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Time-dependent reliability analysis based on probability density of first-passage time point

DOI：

 作者 单位 E-mail 俞水 电子科技大学 yushuiuestc@163.com 汪忠来 电子科技大学 wzhonglai@uestc.edu.cn

基于时变可靠性性能函数首次穿越时间的概率密度(first-passage time probability density，F-PTPD)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，利用均值为零得到性能函数均值的穿越点并选取首次穿越点；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。

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 to zero. The limit state function is then decomposed a quadratic function 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 central moments of the first-passage time point function are estimated by employed the sparse grid based stochastic collocation method. Finally, the probability model of the first-passage time point for the limit state function a can be obtained by the combination of the fourth central moments and the maximum entropy method and so the cumulative probability density function can be estimated.
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