基于降维算法的结构可靠性分析

摘要

为解决工程实际中功能函数为高维非线性的可靠性分析问题,提出了基于降维算法的一种新型的直接结构可靠度的分析方法.利用降维算法,建立了新的n个一维函数模型近似替代原n维功能函数,借助于泰勒级数和统计矩理论,求解结构功能函数的前四阶矩信息,并通过Edgeworth级数拟合结构功能函数的累积分布函数,结合可靠性理论可计算得到结构的失效概率.与传统方法相比,本文方法无需积分求解功能函数的统计矩,也无需迭代搜索最可能失效点.数值算例结果表明本文方法具有较高的计算精度和较好的适应性.%Considering the high-dimensional non-linear performance functions of complex structures,a new structural reliability analysis method based on dimension reduction algorithm was proposed.The n one-dimensional approximate functions were established to substitute the n dimensional performance function by using dimension reduction algorithm.With the help of Taylor series and statistical moment theory,the first four order moments of the performance function were solved.The cumulative distribution function of the performance function was fitted by Edgeworth series and the failure probability of the structure was obtained based on the reliability theory.Compared with the traditional methods,the new method does not need to use integral method to solve the statistical moments of the performance function,and not need to search the most possible failure point iteratively.Numerical results indicate that the proposed method has high precision and good adaptability.