结构体系失效概率计算方法研究
|
摘要
结构可靠度分析包括构件和体系两个层次：构件层次的可靠度经过几十年发展已经成熟,进入了实用阶段；对结构进行体系可靠度分析虽然已经在工程界达成共识,但距实际应用还有一定的距离。主要原因是结构体系可靠度计算中的两大难点“主要失效模式的搜寻”与“体系失效概率的计算”还有待于进一步研究。本文针对“结构体系失效概率的计算方法”开展研究,得到以下主要成果：
(1)针对基于条件概率的PCM方法(Product of Conditional Marginal)在构件可靠指标较大和失效模式间相关性较强时,计算串联体系失效概率误差较大的问题,提出了改进的PCM法。针对等价平面法(Equivalent Plane Method)计算并联体系失效概率误差较大的问题,提出了改进的等价平面法。
(2)基于可靠指标矢量的概念,应用等价失效模式的思想,推导了两个失效模式串联、并联及条件等价失效模式的可靠指标矢量计算公式。用可靠指标矢量来确定体系可靠度计算过程中失效模式间的相关系数,进而推求结构体系的可靠指标矢量。
(3)研究发现,在一定的可靠指标范围内串联体系和并联体系都具有对失效模式间的相关系数不敏感的特性。根据这一特性,提出在采用等价平面法计算结构体系可靠度时用各失效模式间的最大相关系数作为近似等价相关系数,简化了计算。
(4)针对体系可靠度计算时,近似方法结果受计算顺序影响的现象,研究了几种体系可靠度计算方法的特点。提出了按失效模式相关性强弱和可靠指标大小分组计算体系失效概率的方法与原则。
(5)根据分组计算体系失效概率方法和原则,通过可靠指标矢量来确定各组间的失效模式相关性,对实际工程进行了体系可靠度分析。
The development of structural reliability analysis can be divided into two stages, component analysis stage and system analysis stage. After years of diligent research, the component reliability analysis has achieved quite good level and has been applied to the actual projects. Although most of the scholars reached an agreement that the structural system reliability should be spreaded and applied to the engineering, yet there are still quite long way to go for this aim. There are mainly two difficulties for the structural system reliability application:①how to search for the major failure modes?②how to calculate the structural system failure probability? This paper concentrates on the study of structural system failure probability calculation methods. The main research findings are as follows:
(1) If the component reliability index is large and correlation of failure modes is strong, the PCM (Product of Conditional Marginal) method can usually cause quite large error for the series system failure probability calculation. So, a further improved PCM method (FIPCM) is proposed in this paper. The same problem also exists for the parallel system failure probability calculation if the EPM (Equivalent Plane Method) is used. So, an improved EPM method (IEPM) is also put forward.
(2) Based on the conception of reliability index vector and the idea of equivalent failure mode, the reliability index vector formulae are deduced for the series system, parallel system and conditional equivalent failure modes. The correlation coefficient between the failure modes can be determined by the reliability index vectors, and then the structural system failure probability and reliability index vector can be obtained.
(3) It has been found that the correlation coefficient between system failure modes is insensitive for the series and parallel system in a certain range of reliability indices. According to this characteristic, the maximum correlation coefficient between failure modes is taken as the approximate equivalent correlation coefficient when the equivalent plane method is used to calculate the structural system reliability.
(4) Because the calculation accuracy of system reliability by the approximate method is strongly influenced by the calculation sequences, a grouping calculation method is proposed, in which the strength degree of correlations and the magnitude of reliability index are the main controlling factors.
(5) The above mentioned principles and methods are applied to an actual project analysis, in which the grouping calculation method is used and the correlation of failure modes of groups are determined on the principle of reliability index vectors.
(1)针对基于条件概率的PCM方法(Product of Conditional Marginal)在构件可靠指标较大和失效模式间相关性较强时,计算串联体系失效概率误差较大的问题,提出了改进的PCM法。针对等价平面法(Equivalent Plane Method)计算并联体系失效概率误差较大的问题,提出了改进的等价平面法。
(2)基于可靠指标矢量的概念,应用等价失效模式的思想,推导了两个失效模式串联、并联及条件等价失效模式的可靠指标矢量计算公式。用可靠指标矢量来确定体系可靠度计算过程中失效模式间的相关系数,进而推求结构体系的可靠指标矢量。
(3)研究发现,在一定的可靠指标范围内串联体系和并联体系都具有对失效模式间的相关系数不敏感的特性。根据这一特性,提出在采用等价平面法计算结构体系可靠度时用各失效模式间的最大相关系数作为近似等价相关系数,简化了计算。
(4)针对体系可靠度计算时,近似方法结果受计算顺序影响的现象,研究了几种体系可靠度计算方法的特点。提出了按失效模式相关性强弱和可靠指标大小分组计算体系失效概率的方法与原则。
(5)根据分组计算体系失效概率方法和原则,通过可靠指标矢量来确定各组间的失效模式相关性,对实际工程进行了体系可靠度分析。
The development of structural reliability analysis can be divided into two stages, component analysis stage and system analysis stage. After years of diligent research, the component reliability analysis has achieved quite good level and has been applied to the actual projects. Although most of the scholars reached an agreement that the structural system reliability should be spreaded and applied to the engineering, yet there are still quite long way to go for this aim. There are mainly two difficulties for the structural system reliability application:①how to search for the major failure modes?②how to calculate the structural system failure probability? This paper concentrates on the study of structural system failure probability calculation methods. The main research findings are as follows:
(1) If the component reliability index is large and correlation of failure modes is strong, the PCM (Product of Conditional Marginal) method can usually cause quite large error for the series system failure probability calculation. So, a further improved PCM method (FIPCM) is proposed in this paper. The same problem also exists for the parallel system failure probability calculation if the EPM (Equivalent Plane Method) is used. So, an improved EPM method (IEPM) is also put forward.
(2) Based on the conception of reliability index vector and the idea of equivalent failure mode, the reliability index vector formulae are deduced for the series system, parallel system and conditional equivalent failure modes. The correlation coefficient between the failure modes can be determined by the reliability index vectors, and then the structural system failure probability and reliability index vector can be obtained.
(3) It has been found that the correlation coefficient between system failure modes is insensitive for the series and parallel system in a certain range of reliability indices. According to this characteristic, the maximum correlation coefficient between failure modes is taken as the approximate equivalent correlation coefficient when the equivalent plane method is used to calculate the structural system reliability.
