基于改进降维法的可靠性算法及其在重载操作机中的应用
|
摘要
大载荷、大惯量、多自由度的重载操作机具有较强的多维度力位操控能力,与大型的液压机协调作业,可以大大提高制造能力、制造精度、生产效率和材料利用率,降低能耗。如何保证在极端条件下,重载操作机的操作性能、构件之间的力承载能力、界面特性以及操作机关键构件的刚度特性是重载操作装备设计所面临的关键问题。本文结合国家重点基础研究发展计划(973计划,2006CB705403)课题“非连续工况下重载装备的界面行为与力学特性”,开展了重载操作机关键构件的相关研究。将不确定性分析和优化思想应用于重载操作装备,重点研究了基于降维法可靠性算法以及相关变量的可靠性算法,深入讨论了重载操作机关键构件的力学性能、可靠性分析和结构优化设计,为重载操作装备的设计提供相关的理论、方法与技术支持。
本文的主要内容如下：
1.提出归一化的基于矩的积分方法(NMBQR)。针对单变量维数缩减法(降维法)中的MBQR方法存在的数值不稳定问题,提出了改进降维法中NMBQR方法。当求解问题中输入参数的均值很大或者变异系数很小的时候,NMBQR方法通过矩阵系数归一化可以有效地改善线性方程组求解过程中由于系数矩阵奇异导致的数值不稳定问题。
2.通过将改进的降维法与计算响应概率密度函数(PDF)的最大熵方法进行联合,提出了改进降维法的可靠性算法。并通过各种算例验证了改进降维法求解结构可靠度的优点在于不需要求解响应函数的导数以及不需要迭代求解最可失效概率点(MPP点)等,在进行结构可靠性分析的时候具有较高的计算效率。
3.提出了基于改进降维法的相关变量可靠性算法。通过Nataf变换和Winterstein近似可以对任意分布的相关变量进行标准正态化,并采用Cholesky分解进行变量的独立化,最后采用改进降维法求解结构的可靠度。与仅在MPP点进行等概率变换的基于JC法的相关变量可靠性方法相比,Nataf变换方法是在设计空间的全域内进行等概率变换。本文采用二维Gauss-Hermite积分来进行求解Nataf变换前后的相关系数；通过求解多项式方程可以得到Winterstein近似变换后相关系数的解析解,具有较高的计算效率。
4.进行了基于替代模型的操作机侧壁结构的可靠性分析。考虑操作机侧壁结构中不确定性参数,如肋板的厚度、侧板的厚度以及载荷等信息,通过经典的替代模型方法得到这些参数与结构响应的显式函数关系。考虑输入载荷之间具有较强的相关关系,利用本文提出的基于改进降维法的相关变量可靠性算法计算操作机侧壁结构的可靠度。
5.对重载操作机侧壁结构进行了拓扑与尺寸优化设计,提出了一种新型的重载操作机侧壁框架结构,降低了材料用量而且提高了结构的力学性能。针对操作机侧壁框架的初始设计不能充分地利用材料以及有效地提供侧壁框架侧向刚度的问题,本文进行了基于最大化结构刚度的拓扑优化设计。其主导思想是通过拓扑优化确定材料的分布区域,用于指导侧壁肋板的分布,并根据拓扑优化的结果建立新的侧壁框架有限元模型,然后采用了基于替代模型的尺寸优化设计来获得最优的设计尺寸。优化结果显示,在减少材料用量的情况下,仍然能够保持结构的强度和刚度不降低甚至有所提高。
The heavy duty forging manipulator, with the heavy load, large inertia and multi-degree-of freedom, has the capacity of multi-dimensional control of forces and positions, which could greatly improve the capacity and precision of manufacture, production efficiency, material utilization and reduce the energy consumption working together with the heavy duty hydraulic. The key issues for the heavy duty forging manipulator design focus on how to guarantee the operating performance of the forging manipulator, the capacities of strength and stiffness of the components, the interface characteristics between the key components under the extreme conditions. With the support of the973Program "the mechanical properties and interface characteristics of the heavy load manipulator under discontinuous load cases"(No.2006CB705403),this paper introduces the uncertainty analysis and optimization thoughts into the heavy duty equipment concentrates on the reliability algorithm based on the Univariate Dimension Reduction Method(UDRM,DRM) and the correlated random variable for the reliability algorithm, and discusses the key issues, such as the mechanical properties of the key component of the forging manipulator, reliability analysis and the structural optimization design.
Related studies of this paper are listed as follows:
1. The Normalized Moment Based Quadrature Rule (NMBQR) is proposed. The numerical instability of the Moment Based Quadrature Rule (MBQR) in the DRM could occur in the condition of the great mean value or the small coefficient of variation of the input parameters. The NMBQR could effectively improve the numerical instability of singular coefficient matrix by normalizing the parameters when solving the linear equations.
2. The reliability algorithm based on the Improved Dimension Reduction Method is proposed by combining the Improved DRM and Maximum Entropy Method (MEM) which is used to calculate the probability density function (PDF) of the response. The results of the numerical examples show that the reliability algorithm based on the Improved DRM has the great advantages, such as no need of the derivative of the response function and the iterative procedure for the Most Probable failure Point (MPP), resulting in high computational efficiency.
3. The Improved DRM based reliability algorithm for the correlated random variables is proposed. The Nataf transformations and Winterstein approximations could normalize the correlated random variables with arbitrary distributions. The independent random variables could be obtained by the Cholesky factorization and the reliability can be calculated by the improve DRM. Compared to JC method for the correlated variables, the Nataf transformations give the equivalent probability transformations on all domain of the design space. As for the correlation coefficient in the Nataf transformations, the two-dimensional Gauss-Hermite quadrature is carried out instead of the empirical formula. The correlation coefficient is obtained by the polynomial equation for the Winterstein approximations, which has the closed-form solution with high computational efficiency.
4. The reliability analysis for the wall frame of the forging manipulator based on the surrogate model is carried out. The uncertainty factors include the thickness of the ribs, the thickness of the side wall and the load. The explicit function of the structural response with respect to the input parameters can be achieved by the Design of Experiment (DOE) and Response Surface Method (RSM).The reliability of the wall frame of the forging manipulator is calculated by the proposed method considering the strong correlated relationship between the loads.
5. The structural optimization for the wall frame of the forging manipulator is performed and a new type of wall frame structure of the forging manipulator is proposed. The mechanical properties of the new type wall frame structure are improved with the less material consumption. Due to the lack of the effective utilization of the materials and the less contribution to the side stiffness of the original design of the wall frame, the topology optimization for the maximum structural stiffness is given. The results of the topology optimization is introduced to the distribution of the ribs of the wall frame and the new finite element model (FEM) is built. Then the optimal designs are obtained by the sizing optimization based on the surrogate model, which show that the stiffness and strength are improved with the reduction of the materials.
本文的主要内容如下：
1.提出归一化的基于矩的积分方法(NMBQR)。针对单变量维数缩减法(降维法)中的MBQR方法存在的数值不稳定问题,提出了改进降维法中NMBQR方法。当求解问题中输入参数的均值很大或者变异系数很小的时候,NMBQR方法通过矩阵系数归一化可以有效地改善线性方程组求解过程中由于系数矩阵奇异导致的数值不稳定问题。
2.通过将改进的降维法与计算响应概率密度函数(PDF)的最大熵方法进行联合,提出了改进降维法的可靠性算法。并通过各种算例验证了改进降维法求解结构可靠度的优点在于不需要求解响应函数的导数以及不需要迭代求解最可失效概率点(MPP点)等,在进行结构可靠性分析的时候具有较高的计算效率。
3.提出了基于改进降维法的相关变量可靠性算法。通过Nataf变换和Winterstein近似可以对任意分布的相关变量进行标准正态化,并采用Cholesky分解进行变量的独立化,最后采用改进降维法求解结构的可靠度。与仅在MPP点进行等概率变换的基于JC法的相关变量可靠性方法相比,Nataf变换方法是在设计空间的全域内进行等概率变换。本文采用二维Gauss-Hermite积分来进行求解Nataf变换前后的相关系数；通过求解多项式方程可以得到Winterstein近似变换后相关系数的解析解,具有较高的计算效率。
4.进行了基于替代模型的操作机侧壁结构的可靠性分析。考虑操作机侧壁结构中不确定性参数,如肋板的厚度、侧板的厚度以及载荷等信息,通过经典的替代模型方法得到这些参数与结构响应的显式函数关系。考虑输入载荷之间具有较强的相关关系,利用本文提出的基于改进降维法的相关变量可靠性算法计算操作机侧壁结构的可靠度。
5.对重载操作机侧壁结构进行了拓扑与尺寸优化设计,提出了一种新型的重载操作机侧壁框架结构,降低了材料用量而且提高了结构的力学性能。针对操作机侧壁框架的初始设计不能充分地利用材料以及有效地提供侧壁框架侧向刚度的问题,本文进行了基于最大化结构刚度的拓扑优化设计。其主导思想是通过拓扑优化确定材料的分布区域,用于指导侧壁肋板的分布,并根据拓扑优化的结果建立新的侧壁框架有限元模型,然后采用了基于替代模型的尺寸优化设计来获得最优的设计尺寸。优化结果显示,在减少材料用量的情况下,仍然能够保持结构的强度和刚度不降低甚至有所提高。
The heavy duty forging manipulator, with the heavy load, large inertia and multi-degree-of freedom, has the capacity of multi-dimensional control of forces and positions, which could greatly improve the capacity and precision of manufacture, production efficiency, material utilization and reduce the energy consumption working together with the heavy duty hydraulic. The key issues for the heavy duty forging manipulator design focus on how to guarantee the operating performance of the forging manipulator, the capacities of strength and stiffness of the components, the interface characteristics between the key components under the extreme conditions. With the support of the973Program "the mechanical properties and interface characteristics of the heavy load manipulator under discontinuous load cases"(No.2006CB705403),this paper introduces the uncertainty analysis and optimization thoughts into the heavy duty equipment concentrates on the reliability algorithm based on the Univariate Dimension Reduction Method(UDRM,DRM) and the correlated random variable for the reliability algorithm, and discusses the key issues, such as the mechanical properties of the key component of the forging manipulator, reliability analysis and the structural optimization design.
