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分析了结构系统可靠度计算与多维正态积分之间的转化关系,以及原有的用于多维正态积分计算的条件边缘乘积法的不足之处,从条件正态分位数计算和相关系数矩阵修正两方面给出改进措施,形成一种改进的条件边缘乘积法。该方法采用数值积分方法进行二维正态分布函数的计算,提高原有方法中条件正态分位数计算的精度,并在此基础上对各相关系数矩阵进行修正,从而有效提高了原有方法在串联系统可靠度计算中的精度。同时,将这一改进方法与单失效模式下的结构可靠度显式迭代算法相结合,提出从单元到系统的结构系统可靠度分析流程。数值算例表明了这一改进方法的有效性和实用性。
The relationship between structural system reliability calculation and multi-dimensional normal integral is analyzed, and the deficiencies of the original conditional edge product method for multi-dimensional normal integral calculation are analyzed. From the calculation of conditional normal quantile and the correlation coefficient Correction measures are given both in matrix correction and form an improved conditional edge product method. The method uses the numerical integral method to calculate the two-dimensional normal distribution function, improves the accuracy of the calculation of the conditional normal quantile in the original method, and on the basis of which, corrects each correlation coefficient matrix, thereby effectively improving the original The accuracy of the method in the reliability calculation of series system. At the same time, this improved method is combined with the explicit iterative algorithm of structural reliability under single failure mode, and the structural system reliability analysis flow from unit to system is proposed. Numerical examples show the effectiveness and practicability of this improved method.