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基于支持向量机的序列可靠性优化方法
引用本文:王宇,余雄庆,杜小平.基于支持向量机的序列可靠性优化方法[J].计算力学学报,2013,30(4):485-490.
作者姓名:王宇  余雄庆  杜小平
作者单位:1. 南京航空航天大学航空宇航学院,南京,210016
2. 密苏里科技大学机械与航空航天工程系,密苏里州65409
基金项目:中国博士后基金(2011M500919)资助项目.
摘    要:在工程设计中,可靠性优化设计通常计算量较大或精度不够。本文提出了一种基于支持向量机(Support Vector Machine)和MPP(Most Probable Point)的可靠性分析方法。用SVM 在MPP处替代原极限状态函数,并利用极限状态函数的梯度信息,使SVM模型穿过M PP并与原函数相切,再基于SVM采用重要抽样法计算失效概率。然后,将SORA(Sequential Optimization and Reliability Assessment )与基于SVM 的可靠性分析方法相集成,将传统的双循环可靠性优化算法解耦为单循环,并通过基于SVM 的可靠性分析方法修正了SORA中由于线性近似带来的误差,保证了最优设计点处可靠性分析的精度。算例证明,该方法在处理非线性问题时具有精确度高和计算量适度的特点。

关 键 词:可靠性  优化  支持向量机
收稿时间:2012/3/19 0:00:00
修稿时间:7/6/2012 12:00:00 AM

Sequential reliability-based optimization with support vector machines
WANG Yu,YU Xiong-qing and DU Xiao-ping.Sequential reliability-based optimization with support vector machines[J].Chinese Journal of Computational Mechanics,2013,30(4):485-490.
Authors:WANG Yu  YU Xiong-qing and DU Xiao-ping
Institution:School of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;School of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;Department of Mechanical and Aerospace Engineering, Missouri University of Science and Technology, MO, 65409, USA
Abstract:Traditional reliability-based design optimization (RBDO) is either computational intensive or not accurate enough.In this work,a new RBDO method based on Support Vector Machines (SVM) is proposed.For reliability analysis,SVM is used to create a surrogate model of the limit-state function at the Most Probable Point (MPP).The uniqueness of the new method is the use of the gradient of the limit-state function at the MPP.This guarantees that the surrogate model not only passes through the MPP but also is tangent to the limit-state function at the MPP.Then Importance Sampling (IS) is used to calculate the probability of failure based on the surrogate model.This treatment significantly improves the accuracy of reliability analysis.For optimization,the Sequential Optimization and Reliability Assessment (SORA) is employed,which decouples deterministic optimization from the SVM reliability analysis.The decoupling makes RBDO more efficient.The two examples show that the new method is more accurate with a moderately increased computational cost.
Keywords:reliability  optimization  support vector machines
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