Related studies of this paper are listed as follows:
1. The Normalized Moment Based Quadrature Rule (NMBQR) is proposed. The numerical instability of the Moment Based Quadrature Rule (MBQR) in the DRM could occur in the condition of the great mean value or the small coefficient of variation of the input parameters. The NMBQR could effectively improve the numerical instability of singular coefficient matrix by normalizing the parameters when solving the linear equations.
2. The reliability algorithm based on the Improved Dimension Reduction Method is proposed by combining the Improved DRM and Maximum Entropy Method (MEM) which is used to calculate the probability density function (PDF) of the response. The results of the numerical examples show that the reliability algorithm based on the Improved DRM has the great advantages, such as no need of the derivative of the response function and the iterative procedure for the Most Probable failure Point (MPP), resulting in high computational efficiency.
3. The Improved DRM based reliability algorithm for the correlated random variables is proposed. The Nataf transformations and Winterstein approximations could normalize the correlated random variables with arbitrary distributions. The independent random variables could be obtained by the Cholesky factorization and the reliability can be calculated by the improve DRM. Compared to JC method for the correlated variables, the Nataf transformations give the equivalent probability transformations on all domain of the design space. As for the correlation coefficient in the Nataf transformations, the two-dimensional Gauss-Hermite quadrature is carried out instead of the empirical formula. The correlation coefficient is obtained by the polynomial equation for the Winterstein approximations, which has the closed-form solution with high computational efficiency.
4. The reliability analysis for the wall frame of the forging manipulator based on the surrogate model is carried out. The uncertainty factors include the thickness of the ribs, the thickness of the side wall and the load. The explicit function of the structural response with respect to the input parameters can be achieved by the Design of Experiment (DOE) and Response Surface Method (RSM).The reliability of the wall frame of the forging manipulator is calculated by the proposed method considering the strong correlated relationship between the loads.
5. The structural optimization for the wall frame of the forging manipulator is performed and a new type of wall frame structure of the forging manipulator is proposed. The mechanical properties of the new type wall frame structure are improved with the less material consumption. Due to the lack of the effective utilization of the materials and the less contribution to the side stiffness of the original design of the wall frame, the topology optimization for the maximum structural stiffness is given. The results of the topology optimization is introduced to the distribution of the ribs of the wall frame and the new finite element model (FEM) is built. Then the optimal designs are obtained by the sizing optimization based on the surrogate model, which show that the stiffness and strength are improved with the reduction of the materials.
引文
[1]契里舍也夫B A(上海机电设计院设计一室译).操作机结构的发展状况[J].重型机械,1974,8：29-33.
[2]万胜狄,主运鹏,沈元彬等.锻造机械化与自动化[M].北京机械工业版社,1983.
[3]杨文魁.关于锻造操作机设计制造使用中若干问题的认识和体会[J].重型机械,1975,4：101.111.
[4]李佶.锻造操作机的发展近况[J].锻压机械,1978,3：17-22.
[5]李估.锻造操作机设计与计算中几个问题的讨论[J].锻压机械,1978,5：2-4.
[6]余发国,高峰,郭为忠等.锻造操作机的回顾与展望.中国机构与机器科学应用国际会议论文集,2007：12-15.
[7]Harrison R.Forging manipulator:US,3696651[P].1972,10,10.
[8]Eberhard B. Forging manipulator:Germany,E10128451(A1)[P].2002,05,12.
[9]Kutz H.Workpiece manipulator for use in a forging press:US,4031736[P].1977,06,28.
[10]Kost E,FOLTA W.Gripper feed and gripper resilience cylinders on forging manipulators:US,4420287 [P].1983,12,13.
[11]Hemingway et al.Crane and manipulator integration:US,4430041[P].1984,02,07.
[12]Schubert.Workpiece clamping devices in forging manipulators:US,4776199[P].1988,10,11.
[13]Schubert.Forgin manipulator:US,4815311[P].1989,03,28.
[14]Wilson et al.Manipulator for metal ingots:US,4961336[P].1990,10,09.
[15]Brucher.Quick-action coupling for forge and conveyor manipulators:US,5118248[P].1992,06,02.
[16]Westermeyer.Process and apparatus for opertaing a press unit:US,5454262[P].1995,10,03.
[17]尹朝国.自由锻操作机械化及其发展[J].锻压机械,1992,4：40-42.
[18]玉凤喜.锻造操作机技术近期的发展[J].重型机械,1994,4：12-17.
[19]顾震隆.锤上操作机的动力分析探讨[J].哈尔滨工业大学学报,1979,3：1-10.
[20]哈尔滨工业大学操作机小组.锻造操作机动力分析的初步探讨[J].锻压机械,1979,3：19-22.
[21]权修华.锻造操作机动载荷分析与计算[J].重型机械,1987,10：26-29.
[22]权修华.操作机承载状态分析与计算[J].锻压机械,1988,5：41.44.
[23]王凤喜.锻造液压机与操作机的发展[J].锻压机械,1998,6：3.5.
[24]任云鹏,张计磊,韩清凯等.锻造操作机结构系统的动力有限元建模方法研究[J].机械设计与制造,2008,7：103.105.
[25]任云鹏,张天侠,韩清凯等.锻造操作机机械结构的模态匹配分析[J].机械设计与制造,2008,12：186.187.
[26]任云鹏,张天侠.锻造操作机的可视化刚体动力学仿真[J].中国工程机械学报,2008,6(2)：127-132.
[27]陈博翁,关立文,李铁民.基于ADAMS的锻造操作机动力学仿真及优化设计[J].机械设计与制造,2009,3：6-8.
[28]范凡,王皓,赵勇.自由锻造操作机冗余驱动系统的驱动力分配与协调[J].机械设计,2009,26(9)：26-30.
[29]王立平,吴昱,关立文.锻造操作机相似试验台设计和仿真[J].制造技术与机床,2009,8：57-62.
[30]高峰,郭为忠,宋清玉等.重型制造装备国内外研究与发展[J].机械工程学报,2010,46(19)：92.107.
[31]韩雅楠,李刚,罗晓明.基于Simpack的重载操作机刚柔耦合动力学分析[J].动力学与控制学报,2010,8(3)：267-272.
[32]梁音,王馨舶,李洪胜等.锻造操作机钳杆操纵过程的动力学特性分析[J].重型机械,2010,5：38-42.
[33]刘松柏,邓华,何竞飞.巨型重载夹持装置动态夹持力建模与承载能力分析[J].现代制造工程,2010.1：107-111.
[34]任云鹏,韩清凯,张天侠等.基于虚拟样机技术的锻造操作机的动力学仿真[J].东北大学学报(自然科学版)：2010,31(8)：1170-1173.
[35]任云鹏,陈希红,卢祟劭等.基于虚拟样机技术的锻造操作机的刚柔混合仿真分析[J].科技成果纵横,2010,1：50-53.
[36]同新星.基于虚拟样机技术的锻造操作机缓冲装置研究[J].设备,2010,4：46-49.
[37]王红,张涛,杨文玉等.锻造操作机夹持界面接触力学数值分析[J].锻造,2010,1：77-81.
[38]翟富刚,孔祥东,王林等.锻造操作机夹持机构最优夹紧力分析[J].机械设计与研究,2010,26(4)：38-41.
[39]翟富刚,孔祥东,姚静等.锻造操作机夹钳回转系统动态特性仿真研究[J].液压与气动,2010,3：61.63.
[40]翟群杰.锻造操作机钳杆机构的动态分析[J].锻压技术,2010,35(5)：96-99.
[41]李刚,刘德时.锻造操作机大范围顺应运动的动力学行为分析[J].机械工程学报,2010,46(11)：21.28.
[42]关立文,程宁波.锻造操作机相似模型逆动力学建模与非线性控制器设计[J].机械工程学报,2010,46(11)：55-61.