(4) Because the calculation accuracy of system reliability by the approximate method is strongly influenced by the calculation sequences, a grouping calculation method is proposed, in which the strength degree of correlations and the magnitude of reliability index are the main controlling factors.
(5) The above mentioned principles and methods are applied to an actual project analysis, in which the grouping calculation method is used and the correlation of failure modes of groups are determined on the principle of reliability index vectors.
引文
[1]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 50153-92).北京：中国计划出版社,1992.
[2]国家自然课科学基金委员会.自然科学学科发展战略调研报告：水利学科.北京：科学出版社,1994.
[3]王光远.工程软设计理论[M].北京：科学出版社,1992.
[4]黄兴棣.工程结构可靠性设计[M].北京：人民交通出版社,1989.
[5]王光远,陈树勋.工程结构系统软科学设计理论及应用[M].北京：中国建筑工业出版社,1999.
[6]张新培.建筑结构可靠度分析与设计[M].北京：科学出版社,2001.
[7]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.
[8]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.
[9]杨伟军,赵传智.土木工程结构可靠度理论与应用[M].北京：人民交通出版社,1999.
[10]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.
[11]张骏华.结构可靠性设计与分析[M].宇航出版社.1989.
[12]欧进萍,候纲领.建筑结构可靠度设计的影响因素与比较研究[J].建筑科学,1999,15(5)：51-55
[13]林广元.韩国汉城一座桥梁的坍塌事故[J].国外桥梁,1995,(3)：225-229.
[14]秦荣,谢肖礼,彭立文等.钢管混凝土拱桥钢管开裂事故分析[J].土木工程学报,2001,34(3)：74-77.
[15]范立础.桥梁工程安全性与耐久性一展望设计理念进展[J].上海公路,2004,(1)：1-7.
[16]中国土木工程学会第九届年会论文集.工程安全性与耐久性.北京：中国水利水电出版社,2000.
[17]欧进萍,段忠东,肖仪清.海洋平台结构安全评定：理论、方法与应用[M].北京：科学出版社,2003.
[18]曹双寅,邱洪兴,王恒华.结构可靠性鉴定与加固技术[M].中国水利水电出版社.2002.
[19]刘西拉.我国工程结构耐久性问题面临的处境和难点[A].沿海地区混凝土结构耐久性及其设计方法科技论坛与全国第六届混凝土耐久性学术交流会论文集[C],2004.
[20]Ditlevsen O,Madsen H O. Proposal for a code for the direct use of reliability methods in structural design. In:Working Document of Joint Committee on Structural Safety, 1989.
[21]秦荣.大型复杂结构体系可靠度[M].北京：科学出版社,2009.
[22]贡金鑫,仲伟秋,赵国藩.工程结构可靠性基本理论的发展与应用(1)[J].建筑结构学报,2002,23(4)：2-9.
[23]贡金鑫,仲伟秋,赵国藩.工程结构可靠性基本理论的发展与应用(2)[J].建筑结构学报,2002,23(5)：2-10.
[24]贡金鑫,仲伟秋,赵国藩.工程结构可靠性基本理论的发展与应用(3)[J].建筑结构学报,2002,23(6)：2-9.
[25]董聪,杨庆雄.现代结构系统可靠性分析理论发展概况及若干应用[J].力学进展.1993,23(2)：206-213.
[26]高镇同.疲劳应用统计学[M].国防工业出版社.1986.
[27]ISO/DIS2394. General principles on reliability for structures.1986.
[28]ISO/DIS2394. General principles on reliability for structures.1998.
[29]中华人民共和国国家标准.建筑结构设计统一标准(GBJ68-84).北京：中国建筑工业出版社,1984.
[30]中华人民共和国国家标准.港口工程结构可靠度设计统一标准(GB 50158-92).北京：中国计划出版社,1992.
[31]中华人民共和国国家标准.水利水电工程结构可靠度设计统一标准(GB 50199-94).北京：中国计划出版社,1994.
[32]中华人民共和国国家标准.铁路工程结构可靠度设计统一标准(GB 50216-94).北京：中国计划出版社,1994.
[33]中华人民共和国国家标准.公路工程结构可靠度设计统一标准(GB 50283-1999).北京：中国计划出版社,1999.
[34]中华人民共和国国家标准.建筑结构可靠度设计统一标准(GB 50068-2001).北京：中国建筑工业出版社,2001.
[35]李继华.可靠性数学[M].北京：中国建筑工业出版社,1988.
[36]吴世伟.结构可靠度分析[M].北京：交通出版社,1988.
[37]刘宁.可靠度随机有限元法及其工程应用[M].北京：中国水利水电出版社,2001.6.
[38]秦权,林道锦,梅刚.结构可靠度随机有限元-理论及工程运用[M].北京：清华大学出版社,2006.9.
[39]孙新利,陆长捷.工程可靠性教程[M].北京：国防工业出版社,2005.1.
[40]张明.构可靠度分析-方法与程序[M].北京：科学出版社,2009.
[41]贡金鑫.工程结构可靠度计算方法[M].大连：大连理工大学出版社,2003.9.
[42]董聪.现代结构系统可靠性理论及其应用[M].北京：科学出版社,2001.
[43]张爱林.基于功能可靠度的结构全寿命设计理论研究综述[J].北京工业大学学报,2000,26(3) ：55-58.
[44]李刚,程耿东.基于功能的结构体系目标可靠度优化决策[J].计算力学学报,2002,19(2)：127-131.
[45]贡金鑫,赵国藩.相关荷载效应组合及结构可靠度计算[J].工程力学,2001,18(4)：1-6.
[46]李刚,许林,程耿东.基于ANSYS软件的大型复杂结构可靠度分析[J].建筑结构,2002,32(5) ：58-61.
[47]张小庆.结构体系可靠度分析方法研究[D].大连理工大学,2003.
[48]禹智涛.既有钢筋混凝土桥梁可靠性评估的若干问题研究[D].华南理工大学,2003.
[49]许林.基于可靠度的结构优化研究[D].大连理工大学,2004.
[50]董素芹.现役建筑结构可靠性鉴定方法的研究[D].内蒙古农业大学,2005.
[51]吴启和.基于结构可靠度理论的钢筋混凝土桥梁的健康评估[D].西南交通大学,2006.
