考虑加速度频响函数不确定的有限元模型修正

为克服实际应用中缺乏足够的结构统计信息,获得结构参数和响应的极限值,提出了一种基于加速度频响函数的区间有限元模型修正方法。首先,将频响函数小波变换,提取低频小波系数作为模型修正的响应特征量,以待修正参数和响应特征量分别为输入和输出构建径向基代理模型并采用鲸鱼优化算法来优选径向基模型方差值；其次,根据区间重叠率和巴氏距离分别构造两步求解待修正参数区间的两个目标函数和同步求解待修正参数区间的一个目标函数,以评估两个样本区间分布的相似性和相异性；然后,由灰色数学方法估计径向基模型预测响应特征量的区间,运用花朵授粉算法分别实施待修正参数区间中点和半径的两步和同步求解；最后,通过两个数值算例和一个试验算例验证了所提方法的可行性。结果表明,所提区间有限元模型修正方法能够有效地修正结构参数的区间中点和半径,且在不同试验响应区间下对参数区间的修正具有鲁棒性,同时可以有效地解决小样本的不确定性模型修正问题。

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

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.