[43]李刚,陈高杰.锻造操作机钳臂结构的多轴疲劳分析[J].哈尔滨工业大学学报,2011,43(S1)：100.105.
[44]赵勇,林忠钦,王皓.重型锻造操作机的操作性能分析[J].机械工程学报,2010,46(11)：69-75.
[45]林晓文,王皓,赵勇.考虑构件弹性变形的锻造操作机静刚度分析[J].机械设计与研究,2011,27(1)：94-98.
[46]牛勇,张营杰,房志远等1000kN_2500kNm锻造操作机吊挂装置仿真研究[J].重型机械.2011,2：19-22.
[47]赵国藩.结构可靠度理论[M].北京：中国建筑工业出版社,2000.
[48]赵国藩,曹居易,张宽权.工程结构可靠度[M].北京：水利电力出版社,1984.
[49]李春明.优化方法[M].南京：东南大学出版社,2009.
[50]Venkayya V B.Design of Optimum Structures[J]. Computers and Structures,1971,1(1-2):265-309.
[51]Fleury C,Sanders G.Relations between optimality criteria and mathematical programming in structural optimization[C].In:Proceedings of the Symposium on Applications of Computer Methods in Engineering,Univ. of California, Los Angeles,CA,1977:507-520.
[52]钱令希.工程结构优化设计[M].北京：水利电力出版社,1983.
[53]程耿东.工程结构优化设计基础[M].北京：水利电力出版社,1984.
[54]Vanderplaats G N.Structural design optimization status and direction[J] Journal of Aircraft,1999, 36(1):11-20.
[55]Burns S A.Structural engineering institute technical committee on optimal structural design[J].Recent Advances in Optimal Structural Design.ASCE Publications,2002.
[56]Allaire G,Henrot A.On some recent advances in shape optimization[J].Comptes Rendus de l'Academie des Sciences-Series IIB-Mechanics,2001,329(5):383-396.
[57]Eschenauer H A, Olhoff N.Topology optimization of continuum structures:A review[J].Applied Mechanics Reviews,2001,54(4):331-390.
[58]Dorns W S,Gomory R E,Greenberg H J.Automatic design of optimal structure[J].J Mechanics,1964, 3,25-52.
[59]Rossow M P,Taylor J E,A finite element method for the optimal design of variable thickness sheets[J].AIAA Journal,1973,11(11):1566-1569.
[60]Cheng G D,Olhoff N.An investigation concerning optimal design of solid elastic plates[J]. International Journal of Solids and Structures,1981,17(3):305-323.
[61]Cheng G D.On non-smoothness in optimal design of solid elastic plates[J].International Journal of Solids and Structures,1981,17,795-810.
[62]Bendsoe M P,Kikuchi N.Generating optimal topologies in structural design using a homogenization method[J].Computer Methods in Applied Mechanics and Engineering,1988,71:197-224.
[63]Hassani B,Hinton E.A review of homogenization and topology optimization Ⅰ-topology optimization using optimality criteria[J].Computers & Structures,1998,69:707-717.
[64]Hassani B,Hinton E.A review of homogenization and topology optimization Ⅱ-topology optimization using optimality criteria[J].Computers & Structures,1998,69:718-738.
[65]Hassani B,Hinton E.A review of homogenization and topology optimization Ⅲ-topology optimization using optimality criteria[J].Computers & Structures,1998,69:739-756.
[66]刘书田.复合材料性能预测与梯度功能材料优化设计[D].大连理工大学,1994.
[67]刘书田.复合材料应力分析的均匀化方法[J].力学学报,1997,5(29)：306-313.
[68]刘书田,程耿东.基于均匀化理论的梯度功能材料优化设计方法[J].宇航材料工艺,1995,6：21-27.
[69]Zhou M,Rozvany G I N.The COC algorithm,Part II:topological and geometrical and generalized shape optimization[J].Computer Methods in Applied Mechanics and Engineering,1991,89:309-336.
[70]Bendsoe M P,Sigmund O.Material interpolation Schemes in topology Optimization[J].Archive of applied Mechanics,1999,69:653-645.
[71]Sethian J A,Wiegmann A. Structural boundary design via level set and immersed interface methods [J].Journal of Computational Physics,2000,163:489-528.
[72]Wang M Y,Wang X M,Guo D.A level set method for structural topology optimization[J].Computer Methods in Applied Mechanics and Engineering,2003,192:227-246.
[73]梅玉林.拓扑优化的水平集方法及其在刚性结构、柔性结构和材料设计中的应用[D].大连理工大学,2004.
[74]Eschenauer H A,Kobelev H A,Schumacher A.Bubble method for topology and shape optimization of structures [J]. Structural Optimization,1994,8:142-151.
[75]Sokolowski J,Zochowski A.On the topological derivative in shape optimization[J].SIAM Journal of Control Optimzation,1999,37:1251-1272.
[76]Xie Y M,Steven G P.A simple evolutionary procedure for structure optimization[J].Computers and Structures,1993,49:885-896.
[77]Bendsoe M P,Sigmund O.Topology optimization:theory,methods and applications[M].Berlin:Springer Verlag,2003.
[78]贾海朋.结构与柔性机构拓扑优化[D].大连理工大学,2004.
[79]Diaz A R,Kikuchi N.Solutions to shape and topology eigenvalue optimization problems using a homogenization method[J].International Journal for Numerical Methods in Engineering,1992,35 (7):1487-1502.
[80]Cheng G D.Some aspects of truss topology optimization[J].Structural Optimization,1995,10(3-4): 173-179.
[81]程耿东.考虑局部稳定性约束的析架拓扑优化设计[J].大连理工大学学报,1995,35(6)：770-775.
[82]Guo X,Cheng G D,Olhoff N.Optimum design of truss topology under buckling constraints[J]. Structural and Multidisciplinary Optimization,2005,30(3):169-180.
[83]中华人民共和国国家标准.工程结构可靠度设计统一标准.GB 50153.200X(征求意见稿).
[84]Freudenthal A M.The safety of structures [J]. Transactions of ASCE,1947,112:125-180.
[85]Cornell C A.A probability-based structural code[J].Journal of American Concrete Institute,1969, 66(12):974-985.
[86]Hasofer A M,Lind N C.Exact and invariant second moment code format[J].Journal of Engineering Mechanics,1974,100(EM1):111-121.
[87]Rackwitz R,Fiessler B.Structural reliability under combined random load sequences [J].Computers and Structures,1978,9:489-494.
[88]Fiessler B,Neumann H J,Rackwitz R.Quadratic limit states in structural reliability[J].Journal of Engineering,Mechanics Division ASCE,1979,105(EM4):661-676.
[89]Schueller G I,Bucher C G,Bourgund U,et al.On efficient computational schemes to calculate structural failure probabilities[J] Journal of Probabilistic Engineering Mechanics,1989,4(1):10-18.
[90]Ditlevsen O,Melchers R E,Gluver H.General multi-dimensional probability integration by directional simulation[J].Computers and Structures,1990,36(2):355-368.
[91]Barton R R.Metamodel for simulation input-output relations[C].Proceedings of the 1992 winier simulation Conference,1992:289-299.
[92]Faravelli L.Response surface approach for reliability analysis[J].Journal of Engineering Mechanics, 1989,115(12):2763-2781.
[93]赵敏,陈文.基于径向基函数的加权最小二乘无网格法[J].计算力学学报,2011,28(1)：66-71.
[94]刘小民,张文斌.一种基于径向基函数的替代模型构造方法[J].燕山大学学报,2010,34(5)：390-394.
[95]Kaymaz I.Application of kriging method to structural reliability problems[J].Structural Safety,2005, 27(2):133-151.
[96]彭泽.结构可靠度Metamodel方法及其工程应用研究[D].中南大学.2010.
[97]张崎.基于Kriging方法的结构可靠性分析及优化设计[D].大连理工大学,2005.
[98]邓乃扬,田英杰.数据挖掘中的新方法-支持向量机[M].北京：科学出版社.2004.
[99]Vapnik V N(张学工译).统计学习论理的本质.北京：清华大学出社,2000.
[100]李洪双,吕震宙,岳珠峰.结构可靠性分析的支持向量机方法[J].应用数学与力学,2006,27(10)：1135-1143.
[101]李刚,刘志强.基于支持向量机替代模型的可靠性分析[J].计算力学学报,2011,28(5)：676-681.
[102]Rosenblueth E.Point estimation for probalility moments[J].Proceedings of the National Academy of Sciences,1975,72(10):3812-3814.
[103]Rosenblueth E.Two-point estimates in probalility[J]. Application Mathematics Modeling,1981, 5:329-335.
[104]Gorman M R.Reliability of structural system[D].Cleveland:Case Western Reserve University,1980.
[105]Seo H S,Kwak B M.Efficient statistical tolerance analysis for general distributions using three-point information [J]. International Journal of Production Research,2002,40(4):931-944.
