Load identification in structural dynamics is an ill-conditioned inverse problem, and the errors existing in both the frequency response function matrix and the acceleration response have a great influence on the accuracy of identification. The Tikhonov regularized least-squares method, which is a common approach for load identification, takes the effect of the acceleration response errors into account but neglects the effect of the errors of the frequency response function matrix. In this article, a Tikhonov regularized total least-squares method for load identification is presented. First, the total least-squares method which can minimize the errors of the frequency response function matrix and acceleration response simultaneously is introduced into load identification. Then Tikhonov regularization is used to regularize the total least-squares method to improve the ill-conditioning of the frequency response function matrix. The regularization parameter is selected by the L-curve criterion. To validate the performance of the regularized total least-squares method, a load identification simulation with two excitation loads is studied on a plate based on the finite element method and a load identification experiment with two excitation loads is conducted on an aluminum plate. Both simulation and experiment results show that the excitation loads identified by the regularized total least-squares method match the actual loads well although there are errors existing in both the frequency response function matrix and acceleration response. In experiment, the average relative error of the regularized total least-squares method is 13.00% for excitation load 1 and 20.02% for excitation load 2, whereas the average relative error of the regularized least-squares method is 35.86% and 53.09% for excitation load 1 and excitation load 2, respectively. This result reveals that the regularized total least-squares method is more effective than the regularized least-squares method for load identification.

结构动力学中的载荷辨识是一个病态逆问题，频率响应函数矩阵和加速度响应中存在的误差对辨识的精度影响很大。Tikhonov 正则化最小二乘法是一种常用的载荷识别方法，它考虑了加速度响应误差的影响，而忽略了频率响应函数矩阵误差的影响。在本文中，提出了一种用于负荷识别的 Tikhonov 正则化总最小二乘法。首先，将能够同时最小化频率响应函数矩阵和加速度响应误差的全最小二乘法引入载荷识别中。然后利用Tikhonov正则化对总最小二乘法进行正则化，改善频响函数矩阵的病态。正则化参数由 L 曲线准则选择。为验证正则化全最小二乘法的性能，基于有限元方法在一块板上进行了两个激励载荷的载荷识别仿真，并在铝板上进行了两个激励载荷的载荷识别实验。仿真和实验结果均表明，虽然频率响应函数矩阵和加速度响应均存在误差，但正则化总最小二乘法识别的激励载荷与实际载荷匹配良好。在实验中，正则化总最小二乘法的平均相对误差对于励磁负载 1 为 13.00%，对于励磁负载 2 为 20.02%，而正则化最小二乘法对于励磁负载 1 的平均相对误差为 35.86% 和 53.09%，激励负载 2，分别。该结果表明，正则化总最小二乘法比正则化最小二乘法更有效地进行负荷识别。