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论文:2022,Vol:40,Issue(2):450-457 |
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引用本文： |
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任博, 岳珠峰, 崔利杰, 王新河, 张峰. 混合数据信息下不确定性描述的改进最大熵函数法[J]. 西北工业大学学报 |
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REN Bo, YUE Zhufeng, CUI Lijie, WANG Xinhe, ZHANG Feng. An improved entorpy-based representation for mixed uncertainty about intervals and points data[J]. Northwestern polytechnical university |
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| 混合数据信息下不确定性描述的改进最大熵函数法 |
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| 任博1,2, 岳珠峰1, 崔利杰2, 王新河1, 张峰1 |
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1. 西北工业大学 力学与土木建筑学院, 陕西 西安 710072;
2. 空军工程大学 装备管理与无人机工程学院, 陕西 西安 710051 |
| 摘要: |
| 可靠性分析的基础在于不确定性的精确描述。工程实际中由于个别变量信息缺乏只能确定其区间范围，提出描述区间和离散点混合不确定性的改进最大熵函数法。该方法建立不同类型数据不确定性的联合熵函数，应用插值技术得到描述区间和离散点混合数据信息下不确定性的非参数概率密度函数，通过优化联合熵函数最大，确定非参数概率密度函数在原始数据空间上下限内均匀离散点处的概率密度值。相比于传统非参数概率确定方法，所提方法将传统分布参数估计寻优过程转化为在原始数据空间内对自定义随机离散点处的概率密度值优化，进而使用插值技术得到描述区间和离散点数据混合不确定性的最少偏见概率密度函数，其混合不确定性描述精度由自定义的随机离散点多少来确定，精度按需可控。此外，在概率理论框架下，尝试将输入混合不确定性信息向输出传递，完成输出响应的可靠性分析。所提方法计算量和精度可通过自定义离散点数量控制，对原始数据不确定性信息挖掘更充分。算例表明所提方法科学性和合理性，为概率理论用于混合不确定性分析奠定基础。 |
| 关键词:
不确定性
熵函数
区间数据
离散点
概率密度函数
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| An improved entorpy-based representation for mixed uncertainty about intervals and points data |
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| REN Bo1,2, YUE Zhufeng1, CUI Lijie2, WANG Xinhe1, ZHANG Feng1 |
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1. School of Mechanics, Civil Engineering and Architecture, Northwestern Polytechnical University, Xi'an 710072, China;
2. Equipment Management and UAV Engineering College, Air Force Engineering University, Xi'an 710051, China |
| Abstract: |
| In engineering design problems, intervals refer to any kind of lack of information. This paper presents an improved entorpy-based methodology for a probabilistic representation of a stochastic quantity for which only sparse point data and/or interval data may be available. The combined entropy function is used to measure the uncertainty in data, which is evaluated from the non-parametric probability density function for sparse point data and the cumulative distribution function for interval data, Wherein the entire non-parametric distribution can be discretized at a finite number of points and the probability density values at these points can be inferred using the principle of maximum-entropy, thus avoiding the assumption of any particular distribution. The proposed improved Entorpy-based methodology is then employed in the attempt of interval uncertainty propagation, with the results compared with previous studies. Examples are provided to demonstrate the effectiveness of present method. The study reveals great potentials of the probabilistic method for the treatment of the uncertainty in presence of the sparse point data and/or interval data. |
| Key words:
uncertainty
entropy function
intervals
probability density function
point data
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| 收稿日期: 2020-10-14
修回日期:
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| DOI: 10.1051/jnwpu/20224020450 |
| 基金项目: 国家自然科学基金（71701210）、航空科学基金（20165196017）与陕西省自然科学基金（2019JQ-710）资助 |
| 通讯作者:
Email： |
| 作者简介: 任博(1985-),西北工业大学博士后、副教授,主要从事飞行器结构设计、装备安全性及适航研究。e-mail:rabber2003@163.com
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| 作者相关文章 |
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| 任博 在本刊中的所有文章 |
| 岳珠峰 在本刊中的所有文章 |
| 崔利杰 在本刊中的所有文章 |
| 王新河 在本刊中的所有文章 |
| 张峰 在本刊中的所有文章 |
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参考文献: |
|
|
[1] 郭书祥, 吕震宙. 结构的非概率可靠性方法和概率可靠性方法的比较[J]. 应用力学学报, 2003, 20(3):107-110 GUO Shuxiang, LYU Zhenzhou. Comparison between the non-probabilistic and probabilistic reliability method for uncertain structure design[J]. Chinese Joural of Applied Mechanic, 2003, 20(3):107-110 (in Chinese)
