基于BP神经网络和一次二阶矩法的结构可靠度分析  

Structural reliability analysis based on BP neural network and first-order second-moment method

作　　者：刘敬敏 王文涛 夏雨[1] LIU Jingmin;WANG Wentao;XIA Yu(School of Civil Engineering and Architecture,Guangxi University of Science and Technology,Liuzhou 545006,China)

机构地区：[1]广西科技大学土木建筑工程学院,广西柳州545006

出　　处：《广西科技大学学报》2023年第1期36-42,72,共8页Journal of Guangxi University of Science and Technology

基　　金：广西科技基地和人才专项项目(桂科AD19245125);柳州市科技计划项目(2021CBA0105);广西高校中青年教师基础能力提升项目(2019KY0375);广西自然科学基金面上项目(2020GXNSFAA297203)资助。

摘　　要：工程结构的功能函数大多为隐式表达式,使得以功能函数的显式表达式为基础的可靠度计算方法难以应用。为此,基于BP神经网络法和一次二阶矩法,根据结构随机变量的统计特性进行随机抽样获取有限数量的样本点,计算出每组样本点下结构的响应值;然后,将其代入由结构响应容许值与实际响应值建立的功能函数中,得到每组样本点下结构的功能函数值;利用BP神经网络对功能函数进行拟合,得到其显式表达式之后,采用一次二阶矩法计算结构可靠度,提出了一种针对隐式功能函数的结构可靠度分析方法。本文方法可以将结构的隐式功能函数进行拟合,从而得到显式功能函数,并最终利用基于显式功能函数的可靠度算法来计算结构可靠度。算例分析表明,本文方法能正确计算结构的验算点和可靠指标,具有较高的计算精度,为功能函数无法显式表达的结构可靠度分析提供了一种可行的方法。Most of the engineering performance functions are implicit expressions,so it is difficult to apply the reliability calculation method based on the explicit expression of performance functions.In this paper,based on the BP neural network method and the first-order second-moment method,firstly,a limited number of sample points were obtained by random sampling according to the statistical characteristics of structural random variables,and the response values of the structure under each group of sample points were calculated.Then they were substituted into the performance function established by the allowable response value and the actual response value of the structure,and got the function value of the structure under each group of sample points.Then,the BP neural network was used to fit the function value of the structure,and its explicit expression was obtained.Finally,the first-order second-moment method was used to calculate the structural reliability,and a structural reliability analysis method for implicit function was proposed.This method can fit the implicit function of the structure to get the explicit function,and finally the reliability algorithm is used based on the explicit function to calculate the structural reliability.The example analysis shows that the method in this paper can correctly calculate the checking point and reliability index of the structure,and has high calculation accuracy,which provides a feasible method for the structural reliability analysis of which the performance function cannot be explicitly expressed.

关 键 词：一次二阶矩法 BP神经网络 功能函数 可靠度分析 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]