一种新的结构可靠度通用计算方法

根据可靠度指标β的几何定义,运用具有全局优化能力的改进遗传算法,提出一种新的结构可靠度通用计算方法。针对可靠度几何优化模型搜索区域大而可行区域小的特点,在可靠区域和失效区域分别产生初始种群,在两种群之间通过不断迭代的二分法,使二分点不断接近极限状态曲面(线),从而产生可行解。对可行解进行选择、交叉、变异,最后求出全局最优解。该方法不需要使用结构功能函数的偏导数,对于功能函数不能明确表达的可靠度问题尤为适用;对于功能函数可以明确表达但求导复杂的问题,可省去求导过程;可任意设定初始值,且不受结构功能函数凹凸性的限制;通过算例验证,所提方法具有较高的精度和效率。

A New General Approach for Computing Structural Reliability Index

Based on geometric definition of reliability index in the normal space,a new general approach for computing structural reliability index is proposed by applying genetic algorithms for optimization in the whole space. To large search space and small feasible space of the optimization model,two initial populations are generated in the space of G>0 (the safe domain) and G<0 (the failure domain),respectively,and then a bisection method is applied iteratively to generate a new population on the lines between a population located in G>0 and another population located in G<0. In this way,the new population will approach to the limit state function gradually. Reproduction,crossover,and mutation will be applied for the new population till converging to the optimal or approximate optimal solution. This approach is especially suitable for analyzing the reliability of large-scale structures and those possessing the complicit or implicit performance function because it does not utilize gradients of the structural performance function in the search process. Moreover,initial populations are generated randomly and performance function is not restricted by concave and protruding. The method is tested to be very accurate and efficient by two different types of numerical examples.