A novel uncertainty-oriented regularization method for load identification

Abstract

Since conventional regularization methods have been constructed in the deterministic framework, using deterministic regularization methods to address the ill-posedness problem with uncertainties can lead to errors or even mistakes. Therefore, based on the non-probabilistic theory, a novel uncertainty-oriented regularization method for load identification is proposed in this paper to meet the increasing demand of uncertain inverse technology, which may be more appropriate for the inverse problem with poor uncertainty information. By quantifying the uncertainty models and noisy responses as unknown-but-bounded numbers, the inverse formula with an uncertain kernel function is extended into an interval system using uncertainty propagation methods. One of the classical regularization methods, the singular value decomposition method, is developed into an uncertain case using an interval perturbation method and then applied to solve the uncertain inverse problem. If the bounds of uncertain parameters are known, an estimation of the singular value bounds can be obtained. According to the idea of a deterministic regularization parameter for estimating the residual errors and solutions in the inverse formula, a more robust regularization parameter is determined to balance the deterministic and uncertain parts of these two norms, which can be solved using the uncertain optimization objective of the generalized cross-validation method. By using the uncertain singular value decomposition method and selecting a robust regularization parameter, the uncertain inverse problem can be solved and the bounds of the identified loads can also be estimated. The effectiveness is verified through a numerical engineering example. The accurate identified load intervals are examined by four defined criteria and compared by Monte Carlo simulation and the conventional deterministic method. Discussions on different measurement points and uncertainty levels are also presented.