Structural damage detection under unknown environmental conditions using Sparse Bayesian factor analysis

This study develops a novel structural damage detection method using the factor analysis in the sparse Bayesian learning framework. The unknown changing environmental factors that affect structural vibration properties are treated as latent variables. Structural frequencies that are measured within a long period are utilized as the observations in the factor analysis (FA) model. The ARD model is defined on the factor loading matrix for automatic dimension selection. Using the iterative expectation-maximization technique, the number of underlying environmental factors is determined automatically. With the optimized parameters and variables, the measurement data are reconstructed. The reconstruction error is defined as the damage indicator, which will get large with the emergence of damage. One advantage of the proposed Bayesian FA model is that the assumption of independence of vibration modes is not required, as the covariance matrix of the residue vector in the FA model is treated as a full matrix rather than a diagonal matrix. Two laboratory-tested examples are utilized to verify the effectiveness of the proposed method. Results indicate that structural damage can be accurately detected under changing environmental conditions.