[106]Zhao Y G,Ono T.New point estimates for probability moments [J]. Journal of Engineering Mechanics, 2000,126(4):433-436.
[107]Zhou J H,Nowak A S.Integration formulas to evaluate functions of random variables[J].Structural Safety,1998,5:267-284.
[108]Harr M E.Probability estimate for multivariate analysis [J]. Application Mathematics Modellinig,1989, 13(5):313-318.
[109]Cheng C Hating Y Keying J C.Evaluatuon of probability point estimate methods[J]. Application Mathematics Modellinig,1995,19(2):995-105.
[110]Li K S.Point estimate method for calculating statistical moments[J].Journal of Engineering Mechanics, 1992,118(7):1506-1511.
[111]Hong H P.An efficient point estimate method for probabilistic analysis[J].Reliability Engineering and System Safety,1998,59:261-267.
[112]Zhao Y G,Ono T.Moment methods for structural reliability [J]. Structural Safety,2001,23:47-75.
[113]Xu L,Cheng G D.Discussion on:moment methods for Structural reliability[J].Structural safety,2003, 25,193-199.
[114]许林.基于可靠度的结构优化研究[D].大连理工大学,2004.
[115]Rosenblatt M.Remarks on a multivariate transformation[J].Annals Math Stat,1952,23:470-472.
[116]Nataf A.Determination des distribution dont les marges sont donnees[J].ComptesRedus de l'Academie des Sciences,1962,225:42-43.
[117]Liu P L,Kiureghian D A.Multivariate distribution models with prescribed marginals and covariances [J].Probabilistic Engineering Mechanics,1986,1(2):105-112.
[118]Kiureghian D A,Liu P L.Structural reliability under incomplete probability information[J].Journal of Engineering Mechanics,1986,112:85-104.
[119]李国强,李继华.二阶矩矩阵法关于相关随机向量的结构可靠度计算[J].重庆建筑工程学院学报,1987,1：55.67.
[120]武清玺,吕泰仁,吴世伟.变量相关时结构可靠指标的计算[J].高校应用数学学报,1987,2(3)：323-329.
[121]李宏,吴世伟,吕泰仁.变量相关下的JC法[J].港工科技,1991,3：21-25.
[122]李云贵.赵国藩.广义随机空间内的一次可靠度分析方法[J].大连理工大学学报,1993,33(S1)：S1-S5.
[123]傅旭东.相关变量下失效概率的计算机模拟[J].西南交通大学学报,1997,32：319-323.
[124]俞铭华,姚金山.变量相关的船舶结构可靠性分析[J].华东船舶工业学院学报,1997,11(2)：1-7.
[125]李惠强,范涤.变量相关时悬臂桩支护结构可靠性分析[J].华中理工大学学报,1998,26(8)：44-46.
[126]洪昌华,龚晓南.相关情况下Hasofer Lind可靠度指标的求解[J].岩土力学,2000,21(1)：68-72.
[127]罗红,梁波.非线性相关条件下可靠指标的改进计算方法[J].工程力学,2000,17(4)：99.104.
[128]姚继涛,董振平.随机变量的相关性和结构可靠度[J].西安建筑科技大学学报,2000,32(2)：114-118.
[129]严松宏,赵朝前.变量相关条件下可靠指标计算[J].兰州铁道学院学报,2001,20(4)：42-44.
[130]李斌,严松宏.变量相关情况下结构可靠指标的简化算法[J].西南交通大学学报,2004,39(2)：147-151.
[131]江晓俐.相关腐蚀与疲劳及维修对船体可靠性的影响[J].武汉理工大学学报(交通科学与工程版)：2005,29(3)：363-366.
[132]郄禄文.结构可靠度分析中随机变量间相关系数的特性[J].港工科技,2006,4：18-20.
[133]吕大刚.基于线性化Nataf变换的一次可靠度方法[J].工程力学,2007,24(5)：79-86.
[134]吕大刚,于晓辉,王光远.基于改进点估计法的结构整体概率抗震能力分析[J].世界地震工程,2008,24(4)7-14.
[135]李洪双,吕震宙,袁修开.基于Nataf变换的点估计法[J].科学通报,2008,53(6)：627-632.
[136]侯钢领,欧进萍.广义可靠指标矢量及其计算与应用[J].哈尔滨工程大学学报,2009,30(2)：132-137.
[137]刘小辉.一类基本变量相关的结构功能函数的可靠性分析[J].集美大学学报(自然科学版)：2009,14(3)：299-302.
[138]吴振君,王水林,汤华等.边坡可靠度分析的一种新的优化求解方法[J].岩土力学,2010,31(3)：713-718.
[139]李庆典,周创兵,陈益峰等.边坡可靠度分析的随机响应面法及程序实现[J].岩石力学与工程学报,2010,29(8)：1514-1523.
[140]刘金刚,王世鹏,解艳彩.广义随机空间内结构可靠性优化设计[J].机械设计与研究,2010,26(5)：7-9.
[141]吕大刚,宋鹏彦,于晓辉等.基于矩法的结构非线性整体抗震可靠性分析[J].建筑结构学报,2010,S2：119-124.
[142]Ditlevsen O,Madsen H O.Structural reliability methods[M].Chichester:John Wiley & Sons Ltd,2005.
[143]张明.结构可靠度分析.方法与程序[M].北京：科学出版社,2009.
[144]Madsen H O,Krenk S,Lind N C.Methods of structural safety,prentice-hall[M].NJ:Inc., Englewood Cliffs,1986.
[145]Ditlevsen O.Generalized second moment reliability index[J]Journal of Structural Mechanics,1979,7(4): 435-451.
[146]Chen X,Lind N C.Fast probability integration by three parameter normal tail approximation[J]. Structural Safety,1983,1 (4):269-276.
[147]Tichy M.First-order third-moment reliability method[J].Structural Safety,1994,16:189-200.
[148]Shinazuka M.Basic Analysis of structural safety[J].Journal of Structural Engineering,1983,109(3): 721-740.
[149]Harbitz A.An efficient sampling method for probability of failure calculation[J].Structural Safety, 1986,3:109-115.
[150]Schueller G I,Stix R.A critical appraisal of methods to determine failure probabilities[J]. Structural Safety,1987,4(4):293-309.
[151]Bucher C G.Adaptive sampling-an iterative fast Monte Carlo procedure[J].Structural Safety,1988, 5(2):119-126.
[152]Ang G L,Ang A S,Tang W H.Optimal importance sampling density estimator[J] Journal of Engineering Mechanics,1992,118(6):1146-1163.
[153]Maes M A,Breitung K,Dupuis D J.Asymptotic importance sampling[J].Structural Safety,1993, 12:167-183.
[154]Au S K,Beck J L.A new adaptive importance sampling scheme for reliability calculations[J]. Structural Safety,1999,21 (2):135-158.
[155]Mori Y,Kato T.Multinormal integrals by importance sampling for series system reliability[J]. Structural Safety,2003,25(4):363-378.
[156]Bjerager P.Probability integration by directional simulation[J] Journal of Engineering Mechanics, 1988,114(8):1285-1301.
[157]Ditlevsen O,Bjerager P.Plastic reliability analysis by directional simulation[J].Journal of Engineering Mechanics,1989,115(6):1347-1362.
[158]Ditlevsen O,Olesen R,Mohr G.Solution of a class of load combination problems by directional simulation[J].Structural Safety,1987,4:95-109.
[159]Ditlevsen O,Hasofer A M,Pjerager P,et al.Directional simulation in gaussian processes[J]. Probabilistic Engineering Mechanics,1988,3:207-217.
[160]Nie J S,Ellingwood B R.Directional methods for structural reliability analysis[J].Structural Safety,2000,22(3):233-249.
[161]Melchers R E.Radial importance sampling for structural reliability[J]. Journal of Engineering Mechanics,1990,116(1):189-203.
[162]Katsuki S,Frangopol D M.Hyperspace division method for structural reliability [J]. Journal of Engineering Mechanics,1994,120(11):2405-2427.
[163]Stein M.Large sample properties of simulations using latin hypercube sampling [J].Technometrics, 1987,29(2):143-151.
[164]Olsson A,Sandberg G E.Latin hypercube sampling for stochastic finite element analysis[J]. Journal of Engineering Mechanics,2002,128(1):121-125.
[165]Olsson A,Sandberg G E,Dahlblom O.On latin hypercube sampling for structural reliability analysis[J]. Structural Safety,2003,25(1):47-68.
[166]Ono T,Idota H.Development of high-order moment standardization method into structural design and its efficiency[J].J Structural and Construction Engineering,1986,365:40-7.
[167]Hong HP.Point-estimate moment-based reliability analysis[J].Civil Engineering System,1996,13: 281-294.
[168]Rahman S,Xu H.A univariate dimension-reduction method for multi-dimensional Integration in Stochastic Mechanics[J].Probabilistic Engineering Mechanics,2004,19:393-408.
[169]Xu H,Rahman S.A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics[J].International Journal for Numerical Methods in Engineering,2004,61: 1992-2019.
