基于智能算法的结构可靠性分析及优化设计研究
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摘要
结构可靠性作为衡量结构质量的重要指标之一,越来越受到工程界的高度重视。结构可靠性是一门综合性的工程学科,主要包括可靠性分析、优化设计、评价、使用和控制。可靠性分析及优化设计是结构可靠性活动的关键环节,它从根本上决定了结构的可靠性程度和使用寿命。结构可靠性分析及优化设计是将可靠性分析方法与优化设计完美地结合在一起,将结构可靠性指标作为约束条件或追求的目标,从而得到最佳设计变量的一种计算方法。结构可靠性分析及优化设计方法有着比传统结构设计方法更为合理的设计理念和模型,工程实际应用也证明了该方法可以显著提高结构设计质量和结构固有可靠性,并获得明显的经济效益。因此,目前对结构可靠性分析及优化设计的研究已成为国内外学者积极探索的重要领域之一
支持向量机是根据统计学理论中结构风险最小化原则提出的一种利用最优化方法解决机器学习问题的方法。它在解决小样本学习和预测、非线性及高维模式识别问题中具有突出的优势。粒子群算法模拟鸟群飞行觅食行为,通过鸟之间的集体协作使群体达到最优。该算法简洁且易于实现,需要设置的参数较少。粒子群算法是非线性连续优化问题、组合优化问题和整数非线性优化问题的有效优化工具。因此,本论文结合国家自然科学基金项目(51175442),利用支持向量机理论、粒子群算法及其改进算法和结构可靠性模型,进行结构可靠性分析及优化设计。
针对具有隐式极限状态方程的结构,本文结合支持向量机理论和改进一次二阶矩法,提出了一种基于支持向量机回归的结构概率可靠性分析方法。通过一个数值算例和两个实际结构算例验证了支持向量机模型的预测精度,证明了该方法的可行性、计算精度和较高的工程实用价值。结合区间分析方法和支持向量机理论,本文发展了一种基于支持向量机的隐式结构非概率可靠性分析方法。该方法是一种优化迭代算法,构造出合适的迭代流程就可以计算得到高精度的非概率可靠性指标。本文还通过四个算例验证了该方法的可行性、正确性和高精度。因此,该方法对其它不确定性结构的非概率可靠性分析具有一定的参考价值。
针对基本粒子群算法容易早熟的问题,充分利用基本粒子群算法的全局搜索能力和混沌优化的局部搜索能力,将混沌粒子群算法和支持向量机理论融入结构概率可靠性优化设计理论中,提出基于混沌粒子群算法的结构概率可靠性优化方法,并对某平面刚架结构进行优化设计。当结构的极限状态方程为隐式时,利用基于支持向量机的结构概率可靠性分析方法对某平面桁架进行概率可靠性优化设计。两个算例优化结果均表明,利用该方法得到的优化结果优于基本粒子群算法、最佳矢量型法和罚函数法。该方法具有全局收敛且精度高的特性,适用于较复杂结构的概率可靠性优化设计,具有较好的工程实用价值和较强的探索开发能力。
利用凸模型方法进行显式结构非概率可靠性指标的计算,结合区间分析方法和支持向量机回归理论进行隐式结构非概率可靠性指标的计算,提出了基于模拟退火粒子群算法的结构非概率可靠性优化方法,并对两个平面桁架结构进行了非概率可靠性优化设计。两个算例证明了该方法具有全局优化能力和较强的概率突跳能力,能高效快速地找到全局最优解,其优化结果显著优于基本粒子群算法和罚函数法。
利用支持向量机和混合可靠性模型,提出了隐式结构混合可靠性分析方法。本文通过对悬臂梁和平面桁架结构的混合可靠性分析,验证了该方法的正确性和精度,证明了当结构同时含有概率参数和非概率参数时,仍采用概率可靠性模型进行分析,计算结果具有一定风险性。针对多失效模式结构,提出了多失效模式结构的混合可靠性分析方法。利用该方法进行隐式和显式结构系统的混合可靠性分析,所得的结构系统混合可靠性指标为一个区间值。本文结合智能单粒子优化算法和结构混合可靠性分析方法,提出了基于智能单粒子优化算法的结构混合可靠性优化方法。研究结果表明,智能单粒子优化算法的优化性能较混沌粒子群算法和模拟退火粒子群算法有一定的改善,其解更接近全局最优解。
本文利用支持向量机和三种改进粒子群算法进行了结构可靠性分析及优化设计,主要解决了隐式结构概率及非概率可靠性分析及优化,混合结构可靠性分析及优化等问题。本文所提方法具有较高的理论意义和工程实用价值,并为后续的研究工作奠定了坚实的基础。
Structural reliability, as one of major factors to judge quality of structure, has been highly concerned by the engineering. Structural reliability is an integrated engineering course, and it mainly includes reliability analysis, optimization design, evaluation, use and control. Reliability analysis and optimization is the key of structural reliability, and it fundamentally decides structural reliability and service life. Structural reliability analysis and optimization is a calculated way to obtain optimal design variable, which combines reliability analysis method with optimization design completely, and define reliability index as constraint condition or goal. The ideas and models of structural reliability analysis and optimization methods are more reasonable than traditional design methods. The engineering practices also show that the method can significantly improve structure design quality and inherent reliability, and good economy benefit can be obtained. Therefore, the current research on structural reliability analysis and optimization has become an important actively exploring domain for domestic and foreign scholars.
According to the structural risk minimization principle in statistical learning theory, support vector machines theory is a method to deal with machine learning by optimization methods. Support vector machines theory possesses outstanding advantages in solving small sample learning and prediction, nonlinear and high dimensional pattern recognition problem. Particle swarm optimization which simulates birds flock's looking for food can make the flock find the optimal solution through working together. This algorithm is simple and easy to realize, and it has few parameters to set. Particle swarm optimization is an effective optimization tool for nonlinear continuous optimization problem, combination optimization problem and integer nonlinear optimization problem. Therefore, according to support vector machines theory, particle swarm optimization and its improvement method and structure reliability model, the reliability analysis and optimization design of structure combined with the National Science Fundamental Project (51175442) is mainly discussed in this paper.
Combining support vector machines theory with advanced first order second moment method, a structural probabilistic reliability analysis method based on support vector regression is presented for the structure with implicit limit state function. One numerical test and two practical engineering examples in this paper are provided to demonstrate the prognostication precision of the support vector machine model, and the examples also show the feasibility, veracity and higher engineering practical value of the method proposed. Combining interval analysis with support vector machines, a non-probabilistic reliability analysis method based on support vector machines is developed for the structure with implicit limit state function. This method is an iterative method, which has appropriate iterative procedure, and high accuracy non-probabilistic reliability index is calculated by the method. The paper also shows that the method is feasible, correct and accuracy by other four examples. Therefore, the method has a certain reference value to non-prbabilistic reliability analysis of other uncertainty structure.
According to the premature phenomenon of particle swarm optimization, chaos particle swarm optimization takes full advantage of particle swarm optimization's global search capability and chaos optimization's local search ability. Chaos particle swarm optimization and support vector machines are applied in structural probabilistic reliability optimization design. A method of structural probabilistic reliability optimization based on chaos particle swarm optimization is presented and a plane rigid frame is improved. For reliability analysis of implicit limit state function, the probabilistic reliability optimized design of a plane truss structure is performed through the structural probabilistic reliability analysis method, which is based on support vector machines. Two calculation examples both indicate that the results are superior to particle swarm optimization, best vector method and penalty function method. The method has the advantage of global convergence and high accuracy. It applies to complicated structure probabilistic reliability optimization design, and has better practical value and exploitation ability in engineering problem.
Structure non-probabilistic reliability index is obtained by convex model method. Combining interval analysis and support vector regression, implicit structure non-probabilistic reliability index is calculated. The method of structure non-probabilistic reliability optimization is presented on the basis of simulate anneal-particle swarm optimization, and two plane truss structure are improved by the method. The results of examples prove that the method has global optimization quality and strong probabilistic jumping quality. The examples also show that the method can quickly find the global optimal solution, and the optimal results of the method are much better than particle swarm optimization and penalty function method.
A new method for implicit structure hybrid reliability analysis based on support vector machines and hybrid reliability model is proposed in this paper. The validity and precision of the method are verified though hybrid reliability analysis of a cantilever and a plane truss structure, and it also shows that the structure has a certain risk if it is analyzed by probabilistic reliability model, when it includes both probabilistic and non-probabilistic parameters. According to the structure of multi-failure mode, a hybrid reliability analysis method is proposed. Implicit and explicit structure system hybrid reliability is analyzed by the method, and the results is an interval-valued. A method for structure hybrid reliability optimization based on intelligent single particle optimizer is proposed in this paper, combining with intelligent single particle optimizer and hybrid reliability analysis method. The results of the study show that intelligent single particle optimizer is superior to chaos particle swarm optimization and simulate anneal-particle swarm optimization in optimize performance, and its solution much closer to global optimal one.
Structure reliability analysis and optimization is conducted in this paper using support vector machines and three modified particle swarm optimizations. This paper mainly studies the problems of probability and non-probability reliability analysis and optimization of structure with implicit limit state function, and the problem of hybrid structure reliability analysis and optimization. The proposed methods have high value on both theory and engineering practice, and establish the foundations for further research.
