可靠度指标的等步长求法及其收敛性证明

Equal step iteration method for reliability index and its proof of convergence

针对现有一次二阶矩法进行可靠性指标求解不能保证收敛的情况,提出一个等步长迭代模式进行修正,克服了传统方法的不足,从而增大了二阶矩法求解可靠性指标的应用范围.给出了该方法的通用迭代过程,利用可靠度指标在标准正态空间中的几何意义,分别对极限状态面为凸、凹、平坦的情况,进行了该方法收敛性的证明,并提出了确定迭代步长的建议算法.通过实例,分析验证了该迭代方法的可行性.

In order to overcome the disadvantage that the convergence of first order-second moment （FOSM） method is not guaranteed, an equal step iteration method （ESIM） was proposed. The range of problems that can be solved by FOSM was expanded. A general iterative process was presented for ESIM. By utilizing the geometric interpretation of the limit state surface in the original space of random variables, the convergence of the iteration process was proved by classifying the limit state surface into three categories. A method for determining the length of each iteration step was also proposed. The correctness of ESIM was demonstrated by an example.