[170]Youn B D,Xi Z M,Wang P F.Eigenvector dimension reduction (EDR) method for sensitivity-free probability analysis [J]. Structural and Multidisciplinary Optimization,2008,37:13-28.
[171]Ju B H,Lee B C.Improved moment-based Quadrature rule and its application to reliability-based design optimization [J] Journal of Mechanical Science and Technology,2007,21:1162-1171.
[172]Choi C H,Won J H,Choi J H.Improving the dimension reduction method (DRM) in the uncertainty analysis and application to the reliability based design optimization[C],7th World Congress on Structural and Multidisciplinary Optimization COEX Seoul,21 May-25May,2007,Korea.
[173]Ormoneit D, White H.An efficient algorithm to compute maximum entropy densities [J].Econometrics Reviews,1999,18(2):127-140.
[174]Karian Z E,Dudewicz E J,McDonald P.The extended generalized lambda distribution system for fitting distributions to data:history, completion of theory, tables, applications, the "final word" on moment fits[J].Communications in Statistics-Computation and Simulation,1996,25(3):611-642.
[175]Erdem A,Masoud R R,Christopher D E.Reliability estimation using dimension reduction and extended generalized lambda distribution[C].49th AIAA/ASME/ASCE/AHS/ASC Structures Structural Dynamics and Materials Schaumburg USA,2008.
[176]Huang B,Du X.Uncertainty analysis by dimension reduction integration and saddlepoint approximations[J]. Journal of Mechanical Design ASME,2006,126(1):26-33.
[177]Shannon C E.A mathematical theory of communication[J].The Bell System Technical Journal,1948, 27:379-423.
[178]Jaynes E T.Information theory and statistical mechanics[J].Physical Review,1957,106(4):620-630.
[179]Daniels H E.Saddlepoint approximations in statistics[J].Annals of Mathematical Statistics,1954, 25:631-650.
[180]Papoulis A,Pillai S U.Probability, Random variables and stochastic processes,4th edition[M].New York:McGraw-Hill,2002.
[181]Kang H Y,Kwak B M.Application of maximum entropy principle for reliability-based design optimization[J].Structural and Multidisciplinary Optimization,2009,38(4):331-346.
[182]Zellner A,Highfield R A.Calculation of maximum entropy distributions and approximation of marginal posterior distributions[J] Journal of Econometrics,1988,37(2):195-209.
[183]Mukherjee D,Hurst D C.Maximum entropy revisited[J].Statistical Neerlandica,1984,38(1):1-12.
[184]佟晓利.改进的Rosenblueth方法及其在结构可靠度分析中应用[J].大连理工大学学报,1997,37(3)：316-321.
[185]韦征,叶继红,沈世钊.基于最大熵法的单层球面网壳在地震作用下的破坏模式预测[J].振动与冲击,2008,27(6)：64-69.
[186]坚民,郭冰菁,王中宇等.基于最大熵方法的测量结果估计及测量不确定度评定[J].电测与仪表,2005,42(8)：5-8.
[187]席娜丽.基于最大熵原理的工程边坡参数估计及可靠度分析研究[D].西安建筑科技大学,2006.
[188]邹春霞,申向东,王丽萍等.水工建筑物可靠性分析中的最大熵法[J].福州大学学报(自然科学版),2005,S1：115-118.
[189]章光,朱维申,白世伟.计算近似失效概率的最大熵密度函数法[J].岩石力学与工程学报,1995,14(2)：119.129.
[190]李云贵,赵国藩.结构可靠度的四阶矩分析法[J].大连理工大学学报,1992,32(4)：455-459.
[191]韦征,叶继红,沈世钊.最大熵法可靠度理论在工程中的应用[J].振动与冲击,2007,26(6)：146.151.
[192]谭羽非,王晓霞,邹平华.最大熵原理与供热系统元部件可靠性的研究[J].煤气与热力,2003,23(7)：387-390.
[193]陈虬,戴志敏.随机有限元一最大熵法[J].工程力学,1992,13(3)：1.7.
[194]杨令强,练继建,张社荣等.随机有限元与最大熵法联合求混凝土拱坝可靠度[J].水利水运工程学报,2003,2：24-28.
[195]Gu L,Yang R J,Cho C H,et al.Optimization and robustness for crashworthiness of side impact[J]. International Journal of Vehicle Design,2001,26(4):348-360.
[196]Yi P,Cheng G D,Jiang L.A sequential approximate programming strategy for performance-measure-based probabilistic structural design optimization[J].Structural Safety,2008,30(2):91-109.
[197]Winterstein S R.Nonlinear vibration models for extremes and Fatigue[J].Journal of Engineering Mechanics,1988,110(10):1772-1790.
[198]Ditlevsen O,Mohr G,Hoffmeyer P.Integration of non-Gaussian fields[J].Probabilistic Engineering Mechanics,1996,11:15-23.
[199]Noh Y,Choi K K,Du L.Reliability-based design optimization of problems with correlated input variables using a Gaussian Copula[J].Structural and Multidisciplinary Optimization,2009,38:1-16.
[200]Sigmund O.Numerical instabilities in topology optimization:a survey on procedure dealing with checkerboard, mesh-dependencies and local Minima[J].Structural Optimization,1997,16:68-75.
[201]潘丽军,陈锦权.实验设计与数据处理[M].南京：东南大学出版社,2008.
[202]Fang K. T,Li R Z,Sudjianto A.Design and modeling for computer experiments[M].Boca Raton:CRC Press Inc.,2006.
[203]Montgomery D C.Design and analysis of experiments,6thEdition[M].New York:JohnWily&Sons,Ine, 2005.
[204]赵选民.试验设计方法[M].北京：科学出版设,2006.
[205]开泰.均匀试验设计的理论、方法和应用一历史回顾[M].数理统计与管理,2005.
[206]Fang K T,Ge G N,Liu M Q.Construction on E(fNOD)-optimal supersaturated designs via room squares[J].Calcutta Statistical Association Bulletin,2002,52:205-208.
[207]Sacks J,Welch W J,Mitchell T J,et al.Design and analysis of computer experiments[J]. Statistical Science,1989,4(4):409-423.
[208]Koehler J R,Owen A B.Computer experiments[J].Handbook of Statistics,1996,13:261-308.
[209]Jin R,Chen W,Sudjianto A. An efficient algorithm for constructing optimal Design of Computer Experiments[C].ASME Design Automation Conference,Chicago,IL,September:2-6,2003.
[2]万胜狄,主运鹏,沈元彬等.锻造机械化与自动化[M].北京机械工业版社,1983.
[3]杨文魁.关于锻造操作机设计制造使用中若干问题的认识和体会[J].重型机械,1975,4：101.111.
[4]李佶.锻造操作机的发展近况[J].锻压机械,1978,3：17-22.
[5]李估.锻造操作机设计与计算中几个问题的讨论[J].锻压机械,1978,5：2-4.
[6]余发国,高峰,郭为忠等.锻造操作机的回顾与展望.中国机构与机器科学应用国际会议论文集,2007：12-15.
[7]Harrison R.Forging manipulator:US,3696651[P].1972,10,10.
[8]Eberhard B. Forging manipulator:Germany,E10128451(A1)[P].2002,05,12.
[9]Kutz H.Workpiece manipulator for use in a forging press:US,4031736[P].1977,06,28.
[10]Kost E,FOLTA W.Gripper feed and gripper resilience cylinders on forging manipulators:US,4420287 [P].1983,12,13.
[11]Hemingway et al.Crane and manipulator integration:US,4430041[P].1984,02,07.
[12]Schubert.Workpiece clamping devices in forging manipulators:US,4776199[P].1988,10,11.
[13]Schubert.Forgin manipulator:US,4815311[P].1989,03,28.
[14]Wilson et al.Manipulator for metal ingots:US,4961336[P].1990,10,09.
[15]Brucher.Quick-action coupling for forge and conveyor manipulators:US,5118248[P].1992,06,02.
[16]Westermeyer.Process and apparatus for opertaing a press unit:US,5454262[P].1995,10,03.
[17]尹朝国.自由锻操作机械化及其发展[J].锻压机械,1992,4：40-42.
[18]玉凤喜.锻造操作机技术近期的发展[J].重型机械,1994,4：12-17.
[19]顾震隆.锤上操作机的动力分析探讨[J].哈尔滨工业大学学报,1979,3：1-10.
[20]哈尔滨工业大学操作机小组.锻造操作机动力分析的初步探讨[J].锻压机械,1979,3：19-22.
[21]权修华.锻造操作机动载荷分析与计算[J].重型机械,1987,10：26-29.
[22]权修华.操作机承载状态分析与计算[J].锻压机械,1988,5：41.44.
[23]王凤喜.锻造液压机与操作机的发展[J].锻压机械,1998,6：3.5.
[24]任云鹏,张计磊,韩清凯等.锻造操作机结构系统的动力有限元建模方法研究[J].机械设计与制造,2008,7：103.105.
[25]任云鹏,张天侠,韩清凯等.锻造操作机机械结构的模态匹配分析[J].机械设计与制造,2008,12：186.187.
