There are two primary challenges in current fatigue load probability modeling. Firstly, it is difficult to measure the estimation errors in the mixture model for fatigue loads, particularly in the tails with low-probability and high-stress levels. Secondly, the component number of the mixture model cannot be observed. To address these challenges, this research introduces the hierarchical Bayesian mixture model and the Dirichlet process prior. A relative error measure is proposed to reveal the errors of the density tails. The results of an illustrative example show significant relative errors in the tails and a discrete distribution of the mixture number.

中文翻译：

---

使用分层贝叶斯模型的疲劳载荷混合模型的不确定性量化

当前的疲劳载荷概率建模存在两个主要挑战。首先，很难测量疲劳载荷混合模型中的估计误差，特别是在低概率和高应力水平的尾部。其次，无法观察到混合模型的成分数。为了应对这些挑战，本研究引入了分层贝叶斯混合模型和 Dirichlet 过程先验。提出了一种相对误差度量来揭示密度尾部的误差。说明性示例的结果显示了尾部的显着相对误差和混合数的离散分布。