收稿日期: 2016-10-19
修回日期: 2017-06-12
网络出版日期: 2017-06-12
基金资助
国家自然科学基金（51475370）；中央高校基本科研业务费专项基金（3105015BJ （Ⅱ） CG009）
Global sensitivity analysis method for multivariate output based on fuzzy Hausdorff distance
Received date: 2016-10-19
Revised date: 2017-06-12
Online published: 2017-06-12
Supported by
Natural Science Foundation of China (51475370);the Fundamental research funds for the central universities (3102015 BJ (Ⅱ) CG009)
为了度量模糊不确定性条件下输入变量对输出性能的影响，提出了基于模糊向量Hausdorff距离的多输出性能对模糊输入变量的全局灵敏度指标（GSI）。所提指标以模糊向量的Hausdorff距离来度量模糊输入变量被固定后的条件输出性能与无条件输出性能的差异，并在对这种差异进行加权平均的基础上，建立模糊输入变量对多输出性能影响的全局灵敏度指标。另外，所提指标还被推广至随机输入变量的分布参数具有模糊性的情况，用所提指标来衡量模糊分布参数对随机输出性能统计特征的影响，并结合无迹变换和Kriging代理模型方法，建立了模糊分布参数对输出均值影响的灵敏度求解高效方法。在详细给出所提指标的实现步骤后，采用算例说明了所提指标的合理性和算法的高效性。
关键词： Hausdorff距离; 多输出; 模糊不确定性; 灵敏度; Kriging
樊重庆 , 吕震宙 . 基于模糊Hausdorff距离的多输出全局灵敏度分析方法[J]. 航空学报, 2017 , 38(10) : 220870 -220870 . DOI: 10.7527/S1000-6893.2017.120870
To measure the effects of the model fuzzy inputs on the performance of the model outputs,the global sensitivity index (GSI) based on fuzzy vector Hausdorff distance is proposed.In the proposed GSI,the Hausdorff distance is used to measure the difference between the conditional model outputs and the unconditional model outputs while the fuzzy input is fixed.Based on the weighted average of the difference,the global sensitivity index evaluating the effects of the fuzzy input on the model outputs is established.The proposed GSI is also extended to the condition that the distribution parameters of the random inputs have fuzzy uncertainty,and is used to measure the effects of fuzzy distribution parameters on the statistical characteristics of the random model output.An efficient solution to evaluation of the effects of the fuzzy distribution parameters on the mean of the model outputs is established by combining the unscented transformation with the Kriging meta-model.The accuracy and efficiency of the proposed method is demonstrated by some examples after the procedure of the solution for the proposed GSI is presented in detail.
Key words： Hausdorff distance; multivariate output; fuzzy uncertainty; sensitivity; Kriging
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