[26]任云鹏,张天侠.锻造操作机的可视化刚体动力学仿真[J].中国工程机械学报,2008,6(2)：127-132.
[27]陈博翁,关立文,李铁民.基于ADAMS的锻造操作机动力学仿真及优化设计[J].机械设计与制造,2009,3：6-8.
[28]范凡,王皓,赵勇.自由锻造操作机冗余驱动系统的驱动力分配与协调[J].机械设计,2009,26(9)：26-30.
[29]王立平,吴昱,关立文.锻造操作机相似试验台设计和仿真[J].制造技术与机床,2009,8：57-62.
[30]高峰,郭为忠,宋清玉等.重型制造装备国内外研究与发展[J].机械工程学报,2010,46(19)：92.107.
[31]韩雅楠,李刚,罗晓明.基于Simpack的重载操作机刚柔耦合动力学分析[J].动力学与控制学报,2010,8(3)：267-272.
[32]梁音,王馨舶,李洪胜等.锻造操作机钳杆操纵过程的动力学特性分析[J].重型机械,2010,5：38-42.
[33]刘松柏,邓华,何竞飞.巨型重载夹持装置动态夹持力建模与承载能力分析[J].现代制造工程,2010.1：107-111.
[34]任云鹏,韩清凯,张天侠等.基于虚拟样机技术的锻造操作机的动力学仿真[J].东北大学学报(自然科学版)：2010,31(8)：1170-1173.
[35]任云鹏,陈希红,卢祟劭等.基于虚拟样机技术的锻造操作机的刚柔混合仿真分析[J].科技成果纵横,2010,1：50-53.
[36]同新星.基于虚拟样机技术的锻造操作机缓冲装置研究[J].设备,2010,4：46-49.
[37]王红,张涛,杨文玉等.锻造操作机夹持界面接触力学数值分析[J].锻造,2010,1：77-81.
[38]翟富刚,孔祥东,王林等.锻造操作机夹持机构最优夹紧力分析[J].机械设计与研究,2010,26(4)：38-41.
[39]翟富刚,孔祥东,姚静等.锻造操作机夹钳回转系统动态特性仿真研究[J].液压与气动,2010,3：61.63.
[40]翟群杰.锻造操作机钳杆机构的动态分析[J].锻压技术,2010,35(5)：96-99.
[41]李刚,刘德时.锻造操作机大范围顺应运动的动力学行为分析[J].机械工程学报,2010,46(11)：21.28.
[42]关立文,程宁波.锻造操作机相似模型逆动力学建模与非线性控制器设计[J].机械工程学报,2010,46(11)：55-61.
[43]李刚,陈高杰.锻造操作机钳臂结构的多轴疲劳分析[J].哈尔滨工业大学学报,2011,43(S1)：100.105.
[44]赵勇,林忠钦,王皓.重型锻造操作机的操作性能分析[J].机械工程学报,2010,46(11)：69-75.
[45]林晓文,王皓,赵勇.考虑构件弹性变形的锻造操作机静刚度分析[J].机械设计与研究,2011,27(1)：94-98.
[46]牛勇,张营杰,房志远等1000kN_2500kNm锻造操作机吊挂装置仿真研究[J].重型机械.2011,2：19-22.
[47]赵国藩.结构可靠度理论[M].北京：中国建筑工业出版社,2000.
[48]赵国藩,曹居易,张宽权.工程结构可靠度[M].北京：水利电力出版社,1984.
[49]李春明.优化方法[M].南京：东南大学出版社,2009.
[50]Venkayya V B.Design of Optimum Structures[J]. Computers and Structures,1971,1(1-2):265-309.
[51]Fleury C,Sanders G.Relations between optimality criteria and mathematical programming in structural optimization[C].In:Proceedings of the Symposium on Applications of Computer Methods in Engineering,Univ. of California, Los Angeles,CA,1977:507-520.
[52]钱令希.工程结构优化设计[M].北京：水利电力出版社,1983.
[53]程耿东.工程结构优化设计基础[M].北京：水利电力出版社,1984.
[54]Vanderplaats G N.Structural design optimization status and direction[J] Journal of Aircraft,1999, 36(1):11-20.
[55]Burns S A.Structural engineering institute technical committee on optimal structural design[J].Recent Advances in Optimal Structural Design.ASCE Publications,2002.
[56]Allaire G,Henrot A.On some recent advances in shape optimization[J].Comptes Rendus de l'Academie des Sciences-Series IIB-Mechanics,2001,329(5):383-396.
[57]Eschenauer H A, Olhoff N.Topology optimization of continuum structures:A review[J].Applied Mechanics Reviews,2001,54(4):331-390.
[58]Dorns W S,Gomory R E,Greenberg H J.Automatic design of optimal structure[J].J Mechanics,1964, 3,25-52.
[59]Rossow M P,Taylor J E,A finite element method for the optimal design of variable thickness sheets[J].AIAA Journal,1973,11(11):1566-1569.
[60]Cheng G D,Olhoff N.An investigation concerning optimal design of solid elastic plates[J]. International Journal of Solids and Structures,1981,17(3):305-323.
[61]Cheng G D.On non-smoothness in optimal design of solid elastic plates[J].International Journal of Solids and Structures,1981,17,795-810.
[62]Bendsoe M P,Kikuchi N.Generating optimal topologies in structural design using a homogenization method[J].Computer Methods in Applied Mechanics and Engineering,1988,71:197-224.
[63]Hassani B,Hinton E.A review of homogenization and topology optimization Ⅰ-topology optimization using optimality criteria[J].Computers & Structures,1998,69:707-717.
[64]Hassani B,Hinton E.A review of homogenization and topology optimization Ⅱ-topology optimization using optimality criteria[J].Computers & Structures,1998,69:718-738.
[65]Hassani B,Hinton E.A review of homogenization and topology optimization Ⅲ-topology optimization using optimality criteria[J].Computers & Structures,1998,69:739-756.
[66]刘书田.复合材料性能预测与梯度功能材料优化设计[D].大连理工大学,1994.
[67]刘书田.复合材料应力分析的均匀化方法[J].力学学报,1997,5(29)：306-313.
[68]刘书田,程耿东.基于均匀化理论的梯度功能材料优化设计方法[J].宇航材料工艺,1995,6：21-27.
[69]Zhou M,Rozvany G I N.The COC algorithm,Part II:topological and geometrical and generalized shape optimization[J].Computer Methods in Applied Mechanics and Engineering,1991,89:309-336.
[70]Bendsoe M P,Sigmund O.Material interpolation Schemes in topology Optimization[J].Archive of applied Mechanics,1999,69:653-645.
[71]Sethian J A,Wiegmann A. Structural boundary design via level set and immersed interface methods [J].Journal of Computational Physics,2000,163:489-528.
[72]Wang M Y,Wang X M,Guo D.A level set method for structural topology optimization[J].Computer Methods in Applied Mechanics and Engineering,2003,192:227-246.
[73]梅玉林.拓扑优化的水平集方法及其在刚性结构、柔性结构和材料设计中的应用[D].大连理工大学,2004.
[74]Eschenauer H A,Kobelev H A,Schumacher A.Bubble method for topology and shape optimization of structures [J]. Structural Optimization,1994,8:142-151.
[75]Sokolowski J,Zochowski A.On the topological derivative in shape optimization[J].SIAM Journal of Control Optimzation,1999,37:1251-1272.
[76]Xie Y M,Steven G P.A simple evolutionary procedure for structure optimization[J].Computers and Structures,1993,49:885-896.
[77]Bendsoe M P,Sigmund O.Topology optimization:theory,methods and applications[M].Berlin:Springer Verlag,2003.
[78]贾海朋.结构与柔性机构拓扑优化[D].大连理工大学,2004.
[79]Diaz A R,Kikuchi N.Solutions to shape and topology eigenvalue optimization problems using a homogenization method[J].International Journal for Numerical Methods in Engineering,1992,35 (7):1487-1502.
[80]Cheng G D.Some aspects of truss topology optimization[J].Structural Optimization,1995,10(3-4): 173-179.
[81]程耿东.考虑局部稳定性约束的析架拓扑优化设计[J].大连理工大学学报,1995,35(6)：770-775.
[82]Guo X,Cheng G D,Olhoff N.Optimum design of truss topology under buckling constraints[J]. Structural and Multidisciplinary Optimization,2005,30(3):169-180.
[83]中华人民共和国国家标准.工程结构可靠度设计统一标准.GB 50153.200X(征求意见稿).
[84]Freudenthal A M.The safety of structures [J]. Transactions of ASCE,1947,112:125-180.
[85]Cornell C A.A probability-based structural code[J].Journal of American Concrete Institute,1969, 66(12):974-985.
[86]Hasofer A M,Lind N C.Exact and invariant second moment code format[J].Journal of Engineering Mechanics,1974,100(EM1):111-121.
[87]Rackwitz R,Fiessler B.Structural reliability under combined random load sequences [J].Computers and Structures,1978,9:489-494.
