Sparse Bayesian learning for structural damage detection using expectation–maximization technique

Sparse Bayesian learning (SBL) methods have been developed and applied in the context of regression and classification, in which latent variables and hyperparameters are iteratively obtained using type-II maximization likelihood. However, this method is ineffective in structural damage detection using modal parameters, which have a nonlinear relation with structural damage. Consequently, the analytical solution of the type-II maximization likelihood is unavailable. In this study, an iterative expectation–maximization (EM) technique is employed to tackle the difficulty. During the iteration, structural damage and hyperparameters are updated through an expectation and maximization processes alternatively. Two sampling methods are utilized during the expectation procedure. Upon convergence, some hyperparameters approach infinity and the associated damage variables become zero, resulting in the sparsity of damage. Numerical and experimental examples demonstrate that the proposed SBL method can accurately locate and quantify the sparse damage. The proposed EM technique is easy to implement while also containing clear physical meaning.