Random dynamic load identification based on error analysis and weighted total least squares method

In most cases, random dynamic load identification problems in structural dynamics are in general ill-posed. A common approach to treat these problems is to reformulate these problems into some well-posed problems by some numerical regularization methods. In a previous paper by the authors, a random dynamic load identification model was built, and a weighted regularization approach based on the proper orthogonal decomposition (POD) was proposed to identify the random dynamic loads. In this paper, the upper bound of relative load identification error in frequency domain is derived. The selection condition and the specific form of the weighting matrix is also proposed and validated analytically and experimentally, In order to improve the accuracy of random dynamic load identification, a weighted total least squares method is proposed to reduce the impact of these errors. To further validate the feasibility and effectiveness of the proposed method, the comparative study of the proposed method and other methods are conducted with the experiment. The experimental results demonstrated that the weighted total least squares method is more effective than other methods for random dynamic load identification.