[52]敬大德.在役RC桥梁基于可靠度的耐久性分析[D].长安大学,2006
[53]顾祥林,陈少杰,张伟平.既有建筑结构体系可靠性评估实用方法[J].结构工程师,2007,(04).
[54]吴海军.桥梁结构耐久性设计方法研究[D].同济大学,2007.
[55]李志华.隧道结构生命全过程可靠度研究[D].大连理工大学,2008
[56]周锡武.关于混凝土结构耐久性设计的若干问题研究[D].华中科技大学,2008.
[57]马军海.基于全寿命的桥梁设计过程及其在混凝土连续桥梁中的应用[D].同济大学,2008
[58]高常欢.既有结构抗力的劣化概率模型及可靠度计算[D].西安建筑科技大学,2008.
[59]李玉刚.桩式海上风机基础可靠度分析及优化方法研究[D].大连理工大学,2009
[60]李炜.边坡稳定可靠性研究[D].大连理工大学,2009
[61]中国土木工程学会桥梁及结构工程学会结构可靠度委员会.工程结构可靠性全国第三届学术交流会议论文集.南京：1995.
[62]Cornell C A, Structural Safety Specification Based on Second-Moment Reliability, Sym. Int. Assoc. of Bridge and Struct. Engr., London,1969.
[63]Hasofer A M, Lind N C. Exact and invariant second-moment code format[J]. Journal of the Engineering Mechanics,1974,100 (1):111-121.
[64]Paloheimo E, Hannus H, Structural Design Based on Weighted Fractiles, Journal of the Structural Division,1974,100 (77),1367-1378.
[65]Rackwitz R, Practical Probabilistic Approach to Design. Bulletin 112, Comite European du Beton, Paris, France,1976.
[66]Rackwitz R, Fiessler B, Structural Reliability under Combined Random Load Sequences. Computers & Structures,1978,9 (5):489-494.
[67]Rosenblatt M. Remarks on a multivariate transformation. The Annals of Mathematical Statistics,1952,23 (3):470-472.
[68]Hohenbichler M, Rackwitz R. Nonnormal dependent vetors in structural reliability[J]. Journal of Structural Mechanics,1981,107 (6):1227-1238.
[69]李云贵,赵国藩,张保和.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(增1)：1-5.
[70]赵国藩,王恒栋.广义随机空间内的结构可靠度实用分析方法[J].土木工程学报,1996,29(4)：47-51.
[71]董聪.现代结构系统可靠性理论[D],西北工业大学,1993.
[72]赵国藩.结构可靠度的实用分析方法[J].建筑结构学报,1984,5(3)：1-10.
[73]Ditlevsen 0. Principle of normal tail approxiamation[J]. Journal of the Engineering Mechanics,1981,107 (6):1191-1208.
[74]Rosenblueth, Point Estimate for Probability Moment, Proceedings of the National Academy of Sciences (USA),1975.
[75]祝玉学.边坡可靠性分析[M].北京：冶金工业出版社,1983.
[76]张广文,陈祖煜.Rosenblueth方法的探讨及其在工程结构可靠度中的应用[A].中国土木工程学会桥梁及结构工程学会结构可靠度委员会结构可靠性全国第三界学术会议论文集[C].1993,52-59.
[77]佟晓利,赵国藩.改进的Rosenblueth方法及其在结构可靠度分析中的应用[J].大连理工大学学报,1997,37(3)：316-321.
[78]陈安龙,于雷,郑云龙.基于Rosenblatt变换的一阶可靠度分析方法[J].大连理工大学学报,2000,40(6)：741-743.
[79]徐军,郑颖人.有理多项式技术在工程结构可靠度分析中的应用[J].计算力学学报,2001,18(4)：488-491.
[80]Chowdhury R. N, Xu D. W. Rational polynomial technique in slope-reliability analysis[J]. Journal of Geotechnical Engineering Division, ASCE,1993,119 (12):1910-1928.
[81]李继祥,谢桂华.计算结构可靠度的JC法改进方法[J].武汉工业学院学报,2004,23(1)：48-50.
[82]Fiessler B, Rackwitz R, Neumann H. Quadratic limit states in structural reliability [J]. Journal of the Engineering Mechanics Division,1979,105 (44):661-676.
[83]Breitung K. Asymptotic approximations for multinomrmal integrals[J]. Journal Engineering Mechanics Division. ASCE,1984,110 (3):357-366.
[84]Der Kiureghian A,De Stefano M. Efficient algorithm for second-order reliability analysis[J]. Journal of Engineering Mechanics,1991,117 (12):2904-2923.
[85]Zhao Y-G, Ono T. New Approximations for SORM:Part 1[J]. Journal of Engineering Mechanics,1999,125 (1):79-85.
[86]Zhao Y-G, Ono T. New Approximations for SORM:Part 2[J]. Journal of Engineering Mechanics,1999,125 (1):86-93.
[87]李云贵,赵国藩.广义随机空间内的结构可靠度渐近分析方法[J].水利学报,1994,8：36-41.
[88]张新培,葛燕.结构可靠度的当量正态PFSORM算法[J].应用力学学报,2002,19(2)：85-87.
[89]Breitung K. Asymptotic approximations for probability integrals[J]. Probability Engineering Mechanics,1989,4 (4):187-190.
[90]Breitung K. Probability approximations by log likelihood maximization[J]. Journal of Engineering Mechanics.1991,117 (3):457-477.
[91]贡金鑫,赵国藩.原始随机空间内的结构可靠度分析方法.水利学报,1999,(5)：30-34
[92]Der Kiureghian A, Dakessian T. Multiple design points in first and second-order reliability[J]. Structural Safety,1998,20 (1):37-49.
[93]Zhao Y-G, Ono T. A general procedure for first/second-order reliabilitymethod (FORM/SORM) [J]. Structural Safety,1999,21 (2):95-112.
[94]贡金鑫,陈晓宝,赵国藩.结构可靠度分析的Guass-Hermite积分方法.上海交通大学学报,2002,36(11)：1625-1629.
[95]Tichy M. First-order third-moment reliability method[J]. Structural Safety,1994,16 (3):189-200.
[96]Zhao Y-G, Ono T. Third-moment standardization for structural reliability analysis[J]. Journal of Structual Engineering,2000,126 (6):724-732.
