Finite element model updating considering the uncertainty of acceleration frequency response function

Abstract:

To overcome the lack of sufficient structural statistical information in practical application and obtain the limit values of structural parameters and responses, an interval finite element model updating method based on acceleration frequency response function is proposed. Firstly, the frequency response function is transformed by wavelet transform with the low frequency wavelet coefficients extracted as the response characteristic quantity of the model updating. The parameters to be updated and the response characteristic quantity are respectively input and output to construct the radial basis proxy model. The whale optimization algorithm is used to optimize the variance value of radial basis function model. Secondly, two objective functions for two-step solution of the parameter interval to be updated and one objective function for synchronous solution of the parameter interval to be updated are constructed according to the interval overlap ratio and Bhattacharyya distance, so as to evaluate the distribution similarity and heterogeneity of the two samples. Then, the grey mathematics method is implemented to estimate the interval of characteristic quantity predicted by the radial basis model, and the flower pollination algorithm is adopted to solve the two-step synchronous solutions of the midpoint and radius of the parameter interval to be updated. Finally, two numerical examples and one experimental example are provided to verify the feasibility of the proposed method. The results show that the proposed interval finite element model can effectively update the interval midpoint and radius of structural parameters, and prove to be robust to the parameter interval updating under different test response intervals, thus effectively solving the problem of uncertainty model updating for small test samples.