改进的非概率可靠性全局最优解方法
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摘要
对于非概率可靠度指标的求解,改进的一维优化算法计算简便但仅能搜索到部分可能失效点,全局最优解法可搜索所有可能失效点但计算量过大.鉴于此种情况,论文将改进的一维优化算法与全局最优解法相结合,吸收两种方法的优点提出改进的全局最优解法.提出的方法通过变量的单调性来确定变量的取值,在不遗漏可能失效点的前提下,减少根值方程组的数目,从而降低计算量,提高计算效率.通过算例分析,证明了提出的改进的全局最优解法的有效性和可行性.
To solve non-probabilistic reliability,the improved one-dimensional optimization algorithm can be easily used,which,however,only searches part of the probable failure points.The global optimization method,on the other hand,although capable of searching all the probable failure points,requires a large amount of calculation.In view of such situation,an improved global optimization method is proposed in this study by combining the improved one-dimensional optimization algorithm with the global optimization method.The presented method possesses the advantages of both the improved one-dimensional optimization algorithm and the global optimization method,by means of which,the values of variables are determined based on the monotonicity of variables.Without losing any probable failure points,this method is contributive to reducing the number of root point equations,lowering the computational complexity,and improving the computational efficiency.The effectiveness and feasibility of the presented method are verified by examples.
To solve non-probabilistic reliability,the improved one-dimensional optimization algorithm can be easily used,which,however,only searches part of the probable failure points.The global optimization method,on the other hand,although capable of searching all the probable failure points,requires a large amount of calculation.In view of such situation,an improved global optimization method is proposed in this study by combining the improved one-dimensional optimization algorithm with the global optimization method.The presented method possesses the advantages of both the improved one-dimensional optimization algorithm and the global optimization method,by means of which,the values of variables are determined based on the monotonicity of variables.Without losing any probable failure points,this method is contributive to reducing the number of root point equations,lowering the computational complexity,and improving the computational efficiency.The effectiveness and feasibility of the presented method are verified by examples.
引文
[1]Ben Haim Y.A non-probabilistic measure of reliability of linear systems based on expansion of convex models[J].Structural Safety,1995,17(2):91-109.
[2]Ben Haim Y,Elishakoff I.Convex Models of Uncertainty in Applied Mechanics[M].Amsterdam:Elsevier Science,1990.
[3]Ben Haim Y.A non-probabilistic concept of reliability[J].Structural Safety,1994,14(4):227-245.
[4]Ben Haim Y.Robust Reliability in the Mechanical hanical Sciences[M].Berlin:Springer Verlag,1996.
[5]郭书祥,吕震宙,冯元生.基于区间分析的结构非概率可靠性模型[J].计算力学学报,2001,18(1):56-60.(Guo S X,Lv Z Z,Feng Y S.A non-probabilistic model of structural reliability based on interval analysis[J].Chinese Journal of Computational Mechanics,2001,18(1):56-60.(in Chinese))
[6]郭书祥,吕震宙.结构体系的非概率可靠性分析方法[J].计算力学学报,2002,19(3):332-335.(Guo S X,Lv Z Z.A procedure of the analysis of non-probabilistic reliability of structural systems[J].Chinese Journal of Computational Mechanics,2002,19(3):332-335.(in Chinese))
[7]郭书祥,吕震宙.基于非概率模型的结构可靠性优化设计[J].计算力学学报,2002,19(2):198-201.(Guo S X,Lv Z Z.Optimization of uncertain structures based on non-probabilistic reliability[J].Chinese Journal of Computational Mechanics,2002,19(2):198-201.(in Chinese))
[8]郭书祥,吕震宙.基于非概率模型的结构稳健可靠性设计方法[J].航空学报,2001,22(5):451-453.(Guo S X,Lv Z Z.Procedure for the robust reliability design of structures[J].Acta Aeronautica et Astronautica Sinica,2001,22(5):451-453.(in Chinese))
[9]郭书祥,张陵,李颖.结构非概率可靠性指标的求解方法[J].计算力学学报,2005,22(2):227-231.(Guo S X,Zhang L,Li Y.Procedures for computing the nonprobabilistic reliability index of uncertain structures[J].Chinese Journal of Computational Mechanics,2005,22(2):227-231.(in Chinese))
[10]江涛,陈建军,姜培刚,拓耀飞.区间模型非概率可靠性指标的一维优化算法[J].工程力学,2007,24(7):23-27.(Jiang T,Chen J J,Jiang P G,Tuo Y F.A onedimensional optimization algorithm for non-probabilistic reliability index[J].Engineering Mechanics,2007,24(7):23-27.(in Chinese))
[11]Chen X Y,Fan J P.An improved semi-analytic method for calculating non-probabilistic reliabi-lity index based on convex model[J].Acta Mechanica Solida Sinica,2012,23(2):115-120.