[88]Fiessler B,Neumann H J,Rackwitz R.Quadratic limit states in structural reliability[J].Journal of Engineering,Mechanics Division ASCE,1979,105(EM4):661-676.
[89]Schueller G I,Bucher C G,Bourgund U,et al.On efficient computational schemes to calculate structural failure probabilities[J] Journal of Probabilistic Engineering Mechanics,1989,4(1):10-18.
[90]Ditlevsen O,Melchers R E,Gluver H.General multi-dimensional probability integration by directional simulation[J].Computers and Structures,1990,36(2):355-368.
[91]Barton R R.Metamodel for simulation input-output relations[C].Proceedings of the 1992 winier simulation Conference,1992:289-299.
[92]Faravelli L.Response surface approach for reliability analysis[J].Journal of Engineering Mechanics, 1989,115(12):2763-2781.
[93]赵敏,陈文.基于径向基函数的加权最小二乘无网格法[J].计算力学学报,2011,28(1)：66-71.
[94]刘小民,张文斌.一种基于径向基函数的替代模型构造方法[J].燕山大学学报,2010,34(5)：390-394.
[95]Kaymaz I.Application of kriging method to structural reliability problems[J].Structural Safety,2005, 27(2):133-151.
[96]彭泽.结构可靠度Metamodel方法及其工程应用研究[D].中南大学.2010.
[97]张崎.基于Kriging方法的结构可靠性分析及优化设计[D].大连理工大学,2005.
[98]邓乃扬,田英杰.数据挖掘中的新方法-支持向量机[M].北京：科学出版社.2004.
[99]Vapnik V N(张学工译).统计学习论理的本质.北京：清华大学出社,2000.
[100]李洪双,吕震宙,岳珠峰.结构可靠性分析的支持向量机方法[J].应用数学与力学,2006,27(10)：1135-1143.
[101]李刚,刘志强.基于支持向量机替代模型的可靠性分析[J].计算力学学报,2011,28(5)：676-681.
[102]Rosenblueth E.Point estimation for probalility moments[J].Proceedings of the National Academy of Sciences,1975,72(10):3812-3814.
[103]Rosenblueth E.Two-point estimates in probalility[J]. Application Mathematics Modeling,1981, 5:329-335.
[104]Gorman M R.Reliability of structural system[D].Cleveland:Case Western Reserve University,1980.
[105]Seo H S,Kwak B M.Efficient statistical tolerance analysis for general distributions using three-point information [J]. International Journal of Production Research,2002,40(4):931-944.
[106]Zhao Y G,Ono T.New point estimates for probability moments [J]. Journal of Engineering Mechanics, 2000,126(4):433-436.
[107]Zhou J H,Nowak A S.Integration formulas to evaluate functions of random variables[J].Structural Safety,1998,5:267-284.
[108]Harr M E.Probability estimate for multivariate analysis [J]. Application Mathematics Modellinig,1989, 13(5):313-318.
[109]Cheng C Hating Y Keying J C.Evaluatuon of probability point estimate methods[J]. Application Mathematics Modellinig,1995,19(2):995-105.
[110]Li K S.Point estimate method for calculating statistical moments[J].Journal of Engineering Mechanics, 1992,118(7):1506-1511.
[111]Hong H P.An efficient point estimate method for probabilistic analysis[J].Reliability Engineering and System Safety,1998,59:261-267.
[112]Zhao Y G,Ono T.Moment methods for structural reliability [J]. Structural Safety,2001,23:47-75.
[113]Xu L,Cheng G D.Discussion on:moment methods for Structural reliability[J].Structural safety,2003, 25,193-199.
[114]许林.基于可靠度的结构优化研究[D].大连理工大学,2004.
[115]Rosenblatt M.Remarks on a multivariate transformation[J].Annals Math Stat,1952,23:470-472.
[116]Nataf A.Determination des distribution dont les marges sont donnees[J].ComptesRedus de l'Academie des Sciences,1962,225:42-43.
[117]Liu P L,Kiureghian D A.Multivariate distribution models with prescribed marginals and covariances [J].Probabilistic Engineering Mechanics,1986,1(2):105-112.
[118]Kiureghian D A,Liu P L.Structural reliability under incomplete probability information[J].Journal of Engineering Mechanics,1986,112:85-104.
[119]李国强,李继华.二阶矩矩阵法关于相关随机向量的结构可靠度计算[J].重庆建筑工程学院学报,1987,1：55.67.
[120]武清玺,吕泰仁,吴世伟.变量相关时结构可靠指标的计算[J].高校应用数学学报,1987,2(3)：323-329.
[121]李宏,吴世伟,吕泰仁.变量相关下的JC法[J].港工科技,1991,3：21-25.
[122]李云贵.赵国藩.广义随机空间内的一次可靠度分析方法[J].大连理工大学学报,1993,33(S1)：S1-S5.
[123]傅旭东.相关变量下失效概率的计算机模拟[J].西南交通大学学报,1997,32：319-323.
[124]俞铭华,姚金山.变量相关的船舶结构可靠性分析[J].华东船舶工业学院学报,1997,11(2)：1-7.
[125]李惠强,范涤.变量相关时悬臂桩支护结构可靠性分析[J].华中理工大学学报,1998,26(8)：44-46.
[126]洪昌华,龚晓南.相关情况下Hasofer Lind可靠度指标的求解[J].岩土力学,2000,21(1)：68-72.
[127]罗红,梁波.非线性相关条件下可靠指标的改进计算方法[J].工程力学,2000,17(4)：99.104.
[128]姚继涛,董振平.随机变量的相关性和结构可靠度[J].西安建筑科技大学学报,2000,32(2)：114-118.
[129]严松宏,赵朝前.变量相关条件下可靠指标计算[J].兰州铁道学院学报,2001,20(4)：42-44.
[130]李斌,严松宏.变量相关情况下结构可靠指标的简化算法[J].西南交通大学学报,2004,39(2)：147-151.
[131]江晓俐.相关腐蚀与疲劳及维修对船体可靠性的影响[J].武汉理工大学学报(交通科学与工程版)：2005,29(3)：363-366.
[132]郄禄文.结构可靠度分析中随机变量间相关系数的特性[J].港工科技,2006,4：18-20.
[133]吕大刚.基于线性化Nataf变换的一次可靠度方法[J].工程力学,2007,24(5)：79-86.
[134]吕大刚,于晓辉,王光远.基于改进点估计法的结构整体概率抗震能力分析[J].世界地震工程,2008,24(4)7-14.
[135]李洪双,吕震宙,袁修开.基于Nataf变换的点估计法[J].科学通报,2008,53(6)：627-632.
[136]侯钢领,欧进萍.广义可靠指标矢量及其计算与应用[J].哈尔滨工程大学学报,2009,30(2)：132-137.
[137]刘小辉.一类基本变量相关的结构功能函数的可靠性分析[J].集美大学学报(自然科学版)：2009,14(3)：299-302.
[138]吴振君,王水林,汤华等.边坡可靠度分析的一种新的优化求解方法[J].岩土力学,2010,31(3)：713-718.
[139]李庆典,周创兵,陈益峰等.边坡可靠度分析的随机响应面法及程序实现[J].岩石力学与工程学报,2010,29(8)：1514-1523.
[140]刘金刚,王世鹏,解艳彩.广义随机空间内结构可靠性优化设计[J].机械设计与研究,2010,26(5)：7-9.
[141]吕大刚,宋鹏彦,于晓辉等.基于矩法的结构非线性整体抗震可靠性分析[J].建筑结构学报,2010,S2：119-124.
[142]Ditlevsen O,Madsen H O.Structural reliability methods[M].Chichester:John Wiley & Sons Ltd,2005.
[143]张明.结构可靠度分析.方法与程序[M].北京：科学出版社,2009.
[144]Madsen H O,Krenk S,Lind N C.Methods of structural safety,prentice-hall[M].NJ:Inc., Englewood Cliffs,1986.
[145]Ditlevsen O.Generalized second moment reliability index[J]Journal of Structural Mechanics,1979,7(4): 435-451.
[146]Chen X,Lind N C.Fast probability integration by three parameter normal tail approximation[J]. Structural Safety,1983,1 (4):269-276.
[147]Tichy M.First-order third-moment reliability method[J].Structural Safety,1994,16:189-200.
[148]Shinazuka M.Basic Analysis of structural safety[J].Journal of Structural Engineering,1983,109(3): 721-740.
[149]Harbitz A.An efficient sampling method for probability of failure calculation[J].Structural Safety, 1986,3:109-115.
[150]Schueller G I,Stix R.A critical appraisal of methods to determine failure probabilities[J]. Structural Safety,1987,4(4):293-309.
[151]Bucher C G.Adaptive sampling-an iterative fast Monte Carlo procedure[J].Structural Safety,1988, 5(2):119-126.
[152]Ang G L,Ang A S,Tang W H.Optimal importance sampling density estimator[J] Journal of Engineering Mechanics,1992,118(6):1146-1163.