[97]Zhao Y-G,Ono T. Moment methods for structural reliability[J]. Structural Safety,2001,23 (1):47-75.
[98]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.
[99]Hohenbichler R, Rackwitz R. Improvement of second-order reliability estimates by importance sampling[J]. Journal of Engineering Mechanics,1988,114 (12):2195-2199.
[100]Bucher C. G. Adaptive sampling-an iterative fast Monte Carlo procedure[J]. Structural Safety,1988,5 (2):119-126.
[101]金伟良.结构可靠度数值模拟的新方法[J].建筑结构学报,1996,17(3)：63-72.
[102]Jin W-L. Importance sampling method in V-space[J]. China Ocean Engineering,1997,11 (2):127-150.
[103]程耿东,蔡文学.结构可靠度计算的近似重要性抽样方法及其应用[J].工程力学,1997,14(2) ：1-7.
[104]Au S. K, Beck J. L. A new adaptive importance sampling scheme for reliability calculations[J]. Structural Safety,1999,21 (2):135-158.
[105]董聪,郭晓华.基于广义遗传算法的自适应重要抽样理论[J].计算机科学,2000,27(4)：1-4.
[106]吴斌,欧进萍,张纪刚.结构动力可靠度的重要抽样法[J].计算力学学报,2001,18(4)：478-482.
[107]Melchers R. E. Importance sampling in structural systems [J]. Structural Safety,1989,6 (1):3-10.
[108]Engelund S, Rackwitz R. A benchmark study on importance sampling techniques in structural reliability[J]. Structural Safety,1993,12 (4):255-276.
[109]Ditlevsen 0, Melchers R. E, Gluver H. General multi-dimensional probability integration by directional simulation[J]. Computers& Structures,1990,36 (2):355-368.
[110]伍朝晖,赵国藩.数论方法在结构体系可靠度计算中的应用[J].大连理工大学学报,1998,38(1)：92-96.
[111]张建仁,许福友.两种求解可靠指标的实用算法[J].工程力学,2002,19(3)：159-165.
[112]许福友,陈艾荣,张建仁.计算结构可靠指标的循环逼近法[J].同济大学学报,2004,32(4)：426-430.
[113]刘宇,吕泰仁.随机有限元及其工程应用[J].力学进展.1995.25(1)：114-126.
[114]An inference-finite element model for field problems[J]. Applied Mathematical Modeling,1978,2 (2):49-55.
[115]M Shinozuka, G Deodatis. Response variability of stochastic finite element systems. Journal of Engineering Mechanics,1988.114 (3):499-519
[116]Fumio Yamazaki, Masanobu Shinozuka and Gautam Dasgupta, Neumann expansion for stochastic finite element analysis. J. Eng. Mech.1988,114 (8):1335-1354
[117]Armen Der Kiureghian, Jyh-Bin Ke. The stochastic finite element method in structural reliability. Probabilistic Engineering Mechanics,1988,3 (2):83-91
[118]Wong F. S. Slope reliability and response surface method[J]. Journal of Geotechnical Engineering,1985,111 (1):32-53.
[119]Faravelli L. A response surface approach for reliability analysis[J]. Journal of Engineering Mechanics, ASCE,1989,115 (12):2763-2781.
[120]Bucher C. G, Bourgund U. A fast and efficient response surface approach for structural reliabilityproblems[J]. Structural Safety,1990,7 (1):57-66.
[121]Rajashekhar M. R, Ellingwood B. R. A new look at the response surface approach for reliability analysis[J]. Structural Safety,1993,12 (3):205-220.
[122]佟晓利,赵国藩.一种与结构可靠度分析几何法相结合的响应面法[J].土木工程学报,1997,30(4) ：51-57.
[123]武清玺,卓家寿.结构可靠度分析的变f序列响应面法及其应用[J].河海大学学报：自然科学版,2001,29(2)：75-78.
[124]张小庆,康海贵,王复明.求解隐式功能函数可靠度的一种新方法[J].大连理工大学学报.2003,43(5)：650-653.
[125]Hosni Elhewy A.,Mesbahi E.,Pu Y. Reliability analysis of structures using neural network method[J]. Probabilistic Engineering Mechanics,2006,21 (1):44-53.
[126]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.
[127]桂劲松.结构可靠度分析的改进BP神经网络响应面法[J].应用力学学报,2005,22(1)：127-130.
[128]桂劲松,康海贵.结构可靠度分析的全局响应面法研究[J].建筑结构学报,2004,25(4)：100-105.
[129]桂劲松,康海贵.结构可靠度分析的智能计算法[J].中国造船,2005,46(2)：28-34.
[130]袁雪霞.建筑施工模板支撑体系可靠性研究[D].杭州：浙江大学博士学位论文,2006.
[131]刘济科,赵卫.基于支持向量回归的响应面可靠度计算[J].中山大学学报,2008.47(1)：1-4.
[132]Moses F. System reliability developments in structural engineering[J]. Structural Safety,1982,1(1):3-13.
[133]Moses F. New directions and research needs in system reliability research[J]. Structural Safety,1990,7 (2-4):93-100.
[134]Feng Y S. Enumerating significant failure modes of a structural system by using criterion methods[J]. Computers and Structures,1988,30 (5):1153-1157.
[135]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.
[136]董聪,冯元生.枚举结构主要失效模式的一种新方法[J].西北工业大学学报,1991,9(3)：284-289.
[137]董聪,杨庆雄.冗余桁架结构系统可靠性分析理论与算法[J].计算结构力学及其应用,1992,9(4)：393-398.
[138]董聪,杨庆雄.结构系统静强度可靠性分析理论与算法[J],强度与环境,1993,2：1-8.
[139]姚卫星.顾怡.用自动矩阵力法枚举结构的主要失效模式[J].计算结构力学及其应用.1996,13(1)：62-66.
[140]Reashedi M R, Application of linear programming to structural system reliability. Computers and Structures,1986,24 (3):375-384.
[141]刘天云,赵国藩.一种识别结构主要失效模式的有效算法[J].大连理工大学学报,1998,38(1)：97-100.
[142]Murotsu Y, Okada H, Yonezawa M, et al. Automatic generation of stochastically dominant modes of structural failure in frame structure. Structural Safety,1984,28 (2):17-25.
[143]赵鹏飞.对分枝限界法的一种改进[J].四川建筑科学研究,1997,4：40-45.
