多项式基函数神经网络的结构可靠性分析

孟广伟; 李广博; 李锋; 周立明

多项式基函数神经网络的结构可靠性分析

吉林大学机械科学与工程学院, 长春 130025

基金项目: 吉林省科技厅基金资助项目（201205011，201215048）；国家重大科学仪器设备开发专项资助项目（2012YQ030075）

详细信息

中图分类号: TB114.3
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出版历程
- 收稿日期: 2013-03-20
- 网络出版日期: 2013-11-30

Structural reliability analysis based on polynomial basis function neural network

College of Mechanical Science and Engineering, Jilin University, Changchun 130025, China

摘要

摘要: 研究了多项式基函数神经网络法的结构可靠性计算.当结构的极限状态函数复杂，非线性程度较高，功能函数为隐式时，传统的结构可靠度分析方法计算困难，多项式基函数神经网络法为解决结构可靠性分析提供了一种新方法.基于多项式逼近理论，利用神经网络模拟逼近能力，将多输入多项式作为网络的激励函数，利用激励函数的广义逆矩阵形式计算网络隐层与输出层的连接权值，拟合结构的功能函数.利用可靠度的一阶可靠性方法计算结构的失效概率.通过实例计算，表明了本方法计算精度高，同时公式简单，易于编程，具有通用普遍性.
- 结构可靠性 /
- 多项式基函数 /
- 神经网络 /
- 广义逆矩阵 /
- 一阶可靠性方法
Abstract: The polynomial basis function neural network method for structural reliability calculation was adopted. When the limit state function of the structure is highly complex or with nonlinearity, sometimes, limit state function is implicit, the traditional method of structure reliability analysis calculation is time-consuming. The polynomial basis function neural network method provides an effective means for the reliability analysis of large scale structures. Based on the polynomial approximation theory, a pseudo-inverse of random variable input matrix was used to be incentive function to determine the weights between the hidden layer and output layer with the approximation of neural network. The failure probability was calculated by first-order reliability method (FORM). The numerical example results show the proposed method has ability of solving the structural reliability analysis problems. The test results show that the formula of the proposed method is simple and easy to program. A new method for solving the structural reliability analysis was displayed.
- structural reliability /
- polynomial basis function /
- neural network /
- generalized inverse matrix /
- first-order reliability method (FORM)

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参考文献(15)

[1]	张明.结构可靠度分析:方法与程序[M].北京:科学出版社, 2009:8-9 Zhang Ming.Structural reliability analysis:methods and procedures[M].Beijing:Science Press, 2009:8-9 (in Chinese)
[2]	贡金鑫.工程结构可靠度计算方法[M].大连:大连理工大学出版社, 2003:3-6 Gong Jinxin.Computational methods for reliability of engineering structures[M].Dalian:Dalian University of Technology Press, 2003:3-6 (in Chinese)
[3]	Wang Liping, Grandhi R V.Safety index calculation using intervening variables for structural reliability analysis[J].Computers and Structures, 1996, 59 (6):1139-1148
[4]	Kaymaz I, McMahon C A.A response surface method based on weighted regression for structural reliability analysis[J].Probabilistic Engineering Mechanics, 2005, 20 (1):11-17
[5]	Allaix D L, Carbone V I.An improvement of the response surface method[J].Structural Safety, 2011, 33 (2):165-172
[6]	李贵杰, 吕震宙, 赵新攀.基于加权线性响应面的结构可靠性估计的鞍点逼近方法[J].机械强度, 2010, 32 (6):917-921 Li Guijie, LÜ Zhenzhou, Zhao Xinpan.Saddle point approximation of structural reliability on weighted linear response surface method[J].Journal of Mechanical Strength, 2010, 32 (6):917-921 (in Chinese)
[7]	Gomes H M, Awruch A M.Comparison of response surface and neural network with other methods for structural reliability analysis[J].Structural Safety, 2004, 26 (1):49-67
[8]	Elhewy A H, Mesbahi E, Pu Y.Reliability analysis of structures using neural network method[J].Probabilistic Engineering Mechanics, 2006, 21 (1):44-53
[9]	Deng Jian, Gu Desheng, Li Xibing, et al.Structural reliability analysis for implicit performance function using artificial neural network[J].Structural Safety, 2005, 27 (1):25-48
[10]	陆强华.基于径向基函数神经网络的结构可靠性分析[J].中国科技信息, 2008, 20 (5):234-235 Lu Qianghua.Structural reliability analysis based on radial basis function neural network[J].China Science and Technology Information, 2008, 20 (5):234-235 (in Chinese)
[11]	章兢, 邹阿金, 童调生.多项式基函数神经网络模型[J].湖南大学学报, 1996, 23 (2):84-89 Zhang Jing, Zou Ajin, Tong Tiaosheng.A neural network based on polynomial basis functions[J].Journal of Hunan University, 1996, 23 (2):84-89 (in Chinese)
[12]	曹飞龙, 张永全, 张卫国.单隐层神经网络与最佳多项式逼近[J].数学学报, 2007, 50 (2):385-392 Cao Feilong, Zhang Yongquan, Zhang Weiguo.Neural networks with single hidden Layer and the best polynomial approximation[J].Acta Mathematica Sinica, 2007, 50 (2):385-392 (in Chinese)
[13]	梁学章, 李强.多元逼近[M].北京:国防工业出版社, 2005:4-6 Liang Xuezhang, Li Qiang.Multivariate approximation[M].Beijing:National Defense Industry Press, 2005:4-6 (in Chinese)
[14]	吕震宙, 杨子政, 赵洁.基于加权线性响应面法的神经网络可靠性分析方法[J].航空学报, 2006, 27 (6):1063-1067 LÜ Zhenzhou, Yang Zizheng, Zhao Jie.An artificial neural network method for reliability analysis based on weighted Linear response surface[J].Acta Aeronautica Et Astronautica Sinica, 2006, 27 (6):1063-1067 (in Chinese)
[15]	Ren Yuan, Bai Guangchen.New neural network response surface methods for reliability analysis[J].Chinese Journal of Aeronautics, 2011, 24 (1):25-31