支持向量机是根据统计学理论中结构风险最小化原则提出的一种利用最优化方法解决机器学习问题的方法。它在解决小样本学习和预测、非线性及高维模式识别问题中具有突出的优势。粒子群算法模拟鸟群飞行觅食行为,通过鸟之间的集体协作使群体达到最优。该算法简洁且易于实现,需要设置的参数较少。粒子群算法是非线性连续优化问题、组合优化问题和整数非线性优化问题的有效优化工具。因此,本论文结合国家自然科学基金项目(51175442),利用支持向量机理论、粒子群算法及其改进算法和结构可靠性模型,进行结构可靠性分析及优化设计。
针对具有隐式极限状态方程的结构,本文结合支持向量机理论和改进一次二阶矩法,提出了一种基于支持向量机回归的结构概率可靠性分析方法。通过一个数值算例和两个实际结构算例验证了支持向量机模型的预测精度,证明了该方法的可行性、计算精度和较高的工程实用价值。结合区间分析方法和支持向量机理论,本文发展了一种基于支持向量机的隐式结构非概率可靠性分析方法。该方法是一种优化迭代算法,构造出合适的迭代流程就可以计算得到高精度的非概率可靠性指标。本文还通过四个算例验证了该方法的可行性、正确性和高精度。因此,该方法对其它不确定性结构的非概率可靠性分析具有一定的参考价值。
针对基本粒子群算法容易早熟的问题,充分利用基本粒子群算法的全局搜索能力和混沌优化的局部搜索能力,将混沌粒子群算法和支持向量机理论融入结构概率可靠性优化设计理论中,提出基于混沌粒子群算法的结构概率可靠性优化方法,并对某平面刚架结构进行优化设计。当结构的极限状态方程为隐式时,利用基于支持向量机的结构概率可靠性分析方法对某平面桁架进行概率可靠性优化设计。两个算例优化结果均表明,利用该方法得到的优化结果优于基本粒子群算法、最佳矢量型法和罚函数法。该方法具有全局收敛且精度高的特性,适用于较复杂结构的概率可靠性优化设计,具有较好的工程实用价值和较强的探索开发能力。
利用凸模型方法进行显式结构非概率可靠性指标的计算,结合区间分析方法和支持向量机回归理论进行隐式结构非概率可靠性指标的计算,提出了基于模拟退火粒子群算法的结构非概率可靠性优化方法,并对两个平面桁架结构进行了非概率可靠性优化设计。两个算例证明了该方法具有全局优化能力和较强的概率突跳能力,能高效快速地找到全局最优解,其优化结果显著优于基本粒子群算法和罚函数法。
利用支持向量机和混合可靠性模型,提出了隐式结构混合可靠性分析方法。本文通过对悬臂梁和平面桁架结构的混合可靠性分析,验证了该方法的正确性和精度,证明了当结构同时含有概率参数和非概率参数时,仍采用概率可靠性模型进行分析,计算结果具有一定风险性。针对多失效模式结构,提出了多失效模式结构的混合可靠性分析方法。利用该方法进行隐式和显式结构系统的混合可靠性分析,所得的结构系统混合可靠性指标为一个区间值。本文结合智能单粒子优化算法和结构混合可靠性分析方法,提出了基于智能单粒子优化算法的结构混合可靠性优化方法。研究结果表明,智能单粒子优化算法的优化性能较混沌粒子群算法和模拟退火粒子群算法有一定的改善,其解更接近全局最优解。
本文利用支持向量机和三种改进粒子群算法进行了结构可靠性分析及优化设计,主要解决了隐式结构概率及非概率可靠性分析及优化,混合结构可靠性分析及优化等问题。本文所提方法具有较高的理论意义和工程实用价值,并为后续的研究工作奠定了坚实的基础。
Structural reliability, as one of major factors to judge quality of structure, has been highly concerned by the engineering. Structural reliability is an integrated engineering course, and it mainly includes reliability analysis, optimization design, evaluation, use and control. Reliability analysis and optimization is the key of structural reliability, and it fundamentally decides structural reliability and service life. Structural reliability analysis and optimization is a calculated way to obtain optimal design variable, which combines reliability analysis method with optimization design completely, and define reliability index as constraint condition or goal. The ideas and models of structural reliability analysis and optimization methods are more reasonable than traditional design methods. The engineering practices also show that the method can significantly improve structure design quality and inherent reliability, and good economy benefit can be obtained. Therefore, the current research on structural reliability analysis and optimization has become an important actively exploring domain for domestic and foreign scholars.
According to the structural risk minimization principle in statistical learning theory, support vector machines theory is a method to deal with machine learning by optimization methods. Support vector machines theory possesses outstanding advantages in solving small sample learning and prediction, nonlinear and high dimensional pattern recognition problem. Particle swarm optimization which simulates birds flock's looking for food can make the flock find the optimal solution through working together. This algorithm is simple and easy to realize, and it has few parameters to set. Particle swarm optimization is an effective optimization tool for nonlinear continuous optimization problem, combination optimization problem and integer nonlinear optimization problem. Therefore, according to support vector machines theory, particle swarm optimization and its improvement method and structure reliability model, the reliability analysis and optimization design of structure combined with the National Science Fundamental Project (51175442) is mainly discussed in this paper.
Combining support vector machines theory with advanced first order second moment method, a structural probabilistic reliability analysis method based on support vector regression is presented for the structure with implicit limit state function. One numerical test and two practical engineering examples in this paper are provided to demonstrate the prognostication precision of the support vector machine model, and the examples also show the feasibility, veracity and higher engineering practical value of the method proposed. Combining interval analysis with support vector machines, a non-probabilistic reliability analysis method based on support vector machines is developed for the structure with implicit limit state function. This method is an iterative method, which has appropriate iterative procedure, and high accuracy non-probabilistic reliability index is calculated by the method. The paper also shows that the method is feasible, correct and accuracy by other four examples. Therefore, the method has a certain reference value to non-prbabilistic reliability analysis of other uncertainty structure.
According to the premature phenomenon of particle swarm optimization, chaos particle swarm optimization takes full advantage of particle swarm optimization's global search capability and chaos optimization's local search ability. Chaos particle swarm optimization and support vector machines are applied in structural probabilistic reliability optimization design. A method of structural probabilistic reliability optimization based on chaos particle swarm optimization is presented and a plane rigid frame is improved. For reliability analysis of implicit limit state function, the probabilistic reliability optimized design of a plane truss structure is performed through the structural probabilistic reliability analysis method, which is based on support vector machines. Two calculation examples both indicate that the results are superior to particle swarm optimization, best vector method and penalty function method. The method has the advantage of global convergence and high accuracy. It applies to complicated structure probabilistic reliability optimization design, and has better practical value and exploitation ability in engineering problem.
Structure non-probabilistic reliability index is obtained by convex model method. Combining interval analysis and support vector regression, implicit structure non-probabilistic reliability index is calculated. The method of structure non-probabilistic reliability optimization is presented on the basis of simulate anneal-particle swarm optimization, and two plane truss structure are improved by the method. The results of examples prove that the method has global optimization quality and strong probabilistic jumping quality. The examples also show that the method can quickly find the global optimal solution, and the optimal results of the method are much better than particle swarm optimization and penalty function method.
A new method for implicit structure hybrid reliability analysis based on support vector machines and hybrid reliability model is proposed in this paper. The validity and precision of the method are verified though hybrid reliability analysis of a cantilever and a plane truss structure, and it also shows that the structure has a certain risk if it is analyzed by probabilistic reliability model, when it includes both probabilistic and non-probabilistic parameters. According to the structure of multi-failure mode, a hybrid reliability analysis method is proposed. Implicit and explicit structure system hybrid reliability is analyzed by the method, and the results is an interval-valued. A method for structure hybrid reliability optimization based on intelligent single particle optimizer is proposed in this paper, combining with intelligent single particle optimizer and hybrid reliability analysis method. The results of the study show that intelligent single particle optimizer is superior to chaos particle swarm optimization and simulate anneal-particle swarm optimization in optimize performance, and its solution much closer to global optimal one.
Structure reliability analysis and optimization is conducted in this paper using support vector machines and three modified particle swarm optimizations. This paper mainly studies the problems of probability and non-probability reliability analysis and optimization of structure with implicit limit state function, and the problem of hybrid structure reliability analysis and optimization. The proposed methods have high value on both theory and engineering practice, and establish the foundations for further research.
引文
[1]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.
[2]杨瑞刚.机械可靠性设计与应用[M].北京：冶金工业出版社,2008：1-6.
[3]Freudenthal A M. The safety of structures [J]. ASCE Trans.,1947,112:125-129.
[4]孟广伟,李锋,赵云亮.基于随机有限元法的疲劳断裂可靠性分析[J].吉林大学学报,2006,36(3)：16-19.
[5]刘仁云,张义民,刘巧伶.基于多目标优化策略的结构可靠性稳健设计[J].应用力学学报,2007,24(1)：267-271.
[6]孙新利.工程可靠性教程[M].北京：国防工业出版社,2005：1-20.
[7]姜兴渭.可靠性工程技术[M].哈尔滨：哈尔滨工业大学出版社,2005：15-50.
[8]孙志礼,陈良玉.实用机械可靠性设计理论与方法[M].北京：科学出版社,2003：10-30.
[9]张建国,苏多,刘英卫.机械产品可靠性分析与优化[M].北京：电子工业出版社,2008：1-80.
[10]叶晓琰,蒋小平,许建强等.往复泵曲轴疲劳可靠性分析[J].机械工程学报,2008,44(10)：272-276.
[11]郭耀斌,张文明,张国芬.基于蒙特卡罗法的螺旋锥齿轮接触疲劳可靠性分析[J].农业机械学报,2008,39(4)：157-159.
[12]Mainak M, David W C, Kelvin M. A highly efficient Monte Carlo method for assessment of system reliability based on a Markov model [J]. Quality Control and Applied Statistics,2001,46(1):109-112.
[13]安伟光,蔡荫林,陈卫东.随机结构系统可靠性分析与优化设计[M].哈尔滨：哈尔滨工程大学出版社,2007：41-79.
[14]吕震宙,宋述芳,李洪双等.结构机构可靠性及可靠性灵敏度分析[M].北京：科学出版社,2009：9-36.
[15]王军,邱志平.结构的概率-非概率混合可靠性模型[J].航空学报,2009,30(8)：1398-1404.
[16]郭书祥,吕震宙.结构可靠性分析的概率和非概率混合模型[J].机械强度,2002,24(4)：524-526.
[17]白鹏,张喜斌,张斌等.支持向量机理论及工程应用实例[M].西安：西安电子科技大学出版社,2008：30-70.
[18]徐长航,陈国明,谢静.基于支持向量机和蒙特卡洛的结构可靠性分析方法及应用[J].中国石油大学学报,2008,32(4)：103-108.
[19]Kennedy J, Eberhart R. Particle swarm optimization [C]//Proc. of International Conference on Neural Networks:IEEE Press,1995:1942-1948.
[20]段晓东,王存睿,刘向东.粒子群算法及其应用[M].沈阳：辽宁大学出版社,2007：11-41.
[21]赵国藩,金伟良,贡金鑫.结构可靠度理论[M].北京：中国建筑工业出版社,2000：6-23.
[22]Cornell C A. A probability-based structural code[J]. ACI Journal Proceedings, 1969,66(12):974-985.
[23]黄学明,李国芬.结构可靠性研究综述[J].山西建筑,2007,33(11)：76-77.
[24]Hasofer A M, Lind N. An exact and invariant first order reliability format [J]. Journal of Engineering Mechanics,1974,10(EM1):111-127.
[25]Zhao T G, Ono T. New approximations for SORM:Part 1[J]. Journal of Engineering Mechanics,1999,125(1):79-85.
[26]赵维涛,安伟光,严心池.二次二阶矩可靠性指标[J].哈尔滨工程大学学报,2004,25(2)：240-242.