[144]Thoft-Christensen P, Sorensen J, D. Reliability of structural systems with correlated elements. Applied Mathematical Modeling,1982,6 (3):171-178.
[145]董聪,结构系统可靠性分析与优化[D],西北工业大学,1990.
[146]董聪,杨庆雄.冗余桁架结构系统可靠性分析理论与算法[J].计算结构力学及其应用,1992,9(4)：393-398.
[147]蔡迎建,孙炔纯.结构失效模式的快速识别方法[J].大连理工大学学报,1999,39(4)：489-493.
[148]Duunett C. W, Sobel M. Approximation to the probability of integral and certain percentage points of a multivariate analogue of student's distribution[J]. Biometrika, 1955,42 (1-2):258-260.
[149]Johnson N, Kotz S. Distributions in statistics:continuous multivariate distributions. New York, NY:John Wiley & Sons Inc.,1972.
[150]何水清,王善.结构可靠性分析与设计.北京：国防工业出版社,1993.
[151]Cornell CA. Bounds on the reliability of structural systems [J]. Journal of Structural Division,ASCE,1967,93 (ST1).
[152]Kounias EG. Bounds for the probability of a union with applications. Annuals of Mathematical Statistics,1968,39 (6):2154-2158.
[153]Ditlevsen O. Nallow reliability bounds for structural system[J]. Journal of Structural Mechanics,1979,7 (4):453-472.
[154]Thoft-Christensen P. Murotsu Y. Application of structural systems reliability theory. Spring-Verlag, Berlin, Heidelberg, New York, Tokyo,1986.
[155]Feng YS. A Method of computing structural system reliability with high accuracy[J]. Computers and Structures,1989,33 (1):1-5.
[156]Zhang YC. Derivative fitting procedure for computing bivariate normal distribution and some applications [J]. Structural Safety,1994,14 (3):173-183.
[157]贡金鑫,赵国藩.二维正态分布函数值的一个近似算法[J].计算结构力学及其应用,1996,13(4)：494-499.
[158]姚继涛,赵国藩,浦聿修.二维标准正态联合概率的计算[J].建筑结构学报,1996,17(4)：10-19.
[159]吕震宙,冯元生.结构安全概率方法评述[J].机械强度.1993.12.15(4)：1-5.
[160]Ditlevsen 0, Bjerager P. Methods of structural systems reliability[J]. Structural Safety,1986,3 (3-4):195-229.
[161]Ang H-S, Ma HF. On the reliability of structural systems. In:Proceedings of International Conference on Structural Safety and Reliability, Trondheim,1981.
[162]Hohenbichler M, Rackwitz R. First-order concepts in system reliability[J]. Structural Safety,1983,1 (3):177-188.
[163]Tang L. K, Melchers R. E. Improved approximation for multinormal integral[J]. Structural Safety,1986,4 (2):81-93.
[164]Birnbaum ZW. Effect of linear truncation on a multinormal population[J]. The Annals of Mathematical Statistics,1950,21 (2):272-279.
[165]Tallis GM. The moment generating function of the truncated multi-normal distribution[J]. Journal of the Royal Statistical Society, Series B (Methodological),1961,23 (1):223-229.
[166]Terada S, Takahashi T. Failure-conditioned reliability index[J]. Journal of Structural Engineering,1988,114 (4):942-952.
[167]Pandey M. D. An effective approximation to evaluate multinormal integrals[J]. Structural Safety,1998,20 (1):51-67.
[168]Pandey MD, Sarkar A. Comparison of a simple approximation for multinormal integration with an importance sampling-based simulation method[J]. Probabilistic Engineering Mehanics,2002,17 (2):215-218.
[169]X.-X. Yuan, M. D. Pandey. Analysis of approximations for multinormal integration in system reliability computation[J]. Structural Safety,2006,28 (4):361-377.
[170]S. Gollwitzer, R. Rackwitz, Equivalent components in first-order system reliability [J], Reliability Engineering,1983,5 (2):99-115.
[171]贡金鑫.结构体系可靠度计算的逐步当量平面法.水工结构理论与实践,大连：大连海运学院出版社,1993：97-104.
[172]张小庆,康海贵,王复明.改进的微分等价地归算法[J].土木工程学报,2004,37(1)：31-38.
[173]张小庆,康海贵,王复明.一种新的体系可靠度的近似计算方法[J].工程力学.2004,21(1)：93-97.
[174]Vanmarcke E H. Matrix formulation of reliability analysis and reliability based design[J].Computers & Structures,1973.3 (4):757-770.
[175]Tichy M, Vorlica K. Safety of reinforced concrete framed structure, in Mech. Of Reinforcd Concrete. In:Proc of the ASCE ACI Int Sm.1974:171-179.
[176]李云贵,赵国藩.结构体系可靠度的近似计算方法[J].土木工程学报,1993,26(5)：70-76.
[177]郭书祥.结构体系失效概率计算的一种快速有效方法[J].计算力学学报,2007,24(1)：107-110.
[178]Thoft-Christensen P, Sorensen J. D. Reliability of structural systems with correlated elements[J]. Applied Mathematical Modeling,1982,6 (3):171-178.
[179]Ditlevsen O. Taylor expansion of series system reliability[J]. Journal of Engineering Mechanics,1984,110 (2):293-307.
[180]贡金鑫,赵国藩.串联结构体系可靠度的二元泰勒级数展开[J].计算力学学报,1997,14(1)：78-84.
[181]贡金鑫.一类多维正态积分的近似解法[J].西安建筑科技大学学报,1996,28(1)：52-56.
[182]贡金鑫,赵国藩.并联结构体系可靠度计算的二次二阶矩法[J].工程力学(增刊),1996：548-553.
[183]姚继涛,赵国藩,蒲聿修.结构体系失效概率的快速半数值积分方法.中国土木工程学会桥梁及结构工程学会结构可靠度委员会工程结构可靠性第四届全国学术交流会论文集.北京：地震出版社,1996.
[184]侯钢领,欧进萍.结构可靠指标矢量及其计算与应用[J].计算力学学报,2002,19(2)：143-147.
[185]CB271单井平台结构分析报告(No.海工-03038/计)[R].中国石化胜利油田有限公司规划设计研究院,2003.
