基于模糊Hausdorff距离的多输出全局灵敏度分析方法

doi:10.7527/S1000-6893.2017.120870

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基于模糊Hausdorff距离的多输出全局灵敏度分析方法

樊重庆, 吕震宙

西北工业大学航空学院, 西安 710072

收稿日期:2016-10-19 修回日期:2017-06-12 出版日期:2017-10-15 发布日期:2017-06-12
通讯作者: 吕震宙 E-mail:zhenzhoulu@nwpu.edu.cn
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

FAN Chongqing, LYU Zhenzhou

School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China

Received:2016-10-19 Revised:2017-06-12 Online:2017-10-15 Published:2017-06-12
Supported by:
Natural Science Foundation of China (51475370);the Fundamental research funds for the central universities (3102015 BJ (Ⅱ) CG009)

摘要/Abstract

摘要：

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

Abstract:

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

中图分类号:

V215.7

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.

FAN Chongqing, LYU Zhenzhou. Global sensitivity analysis method for multivariate output based on fuzzy Hausdorff distance[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2017, 38(10): 220870-220870.

参考文献

[1] BEN-HAIM Y, ELISHAKOFF I. Convex models of uncertainty in applied mechanics[M]. Amsterdam:Elsevier Science Publisher, 1990:48-52.
[2] ELISHAKOFF I, FERRACUTI B. Fuzzy sets based interpretation of the safety factor[J]. Fuzzy Sets and Systems, 2006, 157(18):2495-2512.
[3] DUBOIS D, PRADE H. Fuzzy sets and systems:Theory and applications[M]. New York:Academic Press, 1997:159-163.
[4] SONG S, LU Z Z. A generalized Borgonovo's importance measure for fuzzy input uncertainty[J]. Fuzzy Sets and Systems, 2012, 189(1):53-62.
[5] SONG S, LU Z Z. The uncertainty importance measures of the structural system in view of mixed uncertain variables[J]. Fuzzy Sets and Systems, 2014, 243:25-35.
[6] TANG Z, LU Z Z,PAN W, et al. An entropy based global sensitivity analysis for the structures with both fuzzy variables and random variables[J]. Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science, 2013, 227(2):195-212.
[7] LI L, LU Z Z. Importance measure system of fuzzy and random input variables and its solution by point estimates[J]. Science China:Technology Science, 2011, 54(8):2167-2179.
[8] LI L, LU Z Z. Importance analysis on the failure probability of the fuzzy and random system and its state dependent parameter solution[J]. Fuzzy Sets and Systems, 2014, 250(2):69-89.
[9] CHENG L, LU Z Z. Global sensitivity analysis of fuzzy distribution parameter on failure probability and its single-loop estimation[J]. Journal of Applied Mathematics, 2014, 49:07-18.
[10] 陈超,吕震宙.模糊分布参数的全局灵敏度分析新方法[J]. 工程力学,2016, 3(2):25-33. CHEN C, LU Z Z. A new method for global sensitivity analysis of fuzzy distribution parameters[J]. Engineering Mechanics, 2016, 3(2):25-33(in Chinese).
[11] PEUQUET D. An algorithm for calculating minimum Euclidean distance between two geographic features[J]. Computers and Geosciences, 1992, 18(8):989-1001.
[12] CHAUDHURI B, ROSENFELD A. On a metric distance between fuzzy sets[J]. Pattern Recognition Letters, 1996, 17(17):1157-1160.
[13] BOXER L. On Hausdorff-like metrics for fuzzy sets[J]. Pattern Recognition Letters, 1997, 18(2):115-118.
[14] CHAUDHURI B, ROSENFELD A. A modified Hausdorff distance between fuzzy sets[J]. Information Sciences, 1999, 118(1-4):159-171.
[15] HELMUT A, LUDMILA S. Computing the Hausdorff distance between curved objects[J]. International Journal of Computational Geometry and Applications, 2008, 18(4):304-320.
[16] CARVALHO D, MARIE C, CHAVENT M, et al. Adaptive Hausdorff distances and dynamic clustering of symbolic interval data[J]. Pattern Recognition Letters, 2006, 27(3):167-179.
[17] CHEN X, DOIHARA T, NASU M. Spatial relations of distance between arbitrary objects in 2D/3D geographic spaces based on the Hausdorff metric[C]//LIESMARS'95, 1995.
[18] JULIER S. The scaled unscented transformation[C]//Proceedings of the American Control Conference. Piscataway(NJ):IEEE Press, 2002, 6:4555-4559.
[19] JULIER S, UHLMANN J. Unscented filtering and nonlinear estimation[J]. Proceedings of the IEEE, 2004, 92(3):401-422.
[20] JULIER S, UHLMANN J. Reduced sigma point filters for the propagation of means and covariance through nonlinear transformations[C]//Proceeding of the American Control Conference. Piscataway, NJ:IEEE Press, 2002,2:887-892.

E-mail：hkxb@buaa.edu.cn

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基于模糊Hausdorff距离的多输出全局灵敏度分析方法

Global sensitivity analysis method for multivariate output based on fuzzy Hausdorff distance

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