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该文目的在于研究二维联合概率密度函数构造方法对结构系统可靠度的影响规律。首先简要介绍了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。提出了基于直接积分方法的并联系统失效概率计算方法。算例结果表明2种近似方法计算的系统失效概率误差取决于系统失效概率的大小、功能函数的形式以及功能函数间相关程度。系统失效概率越小,近似方法计算的系统失效概率误差越大。当系统失效概率小于10 3量级时,近似方法计算的系统失效概率误差较大,工程应用中应该引起足够的重视。功能函数间负相关时近似方法的误差明显大于功能函数间正相关时的误差。此外,系统失效概率误差并不是随着功能函数间相关性的增加而单调增加。
The purpose of this paper is to study the influence of the construction method of two-dimensional joint probability density function on the structural system reliability. Firstly, two approximate methods of constructing joint distribution function are briefly introduced: the approximate method P based on Pearson correlation coefficient and the approximate method S based on Spearman correlation coefficient. A method of calculating the failure probability of parallel system based on direct integral method is proposed. The results show that the probability of system failure probability calculated by two kinds of approximate methods depends on the size of system failure probability, the form of function function and the correlation between function functions. The smaller the probability of system failure, the greater the probability of system failure probability calculated by the approximate method. When the probability of system failure is less than 10 3, the probability of system failure probability calculated by the approximate method is larger, which should be paid enough attention in engineering application. The error of the approximate method when the function is negatively correlated is obviously larger than the error when the function is positively correlated. In addition, the error of system failure probability does not increase monotonically with the increase of the correlation between function functions.