[186]Mori Y, Kato T. Multinormal integrals by importance sampling for series system reliability[J]. Structural Safety 2003;25 (4):363-378.
[187]Sudret B, Kiureghian AD. Comparison of Finite Element Reliability Methods[J], Probabilistic Engineering Mechanics,2002,17 (4):337-348.
[188]吴恒立.拱式体系的稳定计算.北京：人民交通出版社,1979.31-32.
[2]国家自然课科学基金委员会.自然科学学科发展战略调研报告：水利学科.北京：科学出版社,1994.
[3]王光远.工程软设计理论[M].北京：科学出版社,1992.
[4]黄兴棣.工程结构可靠性设计[M].北京：人民交通出版社,1989.
[5]王光远,陈树勋.工程结构系统软科学设计理论及应用[M].北京：中国建筑工业出版社,1999.
[6]张新培.建筑结构可靠度分析与设计[M].北京：科学出版社,2001.
[7]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.
[8]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.
[9]杨伟军,赵传智.土木工程结构可靠度理论与应用[M].北京：人民交通出版社,1999.
[10]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.
[11]张骏华.结构可靠性设计与分析[M].宇航出版社.1989.
[12]欧进萍,候纲领.建筑结构可靠度设计的影响因素与比较研究[J].建筑科学,1999,15(5)：51-55
[13]林广元.韩国汉城一座桥梁的坍塌事故[J].国外桥梁,1995,(3)：225-229.
[14]秦荣,谢肖礼,彭立文等.钢管混凝土拱桥钢管开裂事故分析[J].土木工程学报,2001,34(3)：74-77.
[15]范立础.桥梁工程安全性与耐久性一展望设计理念进展[J].上海公路,2004,(1)：1-7.
[16]中国土木工程学会第九届年会论文集.工程安全性与耐久性.北京：中国水利水电出版社,2000.
[17]欧进萍,段忠东,肖仪清.海洋平台结构安全评定：理论、方法与应用[M].北京：科学出版社,2003.
[18]曹双寅,邱洪兴,王恒华.结构可靠性鉴定与加固技术[M].中国水利水电出版社.2002.
[19]刘西拉.我国工程结构耐久性问题面临的处境和难点[A].沿海地区混凝土结构耐久性及其设计方法科技论坛与全国第六届混凝土耐久性学术交流会论文集[C],2004.
[20]Ditlevsen O,Madsen H O. Proposal for a code for the direct use of reliability methods in structural design. In:Working Document of Joint Committee on Structural Safety, 1989.
[21]秦荣.大型复杂结构体系可靠度[M].北京：科学出版社,2009.
[22]贡金鑫,仲伟秋,赵国藩.工程结构可靠性基本理论的发展与应用(1)[J].建筑结构学报,2002,23(4)：2-9.
[23]贡金鑫,仲伟秋,赵国藩.工程结构可靠性基本理论的发展与应用(2)[J].建筑结构学报,2002,23(5)：2-10.
[24]贡金鑫,仲伟秋,赵国藩.工程结构可靠性基本理论的发展与应用(3)[J].建筑结构学报,2002,23(6)：2-9.
[25]董聪,杨庆雄.现代结构系统可靠性分析理论发展概况及若干应用[J].力学进展.1993,23(2)：206-213.
[26]高镇同.疲劳应用统计学[M].国防工业出版社.1986.
[27]ISO/DIS2394. General principles on reliability for structures.1986.
[28]ISO/DIS2394. General principles on reliability for structures.1998.
[29]中华人民共和国国家标准.建筑结构设计统一标准(GBJ68-84).北京：中国建筑工业出版社,1984.
[30]中华人民共和国国家标准.港口工程结构可靠度设计统一标准(GB 50158-92).北京：中国计划出版社,1992.
[31]中华人民共和国国家标准.水利水电工程结构可靠度设计统一标准(GB 50199-94).北京：中国计划出版社,1994.
[32]中华人民共和国国家标准.铁路工程结构可靠度设计统一标准(GB 50216-94).北京：中国计划出版社,1994.
[33]中华人民共和国国家标准.公路工程结构可靠度设计统一标准(GB 50283-1999).北京：中国计划出版社,1999.
[34]中华人民共和国国家标准.建筑结构可靠度设计统一标准(GB 50068-2001).北京：中国建筑工业出版社,2001.
[35]李继华.可靠性数学[M].北京：中国建筑工业出版社,1988.
[36]吴世伟.结构可靠度分析[M].北京：交通出版社,1988.
[37]刘宁.可靠度随机有限元法及其工程应用[M].北京：中国水利水电出版社,2001.6.
[38]秦权,林道锦,梅刚.结构可靠度随机有限元-理论及工程运用[M].北京：清华大学出版社,2006.9.
[39]孙新利,陆长捷.工程可靠性教程[M].北京：国防工业出版社,2005.1.
[40]张明.构可靠度分析-方法与程序[M].北京：科学出版社,2009.
[41]贡金鑫.工程结构可靠度计算方法[M].大连：大连理工大学出版社,2003.9.
[42]董聪.现代结构系统可靠性理论及其应用[M].北京：科学出版社,2001.
[43]张爱林.基于功能可靠度的结构全寿命设计理论研究综述[J].北京工业大学学报,2000,26(3) ：55-58.
[44]李刚,程耿东.基于功能的结构体系目标可靠度优化决策[J].计算力学学报,2002,19(2)：127-131.
[45]贡金鑫,赵国藩.相关荷载效应组合及结构可靠度计算[J].工程力学,2001,18(4)：1-6.
[46]李刚,许林,程耿东.基于ANSYS软件的大型复杂结构可靠度分析[J].建筑结构,2002,32(5) ：58-61.
[47]张小庆.结构体系可靠度分析方法研究[D].大连理工大学,2003.
[48]禹智涛.既有钢筋混凝土桥梁可靠性评估的若干问题研究[D].华南理工大学,2003.
[49]许林.基于可靠度的结构优化研究[D].大连理工大学,2004.
[50]董素芹.现役建筑结构可靠性鉴定方法的研究[D].内蒙古农业大学,2005.
[51]吴启和.基于结构可靠度理论的钢筋混凝土桥梁的健康评估[D].西南交通大学,2006.
[52]敬大德.在役RC桥梁基于可靠度的耐久性分析[D].长安大学,2006
[53]顾祥林,陈少杰,张伟平.既有建筑结构体系可靠性评估实用方法[J].结构工程师,2007,(04).
