二维联合分布函数构造方法及其对结构可靠度的影响分析

研究了2种构造联合分布函数的近似方法:基于Pearson相关系数的近似方法 P和基于Spearman相关系数的近似方法 S。推导了基于直接积分方法的构件失效概率计算公式。结果表明近似方法 P与近似方法 S构造的联合概率密度函数的唯一差别是相关标准正态空间中Pearson相关系数的不同。2种近似方法的构件失效概率的计算精度取决于失效概率大小、功能函数形式及变量间相关程度。总体来说2种近似方法的计算精度较高,近似方法的失效概率的误差随着失效概率的减小而增加。只有当失效概率小于10 3且失效区域刚好可以反映失效概率差异时,近似方法得到的失效概率才会有较大的误差。

BIVARIATE CONSTRUCTION METHODS AND ITS EFFECT ON STRUCTURAL RELIABILITY

Two bivariate construction methods are investigated,namely,the approximation method P using the Pearson correlation coefficient and the approximate method S using the Spearman correlation coefficient.The formulae for component probability of failure based on a direct integration are derived.The results indicate that the only difference in the joint PDFs between the approximate method P and the approximate method S is the Pearson correlation coefficient between two correlated standard normal variables.The errors in probabilities of failure for the two approximate methods highly depend on the level of probability of failure,the form of a performance function,and the degree of correlation.Such errors increase significantly with decreasing probabilities of failure.Significant errors in component probabilities of failure from the two approximate methods will be obtained only when the failure domain is able to capture the significant difference in the joint PDF surfaces and the component probability of failure is lower than 10-3.