基于偏导全域积分的结构全局敏感性方法  

STRUCTURAL GLOBAL SENSITIVITY METHOD BASED ON PARTIAL DERIVATIVE WHOLE DOMAIN INTEGRAL

作　　者：涂龙威 刘杰[1] 刘光昭[1] 张正[2] TU Long Wei;LIU Jie;LIU GuangZhao;ZHANG Zheng(State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body,Hunan University,Changsha 410082,China;College of Physics and Mechanical&Electrical Engineering,Jishou University,Jishou 416000,China)

机构地区：[1]湖南大学汽车车身先进设计制造国家重点实验室,长沙410082 [2]吉首大学物理与机电工程学院,吉首416000

出　　处：《机械强度》2019年第6期1359-1364,共6页Journal of Mechanical Strength

基　　金：国家自然科学基金项目(11402096,11572115);常州市应用基础研究计划项目(CJ20179009)资助~~

摘　　要：针对传统基于方差的Sobol’法求解效率不高,稳健性不足,且无法进一步对高阶交叉子项的影响进行有效分解和合理分配的问题,文章提出一种实用而有效的基于偏导信息全域统计和最优多项式代理模型的结构全局敏感性方法。首先采用多项式结构选择构建具有良好拟合能力和预测能力的最优代理模型,且便于直接积分操作;其次通过对模型变量的偏导进行全域积分将基于偏导的局部敏感性方法扩展为全局敏感性方法;此外,重新定义了一种更便于求解的敏感性指标,能很好地实现对高阶敏感性指标进行有效分解,使敏感性结果直接对应于模型变量而不存在高阶指标,这更具有工程实际意义。数值算例1说明Sobol’法总敏感性指标在应用中所存在的不足;数值算例2表明提出的方法对复杂高维模型的有效性;工程算例说明本文的方法对于复杂工程结构问题的适用性和有效性。In view of the problems that the traditional variance-based Sobol’method had a low solving efficiency,lacked of enough robustness,and it cannot further effectively decompose and reasonably distribute the influences of the high-order cross subterms,a practical and effective structural global sensitivity method was proposed in this paper based on partial derivative whole domain integral and optimal polynomial surrogate model.Firstly,optimal surrogate model was constructed through polynomial structure-selection,which had good fitting and predictive ability,and it was convenient for direct integral operations.Then,local sensitivity method based on partial derivative was extended to a global sensitivity method by integrating partial derivatives of model variables in variable sapces.In addition,the paper redefined a more conveniently calculated sensitivity indice that can achieve effective decomposition for the high-order sensitivity indices,and the sensitivity results directly corresponded to model variables without the high-order indices,which had more practical engineering significance.Numerical example 1 shows the deficiency of Sobol’total sensitivity indices in application.Numerical example 2 illustrates the validity of the proposed method for complex high-dimensional model.Engineering example demonstrates the applicability and effectiveness of the present method for complex engineering structure problems.

关 键 词：结构敏感性分析 偏导全域积分 多项式结构选择 最优多项式 Sobol’法 

分 类 号：TH122[机械工程—机械设计及理论]