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.
Mapping from parametric characteristics to generalized frequency response functions of non-linear systems
