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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.
The Hermite polynomial approximation method for structural reliability analysis is proposed.First, the basic properties of Hermite polynomials are introduced. Hermite orthogonal polynomials are proved to be good approximation of the probability density function curves of various classical theoretical distributions by numerical tests, especially in the Generally speaking, the 4th order Hermite polynomial can achieve satisfactory accuracy. Secondly, the calculation procedure of structural reliability based on Hermite orthogonal polynomial is given. Finally, the reliability of gravity dam is The results show that the Hermite orthogonal polynomial approximation method is an effective method for the reliability analysis of gravity dam, Hermite orthogonal polynomial approximation method can easily analyze the statistics of the output random response Parameters and the correlation between output response and input variables.