[2] BAUDRIT C, DUBOIS D. Practical representations of incomplete probabilistic knowledge. The fuzzy approach to statistical analysis[J]. Computational Statistical & Data Analysis, 2006, 51(1):86-108
[3] FERSON S, KREINOVICH V, HAJAGOS J, et al. Experimental uncertainty estimation and statistics for data having interval uncertainty[R]. SAND-2007-0939
[4] FERSON S, TUCKER W T. Sensitivity in risk analyses with uncertain numbers[R]. SAND-2006-2801
[5] ZAMAN K, RANGAVAJHALA S, MCDONALD M P, et al. A probabilistic approach for representation of interval uncertainty[J]. Reliability Engineering and System Safety, 2011, 96:117-130
[6] WILLIAMSON R C. Probabilistic arithmetic[D]. Brisbane:University of Queensland, 1989
[7] MONTGOMERY V. New statistical methods in risk assessment by probability bounds[D]. Durham:Durham University, 2009
[8] SANKARARAMAN S, MAHADEVAN S. Likelihood-based representation of epistemic uncertainty due to sparse point data and/or interval data[J]. Reliability Engineering and System Safety, 2011, 96:814-824
[9] ELISHAKOFF I, COLOMBI P. Combination of probabilistic and convex models of uncertainty when scare knowledge is present on acoustic excitation on parameters[J]. Computer Methods in Applied Mechanics and Engineering, 1993,104:187-209
[10] 曹鸿钧, 段宝岩. 基于凸集合模型的非概率可靠性研究[J]. 计算力学学报, 2005, 22(5):546-549 CAO Hongjun, DUAN Baoyan. An approach on the non-probabilitic reliability of structures based on uncertainty convex models[J]. Chinese Joural of Computational Mechanics, 2005, 22(5):546-549 (in Chinese)
[11] QIU Z P, YANG D, ELISHAKOFF I. Probabilistic interval reliability of structural systems[J]. International Journal of Solids and Structures, 2008, 45:2850-2860
[12] SOIZE C. Maximum entropy approach for modeling random uncertainties in transient elastodynamics[J]. Journal of Acoustical Society of America, 2001, 109(5):1979-1996
[13] 吕震宙, 宋述芳, 李洪双, 等. 结构机构可靠性及可靠性灵敏度分析[M]. 北京:科学出版社, 2009 LYU Zhenzhou, SONG Shufang, LI Hongshuang, et al. Reliability and reliability sensitivity analysis of uncertainty structure[M]. Beijing:Science Press, 2009 (in Chinese)
[14] 赵宇. 可靠性数据分析教程[M]. 北京:北京航空航天大学出版社, 2011 ZHAO Yu. Data analysis of reliability[M]. Beijing:Beihang University Press, 2011 (in Chinese)
[15] REZA F M. An introduction to information theory[M]. New York:Dover Publications, 1994
[16] SHANNON C E. A mathematical theory of communication[J]. Bell System Technical Journal, 1948, 27:379-423
[17] SOIZE C. Maximum entropy approach for modeling random uncertainties in transient elastodynamics[J]. Journal of Acoustical Society of America, 2001, 109(5):1979-1996
[18] 龚纯, 王正林. Matlab语言常用算法程序集[M]. 北京:电子工业出版社, 2011 GONG Chun, WANG Zhenglin. Programs collection of algorithm in common use based on Matlab[M]. Beijing:Publishing House of Electronics Industry, 2011 (in Chinese)
[19] OBERKAMPF W L, HELTON J C, JOSLYN C A, et al. Challenge problems:uncertainty in system response given uncertain parameters[J]. Reliability Engineering and System Safety, 2004, 85:11-19
[20] FERSON S, JOSLYN C A, HELTON J C. Summary from the epistemic uncertainty workshop:consensus amid diversity[J]. Reliability Engineering and System Safety, 2004, 85:355-369
[21] ZHANG F, XU X, WANG L, et al. Global sensitivity analysis of twostage thermoelectric refrigeration system based on response variance[J]. Intentional Journal of Energy Research, 2020, 44:6623-6630
[22] 吕震宙, 李璐祎, 宋述芳. 不确定性结构系统的重要性分析理论与求解方法[M]. 北京:科学出版社, 2016 LYU Zhenzhou, LI Luyi, SONG Shufang. Importance analysis theory and solution method of uncertain structural system[M]. Beijing:Science Press, 2016 (in Chinese)
[23] BOTEV Z I, GROTOWSKI J F, KROESE D P. Kernel density estimation via diffusion[J]. The Annals of Statistics, 2010, 38:2916-2957
[24] BOTEV Z I. Kernel density estimation using Matlab[EB/OL].(2015-12-30)[2020-09-19]. http://www.mathworks.us/matlabcentral/fileexchange/authors/27236 |
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