This paper develops a method for the time-dependent reliability analysis of deteriorating structures using phase-type (PH) distributions. The deteriorating model consists of two aspects: the progressive deterioration posed by aging effects, and the shock deterioration caused by random shocks. Evaluating the distribution of the sum of random variables is a tough work in the model. For simplified problems that random variables follow specific distributions with the convolutions being derived analytically, it is effective to utilize semianalytical methods for the time-dependent reliability analysis. For other general problems (the distribution does not have additivity or is even unknown, only with limited datasets), the semianalytical method will no longer be applicable. In dealing with such problems, PH fitting is utilized in the proposed model, i.e., any distribution or general datasets are approximated as PH distributions using Expectation Maximization algorithms. Owing to the good properties in convolution of PH distributions, the time-dependent reliability can be evaluated conveniently. Numerical examples are given to demonstrate the efficiency of the model proposed, and its accuracy is verified by comparing the model results with those of Monte Carlo simulation. The interaction between the degradation process and the shock process is also modeled and displayed with an example and discussion.

中文翻译：

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基于相型分布的劣化结构瞬态可靠性分析

本文开发了一种使用相型 (PH) 分布对老化结构进行瞬态可靠性分析的方法。恶化模型包括两个方面：老化效应造成的渐进恶化和随机冲击引起的冲击恶化。在模型中评估随机变量总和的分布是一项艰巨的工作。对于随机变量遵循特定分布且卷积是解析导出的简化问题，利用半解析方法进行瞬态可靠性分析是有效的。对于其他一般问题（分布没有可加性或什至是未知的，只有有限的数据集），半分析方法将不再适用。在处理此类问题时，所提出的模型中使用了 PH 拟合，即 ，使用期望最大化算法将任何分布或一般数据集近似为 PH 分布。由于 PH 分布的卷积具有良好的特性，因此可以方便地评估时间相关的可靠性。数值算例证明了所提出模型的有效性，并通过将模型结果与蒙特卡罗模拟的结果进行比较来验证其准确性。退化过程和冲击过程之间的相互作用也通过一个例子和讨论进行了建模和展示。数值算例证明了所提出模型的有效性，并通过将模型结果与蒙特卡罗模拟的结果进行比较来验证其准确性。退化过程和冲击过程之间的相互作用也通过一个例子和讨论进行了建模和展示。数值算例证明了所提出模型的有效性，并通过将模型结果与蒙特卡罗模拟的结果进行比较来验证其准确性。退化过程和冲击过程之间的相互作用也通过一个例子和讨论进行了建模和展示。