| 俞水,汪忠来.基于首次穿越时间概率密度的时变可靠性分析[J].计算力学学报,2020,37(3):300~306 |
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| 基于首次穿越时间概率密度的时变可靠性分析 |
| Time-dependent reliability analysis based on probability density of first-passage time point |
| 投稿时间：2019-04-16 修订日期：2019-06-04 |
| DOI：10.7511/jslx20190416001 |
| 中文关键词: 时变可靠性 首次穿越时间概率密度 原点矩 最大熵估计 累计概率密度函数 |
| 英文关键词:time-dependent reliability first-passage time probability density origin moments maximum entropy method cumulative probability density function |
| 基金项目:国家自然科学基金（11472075）资助项目. |
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| 摘要点击次数: 838 |
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| 中文摘要: |
| 基于时变可靠性性能函数首次穿越时间的概率密度F-PTPD（first-passage time probability density）模型，提出了一种求解机械产品全寿命周期可靠性累计概率密度函数的方法（简称F-PTPD方法），为产品在全寿命周期内可靠性分析和设计提供了工具。首先，采用稀疏网络随机配置方法进行时变可靠性性能函数均值的估计，选取性能函数均值为零的第一个时刻点作为首次穿越点；其次，基于均值的首次穿越点将时变可靠性性能函数进行二阶泰勒展开，利用二次函数的性质求解性能函数首次穿越时间关于随机输入变量的函数；再次，针对首次穿越点函数，采用稀疏网络随机配置方法进行首次穿越时间的四阶原点矩估计；最后，基于四阶原点矩利用最大熵概率密度函数估计方法，推导出首次穿越点的概率分布，获得产品寿命周期内时变可靠性的累计概率密度函数。本文方法可获得产品整个寿命周期失效概率的变化趋势，极大地提高了评估效率，对复杂产品的可靠性评估设计有一定的工程指导意义。 |
| 英文摘要: |
| Based on the first-passage time probability density (F-PTPD) for the time-dependent limit state function,an approach for estimating the cumulative probability density function of mechanical products over the whole lifecycle is proposed,which provides an effective analytical method for reliability analysis and design of mechanical products.Firstly,the sparse grid based stochastic collocation method is employed to obtain the mean value function of time-dependent limit state function,and the first-passage time point of the mean value function is obtained while the mean value function equals zero.The limit state function is then decomposed into a second-order Taylor series about time,meanwhile,the first-passage time point function about input random variables is established via using the property of the quadratic function.The fourth origin moments of the first-passage time point function are estimated by employing the sparse grid based stochastic collocation method.Finally,the probability model of the first-passage time point for the limit state function can be obtained by the combination of the fourth origin moments and the maximum entropy method,so the cumulative probability density function can be estimated. |
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