基于Kriging模型和提升小波变换的随机模型修正

Stochastic Model Updating Based on Kriging Model and Lifting Wavelet Transform

为提高随机模型修正效率,减小计算量,提出了一种基于Kriging模型和提升小波变换的随机模型修正方法.首先,对加速度频响函数进行提升小波变换,提取第5层近似系数代替原频响函数.其次,采用拉丁超立方抽样抽取待修正样本,将其作为Kriging模型的输入,对应的近似系数作为输出,构建Kriging模型.提出了一种引入莱维飞行(Lévy flight)的蝴蝶优化算法(LBOA),并将其应用于Kriging模型相关参数的寻优中,提高Kriging模型的精度.最后,以最小化Wasserstein距离为目标,通过鲸鱼优化算法求解待修正参数的均值.测试函数结果表明,LBOA在寻优能力、收敛精度和稳定性等方面有了很大的提升.数值算例的修正误差均低于0.4%,验证了所提模型修正方法具有较高的修正精度和效率.

In order to improve the efficiency of stochastic model updating and reduce the amount of calculation,a stochastic model updating method based on Kriging model and lifting wavelet transform was proposed.Firstly,the lifting wavelet transform was performed on the acceleration frequency response function,and the 5th-level approximate coefficients were extracted to replace the original frequency response function;secondly,the Latin hypercube sampling was applied to sample the parameters to be updated and the corresponding approximate coefficients as the outputs to build the Kriging model.A butterfly optimization algorithm with Lévy flight(LBOA)was proposed and used to improve the accuracy of Kriging model;finally,with the goal of minimizing the Wasserstein distance,the mean values of the parameters to be updated were solved with the whale optimization algorithm.The results of the test function show that,the LBOA greatly improves in terms of optimization,convergence accuracy and stability.The updating errors of the numerical examples are all less than 0.4%,and indicate the high accuracy and efficiency of the proposed model updating method.