考虑随机和认知混合不确定性的稳健性分析与稳健设计方法

郭惠昕; 锁斌; 张干清

doi:10.13433/j.cnki.1003-8728.2018.0517

考虑随机和认知混合不确定性的稳健性分析与稳健设计方法

doi: 10.13433/j.cnki.1003-8728.2018.0517

1.
长沙学院机电工程学院, 长沙 410003;
2.
中国工程物理研究院电子工程研究所, 四川绵阳 621900

基金项目:

湖南省自然科学基金项目（13JJ6095，2015JJ2015）与长沙市科技计划项目（K1705012）资助

详细信息

作者简介:
郭惠昕(1962-),教授,硕士,研究方向为不确定性分析、稳健设计等,xinhuiguo@126.com

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- 文章访问数: 200
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- 被引次数: 0
出版历程
- 收稿日期: 2017-04-06
- 刊出日期: 2018-05-05

A Method for Robustness Analysis and Robust Design with Mixed Aleatory and Epistemic Uncertainties Considered

1.
School of Mechanical and Electrical Engineering, Changsha University, Changsha 410003, China;
2.
Institute of Electronic Engineering, China Academy of Engineering Physics, Sichuan Mianyang 621900, China

摘要

摘要: 针对质量指标Y的影响因素同时具有随机不确定性和认知不确定性的情况，提出一种质量稳健性分析的随机模拟方法。用证据理论认知对不确定性因素进行表征，进而提出一种基于随机集理论的认知不确定性因素随机采样方法，该方法可根据认知不确定性的mass函数对其进行随机采样。随机不确定性因素不必进行分布类型的转换，直接按其概率分布规律进行采样。通过不确定性分析和计算机模拟，对质量指标Y的不确定性分布进行定量计算，进而提出了3个质量稳健性的评价指标，包括Y的期望值区间宽度、期望值中点值以及区间中点分布的标准差。根据质量指标的不同特性对三个稳健性评价指标进行优化，提出了3种不同类型的稳健设计准则。通过两个典型实例，说明了所提出的稳健性评价指标以及稳健设计准则的合理性和实用性。
- 随机不确定性 /
- 认知不确定性 /
- 不确定性分析 /
- 随机模拟方法 /
- 稳健性
Abstract: A stochastic simulation method is proposed to analyze the quality robustness of a product whose quality index Y is influenced by aleatory and epistemic uncertainties. The epistemic uncertainty is characterized by the evidence theory, and then a random sampling method based on the random set theory is proposed for the epistemic uncertainty so that its random samples can be obtained according to its mass function. The aleatory uncertainty is directly sampled according to its probability distribution function, and it is not necessary for the aleatory uncertainty to be transformed into other types of uncertainty. By means of uncertainty analysis and computer simulation based on the above two random sampling methods, the uncertainty distribution of quality index Y is quantified by three statistical magnitudes of Y such as the width of mathematical expectation interval, the midpoint of expectation interval and the standard deviation of the subinterval midpoints. The above three statistical magnitudes are proposed as the evaluation indices of the quality robustness. For quality index Y with different characteristics, three different robust design criteria are put forward so that the robustness evaluation indices can be optimized. Finally, two typical examples prove that the proposed indices and criteria are rational and practical.
- aleatory uncertainty /
- epistemic uncertainty /
- uncertainty analysis /
- computer simulation /
- robustness

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参考文献(17)

[1]	Taguchi G. Introduction to quality engineering:designing quality into products and processes[M]. Tokyo:Asian Productivity Organization, 1986
[2]	Chen W, Allen J K, Tsui K L, et al. A procedure for robust design:minimizing variations caused by noise factors and control factors[J]. Journal of Mechanical Design, 1996,118(4):478-485
[3]	Box G. Signal-to-noise ratios, performance criteria, and transformations[J]. Technometrics, 1988,30(1):1-17
[4]	Rizzuti S, Napoli L D. Some hints for the correct use of the Taguchi method in product design[M]//Eynard B, Nigrelli V, Oliveri S, et al. Advances on Mechanics, Design Engineering and Manufacturing. Cham:Springer International Publishing, 2017
[5]	Parkinson A. Robust mechanical design using engineering models[J]. Journal of Mechanical Design, 1995,117(B):48-54
[6]	刘德顺,岳文辉,朱萍玉,等.基于性能稳健偏差的区间型参数稳健设计优化[J].中国机械工程,2007,18(8):952-957 Liu D S, Yue W H, Zhu P Y, et al. Robust design optimization involving interval parameters based on robust performance variations[J]. China Mechanical Engineering, 2007,18(8):952-957(in Chinese)
[7]	Zuiani F, Vasile M, Gibbings A. Evidence-based robust design of deflection actions for near Earth objects[J]. Celestial Mechanics and Dynamical Astronomy, 2012,114(1-2):107-136
[8]	Hu J M, Wei F Y, Ge R W, et al. Propagation of parameter uncertainty based on evidence theory[C]//Proceedings of 2011 International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering. Xi'an, China:IEEE, 2011:915-919
[9]	Rumpfkeil M P. Robust design under mixed aleatory/epistemic uncertainties using gradients and surrogates[J]. Journal of Uncertainty Analysis and Applications, 2013,1:7
[10]	Shafer G. A mathematical theory of evidence[M]. Princeton:Princeton University Press, 1976
[11]	锁斌,程永生,曾超,等.基于证据理论的异类信息统一表示与建模[J].系统仿真学报,2013,25(1):6-11 Suo B, Cheng Y S, Zeng C, et al. Unified method of describing and modeling heterogeneous information based on evidence theory[J]. Journal of System Simulation, 2013,25(1):6-11(in Chinese)
[12]	Florea M C, Jousselme A L. Fusion of imperfect information in the unified framework of random sets theory:application to target identification[R].Ottawa:Defence R & D Canada-Valcartier, 2007
[13]	Matheron G. Random sets and integral geometry[M]. New York:Wiley, 1975
[14]	Hall J W, Lawry J. Generation, combination and extension of random set approximations to coherent lower and upper probabilities[J]. Reliability Engineering & System Safety, 2004,85(1-3):89-101
[15]	胡钧铭.一种面向随机与认知不确定性的稳健优化设计方法研究[D].绵阳:中国工程物理研究院,2012 Hu J M. A methodology research on robust design optimization considering aleatory and epistemic uncertainty[D]. Mianyang:China Academy of Engineering Physics, 2012(in Chinese)
[16]	长沙学院.基于随机集的随机和认知不确定系统的稳健性分析软件:中国,2016SR021637[P].2016 Changsha University. Robust analysis software for aleatory and epistemic uncertain systems based on random sets:China, 2016SR021637[P]. 2016(in Chinese)
[17]	Du X P. Uncertainty analysis with probability and evidence theories[C]//Proceedings of ASME 2006 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Philadelphia, Pennsylvania, USA:ASME, 2006:1025-1038