[153]Maes M A,Breitung K,Dupuis D J.Asymptotic importance sampling[J].Structural Safety,1993, 12:167-183.
[154]Au S K,Beck J L.A new adaptive importance sampling scheme for reliability calculations[J]. Structural Safety,1999,21 (2):135-158.
[155]Mori Y,Kato T.Multinormal integrals by importance sampling for series system reliability[J]. Structural Safety,2003,25(4):363-378.
[156]Bjerager P.Probability integration by directional simulation[J] Journal of Engineering Mechanics, 1988,114(8):1285-1301.
[157]Ditlevsen O,Bjerager P.Plastic reliability analysis by directional simulation[J].Journal of Engineering Mechanics,1989,115(6):1347-1362.
[158]Ditlevsen O,Olesen R,Mohr G.Solution of a class of load combination problems by directional simulation[J].Structural Safety,1987,4:95-109.
[159]Ditlevsen O,Hasofer A M,Pjerager P,et al.Directional simulation in gaussian processes[J]. Probabilistic Engineering Mechanics,1988,3:207-217.
[160]Nie J S,Ellingwood B R.Directional methods for structural reliability analysis[J].Structural Safety,2000,22(3):233-249.
[161]Melchers R E.Radial importance sampling for structural reliability[J]. Journal of Engineering Mechanics,1990,116(1):189-203.
[162]Katsuki S,Frangopol D M.Hyperspace division method for structural reliability [J]. Journal of Engineering Mechanics,1994,120(11):2405-2427.
[163]Stein M.Large sample properties of simulations using latin hypercube sampling [J].Technometrics, 1987,29(2):143-151.
[164]Olsson A,Sandberg G E.Latin hypercube sampling for stochastic finite element analysis[J]. Journal of Engineering Mechanics,2002,128(1):121-125.
[165]Olsson A,Sandberg G E,Dahlblom O.On latin hypercube sampling for structural reliability analysis[J]. Structural Safety,2003,25(1):47-68.
[166]Ono T,Idota H.Development of high-order moment standardization method into structural design and its efficiency[J].J Structural and Construction Engineering,1986,365:40-7.
[167]Hong HP.Point-estimate moment-based reliability analysis[J].Civil Engineering System,1996,13: 281-294.
[168]Rahman S,Xu H.A univariate dimension-reduction method for multi-dimensional Integration in Stochastic Mechanics[J].Probabilistic Engineering Mechanics,2004,19:393-408.
[169]Xu H,Rahman S.A generalized dimension-reduction method for multi-dimensional integration in stochastic mechanics[J].International Journal for Numerical Methods in Engineering,2004,61: 1992-2019.
[170]Youn B D,Xi Z M,Wang P F.Eigenvector dimension reduction (EDR) method for sensitivity-free probability analysis [J]. Structural and Multidisciplinary Optimization,2008,37:13-28.
[171]Ju B H,Lee B C.Improved moment-based Quadrature rule and its application to reliability-based design optimization [J] Journal of Mechanical Science and Technology,2007,21:1162-1171.
[172]Choi C H,Won J H,Choi J H.Improving the dimension reduction method (DRM) in the uncertainty analysis and application to the reliability based design optimization[C],7th World Congress on Structural and Multidisciplinary Optimization COEX Seoul,21 May-25May,2007,Korea.
[173]Ormoneit D, White H.An efficient algorithm to compute maximum entropy densities [J].Econometrics Reviews,1999,18(2):127-140.
[174]Karian Z E,Dudewicz E J,McDonald P.The extended generalized lambda distribution system for fitting distributions to data:history, completion of theory, tables, applications, the "final word" on moment fits[J].Communications in Statistics-Computation and Simulation,1996,25(3):611-642.
[175]Erdem A,Masoud R R,Christopher D E.Reliability estimation using dimension reduction and extended generalized lambda distribution[C].49th AIAA/ASME/ASCE/AHS/ASC Structures Structural Dynamics and Materials Schaumburg USA,2008.
[176]Huang B,Du X.Uncertainty analysis by dimension reduction integration and saddlepoint approximations[J]. Journal of Mechanical Design ASME,2006,126(1):26-33.
[177]Shannon C E.A mathematical theory of communication[J].The Bell System Technical Journal,1948, 27:379-423.
[178]Jaynes E T.Information theory and statistical mechanics[J].Physical Review,1957,106(4):620-630.
[179]Daniels H E.Saddlepoint approximations in statistics[J].Annals of Mathematical Statistics,1954, 25:631-650.
[180]Papoulis A,Pillai S U.Probability, Random variables and stochastic processes,4th edition[M].New York:McGraw-Hill,2002.
[181]Kang H Y,Kwak B M.Application of maximum entropy principle for reliability-based design optimization[J].Structural and Multidisciplinary Optimization,2009,38(4):331-346.
[182]Zellner A,Highfield R A.Calculation of maximum entropy distributions and approximation of marginal posterior distributions[J] Journal of Econometrics,1988,37(2):195-209.
[183]Mukherjee D,Hurst D C.Maximum entropy revisited[J].Statistical Neerlandica,1984,38(1):1-12.
[184]佟晓利.改进的Rosenblueth方法及其在结构可靠度分析中应用[J].大连理工大学学报,1997,37(3)：316-321.
[185]韦征,叶继红,沈世钊.基于最大熵法的单层球面网壳在地震作用下的破坏模式预测[J].振动与冲击,2008,27(6)：64-69.
[186]坚民,郭冰菁,王中宇等.基于最大熵方法的测量结果估计及测量不确定度评定[J].电测与仪表,2005,42(8)：5-8.
[187]席娜丽.基于最大熵原理的工程边坡参数估计及可靠度分析研究[D].西安建筑科技大学,2006.
[188]邹春霞,申向东,王丽萍等.水工建筑物可靠性分析中的最大熵法[J].福州大学学报(自然科学版),2005,S1：115-118.
[189]章光,朱维申,白世伟.计算近似失效概率的最大熵密度函数法[J].岩石力学与工程学报,1995,14(2)：119.129.
[190]李云贵,赵国藩.结构可靠度的四阶矩分析法[J].大连理工大学学报,1992,32(4)：455-459.
[191]韦征,叶继红,沈世钊.最大熵法可靠度理论在工程中的应用[J].振动与冲击,2007,26(6)：146.151.
[192]谭羽非,王晓霞,邹平华.最大熵原理与供热系统元部件可靠性的研究[J].煤气与热力,2003,23(7)：387-390.
[193]陈虬,戴志敏.随机有限元一最大熵法[J].工程力学,1992,13(3)：1.7.
[194]杨令强,练继建,张社荣等.随机有限元与最大熵法联合求混凝土拱坝可靠度[J].水利水运工程学报,2003,2：24-28.
[195]Gu L,Yang R J,Cho C H,et al.Optimization and robustness for crashworthiness of side impact[J]. International Journal of Vehicle Design,2001,26(4):348-360.
[196]Yi P,Cheng G D,Jiang L.A sequential approximate programming strategy for performance-measure-based probabilistic structural design optimization[J].Structural Safety,2008,30(2):91-109.
[197]Winterstein S R.Nonlinear vibration models for extremes and Fatigue[J].Journal of Engineering Mechanics,1988,110(10):1772-1790.
[198]Ditlevsen O,Mohr G,Hoffmeyer P.Integration of non-Gaussian fields[J].Probabilistic Engineering Mechanics,1996,11:15-23.
[199]Noh Y,Choi K K,Du L.Reliability-based design optimization of problems with correlated input variables using a Gaussian Copula[J].Structural and Multidisciplinary Optimization,2009,38:1-16.
[200]Sigmund O.Numerical instabilities in topology optimization:a survey on procedure dealing with checkerboard, mesh-dependencies and local Minima[J].Structural Optimization,1997,16:68-75.
[201]潘丽军,陈锦权.实验设计与数据处理[M].南京：东南大学出版社,2008.
[202]Fang K. T,Li R Z,Sudjianto A.Design and modeling for computer experiments[M].Boca Raton:CRC Press Inc.,2006.
[203]Montgomery D C.Design and analysis of experiments,6thEdition[M].New York:JohnWily&Sons,Ine, 2005.
[204]赵选民.试验设计方法[M].北京：科学出版设,2006.
[205]开泰.均匀试验设计的理论、方法和应用一历史回顾[M].数理统计与管理,2005.
[206]Fang K T,Ge G N,Liu M Q.Construction on E(fNOD)-optimal supersaturated designs via room squares[J].Calcutta Statistical Association Bulletin,2002,52:205-208.
[207]Sacks J,Welch W J,Mitchell T J,et al.Design and analysis of computer experiments[J]. Statistical Science,1989,4(4):409-423.
[208]Koehler J R,Owen A B.Computer experiments[J].Handbook of Statistics,1996,13:261-308.
[209]Jin R,Chen W,Sudjianto A. An efficient algorithm for constructing optimal Design of Computer Experiments[C].ASME Design Automation Conference,Chicago,IL,September:2-6,2003.
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |