| 程蕾,吕震宙,王攀.状态模糊下主客观不确定性同时存在的重要性测度分析[J].计算力学学报,2014,31(1):72~77 |
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| 状态模糊下主客观不确定性同时存在的重要性测度分析 |
| Importance analysis in the presence of epistemic and aleatory uncertainties under fuzzy state |
| 投稿时间：2012-07-11 修订日期：2012-12-28 |
| DOI：10.7511/jslx201401013 |
| 中文关键词: 状态模糊 主观不确定性 重要性测度 移动最小二乘 比例系数 |
| 英文关键词:fuzzy state epistemic uncertainty importance measure Move Least Square method proportional coefficient |
| 基金项目:国家自然科学基金（51175425）；航天支撑基金（2011XW010001）；航空基金（2011ZA53015）；博士学科点专项科研基金（20116102110003）资助项目. |
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| 中文摘要: |
| 为了分析状态模糊下主观不确定性对失效概率的影响，定义了两种重要性测度指标：相关系数和相关比。针对传统的Monte Carlo方法计算量大的缺点，利用近似方法引入一个比例系数C将三层Monte Carlo循环简化成双层循环。为了进一步减小计算量，本文建立了一种状态模糊下主客观不确定性同时存在时重要性测度指标求解的移动最小二乘MLS（Move Least Square）法。该方法通过移动最小二乘策略拟合主观变量与响应量输出之间的映射关系，并根据此关系可以很方便地得到模型的条件响应输出，进而得到主客观不确定性同时存在情况下的重要性测度。本文算例验证了所提方法的效率和精度。 |
| 英文摘要: |
| To analyze the effect of epistemic uncertainty on failure probability under the condition of fuzzy state,two importance measures:Correlation Coefficient and Correlation Ration are defined. For the problem of large computational cost of Monte Carlo method,an approximate method is utilized by introducing a proportional coefficient to decrease a "three-loop" procedure to a "double-loop" procedure. In order to decrease the computational cost further,a novel Moving Least Square (MLS) method is constructed in the presence of epistemic and aleatory uncertainties. This method fits the approximate mapping relationship between epistemic parameters and output by moving least square strategy,which can be used to compute the conditional expectation of output conveniently,and then the proposed importance measure can be obtained. Some examples are employed to validate the reasonability and efficiency of the proposed method. |
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