30. Bayesian Inference for Damage Detection in Unsupervised Structural Health Monitoring

This paper presents a preliminary study on developing a new algorithm for making inference on the unsupervised structural health monitoring problems in a Bayesian framework. The main constraint in such problems, besides their unsupervised nature, is the small size of data set. Secondly, most often, there is no numerical model or enough empirical data for computing an appropriate prior density for Bayesian data analysis. Gaussian Mixture Model (GMM) and Kernel Density Estimate (KDE) are the main tools which are used in this paper for density estimation under the constraint on the size of data sets. To solve the second issue, an empirical Bayesian approach is employed for computing a prior density without any model; therefore, this algorithm provides an approximation to the standard Bayesian inference technique. An important aspect of the proposed algorithm is that it provides posterior probabilities for the intact or damaged states of the structure. Such results can be directly used for cost analysis and decision making in such unsupervised problems. The efficacy of the algorithm is experimentally verified by testing a three-story two-bay steel laboratory structure. The results show that the algorithm can effectively detect and localize the damages.