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论文:2013,Vol:31,Issue(6):865-870 |
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引用本文： |
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吕召燕, 吕震宙. 基于条件期望的子集模拟法[J]. 西北工业大学 |
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L�Zhaoyan, L�Zhenzhou. A Subset Simulation Method Based on Conditional Expectation[J]. Northwestern polytechnical university |
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| 基于条件期望的子集模拟法 |
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| 吕召燕, 吕震宙 |
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| 西北工业大学 航空学院, 陕西 西安 710072 |
| 摘要: |
| 为减小传统子集模拟法求解失效概率及可靠性灵敏度估计值的方差,提出了一种基于条件期望的子集模拟方法,其理论基础是全方差公式,即多维变量条件期望的方差不大于变量自身的方差。所提方法将传统子集模拟法中计算失效概率和可靠性灵敏度的多维综合变量均值的估计转换为条件期望均值的估计,并将条件期望均值的两重概率估计进一步转换成可采用核密度进行计算的积分形式,从而可以在不增加传统子集模拟法计算量的条件下减小估计值的方差。最后通过算例计算进一步验证了理论分析的正确性:基于条件期望的子集模拟方法有效地减小了失效概率和灵敏度计算结果的方差,提高了计算的收敛性和稳定性。 |
| 关键词:
子集模拟
条件期望
核密度
方差
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| A Subset Simulation Method Based on Conditional Expectation |
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| L�Zhaoyan, L�Zhenzhou |
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| College of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, China |
| Abstract: |
| In order to reduce the variance in estimating the probability failure and reliability sensitivity, an im-proved subset simulation method is put forward.The proposed method is based on total variance formula in which the variance of the multidimensional variables with conditional expectation is not greater than that of the variables themselves.So that the mean of multidimensional variables to estimate the probability failure and reliability sensitiv -ity is transformed into the mean of conditional expectation in this paper.The latter contains twofold probability esti-mation and then is converted into an integral form that can be estimated with kernel density to reduce the variance without calculation increasing.Finally, some examples demonstrate that the theoretical analysis is correct and the proposed method reduces the variance and improves the convergence and stability in calculating the probability fail -ure and reliability effectively. |
| Key words:
subset simulation
conditional expectation
kernel density
variance
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| 收稿日期: 2013-04-15
修回日期:
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| DOI: |
| 基金项目: 国家自然科学基金(51175425);博士学科点专项科研基金(2011610211003)资助 |
| 通讯作者:
Email： |
| 作者简介: 吕召燕(1987-),女,西北工业大学硕士研究生,主要从事飞行器结构设计及可靠性研究。
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参考文献: |
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