结合Cokriging模型和单目标函数的随机模型修正

Stochastic Model Updating Combining Cokriging Model and Single Objective Function

将Cokriging代理模型技术和单目标函数进行结合,提出了一种随机模型修正方法。该方法将不确定性模型修正问题转化为较简单的待修正参数统计特征的修正问题,能够在保证模型修正精度的同时,有效缓解模型修正中由于分步修正和多目标修正造成的计算成本高的问题。首先,假设待修正参数和响应均服从高斯分布,采用拉丁超立方抽样获取训练集样本,构造满足精度要求的Cokriging模型替代复杂的有限元模型参与迭代计算。然后,建立有限元模型计算响应统计特征与试验响应统计特征的加权残差目标函数,引入土狼优化算法最小化该单目标函数来得到待修正参数的统计特征。最后,通过二维和三维桁架结构验证了所提方法的可行性。

A stochastic model updating method is proposed by combining the Cokriging surrogate model technique with the single objective function.The method transforms the uncertainty model updating problem into a simple updating problem of the statistical characteristics of the parameters to be updated,which can effectively alleviate the high computational cost problem caused by the stepwise and multi⁃objective updating while ensuring the updating accuracy.Firstly,assuming that the parameters to be updated and the corresponding responses obey Gaussian distribution,the Latin hypercube sampling is used to obtain the training set samples,and the Cokriging model satisfying the accuracy requirement is constructed to replace the complex finite element model in the iterative calculation.Then,the weighted residual objective function between the statistical characteristics of the finite element model calculated responses and the statistical characteristics of the test responses is established,and the coyote optimization algorithm is introduced to minimize the single objective function to obtain the statistical characteristics of the parameters to be updated.Finally,the proposed method is verified by the two⁃dimensional and the three⁃dimensional truss structures.