岩土工程可靠度分析的神经网络四阶矩法  

An ANN-based four order moments method for geotechnical engineering reliability analysis

作　　者：左育龙[1,2] 朱合华[1,2] 李晓军[1,2] 

机构地区：[1]同济大学岩土及地下工程教育部重点实验室,上海200092 [2]同济大学土木工程学院地下建筑与工程系,上海200092

出　　处：《岩土力学》2013年第2期513-518,共6页Rock and Soil Mechanics

摘　　要：针对岩土工程的功能函数强非线性且难以显式表达的特点,提出了基于人工神经网络的四阶矩法,充分利用了基本随机变量的统计信息。首先利用神经网络对结构的隐式功能函数进行拟合,求得基本随机变量在均值点处的功能函数值及其偏导数,然后利用泰勒级数展开的方法由基本随机变量的前四阶矩求得功能函数的前四阶矩,并借助于Pearson系统获得功能函数的更高阶矩。在此基础上,通过最大熵原理确定以功能函数各阶矩为约束的功能函数的概率密度函数,最后由一次积分得到结构的失效概率。通过数值算例和工程实例不同方法的对比分析,表明基于神经网络的结构可靠度分析四阶矩方法是可行的,有效的,能够满足岩土工程可靠度分析的要求。Strong nonlinear and implicit performance functions are normally encountered when geotechnical engineering is complicated.An artificial neural network（ANN）-based four order moments method,allowing to make full use of statistical information of basic random variables,is proposed to address this issue.In this method,the relation between the basic random variables and responses is established to approximate the implicit performance function;then the values of the implicit performance function in the mean point as well as partial derivatives can be obtained for the four order moments method.The first four order moments are approximated by expanding the implicit performance function into a second-order Taylor series;the corresponding higher-order moments can be estimated via Pearson curves.In restraint of the assigned moments of the implicit performance function,the probability density function of the performance function can be expressed by applying the maximum entropy theory.Subsequently,the reliability results are easily worked out.From the comparison between the results of numerical example and practical engineering calculated by different methods,it is shown that the proposed method is valuable and applicable to reliability analysis of complex geotechnical engineering involving implicit performance functions.

关 键 词：岩土工程 可靠度分析 隐式功能函数 BP神经网络 四阶矩 最大熵 

分 类 号：TU47[建筑科学—结构工程]