基于显式迭代算法的可靠性灵敏度分析

Reliability Sensitivity Analysis based on Explicit Iterating Algorithm

随着科学技术的发展,机械产品的组成和功能日益庞大,其性能极限状态函数也越趋复杂。改进一次二阶矩法在机械结构的可靠性灵敏度分析中应用最为广泛,但是对于复杂极限状态函数而言,其计算效率却非常低,原因是该方法的每个迭代过程都需要通过求解极限状态方程来获得可靠度指标。基于改进的一次二阶矩法,通过极限状态函数的均值、标准差和灵敏度系数显式表达出可靠度指标,根据表达式的不同,提出了2种可靠度的显式迭代算法,该方法能够有效地避免改进的一次二阶矩法需要列方程求解可靠度指标的缺点,具有简单的计算形式,利于编程的实现。算例表明,提出的2种显式迭代算法的迭代结果相同且近似等于改进的一次二阶矩法的结果,提高了计算效率和精度。

With the development of science and technology,the components and functions of mechanical products,along with their performance limit state functions,have become increasingly complex.The improved first-order second-moment method was most widely used in the reliability sensitivity analysis of mechanical structures,while the computational efficiency was extremely inefficient for complex limit state functions,because the each iteration of the method needed to calculate the reliability index by solving the limit state equation.The reliability index was obtained by using the normalized mean and standard deviation and sensitivity coefficient of limit state functions.Based on the improved first-order second-moment method,two explicit iterating algorithms for reliability were proposed.This method can effectively avoid the disadvantage of solving the equation for reliability index of the improved first-order second-moment method,which had the simple computation form and was conducive to realize programming.The example showed that the iterative results of the two explicit iterating algorithms proposed were the same and approximately equal to the results of the improved first-order second-moment algorithm,which improved both the computational efficiency and the computational accuracy.