[12]樊建平,李世军,陈旭勇.非概率可靠性指标空间搜索算法[J].计算力学学报,2012,29(6):831-840.(Fan J P,Li S j,Chen X Y.Optimal searching algorithm for non-proba-bilistic reliability[J].Chinese Journal of Compu tational Mechanics,2012,29(6):831-840.(in Chinese))
[13]陈旭勇,樊建平.非概率可靠性中一维优化算法的改进及其在桥梁评估中应用[J].工程力学,2010,28(5):21-26.(Chen X Y,Fan J P.An improved one-dimensional optimization algorithm non-probabilistic reliability investigation and its application in bridge assessment[J].Engineering Mechanics,2010,28(5):21-26.(in Chinese))
[14]樊建平,陈旭勇.区间模型非概率可靠性全局最优解[J].固体力学学报,2014,35(5):476-484.(Fan J P,Chen X Y.Theoretical analysis of non-probabilistic reliability based on interval model[J].Chinese Journal of Solid Mechanics,2014,35(5):476-484.(in Chinese))
[2]Ben Haim Y,Elishakoff I.Convex Models of Uncertainty in Applied Mechanics[M].Amsterdam:Elsevier Science,1990.
[3]Ben Haim Y.A non-probabilistic concept of reliability[J].Structural Safety,1994,14(4):227-245.
[4]Ben Haim Y.Robust Reliability in the Mechanical hanical Sciences[M].Berlin:Springer Verlag,1996.
[5]郭书祥,吕震宙,冯元生.基于区间分析的结构非概率可靠性模型[J].计算力学学报,2001,18(1):56-60.(Guo S X,Lv Z Z,Feng Y S.A non-probabilistic model of structural reliability based on interval analysis[J].Chinese Journal of Computational Mechanics,2001,18(1):56-60.(in Chinese))
[6]郭书祥,吕震宙.结构体系的非概率可靠性分析方法[J].计算力学学报,2002,19(3):332-335.(Guo S X,Lv Z Z.A procedure of the analysis of non-probabilistic reliability of structural systems[J].Chinese Journal of Computational Mechanics,2002,19(3):332-335.(in Chinese))
[7]郭书祥,吕震宙.基于非概率模型的结构可靠性优化设计[J].计算力学学报,2002,19(2):198-201.(Guo S X,Lv Z Z.Optimization of uncertain structures based on non-probabilistic reliability[J].Chinese Journal of Computational Mechanics,2002,19(2):198-201.(in Chinese))
[8]郭书祥,吕震宙.基于非概率模型的结构稳健可靠性设计方法[J].航空学报,2001,22(5):451-453.(Guo S X,Lv Z Z.Procedure for the robust reliability design of structures[J].Acta Aeronautica et Astronautica Sinica,2001,22(5):451-453.(in Chinese))
[9]郭书祥,张陵,李颖.结构非概率可靠性指标的求解方法[J].计算力学学报,2005,22(2):227-231.(Guo S X,Zhang L,Li Y.Procedures for computing the nonprobabilistic reliability index of uncertain structures[J].Chinese Journal of Computational Mechanics,2005,22(2):227-231.(in Chinese))
[10]江涛,陈建军,姜培刚,拓耀飞.区间模型非概率可靠性指标的一维优化算法[J].工程力学,2007,24(7):23-27.(Jiang T,Chen J J,Jiang P G,Tuo Y F.A onedimensional optimization algorithm for non-probabilistic reliability index[J].Engineering Mechanics,2007,24(7):23-27.(in Chinese))
[11]Chen X Y,Fan J P.An improved semi-analytic method for calculating non-probabilistic reliabi-lity index based on convex model[J].Acta Mechanica Solida Sinica,2012,23(2):115-120.
[12]樊建平,李世军,陈旭勇.非概率可靠性指标空间搜索算法[J].计算力学学报,2012,29(6):831-840.(Fan J P,Li S j,Chen X Y.Optimal searching algorithm for non-proba-bilistic reliability[J].Chinese Journal of Compu tational Mechanics,2012,29(6):831-840.(in Chinese))
[13]陈旭勇,樊建平.非概率可靠性中一维优化算法的改进及其在桥梁评估中应用[J].工程力学,2010,28(5):21-26.(Chen X Y,Fan J P.An improved one-dimensional optimization algorithm non-probabilistic reliability investigation and its application in bridge assessment[J].Engineering Mechanics,2010,28(5):21-26.(in Chinese))
[14]樊建平,陈旭勇.区间模型非概率可靠性全局最优解[J].固体力学学报,2014,35(5):476-484.(Fan J P,Chen X Y.Theoretical analysis of non-probabilistic reliability based on interval model[J].Chinese Journal of Solid Mechanics,2014,35(5):476-484.(in Chinese))