[27]Rackwitz R, Fiessler B. An algorithm for calculation of structural reliability under combined loading. Munchen,1977.
[28]贡金鑫,赵国藩.国外结构可靠性理论的应用与发展[J].土木工程学报,2005,38(2)：1-7.
[29]Sami W. Tabsh. Safety of reinforced concrete members designed following ACI 318 building code[J]. Engineering Structures,1997,19(10):843-850.
[30]航空工业部科学技术委员会编著.飞机结构损伤容限设计指南.航空工业部科学技术情报研究所,1985.
[31]航空工业部科学技术研究院编.飞机结构耐久性损伤容限设计手册(2).飞机结构的疲劳分析.航空工业部科学技术情况研究所,1989.
[32]冯元生,董聪.枚举结构主要失效模式的一种方法[J].航空学报1991,12(9)：537-541.
[33]安伟光,蔡荫林.冗余桁架结构的故障分析[J].哈尔滨船舶工程学院学报,1989,10(4)：479-485.
[34]安伟光,蔡荫林.冗余度结构故障概率计算的一种方法[J].兵工学报,1992(2)：92-96.
[35]蔡荫林,安伟光,陈卫东.空间桁架结构基于可靠性的优化设计[C].第六届空间结构学术会议论文集.北京：地震出版社,1992：210-217.
[36]Ditlevsen O. Narrow reliability bounds for structural system[J]. Journal of Structural Mechanics,1979,7(4):453-472.
[37]Alfredo H.-S. A, Tang W H. Probability concepts in engineering planning and design[M]. John Wiley and Sons,1984:23-56.
[38]Song B F. A numerical integration method in affine space and a method with high accuracy for computing structural system reliability[J]. computer and Structures, 1992,42(2):255-262.
[39]蔡荫林,周健生.结构系统失效概率的近似公式[J].航空学报,1992,13(3)：219-223.
[40]陈卫东,王善,蔡荫林.杆板结构系统的可靠性分析[J].哈尔滨工程大学学报,1997,18(6)：68-74.
[41]安伟光.载荷效应组合时的失效概率[J].哈尔滨船舶工程学院学报,1988,9(2)：126-136.
[42]安伟光, 陈卫东.结构系统在随机组合力作用下的可靠性分析[J].哈尔滨工程大学学报,1996,17(1)：15-23.
[43]蔡荫林,安伟光.随机组合力下冗余结构的故障概率计算[J].哈尔滨船舶工程学院学报,1989,10(2)：135-144.
[44]郭书祥.非随机不确定结构的可靠性方法和优化设计研究[D].西北工业大学博士学位论文.2002：4-10.
[45]Ben-Haim Y, Elishakoff I. Convex models of uncertainty in applied mechanics [M]. Amsterdam:Elsevier Science Publishers,1990:12-45.
[46]Elishakoff I. Essay on uncertainties in elastic and viscoelastic structures:form A M Freudenthal's criticisms to modern convex modeling [J]. Computers and Structures, 1995,56(6):871-895.
[47]邱志平,王晓军.不确定性结构力学问题的集合理论凸方法[M].北京：科学出版社,2008：1-9.
[48]曹鸿钧,段宝岩.基于凸集合模型的非概率可靠性研究[J].计算力学学报,2005,22(5)：546-549.
[49]罗阳军,亢战.超椭球模型下结构非概率可靠性指标的迭代算法[J].计算力学学报,2008,25(6)：747-752.
[50]Ben-Haim Y. A non-probabilistic concept of reliability[J]. Structural Safety, 1994,14(4):227-245.
[51]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.
[52]Elishakoff I. Discussion on a non-probabilistic concept of reliability [J]. Structural Safety,1995,17(3):195-199.
[53]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.
[54]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.
[55]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.
[56]Qiu Z P, Mueller P C, Frommer A. The new non-probabilistic criterion of failure for dynamical systems based on convex models[J]. Mathematical and Computer Modelling,2004,40(1/2):201-215.
[57]王晓军,邱志平.结构振动的鲁棒可靠性[J].北京航空航天大学学报,2003,29(11)：1006-1010.
[58]王晓军,邱志平,武哲.结构非概率集合可靠性模型[J].力学学报2007,39(5)：641-646.
[59]江涛,陈建军,姜培刚等.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.
[60]乔心州,仇原鹰,孔宪光.一种基于椭球凸集的结构非概率可靠性模型[J].工程力学,2009,26(11)：203-208.
[61]Elishakoff I. Are probabilistic and anti-optimization approaches compatible? Whys and hows in uncertainty modeling:Probability, fuzziness and anti-optimization[M]. New York:Springer Wien,1999:11-34.
[62]吕震宙,冯蕴雯.结构可靠性问题研究的若干进展[J].力学进展,2000,30(1)：21-28.
[63]郭书祥,吕震宙,刘成立等.概率-非概率混合结构体系失效概率的区间分析[J].西北工业大学学报,2003,21(6)：667-670.
[64]孙文彩,杨自春,唐卫平.随机和区间混合变量下结构可靠性分析方法研究[J].工程力学,2010,27(11)：22-27.
[65]Cai Y L, Jiang Y Z. Optimum design of structures by using method of multiple constraint deletion [J]. Proc. of the Int. Conf. on Finite Element Methods. Shanghai, China,1982,(8):845-848.
[66]钱令希.工程结构优化设计[M].北京：水利电力出版社,1983：21-43.
[67]蔡荫林.结构优化设计的若干进展[J].力学进展,1984,14(3)：275-286.
[68]Cai Y L. An efficient structural optimization method based on constraints redetection and dual formulation[J]. Proceedings of the First East Asian Conference on Structural Engineering and Construction. Bangkok, Thailand.1986,(1):1977-2003.
[69]Moses F. Approaches to structural reliability and optimization [J]. An Introduction to Structural Optimization,1969,(1):81-120.
[70]Moses F. Design for reliability-concepts and applications. Optimum Structural design, New York,1973:241-261.
[71]廖炯生.用优选法解系统可靠性最优化问题一个简捷算法[J].自动化学报,1980,6(1)：18-24.
[72]Feng Y S, Moses F. A method of structural optimization based on structural system reliability [J]. Mechanics Based Design of Structures and Machines, 1986,14(4):437-453.
[73]李惠珍,李君,方华.曲轴可靠性优化设计[J].内燃机学报,1991,9(3)：221-226.
[74]羊妗,马祖康,庄力舟.采用多级优化技术进行复合材料结构可靠性优化设计[J].航空学报,1993,14(8)：B408-B411.
[75]黄炳生,王文涛.工程系统可靠度优化的多阶段决策算子法[J].工程力学,1997,14(2)：69-78.
[76]蔡迎建,孙焕纯.框架结构的可靠性优化[J].计算力学学报,1999,16(3)：288-294.
[77]陈建军,曹一波,段宝岩.基于可靠性的桁架结构拓扑优化设计[J].力学学报,1998,30(3)：277-284.
[78]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.
[79]程远胜,曾广武.结构非概率可靠性优化设计[J].华中科技大学学报(自然科学版),2002,30(3)：30-32.
[80]曹鸿钧,段宝岩.基于非概率可靠性的结构优化设计研究[J].应用力学学报,2005,22(3)：381-386.
[81]亢战,罗阳军.基于凸模型的结构非概率可靠性优化[J].力学学报,2006,38(6)：807-814.
[82]罗阳军,亢战.连续体结构非概率可靠性拓扑优化[J].力学学报2007,39(1)：125-131.
[83]宋宗风,陈建军,朱增青等.基于非概率可靠性的连续体结构拓扑优化设计[J].机械强度,2008,30(6)：935-940
[84]王军,邱志平.基于概率-非概率混合可靠性模型的结构优化设计[J].南京航空航天大学学报,2010,42(3)：278-282.
[85]黄席樾,张著洪,何传江等.现代智能算法理论及应用[M].北京：科学出版社,2005：1-12.
[86]高尚,杨静宇.群智能算法及其应用[M].北京：中国水利水电出版社,2006：1-17.
[87]梁艳春,吴春国,时小虎等.群智能优化算法理论与应用[M].北京：科学出版社,2009：1-9.
[88]张青贵.人工神经网络导论[M].北京：中国水利水电出版社,2004：1-50.
[89]姚新,陈国良,徐惠敏等.进化算法的研究进展[J].计算机学报1995,18(9)：694-706.
[90]张晓,戴冠中,徐乃平.一种新的优化搜索算法—遗传算法[J].控制理论与应用.1995,12(3)：265-273.
[91]汪定伟,王俊伟,王洪峰等.智能优化方法[M].北京：高等教育出版社,2007：1-11.
[92]高鹰,谢胜利.基于模拟退火的粒子群优化算法[J].计算机工程与应用,2004,(1)：47-50.
[93]龚纯,王正林.精通MATLAB最优化计算[M].北京：电子工业出版社,2009：299-303.
[94]康立山.非数值并行算法(第1册)——模拟退火算法[M].北京：科学出版社,1997：22-55.
[95]李海生.支持向量机回归算法与应用研究[D].华南理工大学博士学位论文,2005：1-18.
[96]Suykens J A K, J Vandewalle. Least squares support vector machine classifiers[J]. Neural Processing Letters,1999,9(3):293-300.
[97]Olvi L M, David RM. Successive over relaxiation for support vector machines[J]. Neural Networks,1999,10(5):1032-1037.
[98]Lau K W, Q H Wu. Online training of support vector classifier[J]. Pattern Recognition, 2003,36(8):1913-1920.
[99]Chapelle O, Vapnik V. Choosing multiple parameters for support vector machines[J]. Machine Learning,2002,46(1):131-159.
[100]忻斌健,汪镭,吴启迪.蚁群算法的研究现状和应用及蚂蚁智能体的硬件实现[J].同济大学学报,2002,30(1)：82-87.
[101]Akihide H, Toshiya K, Nobuhiro I, et al. Cooperative behavior of various agents in dynamic environment[J]. Computers and Industrial Engineering,1997,33(3):601-604.
[102]李全通,景小宁,吕文林.基于人工神经网络的涡轮盘蠕变可靠性分析方法[J].航空动力学报,2003,18(2)：211-215.
[103]张义民,张雷.基于神经网络的结构可靠性优化设计[J].应用力学学报,2005,22(1)：49-54.
[104]张义民,张雷.基于神经网络的机械零部件可靠性优化设计[J].农业机械学报,2005,36(4)：112-122.
[105]张义民,高娓,贺向东等.基于神经网络的机械零部件可靠性稳健设计[J].应用力学学报,2009,26(1)：172-175.
