基于神经网络和Laplace渐近方法的边坡可靠度分析  

Reliability Analysis of Slope Based on Neural Network and Laplace Asymptotic Method

作　　者：张东升[1] 舒苏荀 龚文惠[1] ZHANG Dongsheng;SHU Suxun;GONG Wenhui(School of Civil and Hydraulic Engineering,Huazhong University of Science and Technology,Wuhan 430074,China;School of Civil Engineering and Architecture,Wuhan Institute of Technology,Wuhan 430074,China)

机构地区：[1]华中科技大学土木与水利工程学院,湖北武汉430074 [2]武汉工程大学土木工程与建筑学院,湖北武汉430074

出　　处：《土木工程与管理学报》2022年第4期131-136,共6页Journal of Civil Engineering and Management

基　　金：国家自然科学基金(52178217,52008319)。

摘　　要：针对功能函数高度非线性且难以显式表达的岩土工程问题,考虑高度非线性问题采用传统一次可靠度求解方法有较大误差,提出利用BP神经网络模型来拟合岩土体的隐式功能函数,并结合精度较高的二次二阶矩法中的Laplace渐近方法求解可靠度;采用拉丁超立方抽样法对各随机变量进行抽样,将样本数据带入BP神经网络训练并验证其精度,基于神经元之间的函数关系推导功能函数的拟合表达式,采用二次二阶矩方法中的Laplace渐近方法,结合含有大参数的Laplace型积分公式推导对应的失效概率表达式;通过边坡算例表明:本文提出的方法是可行有效的,具有较高的计算效率和计算精度,在岩土工程的可靠度分析研究中有较强的实用价值。For geotechnical problems that are highly non-linear in performance functions and difficult to express explicitly, and the traditional first-order reliability solution method for highly non-linear problems has larger errors, we can use the BP neural network model with strong nonlinear fitting ability to fit the implicit performance function of rock and soil, combine with Laplace asymptotic method in the second-order second moment method with higher accuracy to solve the reliability. Latin hypercube sampling method is used to sample each random variable, the sample data is brought into the BP neural network training and its accuracy is verified, and the fitting expression of the performance function is derived based on the functional relationship between neurons. Laplace asymptotic method in the second-order second moment method is used to derive the corresponding failure probability expression in combination with the Laplace type integral formula containing large parameters. A slope calculation example shows that the method proposed in this paper is feasible and effective with high calculation accuracy and efficiency, and has strong practical value in the reliability analysis and research of geotechnical engineering.

关 键 词：可靠度 BP神经网络 拉丁超立方抽样 Laplace渐近方法 边坡 

分 类 号：TU43[建筑科学—岩土工程] TB114.3[建筑科学—土工工程]