基于加速度频响函数小波分解的模型修正方法

Model updating method based on wavelet decomposition of acceleration frequency response function

为提高模型修正效率,满足修正方法对于实测环境噪声的鲁棒性,将Kriging模型和小波分解引入加速度频响函数模型修正。首先,将加速度频响函数进行小波分解,用得到的第1层幅值较大的小波系数来表征原频响函数。其次,采用拉丁超立方抽样对初选待修正参数进行设计,根据设计结果对各参数进行灵敏度分析,从而确定模型修正的待修正参数,以待修正参数作为Kriging模型输入,所对应的小波系数作为Kriging模型输出,通过混合灰狼算法寻得最优Kriging模型相关系数,建立精确有效的Kriging模型。最后,以目标加速度频响函数小波分解的小波系数与Kriging模型输出的小波系数差值最小为目标,通过水循环算法求解模型待修正参数。数值算例表明,所提模型修正方法具有良好的修正效果,即使在加速度频响函数中加入信噪比为5dB的高斯白噪声时,修正误差也低于4%,证明了该方法对于随机噪声的鲁棒性。

To improve the efficiency of model updating and satisfy its robustness for the measured environmental noise,the Kriging model and wavelet decomposition are introduced into the model updating of the acceleration frequency response function.Firstly,the acceleration frequency response function is decomposed by wavelets,and the obtained wavelet coefficients with large amplitudes in the first layer are used to represent the original frequency response function.Secondly,the Latin hypercube sampling is utilized to design the primary parameters to be updated,and the sensitivity analysis of each parameter carried out according to the design results to determine the parameters to be modified,which are then used as the inputs of the Kriging model,while the corresponding wavelet coefficients as the outputs of the model.The optimal correlation coefficients of the Kriging model are found through the mixed grey wolf algorithm,with which an accurate and effective Kriging model is established.Finally,with the error between the wavelet coefficients calculated from the Kriging model and those from tests as the objective function,a minimization problem is solved by the water cycle algorithm for parameter updating.Numerical examples show the effectiveness of the proposed model updating method.When Gaussian white noise with a signal-to-noise ratio of 5 dB is added to the acceleration frequency response function,the updating error is smaller than 4%,proving the robustness of the method against random noise.