[106]杨多和,安伟光,李铁钧.基于人工神经网络的结构可靠性分析[J].兵工学报,2007,28(4)：495-498.
[107]孟广伟,沙丽荣,李锋等.基于径向基函数神经网络响应面的装载机动臂疲劳可靠性[J].吉林大学学报(工学版),2009,39(6)：1516-1520.
[108]孟广伟,沙丽荣,李锋等.基于神经网络的结构疲劳可靠性优化设计[J].兵工学报,2010,31(6)：765-769.
[109]王国庆,郭振邦,张连营等.基于改进遗传算法的离散变量结构可靠性优化设计[J].天津大学学报,1998,31(5)：569-575.
[110]王向阳,陈建桥,罗成.基于遗传算法的层合板结构的可靠性优化设计[J].华中科技大学学报,2004,32(1)：10-12.
[111]祁长青,吴青柏,施斌等.基于遗传算法的冻土路基融沉可靠性分析[J].岩土力学,2006,27(8)：1429-1436.
[112]姜封国,安伟光.基于混合遗传算法的随机结构可靠性优化设计[J].华南理工大学学报(自然科学版),2008,36(1)：152-156.
[113]张进华,张鄂.基于免疫算法的齿轮减速器模糊可靠性优化设计[J].机械科学与技术,2003,22(11)：37-40.
[114]刘志祥,李夕兵,张义平.基于混沌优化的高阶段充填体可靠性分析[J].岩土工程学报,2006,28(3)：348-352.
[115]廖雯竹,潘尔顺,奚立峰.基于Tabu搜索和蚂蚁算法的系统可靠性分析[J].上海交通大学学报,2008,42(8)：1291-1295.
[116]Eamon C D, Rais R M. Structural reliability analysis of composite advanced sail for virginia class submarine[J]. Journal of Ship Research,2008,52(3):165-174.
[117]Barnett T S, Grady M, Purdy K G. Combining negative binomial and weibull distributions for yield and reliability prediction[J]. IEEE Design and Test of Computers, 2006,23(2):110-116.
[118]王新锐,丁勇,李国顺.铁路货车可靠性试验方法及评价标准的研究[J].中国铁道科学,2010,31(1)：116-122.
[119]Eamon C D, Rais R M. Integrated reliability and sizing optimization of a large composite structure[J]. Marine Structures,2009,22(2):315-334.
[120]李创第,黄天立,葛新广.隔震结构基于动力可靠性约束的优化设计[J].哈尔滨工业大学学报,2009,41(8)：169-171.
[121]Lambert S, Paqnacco E, Khalii L. A probabilistic model for the fatigue reliability of structures under random loadings with phase shift effects[J]. International Journal of Fatigue,2010,32(2):463-474.
[122]孟广伟,赵云亮,李锋等.含多裂纹结构的断裂可靠性分析[J].吉林大学学报(工学版),2008,38(3)：614-618.
[123]张伟.结构可靠性理论与应用[M].北京：科学出版社,2008：17-40.
[124]黄席樾,向长城,殷礼胜.现代智能算法理论及应用[M].北京：科学出版社,2009：213-220.
[125]张明.结构可靠度分析—方法与程序[M].北京：科学出版社,2009：130-142.
[126]安伟光,蔡荫林,陈卫东.随机结构系统可靠性分析与优化设计[M].哈尔滨：哈尔滨工程大学出版社,2005：33-86.
[127]Di S M, Lomario D. A comparison between Monte Carlo and FORMs in calculating the reliability of a composite structure[J]. Composite Structures,2003,59(1):155-162.
[128]Melchers R E, Ahammed M, Middleton C. FORM for discontinuous and truncated probability density functions [J]. Structural Safety,2003,25(3):305-313.
[129]Der K A. The geometry of random vibrations and solutions by FORM and SORM[J]. Probabilistic Engineering Mechanics,2000,15(1):81-90.
[130]Du X, Chen W. A most probable point-based method for efficient uncertainty analysis[J]. Design Manufacturing,2001,4(1):47-66.
[131]Du X, Sudjianto A. The first order saddlepoint approximation for reliability analysis[J]. American Institute of Aeronautics and Astronautics Journal,2004,42(6):1199-1207.
[132]宋云连,李树军,刘文白.结构可靠性分析方法——AFOSM的进一步精确化[J].计算力学学报,2003,20(1)：121-126.
[133]Lee T, Mosalam K M. Seismic demand sensitivity of reinforced concrete shear-wall building using FOSM method[J]. Earthquake Engineering and Structural Dynamics, 2005,34(14):1719-1736.
[134]金星,洪延姬.工程系统可靠性数值分析方法[M].北京：国防工业出版社,2002：22-64.
[135]Wu Y T, Sitakanta M. Variable screening and ranking using sampling-based sensitivity measures[J]. Reliability Engineering and System Safety,2006,91(6):634-647.
[136]Liu J S. Monte Carlo strategies in scientific computing [M]. New York:Springer-Verlag Press,2002:4-32.
[137]Guan X L, Melchers R E. Effect of response surface parameter variation on structural reliability estimates[J]. Structural Safety,2001,23(4):429-444.
[138]Gayton N, Bourinet J M, Lemaire M. CQ2RS:A new statistical approach to the response surface method for reliability analysis[J]. Structural Safety, 2003,25(1):99-121.
[139]Falson G, Impollonia N. About the accuracy of a novel response surface method for the analysis of finite element modeled uncertain structures [J]. Probabilistic Engineering Mechanics,2004,19(1-2):53-63.
[140]桂劲松,康海贵.结构可靠度分析的响应面法及其Matlab实现[J].计算力学学报, 2004,21(6):683-687.
[141]Hurtado J E. An examination of methods for approximating implicit limit state functions from the viewpoint of statistical learning theory [J]. Structural Safety, 2004,26(3):271-293.
[142]Gupta S, Manohar C S. An improved response surface method for the determination of failure probability and importance measures[J]. Structural Safety,2004,26(2):123-139.
[143]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.
[144]Wong S M, Hobbs R E, Onof C. An adaptive response surface method for reliability analysis of structures with multiple loading sequences [J]. Structural Safety, 2005,27(4):287-308.
[145]徐军,郑颖人.响应面重构的若干方法研究及其在可靠性分析中的应用[J].计算力学学报,2002,19(2)：217-222.
[146]Bucher C G, Bourgund U. A fast and efficient response surface approach for structural reliability problems[J]. Structural Safety,1990,7(1):57-66.
[147]Rajashekhar M R, Ellingwood B R. A new look at the response surface approach for reliability[J]. Structural Safety,1993,12(3):205-220.
[148]Irfan K, Chris A M. A responsive surface method based on weighted regression for structural reliability analysis[J]. Probabilistic Engineering Mechanics,2005,20:11-17.
[149]Xuan S N, Alian S, Frederic D, et al. Adaptive response surface metod based on a double weighted regression technique [J]. Probabilistic Engineering Mechanics, 2009,24(2):135-143.
[150]安伟光,孙克淋,陈卫东等.随机结构系统基于可靠性的优化设计[J].应用数学和力学,2005,26(10)：1175-1182.
[151]程跃,程文明,郑严,张则强.基于混沌粒子群算法的结构可靠性优化设计[J].中南大学学报(自然科学版),2011,42(3)：671-676.
[152]赵维涛,张凌云,安伟光.最佳矢量与遗传算法在结构系统可靠性优化中的应用[J].宇航学报,2007,28(3)：735-739.
[153]郑严,程文明,程跃.基于SVR的万向节机构可靠性及灵敏度分析[J].华中科技大学学报(自然科学版),2010,38(7)：12-15.
[154]邓乃扬,田英杰.支持向量机—理论、算法与拓展[M].北京：科学出版社2009：20-64.
[155]杨志民,刘广利.不确定性支持向量机原理及应用[M].北京：科学出版社2007：25-87.
[156]Blanchard G, Bousquet O, Massar P. Statistical performance of support vector machines [J]. Annals of Statistics,2008,36(2):489-531.
[157]Guyon I, Weston J, Barnhill S. Gene selection for cancer classification using support vector machines[J]. Machine Learning,2002,46:389-422.
[158]Li D C, Fang Y H. An algorithm to cluster data for efficient classification of support vector machines[J]. Expert Systems with Applications,2008,34(3):2013-2018.
[159]Lin C J. Formulations of support vector machines:A note from an optimization point of view[J]. Neural Computation,2001,13(2):307-317.
[160]Nello C, John S. An introduction to support vector machines and other kernel-based learning methods [M]. Cambridge:Cambridge University Press,2000:13-56.
[161]崔伟东,周志华,李星.支持向量机研究[J].计算机工程与应用,2001(1)：58-61.
[162]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,2004：10-43.
[163]赵洪波,茹忠亮,张士科.SVM在地下工程可靠性分析中的应用[J].岩土力学,2009,30(2)：526-530.
[164]Rocco C M, Moreno J A. Fast Monte Carlo reliability evaluation using support vector machine[J]. Reliability Engineering and System Safety,2002,76(3):237-243.
[165]马超,吕震宙.结构可靠性分析的支持向量机分类迭代算法[J].中国机械工程,2007,18(7)：816-819.
[166]郑严,程文明,程跃.基于支持向量机回归的结构可靠性分析[J].机械科学与技术,2011,30(1)：52-56.
[167]GUO Zhiwei, BAI Guangchen. Application of least squares support vector machine for regression to reliability analysis[J]. Chinese Journal of Aeronautics, 2009,22(2):160-166.
[168]ZHAO Hongbo. Slope reliability analysis using a support vector machine[J]. Computers and Geotechnics,2008,35(3):459-467.
[169]Chen K Y. Forecasting systems reliability based on support vector regression with genetic algorithms [J]. Reliability Engineering and System Safety,2007,92(4):423-432.
[170]Narwaria M, Lin W. Objective image quality assessment based on support vector regression[J]. IEEE Transactions on Neural Networks,2010,21(3):515-519.
[171]Suresh S, Sujit P B, Rao A K. Particle swarm optimization approach for multi-objective composite box-beam design[J]. Composite Structures,2007,81(4):598-605.
[172]Juan J. Particle swarm optimization application in power system engineering[D]. Puerto Rico:University of Puerto Rico,2004:26-63.
[173]Shi Y, Eberhart R C. A modified particle swarm optimizer [C]//Proceedings of IEEE International Conference on Evolutionary Computation Anchorage,1998:69-73.
[174]Tayal M. Particle swarm optimization for mechanical design[D]. Texas:University of Texas,2003:15-44.
[175]EBERHART R, KENNEDY J. A New Optimizer Using Particle Swarm Theory [C]// Proc. of 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan:IEEE Press,1995:39-43.
