复杂混联体系失效区域的确定与积分方法比较

Determination of failure domain and comparison of integral methods for complex compound systems

为研究复杂混联体系失效区域的快速确定,采用体系失效域可视为若干维变量取定值时条件失效区间的集合的思路,提出了一种基于体系组成方式的失效域确定方法。该方法依据体系失效曲面的混联组成方式,确定出当其余维变量取定值时沿某坐标轴方向直线与体系失效边界的交点,获得对应的条件失效区间。应用该方法对多个算例进行了可靠度分析,结果证实:当失效边界较为复杂时,采用较多积分节点的梯形积分(Trapezoid integration)方法精度较好且稳定;而Gauss-Hermite或Gauss-Legendre积分方法的精度则依赖于计算时选用的坐标系或积分区间,若选用不当则失效概率将会相差数倍以上。研究表明基于体系组成方式的失效域确定方法具有较好的效果;当能接受较多计算量时,采用梯形积分方法来计算复杂混联体系可靠度是一个较好的选择。

To rapidly determine the failure domains for a complex compound system,a method based on system constitution is proposed to rapidly determine the failure domain by a strategy that the system failure domain is a set of conditional failure domains with several variables that have given values.This method follows the criterions of the compound system failure surface to search for the intersections between a line parallel to a certain coordinate axis and the system failure boundary when other variables have given values.Therefore,the conditional failure domains can be obtained accordingly.Based on this method,reliability analyses of multiple numerical examples are carried out.The results show that when the failure boundary is a complex one,the accuracy of the trapezoid integration would be stable by increasing the number of integral nodes; that the accuracy of the Gauss-Hermite integration or the Gauss-Legendre integration would depend on the coordinates or the integration ranges used for calculation,and if they are used to choose inappropriately,the failure probability would be as much as several times of the actual one.The studies indicate that the pro-posed method based on system constitution perform well for the determination of the system failure domain; that the trapezoid integration method would be better choice for the reliability calculation of complex compound systems if higher computation cost is acceptable.