A robust sparse Bayesian learning method for the structural damage identification by a mixture of Gaussians

Sparse Bayesian learning methods have been successfully applied to the community of structural damage identification, which commonly assumes that the uncertainties from modeling errors and measurement noises follow Gaussian distribution. However, this assumption typically compromises the accuracy of damage identification because these real uncertainties may not follow a Gaussian distribution. A mixture of Gaussian distributions can more accurately quantify the real uncertainties of damage identification than a Gaussian distribution because it can theoretically approximate any continuous distribution. Motivated by this, we utilized a robust sparse Bayesian learning method to investigate the problem of structural damage identification and further improve the accuracy of damage identification. This method includes a sparse Bayesian learning model with a mixture of Gaussians and an expectation–maximization algorithm based on the Laplace approximation technique. The numerical and experimental results illustrate that our method improves the damage identification accuracy by 6.78% and 11.92% than the existing two sparse Bayesian learning ones, respectively.