正态相关变量主客观不确定性分离和参数影响分析

吴丹清; 吕震宙; 程蕾

doi:10.6052/0459-1879-14-014

正态相关变量主客观不确定性分离和参数影响分析

doi: 10.6052/0459-1879-14-014

西北工业大学航空学院, 西安710072

基金项目: 国家自然科学基金（51175425）和博士学科点专项科研基金（20116102110003）资助项目.

详细信息

作者简介:
吕震宙，教授，主要研究方向：可靠性工程.E-mail：zhenzhoulu@nwpu.edu.cn

中图分类号: TB114.3
计量
- 文章访问数: 978
- HTML全文浏览量: 73
- PDF下载量: 680
- 被引次数: 0
出版历程
- 收稿日期: 2014-01-16
- 修回日期: 2014-04-18
- 刊出日期: 2014-09-18

AN SEPARATION OF THE ALEATORY AND EPISTEMIC UNCERTAINTIES WITH CORRELATED NORMAL VARIABLES AND ANALYSIS OF THE INFLUENCE OF PARAMETERS

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

Funds: The project was supported by the National Natural Science Foundation of China (51175425) and the Research Fund of Doctoral Program of High Education of China (20116102110003).

摘要

摘要: 针对主观和客观不确定性同时存在且输入变量相关的结构系统，研究分析了分布参数的主观不确定性对系统输出响应的影响. 首先采用正交变换进行了相关输入变量情况下主、客观不确定性的分离，通过引入独立标准正态空间辅助变量，使得分布参数的主观不确定性能够从输入变量客观不确定性中分离，进而分析分布参数的主观不确定性对输出响应的主效应指标. 其次验证了分布参数对模型输出响应期望影响的一阶方差贡献与主、客观不确定性分离后其对响应量一阶方差贡献的相等关系. 算例结果表明了文中所用主、客观不确定性分离方法的合理性和有效性.
- 主观不确定性 /
- 客观不确定性 /
- 分布参数 /
- 正交变换 /
- 一阶方差贡献
Abstract: For the structural system with correlated variables with aleatory and epistemic uncertainties, the influence of distribution parameters with epistemic uncertainty to the output is studied. Firstly, orthogonal transformation is used to separate the aleatory and epistemic uncertainties. The epistemic uncertainty is separated from the aleatory uncertainty of input variables through the auxiliary variable. After that, the main effect of distribution parameters to the model output is discussed. Secondly, the equality between the first order variance of parameters to the expectation of the output and the first order variance contribution of parameters to the output after separating uncertainties is validated. At last, some examples are utilized to demonstrate the rationality and efficiency of method used to separate the aleatory and epistemic uncertainties.
- epistemic uncertainty /
- aleatory uncertainty /
- distribution parameters /
- orthogonal transformation /
- first order variance contribution

HTML全文

参考文献(13)

Kiureqhian AD, Ditlevsen O. Aleatory or epistemic? Does it matter?. Structural Safety, 2009, 31(2): 105-112

Okerkampf WL, Helton JC, Joslyn CA, et al. Challenge problems: Uncertainty in system response given uncertain parameters. Reliability Engineering and System Safety, 2004, 85(1-3): 11-19

Guo J, Du XP. Sensitivity analysis with mixture epistemic and aleatory uncertainties. AIAA J, 2007, 45(9): 2337-2349

Hofer E, Kloos M, Krzykacz-Hansmann B, et al. An approximate epistemic uncertainty analysis approach in the presence of epistemic and aleatory uncertainties. Reliability Engineer System Safety, 2002, 77(3): 229-238

Helton JC, Johnson JD, Sallaberry CJ, et al. Survey of sampling-based method for uncertainty and sensitivity analysis. Reliability Engineering and System Safety, 2006, 91(10-11): 1175-1209

Saltelli A. Sensitivity analysis for importance assessment. Risk Analysis, 2002, 22(3): 579-590

Borgonovo E. Measuring uncertainty importance: Investigation and comparison of alternative approaches. Risk Analysis, 2006, 26(5): 1349-1361

Wang P, Lü ZZ. A generalized separation for the variance contributions of the aleatory and epistemic uncertainties. Structural Safety, with edit.

Wang P, Lü ZZ, Tang ZC. An application of the Kriging method in global sensitivity analysis with parameter uncertainty. Applied Mathematical Modeling, 2013, 37(9): 6543-6555

Sankararaman S, Mahadevan S. Separating the contributions of variability and parameter uncertainty in probability distributions. Reliability Engineering and System Safety, 2013, 112: 187-199

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. 北京: 科学出版社, 2009 (Lü Zhenzhou, Song Shufang, Li Hongshuang, et al. The Reliability and Reliability Sensitivity Analysis for Structure and Machine System. Beijing: Science Press, 2009 (in Chinese))

Saltelli A, Annoni P, Azzini I, et al. Variance based sensitivity analysis of model output. Design and estimator for the total sensitivity index. Computer Physics Communications, 2010, 181: 259-270

Allaire DL, Willcox K. A variance-based sensitivity index function for factor prioritization. Reliability Engineering and System Safety , 2012, 107: 107-114

施引文献

资源附件(0)

访问统计