid the robustness problem which is caused by the optimizations of hyper-parameter in the traditional sparse Bayesian learning procedure. Two Gibbs sampling algorithms were established in which samples consistent with the posterior PDF of the model parameters are generated. The generated samples also characterize the marginal posterior distribution of the structural stiffness parameters, which can achieve the goal for damage assessment.With the theory and algorithms developed in this thesis, pseudo-codes were written by Matlab. To demonstrate the validity of the proposed methods, a braced-frame structural model is employed for analysis. The results demonstrate that the approach is capable to localize and assess damage reliably even contaminated with high-level noise.