Sparse Bayesian factor analysis for structural damage detection under unknown environmental conditions

Abstract Damage detection of civil engineering structures needs to consider the effect of normal environmental variations on structural dynamic properties. This study develops a novel structural damage detection method using factor analysis in the sparse Bayesian learning framework. The unknown changing environmental factors that affect the structural dynamic properties are treated as latent variables in the model. The automatic relevance determination prior is adopted for the factor loading matrix for model selection. All variables and parameters, including the factor loading matrix, error vector and latent variables, are solved using the iterative expectation-maximization technique. The variables are then used to reconstruct structural responses. The Euclidean norm of the error vector is calculated as the damage indicator to detect possible damage when limited vibration data are available. Two laboratory-tested examples are utilized to verify the effectiveness of the proposed method. Results demonstrate that the number of underlying environmental factors and structural damage can be accurately identified, even though the changing environmental data are unavailable. The proposed method has the advantages of online monitoring and automatic identification of underlying environmental factors.