建立船体结构疲劳设计曲线的贝叶斯方法

Bayesian Method for Establishing Fatigue Design Curves of Ship Structures

基于船体结构疲劳试验的小样本特点 ,探讨了建立疲劳设计曲线 (S N或P S N曲线 )的贝叶斯方法。将传统疲劳模型中的未知参数处理成离散型随机变量 ,利用贝叶斯公式求出参数向量的后验概率密度 ,在此基础上建立不同存活率下的贝叶斯疲劳设计曲线方程并编程求解。算例表明 ,贝叶斯方法不仅弥补了样本小带来的统计误差 。

It is important to establish reliable fatigue design curves( P S N curves) of ship structures based on laboratory fatigue test data. And it is also necessary to adapt a proper statistical method because of the relatively small fatigue data set of ship structures. In this paper, Bayesian method for establishing P S N curves is discussed. In this method, the unknown parameters in the fatigue method are considered as random quantities. By Bayesian theorem, a posterior joint propbability mass function of parameters is calculated, on the foundation of which, an equation of Bayesian P S N curves is established, and a computer program is developed. It is illustrated that the Bayesian method not only reduces the statistical error from small samples but also solves the problem of run out in the fatigue test data.