Low frequency load identification under high noise level using weighted total least squares

Abstract

Load identification in structural dynamics is an ill-conditioned inverse problem, and the errors exist in both the transfer function matrix and the response vector, which have a great influence on the accuracy of the identification, especially at the low frequency and high noise. Although the Total Least Squares (TLS) method can consider the errors in the transfer function matrix and the response vector, the problem of unequal precision between them has not been properly solved. In this article, the Weighted Total Least Squares (WTLS) method for load identification is presented. First, the variance–covariance matrices are constructed using stochastic information, which can consider the unequal precision of the data and make the solution less biased and more precise. Then, Tikhonov regularization is used to regularize the WTLS method to reduce the ill-condition of the transfer function matrix. To validate the performance of the WTLS method under different noise levels, a load identification simulation with four excitation loads on a plate and a load identification experiment with three excitation loads on a steel plate were studied. The results show that when the noise levels of the transfer function and the response are different, the accuracy of the TLS solution is poor. Especially when the noise levels are high, the identification deviations are large. The WTLS method considers the unequal noise levels using the weight matrices, which provides more stable load estimates at different noise levels. And the identification deviations are greatly reduced compared to the TLS method.