[176]蔡自兴,徐光祜.人工智能及其应用[M].北京：清华大学出版社,2004：40-96.
[177]Parsopoulos K E, Vrahatis M N. Recent approaches to global optimization problems through particle swarm optimization [J]. Natural Computing,2002,1(2-3):235-306.
[178]Shi Y, Eberhart R C. Empirical study of particle swarm optimization[C]//Proceedings of IEEE Congress on Evolutionary Computation. Piscataway:IEEE,1999:1945-1950.
[179]Clerc M. The swarm and the queen:Towards a deterministic and adaptive paticle swarm optimization [C]//Proceedings of the Congress on Evolutionary Computation. Washington:IEEE Service Center,1999.1927-1930.
[180]Eberhart R C, Shi Y. Comparing inertia weights and constriction factors in particle swarm optimization [C]//Proceedings of the Congress Evolutionary Computation, San Diego:IEEE Press,2000:84-88.
[181]Kennedy J, Eberhart R C. A discrete binary version of the particle swarm algorithm [C]//Proceedings of the World Multri-Conference on Systemics, Cybernetics and Informatics, IEEE Press,1997:4104-4109.
[182]Secrest B, Lamont G. Communication in particle swarm optimization illustrated by the traveling salesman problem [C]//Proceedings of the Workshop on Particle Swarm Optimization, Indianapolis, IN:Purdue School of Engineering and Technology, IUPUI, 2001:230-238.
[183]Lovbjerg M, Rasmussen Tk, Krink T. Hybrid particle swarm optimization with breeding and subpopulations [C]//Proceedings of IEEE International Conference on Evolutionary Computation, San, Diego:IEEE,2000:1217-1222.
[184]史妍妍,孙志礼,闫明.基于响应面法的隐式极限状态函数可靠性灵敏度分析方法[J].机械科学与技术,2009,28(5)：648-651.
[185]Deng Jian, Gu Desheng, Li Xibing, et al. Structural Reliability Analysis for Implicit Performance [J]. Structural Safety,2005,27(1):25-48.
[186]Hurtado J E, Alvarez D A. Classification Approach for Reliability Analysis with Stochastic Finite-element Modeling [J].Journal of Structural Engineering, 2003,129:1141-1149.
[187]何水清,王善.结构可靠性分析与设计[M].北京：国防工业出版社,1993：22-35.
[188]赵洪波.基于支持向量机的边波可靠性分析[J].岩土工程学报,2007,29(6)：819-823.
[189]李洪双,吕震宙.支持向量回归机在结构可靠性分析中的应用[J].航空学报,2007,28(1)：94-99.
[190]赵国藩.工程结构可靠性理论与应用[M].大连：大连理工大学出版社,1996：14-42.
[191]Givolid, Elishakoff I. Stress concentration at a nearly circular hole with uncertain irregularities [J]. Journal of Applied Mechanics,1992,59:67-71.
[192]Ibrahim R A. Structural dynamics with parameter uncertainties[J]. Applied Mechanics, Reviews,1987,40(3):309-328.
[193]Elishakoff I, Cai G Q. Non-linear buckling of a column with initial imperfection via stochastic and Non-stochastic convex models[J]. International Journal of Non-linear Mechanics,1994,29(1):71-82.
[194]Elishakoff I, Elisseeff P, Glegg S A L. Non-probabilistic, convex-theoretic modeling of scatter in material properties [J]. AIAA Journal,1994,32(4):843-849.
[195]李洪双,吕震宙.结构可靠性分析的支持向量机响应面法[J].计算力学学报,2009,26(2)：199-203.
[196]邱志平.非概率集合理论凸方法及其应用[M].北京：国防工业出版社,2005：46-58.
[197]刘成立.复杂结构可靠性分析及设计研究[D].西北工业大学博士学位论文,2007：43-54.
[198]邵信光,杨慧中,陈刚.基于粒子群优化算法的支持向量机参数选择及其应用[J].控制理论与应用,2006,23(5)：740-743.
[199]张强,毛君,田大丰.基于遗传算法掘进机截割头多目标模糊可靠性优化[J].煤炭学报,2008,33(12)：1435-1437.
[200]YU Ying, YU Xiao-chun, LI Yong-sheng. New discrete particle swarm optimization based on huge value penalty for solving engineering problem[J]. Chinese Journal of Mechanical Engineering,2009,22(3):410-418.
[201]金一粟,周永华,梁逸曾.改进粒子群优化算法对反应动力学参数的估计[J].中南大学学报,2008,39(4)：694-699.
[202]El-Gohary A, Al-Ruzaiza A S. Chaos and adaptive control in two prey, one predator system with nonlinear feedback[J]. Chaos, Solitons and Fractals,2007,34(2):443-453.
[203]LIU Bo, WANG Ling, JIN Yi-hui, et al. Improved particle swarm optimization combined with chaos[J]. Chaos, Solitons and Fractals,2005,25(5):1261-1271.
[204]YANG Di-xiong, LI Gang, CHENG Geng-dong. On the efficiency of chaos optimization algorithms for global optimization[J]. Chaos, Solitons and Fractals,2007, 34(4):1366-1375.
[205]张义民,刘仁云,于繁华.基于计算智能技术的结构系统可靠性优化设计[J].工程力学,2007,24(8)：27-31.
[206]LI Bing, JIANG Wei-sun. Optimizing complex functions by chaos search[J]. Cybernetics and Systems,1998,29(4):409-419.
[207]李兵,蒋慰孙.混沌优化方法及其应用[J].控制理论与应用,1997,14(4)：613-615.
[208]张浩,张铁男,沈继红,等Tent混沌粒子群算法及其在结构优化决策中的应用[J].控制与决策,2008,23(8)：857-862.
[209]谷良贤,王轶鹏,龚春林.基于概率突跳和模拟退火的改进自适应微粒群算法[J].控制与决策,2009,24(4)：617-620.
[210]焦巍,刘光斌,张艳红.求解约束优化的模拟退火PSO算法[J].系统工程与电子技术,2010,32(7)：1532-1536.
[211]申建建,程春田,廖胜利等.基于模拟退火的粒子群算法在水电站水库优化调度中的应用[J].水力发电学报,2009,(1)：47-50.
[212]陈华根,吴健生,王家林等.模拟退火算法机理研究[J].同济大学学报(自然科学版),2004,32(6)：802-805.
[213]祝恒云,叶文华.模拟退火粒子群算法在动态单元布局中的应用[J].中国机械工程,2009,20(2)：181-185
[214]Wang T Y, Wu K B, Liu Y W. A Simulated Annealing Algorithm for Facility Layout Problems under Variable Demand in Cellular Manufacturing System[J]. Computers in Industry,2001,46(1):181-188.
[215]周龙,牟怿,尤新革.模拟退火算法在粮虫图像分割中的应用[J].华中科技大学学报(自然科学版),2010,38(5)：72-74.
[216]纪震,廖惠连,吴青华.粒子群算法及应用[M].北京：科学出版社,2009：25-57.
[217]Boeringer D W, Werner D H. Particle swarm optimization versus genetic algorithms for phased array synthesis. IEEE Trans. Antennas Propagation,2004,52(3):771-779.
[218]王华秋,曹长修.基于模拟退火的并行粒子群优化研究[J].控制与决策,2005,20(5)：500-504.
[219]刘朝,祁荣宾,钱锋.融合交叉变异和混沌的新型混合粒子群算法[J].化工学报,2010,61(11)：2862-2867.
[220]易平.对区间不确定性问题的可靠性度量的探讨[J].计算力学学报2006,23(2)：152-156.
[221]亢战,罗阳军.桁架结构非概率可靠性拓扑优化[J].计算力学学报,2008,25(5)：589-594.
[222]Kounias E G. Bounds for the probability of a union with applications[J]. Annals of Mathematical Statistics,1968,39(6):2154-2158.
[223]Ditlevsen O. Narrow reliability bounds for structural systems[J]. Journal of Structural Mechanics,1979,7(4):453-472.
[224]Greig G L. An assessment of high-order bounds for structural reliability[J]. Structural Safety,1992,11(3-4):213-225.
[225]盛骤,谢式千,潘承毅.概率论与数理统计[M](第二版).北京：高等教育出版社,1999：30-55.
[226]纪震,周家锐,廖惠连等.智能单粒子优化算法[J].计算机学报,2010,33(3)：556-561.
[227]储颖,糜华,纪震等.基于智能单粒子的联合代数重建算法[J].深圳大学学报(理工版),2009,26(2)：111-115.
[228]张明瑞,陈征宙,吴强等.基于智能单粒子算法的复杂边坡最危险滑动面搜索[J].中国水运,2010,10(12)：208-209.
[229]乔心州.不确定结构可靠性分析与优化设计研究[D].西安电子科技大学博士学位论文,2008：71-81.
[2]杨瑞刚.机械可靠性设计与应用[M].北京：冶金工业出版社,2008：1-6.
[3]Freudenthal A M. The safety of structures [J]. ASCE Trans.,1947,112:125-129.
[4]孟广伟,李锋,赵云亮.基于随机有限元法的疲劳断裂可靠性分析[J].吉林大学学报,2006,36(3)：16-19.
[5]刘仁云,张义民,刘巧伶.基于多目标优化策略的结构可靠性稳健设计[J].应用力学学报,2007,24(1)：267-271.
[6]孙新利.工程可靠性教程[M].北京：国防工业出版社,2005：1-20.
[7]姜兴渭.可靠性工程技术[M].哈尔滨：哈尔滨工业大学出版社,2005：15-50.
[8]孙志礼,陈良玉.实用机械可靠性设计理论与方法[M].北京：科学出版社,2003：10-30.
[9]张建国,苏多,刘英卫.机械产品可靠性分析与优化[M].北京：电子工业出版社,2008：1-80.
[10]叶晓琰,蒋小平,许建强等.往复泵曲轴疲劳可靠性分析[J].机械工程学报,2008,44(10)：272-276.
[11]郭耀斌,张文明,张国芬.基于蒙特卡罗法的螺旋锥齿轮接触疲劳可靠性分析[J].农业机械学报,2008,39(4)：157-159.
[12]Mainak M, David W C, Kelvin M. A highly efficient Monte Carlo method for assessment of system reliability based on a Markov model [J]. Quality Control and Applied Statistics,2001,46(1):109-112.
[13]安伟光,蔡荫林,陈卫东.随机结构系统可靠性分析与优化设计[M].哈尔滨：哈尔滨工程大学出版社,2007：41-79.
[14]吕震宙,宋述芳,李洪双等.结构机构可靠性及可靠性灵敏度分析[M].北京：科学出版社,2009：9-36.
