一个以遗传算法为基础的结构可靠性分析方法
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摘要
本文首先总结了一次二阶矩法在结构可靠性分析时的五个弱点。针对其在寻求验算点时需要求极限状态函数的导数以及在处理多峰性极限状态函数时存在的不收敛或收敛于局部验算点等弱点,探讨了将遗传算法应用于结构可靠性分析的可能性,并在分析其应用时存在的具体问题的基础上提出了一个以智能生物为基础的遗传算法。本文的分析计算表明:遗传算法在结构可靠性分析中是适用的,它可以克服一次二阶矩法在求解验算点时存在的几个弱点。本文提出的以智能生物为基础的遗传算法计算格式是对普通遗传算法的改良,它可以有效地改善遗传算法在结构可靠性分析中应用时存在的染色体长度问题及遗传算法欺瞒问题。
First Order Reliability Method (FORM) is considered as one of the most acceptable computational approximation in which the most likely failure point is searched by mathematical programing methods applying the gradients of performance function. It is difficult to be applied to reliability problems with smoothless,discrete,multi-peaked performance function,or with difficulty to obtain the gradients of performance function. This paper presents a genetic algorithm for searching the most likely failure point which is not limited by restrictive assumptions about search space such as continuity or existence of derivatives. The workings of genetic algorithm in structural reliability are investigated and three intellectual faculties are introduced to improve the search process. From some structural reliability examples using the GA search with the three intellectual faculties,it is found that the problems in deciding the length of strings can be effectively improved the genetic algorithm is applicable to structural reliability analysis and the weaknesses of FORM can be effectively avoided.
First Order Reliability Method (FORM) is considered as one of the most acceptable computational approximation in which the most likely failure point is searched by mathematical programing methods applying the gradients of performance function. It is difficult to be applied to reliability problems with smoothless,discrete,multi-peaked performance function,or with difficulty to obtain the gradients of performance function. This paper presents a genetic algorithm for searching the most likely failure point which is not limited by restrictive assumptions about search space such as continuity or existence of derivatives. The workings of genetic algorithm in structural reliability are investigated and three intellectual faculties are introduced to improve the search process. From some structural reliability examples using the GA search with the three intellectual faculties,it is found that the problems in deciding the length of strings can be effectively improved the genetic algorithm is applicable to structural reliability analysis and the weaknesses of FORM can be effectively avoided.
引文
1． Madsen,H.O.,Krenk,S.,and Lind,N.C.,Method of Structural Safety,Prentice-Hall.Inc.,Englewood Cliffs,N.J.,1986．
2． P., Bjerager, Methods for Structural Reliability Computation ,Reliability Problems:General Principles and Applications in Mechanics of Solid and Structures,Chapter3,Springer Varlag Wien-New York, 1991．
3． M, Shinozuka, Basic Analysis of Structural Safety,ASCE,Vol.109,ST3,1983．
4． 赵衍刚,江近仁,陈君娇.结构可靠性分析中各类不确定性的综合处理方法.地震工程与工程振动(投稿中)
5． Y.K.,Wen,H.C.,Chen,On Fast Integration for Time Variant Structural Reliability,Probabilistic Engineering Mechanics,Vol.2,No.3,1987．
6． 赵衍刚,江近仁.一个推广的一次二阶矩方法.地震工程与工程振动.12卷4期.1992．
7． Tvedt, L., Distribution of Quadratic Forms in the Normal Space-Application to Structural Reliability,J.of Engineering Mechanics,ASCE, 116(6) . 1990．
8． Der Kiureghian,A.,De Stefano,M.An Efficient Algorithm for Second Order Reliability Analysis,J.of Engineering Mechanics,ASCE,117(2) ,1991．
9． S.Englund,R.,Rackwitz,A Benchmark Study on Importance Sampling,Techniques in Structural Reliability,Structural Safety, Vol.2,p255-276,1993．
10． Bucher,C.G.,Adaptative Sampling: An Iferative Fast Monte Carlo Procedure,Structural Safety,Vol.5,No.2,1988．
11． Goldberg,D.E., Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley Publishing Company, 1989．
12． S.Rajeev, C.S., Krishnamoorthy, Discrete Optimization of Structures Using Genetic Algorithms,J.of Structural Engineering, ASCE,118(5) ,1992．
13． 杉本博之,鹿汴丽.离散的构造最适设计GA信赖性向上关研究,JSCE.No.471/I-24． 1993．
14． M.Hohenbichler,R.,Rackwitz,Non-Normal Dependent Vectors in Structural Safety,ASCE,Vol.107,EM6,1981．
2． P., Bjerager, Methods for Structural Reliability Computation ,Reliability Problems:General Principles and Applications in Mechanics of Solid and Structures,Chapter3,Springer Varlag Wien-New York, 1991．
3． M, Shinozuka, Basic Analysis of Structural Safety,ASCE,Vol.109,ST3,1983．
4． 赵衍刚,江近仁,陈君娇.结构可靠性分析中各类不确定性的综合处理方法.地震工程与工程振动(投稿中)
5． Y.K.,Wen,H.C.,Chen,On Fast Integration for Time Variant Structural Reliability,Probabilistic Engineering Mechanics,Vol.2,No.3,1987．
6． 赵衍刚,江近仁.一个推广的一次二阶矩方法.地震工程与工程振动.12卷4期.1992．
7． Tvedt, L., Distribution of Quadratic Forms in the Normal Space-Application to Structural Reliability,J.of Engineering Mechanics,ASCE, 116(6) . 1990．
8． Der Kiureghian,A.,De Stefano,M.An Efficient Algorithm for Second Order Reliability Analysis,J.of Engineering Mechanics,ASCE,117(2) ,1991．
9． S.Englund,R.,Rackwitz,A Benchmark Study on Importance Sampling,Techniques in Structural Reliability,Structural Safety, Vol.2,p255-276,1993．
10． Bucher,C.G.,Adaptative Sampling: An Iferative Fast Monte Carlo Procedure,Structural Safety,Vol.5,No.2,1988．
11． Goldberg,D.E., Genetic Algorithms in Search, Optimization, and Machine Learning, Addison-Wesley Publishing Company, 1989．
12． S.Rajeev, C.S., Krishnamoorthy, Discrete Optimization of Structures Using Genetic Algorithms,J.of Structural Engineering, ASCE,118(5) ,1992．
13． 杉本博之,鹿汴丽.离散的构造最适设计GA信赖性向上关研究,JSCE.No.471/I-24． 1993．
14． M.Hohenbichler,R.,Rackwitz,Non-Normal Dependent Vectors in Structural Safety,ASCE,Vol.107,EM6,1981．
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