基于Tikhonov正则化及奇异值分解的载荷识别方法

针对矩阵求逆法应用中存在的病态逆问题，用Tikhonov正则化及奇异值分解法解决。通过对平板模型仿真分析，利用频响函数法矩阵条件数评价系统的病态性，系统病态性不同时用奇异值分解法与基于不同正则化参数选择的Tikhonov方法对载荷进行识别。研究表明，条件数大于1000时，Tikhonov正则化方法识别误差较小；反之，奇异值分解法较优。提出综合使用Tikhonov正则化与奇异值分解的载荷识别方法，给出方法流程。仿真与实验结果表明该方法可提高结构载荷识别精度，具有一定工程应用价值。

A novel load identification method based on the combination of Tikhonov regularization and singular value decomposition

The inverse matrix of frequency response function is a common method for load identification in practice. The key point of the method is to solve the ill-conditioned problem, which was dealt with Tikhonov regularization and singular value decomposition (SVD) in the paper. Simulation of a plate was carried out to compare the load identification accuracy of the two methods under different ill-conditions, which were evaluated by the condition number of the normal matrix of frequency response function. Conclusions show that Tikhonov regularization is more suitable when the condition number is greater than 1000 and SVD method is better for other situations. What’s more, a novel method is proposed to identify loads with the combination of the two methods based on the condition number. Comparing with SVD and Tikhonov regularization methods through results of simulation and experiment, the novel method can obviously improve the load identification accuracy, and provides a certain guide for practical engineering.