[15]王军,邱志平.结构的概率-非概率混合可靠性模型[J].航空学报,2009,30(8)：1398-1404.
[16]郭书祥,吕震宙.结构可靠性分析的概率和非概率混合模型[J].机械强度,2002,24(4)：524-526.
[17]白鹏,张喜斌,张斌等.支持向量机理论及工程应用实例[M].西安：西安电子科技大学出版社,2008：30-70.
[18]徐长航,陈国明,谢静.基于支持向量机和蒙特卡洛的结构可靠性分析方法及应用[J].中国石油大学学报,2008,32(4)：103-108.
[19]Kennedy J, Eberhart R. Particle swarm optimization [C]//Proc. of International Conference on Neural Networks:IEEE Press,1995:1942-1948.
[20]段晓东,王存睿,刘向东.粒子群算法及其应用[M].沈阳：辽宁大学出版社,2007：11-41.
[21]赵国藩,金伟良,贡金鑫.结构可靠度理论[M].北京：中国建筑工业出版社,2000：6-23.
[22]Cornell C A. A probability-based structural code[J]. ACI Journal Proceedings, 1969,66(12):974-985.
[23]黄学明,李国芬.结构可靠性研究综述[J].山西建筑,2007,33(11)：76-77.
[24]Hasofer A M, Lind N. An exact and invariant first order reliability format [J]. Journal of Engineering Mechanics,1974,10(EM1):111-127.
[25]Zhao T G, Ono T. New approximations for SORM:Part 1[J]. Journal of Engineering Mechanics,1999,125(1):79-85.
[26]赵维涛,安伟光,严心池.二次二阶矩可靠性指标[J].哈尔滨工程大学学报,2004,25(2)：240-242.
[27]Rackwitz R, Fiessler B. An algorithm for calculation of structural reliability under combined loading. Munchen,1977.
[28]贡金鑫,赵国藩.国外结构可靠性理论的应用与发展[J].土木工程学报,2005,38(2)：1-7.
[29]Sami W. Tabsh. Safety of reinforced concrete members designed following ACI 318 building code[J]. Engineering Structures,1997,19(10):843-850.
[30]航空工业部科学技术委员会编著.飞机结构损伤容限设计指南.航空工业部科学技术情报研究所,1985.
[31]航空工业部科学技术研究院编.飞机结构耐久性损伤容限设计手册(2).飞机结构的疲劳分析.航空工业部科学技术情况研究所,1989.
[32]冯元生,董聪.枚举结构主要失效模式的一种方法[J].航空学报1991,12(9)：537-541.
[33]安伟光,蔡荫林.冗余桁架结构的故障分析[J].哈尔滨船舶工程学院学报,1989,10(4)：479-485.
[34]安伟光,蔡荫林.冗余度结构故障概率计算的一种方法[J].兵工学报,1992(2)：92-96.
[35]蔡荫林,安伟光,陈卫东.空间桁架结构基于可靠性的优化设计[C].第六届空间结构学术会议论文集.北京：地震出版社,1992：210-217.
[36]Ditlevsen O. Narrow reliability bounds for structural system[J]. Journal of Structural Mechanics,1979,7(4):453-472.
[37]Alfredo H.-S. A, Tang W H. Probability concepts in engineering planning and design[M]. John Wiley and Sons,1984:23-56.
[38]Song B F. A numerical integration method in affine space and a method with high accuracy for computing structural system reliability[J]. computer and Structures, 1992,42(2):255-262.
[39]蔡荫林,周健生.结构系统失效概率的近似公式[J].航空学报,1992,13(3)：219-223.
[40]陈卫东,王善,蔡荫林.杆板结构系统的可靠性分析[J].哈尔滨工程大学学报,1997,18(6)：68-74.
[41]安伟光.载荷效应组合时的失效概率[J].哈尔滨船舶工程学院学报,1988,9(2)：126-136.
[42]安伟光, 陈卫东.结构系统在随机组合力作用下的可靠性分析[J].哈尔滨工程大学学报,1996,17(1)：15-23.
[43]蔡荫林,安伟光.随机组合力下冗余结构的故障概率计算[J].哈尔滨船舶工程学院学报,1989,10(2)：135-144.
[44]郭书祥.非随机不确定结构的可靠性方法和优化设计研究[D].西北工业大学博士学位论文.2002：4-10.
[45]Ben-Haim Y, Elishakoff I. Convex models of uncertainty in applied mechanics [M]. Amsterdam:Elsevier Science Publishers,1990:12-45.
[46]Elishakoff I. Essay on uncertainties in elastic and viscoelastic structures:form A M Freudenthal's criticisms to modern convex modeling [J]. Computers and Structures, 1995,56(6):871-895.
[47]邱志平,王晓军.不确定性结构力学问题的集合理论凸方法[M].北京：科学出版社,2008：1-9.
[48]曹鸿钧,段宝岩.基于凸集合模型的非概率可靠性研究[J].计算力学学报,2005,22(5)：546-549.
[49]罗阳军,亢战.超椭球模型下结构非概率可靠性指标的迭代算法[J].计算力学学报,2008,25(6)：747-752.
[50]Ben-Haim Y. A non-probabilistic concept of reliability[J]. Structural Safety, 1994,14(4):227-245.
[51]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.
[52]Elishakoff I. Discussion on a non-probabilistic concept of reliability [J]. Structural Safety,1995,17(3):195-199.
[53]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.
[54]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.
[55]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.
[56]Qiu Z P, Mueller P C, Frommer A. The new non-probabilistic criterion of failure for dynamical systems based on convex models[J]. Mathematical and Computer Modelling,2004,40(1/2):201-215.
[57]王晓军,邱志平.结构振动的鲁棒可靠性[J].北京航空航天大学学报,2003,29(11)：1006-1010.
[58]王晓军,邱志平,武哲.结构非概率集合可靠性模型[J].力学学报2007,39(5)：641-646.
[59]江涛,陈建军,姜培刚等.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.
[60]乔心州,仇原鹰,孔宪光.一种基于椭球凸集的结构非概率可靠性模型[J].工程力学,2009,26(11)：203-208.
[61]Elishakoff I. Are probabilistic and anti-optimization approaches compatible? Whys and hows in uncertainty modeling:Probability, fuzziness and anti-optimization[M]. New York:Springer Wien,1999:11-34.
[62]吕震宙,冯蕴雯.结构可靠性问题研究的若干进展[J].力学进展,2000,30(1)：21-28.
[63]郭书祥,吕震宙,刘成立等.概率-非概率混合结构体系失效概率的区间分析[J].西北工业大学学报,2003,21(6)：667-670.
[64]孙文彩,杨自春,唐卫平.随机和区间混合变量下结构可靠性分析方法研究[J].工程力学,2010,27(11)：22-27.
[65]Cai Y L, Jiang Y Z. Optimum design of structures by using method of multiple constraint deletion [J]. Proc. of the Int. Conf. on Finite Element Methods. Shanghai, China,1982,(8):845-848.
[66]钱令希.工程结构优化设计[M].北京：水利电力出版社,1983：21-43.
[67]蔡荫林.结构优化设计的若干进展[J].力学进展,1984,14(3)：275-286.
[68]Cai Y L. An efficient structural optimization method based on constraints redetection and dual formulation[J]. Proceedings of the First East Asian Conference on Structural Engineering and Construction. Bangkok, Thailand.1986,(1):1977-2003.
[69]Moses F. Approaches to structural reliability and optimization [J]. An Introduction to Structural Optimization,1969,(1):81-120.
[70]Moses F. Design for reliability-concepts and applications. Optimum Structural design, New York,1973:241-261.
[71]廖炯生.用优选法解系统可靠性最优化问题一个简捷算法[J].自动化学报,1980,6(1)：18-24.
[72]Feng Y S, Moses F. A method of structural optimization based on structural system reliability [J]. Mechanics Based Design of Structures and Machines, 1986,14(4):437-453.
[73]李惠珍,李君,方华.曲轴可靠性优化设计[J].内燃机学报,1991,9(3)：221-226.
[74]羊妗,马祖康,庄力舟.采用多级优化技术进行复合材料结构可靠性优化设计[J].航空学报,1993,14(8)：B408-B411.
[75]黄炳生,王文涛.工程系统可靠度优化的多阶段决策算子法[J].工程力学,1997,14(2)：69-78.
[76]蔡迎建,孙焕纯.框架结构的可靠性优化[J].计算力学学报,1999,16(3)：288-294.
[77]陈建军,曹一波,段宝岩.基于可靠性的桁架结构拓扑优化设计[J].力学学报,1998,30(3)：277-284.
[78]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.
[79]程远胜,曾广武.结构非概率可靠性优化设计[J].华中科技大学学报(自然科学版),2002,30(3)：30-32.
[80]曹鸿钧,段宝岩.基于非概率可靠性的结构优化设计研究[J].应用力学学报,2005,22(3)：381-386.
[81]亢战,罗阳军.基于凸模型的结构非概率可靠性优化[J].力学学报,2006,38(6)：807-814.
[82]罗阳军,亢战.连续体结构非概率可靠性拓扑优化[J].力学学报2007,39(1)：125-131.
[83]宋宗风,陈建军,朱增青等.基于非概率可靠性的连续体结构拓扑优化设计[J].机械强度,2008,30(6)：935-940
[84]王军,邱志平.基于概率-非概率混合可靠性模型的结构优化设计[J].南京航空航天大学学报,2010,42(3)：278-282.
[85]黄席樾,张著洪,何传江等.现代智能算法理论及应用[M].北京：科学出版社,2005：1-12.
[86]高尚,杨静宇.群智能算法及其应用[M].北京：中国水利水电出版社,2006：1-17.
[87]梁艳春,吴春国,时小虎等.群智能优化算法理论与应用[M].北京：科学出版社,2009：1-9.
[88]张青贵.人工神经网络导论[M].北京：中国水利水电出版社,2004：1-50.
[89]姚新,陈国良,徐惠敏等.进化算法的研究进展[J].计算机学报1995,18(9)：694-706.
[90]张晓,戴冠中,徐乃平.一种新的优化搜索算法—遗传算法[J].控制理论与应用.1995,12(3)：265-273.
[91]汪定伟,王俊伟,王洪峰等.智能优化方法[M].北京：高等教育出版社,2007：1-11.
[92]高鹰,谢胜利.基于模拟退火的粒子群优化算法[J].计算机工程与应用,2004,(1)：47-50.
[93]龚纯,王正林.精通MATLAB最优化计算[M].北京：电子工业出版社,2009：299-303.