[54]吴海军.桥梁结构耐久性设计方法研究[D].同济大学,2007.
[55]李志华.隧道结构生命全过程可靠度研究[D].大连理工大学,2008
[56]周锡武.关于混凝土结构耐久性设计的若干问题研究[D].华中科技大学,2008.
[57]马军海.基于全寿命的桥梁设计过程及其在混凝土连续桥梁中的应用[D].同济大学,2008
[58]高常欢.既有结构抗力的劣化概率模型及可靠度计算[D].西安建筑科技大学,2008.
[59]李玉刚.桩式海上风机基础可靠度分析及优化方法研究[D].大连理工大学,2009
[60]李炜.边坡稳定可靠性研究[D].大连理工大学,2009
[61]中国土木工程学会桥梁及结构工程学会结构可靠度委员会.工程结构可靠性全国第三届学术交流会议论文集.南京：1995.
[62]Cornell C A, Structural Safety Specification Based on Second-Moment Reliability, Sym. Int. Assoc. of Bridge and Struct. Engr., London,1969.
[63]Hasofer A M, Lind N C. Exact and invariant second-moment code format[J]. Journal of the Engineering Mechanics,1974,100 (1):111-121.
[64]Paloheimo E, Hannus H, Structural Design Based on Weighted Fractiles, Journal of the Structural Division,1974,100 (77),1367-1378.
[65]Rackwitz R, Practical Probabilistic Approach to Design. Bulletin 112, Comite European du Beton, Paris, France,1976.
[66]Rackwitz R, Fiessler B, Structural Reliability under Combined Random Load Sequences. Computers & Structures,1978,9 (5):489-494.
[67]Rosenblatt M. Remarks on a multivariate transformation. The Annals of Mathematical Statistics,1952,23 (3):470-472.
[68]Hohenbichler M, Rackwitz R. Nonnormal dependent vetors in structural reliability[J]. Journal of Structural Mechanics,1981,107 (6):1227-1238.
[69]李云贵,赵国藩,张保和.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(增1)：1-5.
[70]赵国藩,王恒栋.广义随机空间内的结构可靠度实用分析方法[J].土木工程学报,1996,29(4)：47-51.
[71]董聪.现代结构系统可靠性理论[D],西北工业大学,1993.
[72]赵国藩.结构可靠度的实用分析方法[J].建筑结构学报,1984,5(3)：1-10.
[73]Ditlevsen 0. Principle of normal tail approxiamation[J]. Journal of the Engineering Mechanics,1981,107 (6):1191-1208.
[74]Rosenblueth, Point Estimate for Probability Moment, Proceedings of the National Academy of Sciences (USA),1975.
[75]祝玉学.边坡可靠性分析[M].北京：冶金工业出版社,1983.
[76]张广文,陈祖煜.Rosenblueth方法的探讨及其在工程结构可靠度中的应用[A].中国土木工程学会桥梁及结构工程学会结构可靠度委员会结构可靠性全国第三界学术会议论文集[C].1993,52-59.
[77]佟晓利,赵国藩.改进的Rosenblueth方法及其在结构可靠度分析中的应用[J].大连理工大学学报,1997,37(3)：316-321.
[78]陈安龙,于雷,郑云龙.基于Rosenblatt变换的一阶可靠度分析方法[J].大连理工大学学报,2000,40(6)：741-743.
[79]徐军,郑颖人.有理多项式技术在工程结构可靠度分析中的应用[J].计算力学学报,2001,18(4)：488-491.
[80]Chowdhury R. N, Xu D. W. Rational polynomial technique in slope-reliability analysis[J]. Journal of Geotechnical Engineering Division, ASCE,1993,119 (12):1910-1928.
[81]李继祥,谢桂华.计算结构可靠度的JC法改进方法[J].武汉工业学院学报,2004,23(1)：48-50.
[82]Fiessler B, Rackwitz R, Neumann H. Quadratic limit states in structural reliability [J]. Journal of the Engineering Mechanics Division,1979,105 (44):661-676.
[83]Breitung K. Asymptotic approximations for multinomrmal integrals[J]. Journal Engineering Mechanics Division. ASCE,1984,110 (3):357-366.
[84]Der Kiureghian A,De Stefano M. Efficient algorithm for second-order reliability analysis[J]. Journal of Engineering Mechanics,1991,117 (12):2904-2923.
[85]Zhao Y-G, Ono T. New Approximations for SORM:Part 1[J]. Journal of Engineering Mechanics,1999,125 (1):79-85.
[86]Zhao Y-G, Ono T. New Approximations for SORM:Part 2[J]. Journal of Engineering Mechanics,1999,125 (1):86-93.
[87]李云贵,赵国藩.广义随机空间内的结构可靠度渐近分析方法[J].水利学报,1994,8：36-41.
[88]张新培,葛燕.结构可靠度的当量正态PFSORM算法[J].应用力学学报,2002,19(2)：85-87.
[89]Breitung K. Asymptotic approximations for probability integrals[J]. Probability Engineering Mechanics,1989,4 (4):187-190.
[90]Breitung K. Probability approximations by log likelihood maximization[J]. Journal of Engineering Mechanics.1991,117 (3):457-477.
[91]贡金鑫,赵国藩.原始随机空间内的结构可靠度分析方法.水利学报,1999,(5)：30-34
[92]Der Kiureghian A, Dakessian T. Multiple design points in first and second-order reliability[J]. Structural Safety,1998,20 (1):37-49.
[93]Zhao Y-G, Ono T. A general procedure for first/second-order reliabilitymethod (FORM/SORM) [J]. Structural Safety,1999,21 (2):95-112.
[94]贡金鑫,陈晓宝,赵国藩.结构可靠度分析的Guass-Hermite积分方法.上海交通大学学报,2002,36(11)：1625-1629.
[95]Tichy M. First-order third-moment reliability method[J]. Structural Safety,1994,16 (3):189-200.
[96]Zhao Y-G, Ono T. Third-moment standardization for structural reliability analysis[J]. Journal of Structual Engineering,2000,126 (6):724-732.
[97]Zhao Y-G,Ono T. Moment methods for structural reliability[J]. Structural Safety,2001,23 (1):47-75.
[98]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.
