Damage identification method based on interval regularization theory

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.