[94]康立山.非数值并行算法(第1册)——模拟退火算法[M].北京：科学出版社,1997：22-55.
[95]李海生.支持向量机回归算法与应用研究[D].华南理工大学博士学位论文,2005：1-18.
[96]Suykens J A K, J Vandewalle. Least squares support vector machine classifiers[J]. Neural Processing Letters,1999,9(3):293-300.
[97]Olvi L M, David RM. Successive over relaxiation for support vector machines[J]. Neural Networks,1999,10(5):1032-1037.
[98]Lau K W, Q H Wu. Online training of support vector classifier[J]. Pattern Recognition, 2003,36(8):1913-1920.
[99]Chapelle O, Vapnik V. Choosing multiple parameters for support vector machines[J]. Machine Learning,2002,46(1):131-159.
[100]忻斌健,汪镭,吴启迪.蚁群算法的研究现状和应用及蚂蚁智能体的硬件实现[J].同济大学学报,2002,30(1)：82-87.
[101]Akihide H, Toshiya K, Nobuhiro I, et al. Cooperative behavior of various agents in dynamic environment[J]. Computers and Industrial Engineering,1997,33(3):601-604.
[102]李全通,景小宁,吕文林.基于人工神经网络的涡轮盘蠕变可靠性分析方法[J].航空动力学报,2003,18(2)：211-215.
[103]张义民,张雷.基于神经网络的结构可靠性优化设计[J].应用力学学报,2005,22(1)：49-54.
[104]张义民,张雷.基于神经网络的机械零部件可靠性优化设计[J].农业机械学报,2005,36(4)：112-122.
[105]张义民,高娓,贺向东等.基于神经网络的机械零部件可靠性稳健设计[J].应用力学学报,2009,26(1)：172-175.
[106]杨多和,安伟光,李铁钧.基于人工神经网络的结构可靠性分析[J].兵工学报,2007,28(4)：495-498.
[107]孟广伟,沙丽荣,李锋等.基于径向基函数神经网络响应面的装载机动臂疲劳可靠性[J].吉林大学学报(工学版),2009,39(6)：1516-1520.
[108]孟广伟,沙丽荣,李锋等.基于神经网络的结构疲劳可靠性优化设计[J].兵工学报,2010,31(6)：765-769.
[109]王国庆,郭振邦,张连营等.基于改进遗传算法的离散变量结构可靠性优化设计[J].天津大学学报,1998,31(5)：569-575.
[110]王向阳,陈建桥,罗成.基于遗传算法的层合板结构的可靠性优化设计[J].华中科技大学学报,2004,32(1)：10-12.
[111]祁长青,吴青柏,施斌等.基于遗传算法的冻土路基融沉可靠性分析[J].岩土力学,2006,27(8)：1429-1436.
[112]姜封国,安伟光.基于混合遗传算法的随机结构可靠性优化设计[J].华南理工大学学报(自然科学版),2008,36(1)：152-156.
[113]张进华,张鄂.基于免疫算法的齿轮减速器模糊可靠性优化设计[J].机械科学与技术,2003,22(11)：37-40.
[114]刘志祥,李夕兵,张义平.基于混沌优化的高阶段充填体可靠性分析[J].岩土工程学报,2006,28(3)：348-352.
[115]廖雯竹,潘尔顺,奚立峰.基于Tabu搜索和蚂蚁算法的系统可靠性分析[J].上海交通大学学报,2008,42(8)：1291-1295.
[116]Eamon C D, Rais R M. Structural reliability analysis of composite advanced sail for virginia class submarine[J]. Journal of Ship Research,2008,52(3):165-174.
[117]Barnett T S, Grady M, Purdy K G. Combining negative binomial and weibull distributions for yield and reliability prediction[J]. IEEE Design and Test of Computers, 2006,23(2):110-116.
[118]王新锐,丁勇,李国顺.铁路货车可靠性试验方法及评价标准的研究[J].中国铁道科学,2010,31(1)：116-122.
[119]Eamon C D, Rais R M. Integrated reliability and sizing optimization of a large composite structure[J]. Marine Structures,2009,22(2):315-334.
[120]李创第,黄天立,葛新广.隔震结构基于动力可靠性约束的优化设计[J].哈尔滨工业大学学报,2009,41(8)：169-171.
[121]Lambert S, Paqnacco E, Khalii L. A probabilistic model for the fatigue reliability of structures under random loadings with phase shift effects[J]. International Journal of Fatigue,2010,32(2):463-474.
[122]孟广伟,赵云亮,李锋等.含多裂纹结构的断裂可靠性分析[J].吉林大学学报(工学版),2008,38(3)：614-618.
[123]张伟.结构可靠性理论与应用[M].北京：科学出版社,2008：17-40.
[124]黄席樾,向长城,殷礼胜.现代智能算法理论及应用[M].北京：科学出版社,2009：213-220.
[125]张明.结构可靠度分析—方法与程序[M].北京：科学出版社,2009：130-142.
[126]安伟光,蔡荫林,陈卫东.随机结构系统可靠性分析与优化设计[M].哈尔滨：哈尔滨工程大学出版社,2005：33-86.
[127]Di S M, Lomario D. A comparison between Monte Carlo and FORMs in calculating the reliability of a composite structure[J]. Composite Structures,2003,59(1):155-162.
[128]Melchers R E, Ahammed M, Middleton C. FORM for discontinuous and truncated probability density functions [J]. Structural Safety,2003,25(3):305-313.
[129]Der K A. The geometry of random vibrations and solutions by FORM and SORM[J]. Probabilistic Engineering Mechanics,2000,15(1):81-90.
[130]Du X, Chen W. A most probable point-based method for efficient uncertainty analysis[J]. Design Manufacturing,2001,4(1):47-66.
[131]Du X, Sudjianto A. The first order saddlepoint approximation for reliability analysis[J]. American Institute of Aeronautics and Astronautics Journal,2004,42(6):1199-1207.
[132]宋云连,李树军,刘文白.结构可靠性分析方法——AFOSM的进一步精确化[J].计算力学学报,2003,20(1)：121-126.
[133]Lee T, Mosalam K M. Seismic demand sensitivity of reinforced concrete shear-wall building using FOSM method[J]. Earthquake Engineering and Structural Dynamics, 2005,34(14):1719-1736.
[134]金星,洪延姬.工程系统可靠性数值分析方法[M].北京：国防工业出版社,2002：22-64.
[135]Wu Y T, Sitakanta M. Variable screening and ranking using sampling-based sensitivity measures[J]. Reliability Engineering and System Safety,2006,91(6):634-647.
[136]Liu J S. Monte Carlo strategies in scientific computing [M]. New York:Springer-Verlag Press,2002:4-32.
[137]Guan X L, Melchers R E. Effect of response surface parameter variation on structural reliability estimates[J]. Structural Safety,2001,23(4):429-444.
[138]Gayton N, Bourinet J M, Lemaire M. CQ2RS:A new statistical approach to the response surface method for reliability analysis[J]. Structural Safety, 2003,25(1):99-121.
[139]Falson G, Impollonia N. About the accuracy of a novel response surface method for the analysis of finite element modeled uncertain structures [J]. Probabilistic Engineering Mechanics,2004,19(1-2):53-63.
[140]桂劲松,康海贵.结构可靠度分析的响应面法及其Matlab实现[J].计算力学学报, 2004,21(6):683-687.
[141]Hurtado J E. An examination of methods for approximating implicit limit state functions from the viewpoint of statistical learning theory [J]. Structural Safety, 2004,26(3):271-293.
[142]Gupta S, Manohar C S. An improved response surface method for the determination of failure probability and importance measures[J]. Structural Safety,2004,26(2):123-139.
[143]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.
[144]Wong S M, Hobbs R E, Onof C. An adaptive response surface method for reliability analysis of structures with multiple loading sequences [J]. Structural Safety, 2005,27(4):287-308.
[145]徐军,郑颖人.响应面重构的若干方法研究及其在可靠性分析中的应用[J].计算力学学报,2002,19(2)：217-222.
[146]Bucher C G, Bourgund U. A fast and efficient response surface approach for structural reliability problems[J]. Structural Safety,1990,7(1):57-66.
[147]Rajashekhar M R, Ellingwood B R. A new look at the response surface approach for reliability[J]. Structural Safety,1993,12(3):205-220.
[148]Irfan K, Chris A M. A responsive surface method based on weighted regression for structural reliability analysis[J]. Probabilistic Engineering Mechanics,2005,20:11-17.
[149]Xuan S N, Alian S, Frederic D, et al. Adaptive response surface metod based on a double weighted regression technique [J]. Probabilistic Engineering Mechanics, 2009,24(2):135-143.
[150]安伟光,孙克淋,陈卫东等.随机结构系统基于可靠性的优化设计[J].应用数学和力学,2005,26(10)：1175-1182.
[151]程跃,程文明,郑严,张则强.基于混沌粒子群算法的结构可靠性优化设计[J].中南大学学报(自然科学版),2011,42(3)：671-676.
[152]赵维涛,张凌云,安伟光.最佳矢量与遗传算法在结构系统可靠性优化中的应用[J].宇航学报,2007,28(3)：735-739.
[153]郑严,程文明,程跃.基于SVR的万向节机构可靠性及灵敏度分析[J].华中科技大学学报(自然科学版),2010,38(7)：12-15.
[154]邓乃扬,田英杰.支持向量机—理论、算法与拓展[M].北京：科学出版社2009：20-64.
[155]杨志民,刘广利.不确定性支持向量机原理及应用[M].北京：科学出版社2007：25-87.
[156]Blanchard G, Bousquet O, Massar P. Statistical performance of support vector machines [J]. Annals of Statistics,2008,36(2):489-531.
[157]Guyon I, Weston J, Barnhill S. Gene selection for cancer classification using support vector machines[J]. Machine Learning,2002,46:389-422.
[158]Li D C, Fang Y H. An algorithm to cluster data for efficient classification of support vector machines[J]. Expert Systems with Applications,2008,34(3):2013-2018.
[159]Lin C J. Formulations of support vector machines:A note from an optimization point of view[J]. Neural Computation,2001,13(2):307-317.
[160]Nello C, John S. An introduction to support vector machines and other kernel-based learning methods [M]. Cambridge:Cambridge University Press,2000:13-56.
[161]崔伟东,周志华,李星.支持向量机研究[J].计算机工程与应用,2001(1)：58-61.
[162]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,2004：10-43.
[163]赵洪波,茹忠亮,张士科.SVM在地下工程可靠性分析中的应用[J].岩土力学,2009,30(2)：526-530.
