An Equivalent Nonconvex Regularization Model Based on the Capped-l1 Function for Structural Damage Identification

Structural damage identification based on sensitivity analysis can be modeled as a sparse recovery problem, with the original formulation being an l0-norm regularization model. However, this original model is NP-hard due to the discrete and discontinuous nature of the l0-norm. As an alternative, relaxation models are used to approximate the original model. This substitution, however, introduces deviations between the optimal solutions of these relaxation models and the original model, thereby reducing the accuracy of damage identification. In this paper, the equivalent regularization model of the original model is introduced into structural damage identification for the first time to eliminate this deviation. The nonconvex regularization model resulting from the Capped-l1 function is adopted to enhance the accuracy of structural damage identification. The proximal gradient descent algorithm is employed to solve the Capped-l1 regularization model, with the optimal parameters λ and θ determined using the generalized cross-validation criterion. Numerical simulations on a steel cantilever plate and experimental studies on a steel cantilever beam indicate that the Capped-l1 regularization model resulted in fewer misjudgments in damage localization and higher accuracy in quantification.