An Improved Elastic Net Method for Accurate Identification of Structural Damage by Considering Uncertainties

The elastic net-based damage identification method has effectively improved the stability of damage identification by integrating the [Formula: see text] and [Formula: see text] regularization techniques, but it neglects the inevitable uncertainties arising from modeling errors and measurement noise, thereby compromising the accuracy of damage identification. In order to remedy this problem, this study improves the elastic net-based damage identification method within a Bayesian framework by explicitly specifying probability distributions over damage parameters. In detail, the proposed model leverages Laplace and Gaussian priors, equivalently modeling the [Formula: see text] and [Formula: see text] regularization to ensure the stability of damage identification, and employs the mixture of Gaussians (MoG) to accurately quantify the practical uncertainties in damage identification, by exploiting the theoretical property of MoG to approximate any continuous distribution. The iterative expectation–maximization algorithm, combined with the Laplace approximation technique, is employed to perform maximum a posteriori estimation of the damage parameter. Numerical simulations and experimental studies demonstrate that the proposed method achieves maximum improvements of 8.3% and 12.54% over the traditional elastic net method, and 8.12% and 12.06% over the robust sparse Bayesian learning (RSBL) method, in damage identification accuracy, respectively.