[164]Rocco C M, Moreno J A. Fast Monte Carlo reliability evaluation using support vector machine[J]. Reliability Engineering and System Safety,2002,76(3):237-243.
[165]马超,吕震宙.结构可靠性分析的支持向量机分类迭代算法[J].中国机械工程,2007,18(7)：816-819.
[166]郑严,程文明,程跃.基于支持向量机回归的结构可靠性分析[J].机械科学与技术,2011,30(1)：52-56.
[167]GUO Zhiwei, BAI Guangchen. Application of least squares support vector machine for regression to reliability analysis[J]. Chinese Journal of Aeronautics, 2009,22(2):160-166.
[168]ZHAO Hongbo. Slope reliability analysis using a support vector machine[J]. Computers and Geotechnics,2008,35(3):459-467.
[169]Chen K Y. Forecasting systems reliability based on support vector regression with genetic algorithms [J]. Reliability Engineering and System Safety,2007,92(4):423-432.
[170]Narwaria M, Lin W. Objective image quality assessment based on support vector regression[J]. IEEE Transactions on Neural Networks,2010,21(3):515-519.
[171]Suresh S, Sujit P B, Rao A K. Particle swarm optimization approach for multi-objective composite box-beam design[J]. Composite Structures,2007,81(4):598-605.
[172]Juan J. Particle swarm optimization application in power system engineering[D]. Puerto Rico:University of Puerto Rico,2004:26-63.
[173]Shi Y, Eberhart R C. A modified particle swarm optimizer [C]//Proceedings of IEEE International Conference on Evolutionary Computation Anchorage,1998:69-73.
[174]Tayal M. Particle swarm optimization for mechanical design[D]. Texas:University of Texas,2003:15-44.
[175]EBERHART R, KENNEDY J. A New Optimizer Using Particle Swarm Theory [C]// Proc. of 6th International Symposium on Micro Machine and Human Science, Nagoya, Japan:IEEE Press,1995:39-43.
[176]蔡自兴,徐光祜.人工智能及其应用[M].北京：清华大学出版社,2004：40-96.
[177]Parsopoulos K E, Vrahatis M N. Recent approaches to global optimization problems through particle swarm optimization [J]. Natural Computing,2002,1(2-3):235-306.
[178]Shi Y, Eberhart R C. Empirical study of particle swarm optimization[C]//Proceedings of IEEE Congress on Evolutionary Computation. Piscataway:IEEE,1999:1945-1950.
[179]Clerc M. The swarm and the queen:Towards a deterministic and adaptive paticle swarm optimization [C]//Proceedings of the Congress on Evolutionary Computation. Washington:IEEE Service Center,1999.1927-1930.
[180]Eberhart R C, Shi Y. Comparing inertia weights and constriction factors in particle swarm optimization [C]//Proceedings of the Congress Evolutionary Computation, San Diego:IEEE Press,2000:84-88.
[181]Kennedy J, Eberhart R C. A discrete binary version of the particle swarm algorithm [C]//Proceedings of the World Multri-Conference on Systemics, Cybernetics and Informatics, IEEE Press,1997:4104-4109.
[182]Secrest B, Lamont G. Communication in particle swarm optimization illustrated by the traveling salesman problem [C]//Proceedings of the Workshop on Particle Swarm Optimization, Indianapolis, IN:Purdue School of Engineering and Technology, IUPUI, 2001:230-238.
[183]Lovbjerg M, Rasmussen Tk, Krink T. Hybrid particle swarm optimization with breeding and subpopulations [C]//Proceedings of IEEE International Conference on Evolutionary Computation, San, Diego:IEEE,2000:1217-1222.
[184]史妍妍,孙志礼,闫明.基于响应面法的隐式极限状态函数可靠性灵敏度分析方法[J].机械科学与技术,2009,28(5)：648-651.
[185]Deng Jian, Gu Desheng, Li Xibing, et al. Structural Reliability Analysis for Implicit Performance [J]. Structural Safety,2005,27(1):25-48.
[186]Hurtado J E, Alvarez D A. Classification Approach for Reliability Analysis with Stochastic Finite-element Modeling [J].Journal of Structural Engineering, 2003,129:1141-1149.
[187]何水清,王善.结构可靠性分析与设计[M].北京：国防工业出版社,1993：22-35.
[188]赵洪波.基于支持向量机的边波可靠性分析[J].岩土工程学报,2007,29(6)：819-823.
[189]李洪双,吕震宙.支持向量回归机在结构可靠性分析中的应用[J].航空学报,2007,28(1)：94-99.
[190]赵国藩.工程结构可靠性理论与应用[M].大连：大连理工大学出版社,1996：14-42.
[191]Givolid, Elishakoff I. Stress concentration at a nearly circular hole with uncertain irregularities [J]. Journal of Applied Mechanics,1992,59:67-71.
[192]Ibrahim R A. Structural dynamics with parameter uncertainties[J]. Applied Mechanics, Reviews,1987,40(3):309-328.
[193]Elishakoff I, Cai G Q. Non-linear buckling of a column with initial imperfection via stochastic and Non-stochastic convex models[J]. International Journal of Non-linear Mechanics,1994,29(1):71-82.
[194]Elishakoff I, Elisseeff P, Glegg S A L. Non-probabilistic, convex-theoretic modeling of scatter in material properties [J]. AIAA Journal,1994,32(4):843-849.
[195]李洪双,吕震宙.结构可靠性分析的支持向量机响应面法[J].计算力学学报,2009,26(2)：199-203.
[196]邱志平.非概率集合理论凸方法及其应用[M].北京：国防工业出版社,2005：46-58.
[197]刘成立.复杂结构可靠性分析及设计研究[D].西北工业大学博士学位论文,2007：43-54.
[198]邵信光,杨慧中,陈刚.基于粒子群优化算法的支持向量机参数选择及其应用[J].控制理论与应用,2006,23(5)：740-743.
[199]张强,毛君,田大丰.基于遗传算法掘进机截割头多目标模糊可靠性优化[J].煤炭学报,2008,33(12)：1435-1437.
[200]YU Ying, YU Xiao-chun, LI Yong-sheng. New discrete particle swarm optimization based on huge value penalty for solving engineering problem[J]. Chinese Journal of Mechanical Engineering,2009,22(3):410-418.
[201]金一粟,周永华,梁逸曾.改进粒子群优化算法对反应动力学参数的估计[J].中南大学学报,2008,39(4)：694-699.
[202]El-Gohary A, Al-Ruzaiza A S. Chaos and adaptive control in two prey, one predator system with nonlinear feedback[J]. Chaos, Solitons and Fractals,2007,34(2):443-453.
[203]LIU Bo, WANG Ling, JIN Yi-hui, et al. Improved particle swarm optimization combined with chaos[J]. Chaos, Solitons and Fractals,2005,25(5):1261-1271.
[204]YANG Di-xiong, LI Gang, CHENG Geng-dong. On the efficiency of chaos optimization algorithms for global optimization[J]. Chaos, Solitons and Fractals,2007, 34(4):1366-1375.
[205]张义民,刘仁云,于繁华.基于计算智能技术的结构系统可靠性优化设计[J].工程力学,2007,24(8)：27-31.
[206]LI Bing, JIANG Wei-sun. Optimizing complex functions by chaos search[J]. Cybernetics and Systems,1998,29(4):409-419.
[207]李兵,蒋慰孙.混沌优化方法及其应用[J].控制理论与应用,1997,14(4)：613-615.
[208]张浩,张铁男,沈继红,等Tent混沌粒子群算法及其在结构优化决策中的应用[J].控制与决策,2008,23(8)：857-862.
[209]谷良贤,王轶鹏,龚春林.基于概率突跳和模拟退火的改进自适应微粒群算法[J].控制与决策,2009,24(4)：617-620.
[210]焦巍,刘光斌,张艳红.求解约束优化的模拟退火PSO算法[J].系统工程与电子技术,2010,32(7)：1532-1536.
[211]申建建,程春田,廖胜利等.基于模拟退火的粒子群算法在水电站水库优化调度中的应用[J].水力发电学报,2009,(1)：47-50.
[212]陈华根,吴健生,王家林等.模拟退火算法机理研究[J].同济大学学报(自然科学版),2004,32(6)：802-805.
[213]祝恒云,叶文华.模拟退火粒子群算法在动态单元布局中的应用[J].中国机械工程,2009,20(2)：181-185
[214]Wang T Y, Wu K B, Liu Y W. A Simulated Annealing Algorithm for Facility Layout Problems under Variable Demand in Cellular Manufacturing System[J]. Computers in Industry,2001,46(1):181-188.
[215]周龙,牟怿,尤新革.模拟退火算法在粮虫图像分割中的应用[J].华中科技大学学报(自然科学版),2010,38(5)：72-74.
[216]纪震,廖惠连,吴青华.粒子群算法及应用[M].北京：科学出版社,2009：25-57.
[217]Boeringer D W, Werner D H. Particle swarm optimization versus genetic algorithms for phased array synthesis. IEEE Trans. Antennas Propagation,2004,52(3):771-779.
[218]王华秋,曹长修.基于模拟退火的并行粒子群优化研究[J].控制与决策,2005,20(5)：500-504.
[219]刘朝,祁荣宾,钱锋.融合交叉变异和混沌的新型混合粒子群算法[J].化工学报,2010,61(11)：2862-2867.
[220]易平.对区间不确定性问题的可靠性度量的探讨[J].计算力学学报2006,23(2)：152-156.
[221]亢战,罗阳军.桁架结构非概率可靠性拓扑优化[J].计算力学学报,2008,25(5)：589-594.
[222]Kounias E G. Bounds for the probability of a union with applications[J]. Annals of Mathematical Statistics,1968,39(6):2154-2158.
[223]Ditlevsen O. Narrow reliability bounds for structural systems[J]. Journal of Structural Mechanics,1979,7(4):453-472.
[224]Greig G L. An assessment of high-order bounds for structural reliability[J]. Structural Safety,1992,11(3-4):213-225.
[225]盛骤,谢式千,潘承毅.概率论与数理统计[M](第二版).北京：高等教育出版社,1999：30-55.
[226]纪震,周家锐,廖惠连等.智能单粒子优化算法[J].计算机学报,2010,33(3)：556-561.
[227]储颖,糜华,纪震等.基于智能单粒子的联合代数重建算法[J].深圳大学学报(理工版),2009,26(2)：111-115.
[228]张明瑞,陈征宙,吴强等.基于智能单粒子算法的复杂边坡最危险滑动面搜索[J].中国水运,2010,10(12)：208-209.
[229]乔心州.不确定结构可靠性分析与优化设计研究[D].西安电子科技大学博士学位论文,2008：71-81.