In the field of damage identification, traditional regularization methods neglect the impact of uncertainty factors on the selection of regularization parameters, leading to a decrease in the accuracy of damage identification. Therefore, this study proposes a damage identification based on interval truncated singular value decomposition (DI-ITSVD) method that considers the uncertainty in the selection of regularization parameter. This method treats model errors and measurement noise as interval uncertainties, and introduces the quantified uncertainties into the damage identification solutions through uncertainty propagation methods to determine the interval boundary. Uncertainty regularization parameters are selected to balance residuals and solutions using interval and generalized cross-validation methods. The key aspect of the proposed method in this paper is the integration of interval uncertainty propagation with the truncated singular value decomposition method to ensure the accuracy and stability of the damage identification equation solution. A numerical example of a 29-bar planar truss has been performed to test the effectiveness of the proposed method. The superiority of this method is verified by comparing the identification results with other improved truncated singular value decomposition methods. Finally, the practical application effect of the proposed method was also verified through an experimental work.

中文翻译：

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基于区间正则化理论的损伤识别方法


在损伤识别领域，传统的正则化方法忽略了不确定性因素对正则化参数选择的影响，导致损伤识别的准确率下降。因此，本研究提出一种考虑正则化参数选择的不确定性的基于区间截断奇异值分解（DI-ITSVD）的损伤识别方法。该方法将模型误差和测量噪声视为区间不确定性，通过不确定性传播方法将量化的不确定性引入到损伤识别解中，以确定区间边界。使用区间和广义交叉验证方法选择不确定性正则化参数来平衡残差和解。本文提出的方法的关键是将区间不确定性传播与截断奇异值分解方法相结合，以保证损伤识别方程解的准确性和稳定性。通过 29 杆平面桁架的数值算例验证了该方法的有效性。通过与其他改进的截断奇异值分解方法的辨识结果比较，验证了该方法的优越性。最后，通过实验工作也验证了该方法的实际应用效果。