基于Hermite正交多项式逼近法的重力坝可靠度分析

Reliability analysis of gravity dam using Hermite orthogonal polynomials approximation method

提出了结构可靠度分析的Hermite正交多项式逼近法.首先介绍了Hermite多项式的基本性质,通过数值检验,证明Hermite正交多项式可以很好地逼近各种经典理论分布的概率密度函数曲线,尤其在宽区间两端拟合得非常好,一般来说,4阶Hermite多项式就可以达到满意的精度;其次,给出了基于Hermite正交多项式的结构可靠度计算步骤;最后以重力坝可靠度问题为例证明了所提方法的正确性和有效性.结果表明:Hermite正交多项式逼近法是重力坝可靠度分析的一种有效方法,Hermite正交多项式逼近法可以方便地分析输出随机响应量的统计参数以及输出响应量和输入变量间的相关性.

This paper aims to propose a reliability method based on Hermite orthogonal plynomials approximation.Firstly,the Hermite polynomials are briefly introduced,which can approximate the probability density function of various classical distributions well,especially for the tail shape of the probability density function curve.In general,a fourth order Hermite polynomial can obtain the results with sufficient accuracy.Secondly,the procedure for reliability analysis using the Hermite polynomial is presented in detail.Finally,an example of reliability analysis for gravity dam is investigated to demonstrate the validity and effectiveness of the proposed method.The results indicate that the Hermite orthogonal polynomial approximation method can evaluate the reliability of gravity dam accurately and efficiently.Furthermore,the statistics of output response,the correlation between the output and the input variables can be calculated readily by the proposed method.