基于序贯设计和高斯过程模型的结构动力不确定性量化方法  

Uncertainty quantification of structural dynamic characteristics based on sequential design and Gaussian process model

作　　者：万华平 张梓楠 周家伟[2,3] 任伟新 WAN Huaping;ZHANG Zinan;ZHOU Jiawei;REN Weixin(College of Civil Engineering and Architecture,Zhejiang University,Hangzhou 310058,China;Center for Balance Architecture,Zhejiang University,Hangzhou 310028,China;The Architectural Design and Research Institute of Zhejiang University,Hangzhou 310028,China;College of Civil and Transportation Engineering,Shenzhen University,Shenzhen 518060,China)

机构地区：[1]浙江大学建筑工程学院,浙江杭州310058 [2]浙江大学平衡建筑研究中心,浙江杭州310028 [3]浙江大学建筑设计研究院有限公司,浙江杭州310028 [4]深圳大学土木与交通工程学院,广东深圳518060

出　　处：《浙江大学学报（工学版）》2024年第3期529-536,共8页Journal of Zhejiang University：Engineering Science

基　　金：国家重点研发计划资助项目(2021YFF0501001);浙江省重点研发计划资助项目(2021C03154);国家自然科学基金资助项目(51878235)。

摘　　要：将直接基于有限元模型的蒙特卡罗方法用于结构动力不确定性量化较耗时,为此采用高斯过程模型取代耗时的有限元模型,提高不确定性量化的计算效率.提出基于序贯设计和高斯过程模型的结构动力不确定性量化方法,通过样本填充准则迭代,选择最优样本点建立自适应高斯过程模型,提升动力不确定性量化精度.在建立的自适应高斯过程模型框架下,动力特性统计矩的高维积分转化为一维积分,进而进行解析计算.采用2个数学函数来展示自适应高斯模型的拟合过程,高斯过程模型的拟合精度随着迭代次数增加而明显增加.将所提方法应用于柱面网壳的固有频率统计矩计算,计算精度与蒙特卡罗法的结果相当.与传统高斯过程模型对比,所提算法的计算效率优势明显,表明所提方法具有计算精度高和效率高的优势.The Monte Carlo method,which is based on finite element models directly,is extremely time-consuming for quantifying the uncertainty of structural dynamic characteristics.To address the above issue,Gaussian process model was introduced to replace the time-intensive finite element model to enhance the computational efficiency of uncertainty quantification.A method for uncertainty quantification of structural dynamic characteristics was proposed based on sequential design and Gaussian process models.Optimal sample points were selected to establish an adaptive Gaussian process model through iterative sample enrichment criteria,thereby improving the accuracy of uncertainty quantification.The high-dimensional integration of statistical moments of dynamic characteristics was transformed into one-dimensional integration under the framework of the established adaptive Gaussian process model,allowing for analytical computation.Two mathematical functions were used to illustrate the fitting process of the adaptive Gaussian model,indicating a noticeable increase of the fitting accuracy with the increase of the number of iterations.Subsequently,the proposed method was applied to the calculation of the statistical moments of natural frequencies for a cylindrical shell,with computational accuracy comparable to that of the Monte Carlo method.The proposed method demonstrated significant advantage in computational accuracy and efficiency,in comparison with the traditional Gaussian process models.

关 键 词：结构动力特性 不确定性量化 序贯设计 高斯过程模型 统计矩 

分 类 号：TB114[理学—概率论与数理统计]