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.

中文翻译：

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基于凸模型的力重构正则化方法

在重建结构力的过程中，测量误差和固有模型误差的影响不容忽视。这些误差表现出一定程度的相关性，这种相关性的存在不可避免地影响力重建中不确定性的量化。客观上，结构反问题固有的不适定性质使其难以获得待识别的力，且具有不确定性且极易受到扰动。因此，本文引入了一种力重构正则化方法，该方法基于截断奇异值正则化方法显式考虑不确定性参数的相关性。主要目标是更精确地细化不确定性对重建力边界的影响。在确定鲁棒正则化参数时，引入广义交叉验证方法和凸建模方法来考虑求解反问题时的不确定性及其相关性。所提出的方法通过全面的数值案例研究得到了严格验证。采用误差指数和离散指数分析不同噪声水平和相关性对力重构结果的影响。使用所提出的方法获得的力范围与蒙特卡罗模拟结果进行了比较。最后通过四层剪力框架实验验证了该方法的有效性。