多输出情况下重要性测度新指标及其高效求解 -- 西北工业大学学报,2015,33(4):546-552
论文:2015,Vol:33,Issue(4):546-552
引用本文:
王飞, 吕震宙, 肖思男. 多输出情况下重要性测度新指标及其高效求解[J]. 西北工业大学学报
Wang Fei, Lu Zhenzhou, Xiao Sinan. New Global Sensitivity Indices for Structure System with Multivariate Outputs and Their Effective Solution[J]. Northwestern polytechnical university

多输出情况下重要性测度新指标及其高效求解
王飞, 吕震宙, 肖思男
西北工业大学 航空学院, 陕西 西安 710072
摘要:
输入随机变量的重要性测度分析是结构安全评估和工程优化设计的重要组成部分。针对工程结构系统中普遍存在的多维输出情况,提出一种使用无量纲模型的基于方差的重要性测度新指标,可以方便地综合衡量输入随机变量的变异性对多输出结构系统变异性影响的重要程度,而且能够有效地保留各输出提供的重要性测度信息。同时,针对Monte Carlo数字模拟方法巨大的计算代价问题,采用一种乘法降维的功能函数替代模型来求解指标。该方法可在保证求解精度的同时极大地降低了模型调用次数,节约了计算成本。最后,通过数值算例和工程算例说明所提指标的合理性以及求解模型的高效性。
关键词:    多输出    重要性测度    系统不确定性    方差分析    降维模型    降低成本   
New Global Sensitivity Indices for Structure System with Multivariate Outputs and Their Effective Solution
Wang Fei, Lu Zhenzhou, Xiao Sinan
College of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China
Abstract:
Global sensitivity analysis for input random variables is an important component of safety evaluation and optimal design in engineering structure. For many mathematical models encountered in engineering structure system involving multivariate outputs, this paper defines a set of new variance-based global sensitivity indices based on dimensionless model. These indices can synthetically measure the uncertainty effect on the multivariate outputs induced by the corresponding input random variable expediently and can effectively keep global sensitivity analysis information of each output. Simultaneously, to solve the costly computation problem in the Monte Carlo simulation, we calculate the new index by using a surrogate model which is based on a multiplicative version of the dimensional reduction method. The algorithm can greatly reduce model calls and save the calculation cost without decreasing its accuracy. Lastly, a numerical example and an engineering example are presented to show the reasonableness of the proposed index and the efficiency of the algorithm.
Key words:    multivariate outputs    global sensitivity analysis    uncertainty of system    analysis of variance (ANOVA)    dimensional reduction model (DRM)    cost reduction   
收稿日期: 2015-03-10     修回日期:
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作者简介: 王飞(1991—),西北工业大学硕士研究生,主要从事飞行器可靠性研究。
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