A novel semi-convex function for simultaneous identification of moving vehicle loads and bridge damage

For the simultaneous identification (SI) problem on the moving vehicle loads and bridge damage, the existing methods fail to appropriately consider the sparse characteristics of structural damage and ignore the prior information of vehicle loads, which make them suffering from challenges such as prolonged computation cost, poor noise robustness, and limited identification accuracy. To address this issue, a novel semi-convex function is proposed to construct a theoretical framework for the SI problem using the bridge dynamic responses subjected to moving vehicles in this study. Firstly, the bridge damage-induced virtual forces are conceptualized as a new form of moving residual forces characterized by block sparsity properties, and the damage location is then determined by the frequency characteristics with the largest fundamental frequency amplitude of moving residual forces. Secondly, a semi-convex function model encompassing moving forces and moving residual forces is defined. Combined with sparse regularization strategy, an improved alternating direction method of multipliers algorithm is proposed and applied to simultaneously solve for both moving vehicle loads and damage degrees. To assess the effectiveness and feasibility of the proposed method, extensive numerical validations are conducted in various bridge damage scenarios. Additionally, a series of truss bridge experiments are performed in laboratory under multiple damage and vehicle axle-weight conditions. The results show that compared with the existing outstanding methods, the proposed semi-convex function method can significantly reduce the identification cost, enhance robustness to noise, and demonstrate notable improvements in accuracy for the SI problem, which provides an innovative and more efficient solution to the SI problem in bridge engineering.