Convex model-based regularization method for force reconstruction

In the process of reconstructing structural forces, the influence of measurement errors and inherent model inaccuracies cannot be ignored. These errors exhibit a degree of correlation, and the presence of such correlation inevitably affects the quantification of uncertainties in force reconstruction. Objectively, the inherent ill-posed nature of structural inverse problems makes it difficult to obtain the forces to be identified, subject to uncertainties and highly susceptible to perturbations. Consequently, this paper introduces a force reconstruction regularization approach that explicitly considers the correlation of uncertainty parameters based on the truncated singular value regularization method. The primary objective is to refine the influence of uncertainties on the reconstructed force bounds with greater precision. When determining robust regularization parameters, the generalized cross-validation method and convex modelling approach are introduced to consider the uncertainty and its correlation in solving inverse problems. The proposed approach is rigorously validated through a comprehensive numerical case study. Error indexes and dispersion indices are employed to analyze the impact of different levels of noise and correlation on force reconstruction results. The force bounds obtained using the proposed method are compared with Monte Carlo simulation results. Finally, the validity of the proposed method is verified by an experiment with a four-story shear frame.