正则化方法求解偶应力反问题

Solving Inverse Couple Stress Problem via Regularization Method

引入Bregman函数及其加权函数作为正则项,应用Tikhonov正则化方法,对偶应力反问题相关参数进行识别。利用相关测量信息和计算信息构造最小二乘函数。在考虑材料非均质的同时,建立了便于敏度分析的偶应力正/反问题数值求解模型。给出了相关的数值算例,并对信息误差以及不同正则项的计算效率作了探讨。数值结果表明所提的求解策略不仅能够对相关的材料参数进行有效识别,而且具有较高的计算精度、较好的稳定性和一定的抗噪性。采用加权的Bregman距离函数作正则项可以提高计算效率。

Tikhonov′s regularization approach has been used to identify parameters for the inverse couple-stress problem based on Bregman distances and weighted Bregman distances in the construction of regularization terms for the Tikhonov＇s function.The inverse problem is formulated implicitly as an optimization problem with the cost functional of squared residues between calculated and measured quantities.A FE model is given,taking account of inhomogeneity and facilitating to sensitivity analysis for direct and inverse problems.Satisfactory numerical validation is given including a preliminary investigation of effect of noise data on the results and the computational efficiency for different regularization terms.Results show that the proposed method can identify parameters for the inverse couple-stress problem with high computational precision/efficiiency and the ability of anti-noisy data.It could improve computational efficiency for the weighted Bregman distances function as regularization terms.