[99]Hohenbichler R, Rackwitz R. Improvement of second-order reliability estimates by importance sampling[J]. Journal of Engineering Mechanics,1988,114 (12):2195-2199.
[100]Bucher C. G. Adaptive sampling-an iterative fast Monte Carlo procedure[J]. Structural Safety,1988,5 (2):119-126.
[101]金伟良.结构可靠度数值模拟的新方法[J].建筑结构学报,1996,17(3)：63-72.
[102]Jin W-L. Importance sampling method in V-space[J]. China Ocean Engineering,1997,11 (2):127-150.
[103]程耿东,蔡文学.结构可靠度计算的近似重要性抽样方法及其应用[J].工程力学,1997,14(2) ：1-7.
[104]Au S. K, Beck J. L. A new adaptive importance sampling scheme for reliability calculations[J]. Structural Safety,1999,21 (2):135-158.
[105]董聪,郭晓华.基于广义遗传算法的自适应重要抽样理论[J].计算机科学,2000,27(4)：1-4.
[106]吴斌,欧进萍,张纪刚.结构动力可靠度的重要抽样法[J].计算力学学报,2001,18(4)：478-482.
[107]Melchers R. E. Importance sampling in structural systems [J]. Structural Safety,1989,6 (1):3-10.
[108]Engelund S, Rackwitz R. A benchmark study on importance sampling techniques in structural reliability[J]. Structural Safety,1993,12 (4):255-276.
[109]Ditlevsen 0, Melchers R. E, Gluver H. General multi-dimensional probability integration by directional simulation[J]. Computers& Structures,1990,36 (2):355-368.
[110]伍朝晖,赵国藩.数论方法在结构体系可靠度计算中的应用[J].大连理工大学学报,1998,38(1)：92-96.
[111]张建仁,许福友.两种求解可靠指标的实用算法[J].工程力学,2002,19(3)：159-165.
[112]许福友,陈艾荣,张建仁.计算结构可靠指标的循环逼近法[J].同济大学学报,2004,32(4)：426-430.
[113]刘宇,吕泰仁.随机有限元及其工程应用[J].力学进展.1995.25(1)：114-126.
[114]An inference-finite element model for field problems[J]. Applied Mathematical Modeling,1978,2 (2):49-55.
[115]M Shinozuka, G Deodatis. Response variability of stochastic finite element systems. Journal of Engineering Mechanics,1988.114 (3):499-519
[116]Fumio Yamazaki, Masanobu Shinozuka and Gautam Dasgupta, Neumann expansion for stochastic finite element analysis. J. Eng. Mech.1988,114 (8):1335-1354
[117]Armen Der Kiureghian, Jyh-Bin Ke. The stochastic finite element method in structural reliability. Probabilistic Engineering Mechanics,1988,3 (2):83-91
[118]Wong F. S. Slope reliability and response surface method[J]. Journal of Geotechnical Engineering,1985,111 (1):32-53.
[119]Faravelli L. A response surface approach for reliability analysis[J]. Journal of Engineering Mechanics, ASCE,1989,115 (12):2763-2781.
[120]Bucher C. G, Bourgund U. A fast and efficient response surface approach for structural reliabilityproblems[J]. Structural Safety,1990,7 (1):57-66.
[121]Rajashekhar M. R, Ellingwood B. R. A new look at the response surface approach for reliability analysis[J]. Structural Safety,1993,12 (3):205-220.
[122]佟晓利,赵国藩.一种与结构可靠度分析几何法相结合的响应面法[J].土木工程学报,1997,30(4) ：51-57.
[123]武清玺,卓家寿.结构可靠度分析的变f序列响应面法及其应用[J].河海大学学报：自然科学版,2001,29(2)：75-78.
[124]张小庆,康海贵,王复明.求解隐式功能函数可靠度的一种新方法[J].大连理工大学学报.2003,43(5)：650-653.
[125]Hosni Elhewy A.,Mesbahi E.,Pu Y. Reliability analysis of structures using neural network method[J]. Probabilistic Engineering Mechanics,2006,21 (1):44-53.
[126]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.
[127]桂劲松.结构可靠度分析的改进BP神经网络响应面法[J].应用力学学报,2005,22(1)：127-130.
[128]桂劲松,康海贵.结构可靠度分析的全局响应面法研究[J].建筑结构学报,2004,25(4)：100-105.
[129]桂劲松,康海贵.结构可靠度分析的智能计算法[J].中国造船,2005,46(2)：28-34.
[130]袁雪霞.建筑施工模板支撑体系可靠性研究[D].杭州：浙江大学博士学位论文,2006.
[131]刘济科,赵卫.基于支持向量回归的响应面可靠度计算[J].中山大学学报,2008.47(1)：1-4.
[132]Moses F. System reliability developments in structural engineering[J]. Structural Safety,1982,1(1):3-13.
[133]Moses F. New directions and research needs in system reliability research[J]. Structural Safety,1990,7 (2-4):93-100.
[134]Feng Y S. Enumerating significant failure modes of a structural system by using criterion methods[J]. Computers and Structures,1988,30 (5):1153-1157.
[135]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.
[136]董聪,冯元生.枚举结构主要失效模式的一种新方法[J].西北工业大学学报,1991,9(3)：284-289.
[137]董聪,杨庆雄.冗余桁架结构系统可靠性分析理论与算法[J].计算结构力学及其应用,1992,9(4)：393-398.
[138]董聪,杨庆雄.结构系统静强度可靠性分析理论与算法[J],强度与环境,1993,2：1-8.
[139]姚卫星.顾怡.用自动矩阵力法枚举结构的主要失效模式[J].计算结构力学及其应用.1996,13(1)：62-66.
[140]Reashedi M R, Application of linear programming to structural system reliability. Computers and Structures,1986,24 (3):375-384.
[141]刘天云,赵国藩.一种识别结构主要失效模式的有效算法[J].大连理工大学学报,1998,38(1)：97-100.
[142]Murotsu Y, Okada H, Yonezawa M, et al. Automatic generation of stochastically dominant modes of structural failure in frame structure. Structural Safety,1984,28 (2):17-25.
[143]赵鹏飞.对分枝限界法的一种改进[J].四川建筑科学研究,1997,4：40-45.
[144]Thoft-Christensen P, Sorensen J, D. Reliability of structural systems with correlated elements. Applied Mathematical Modeling,1982,6 (3):171-178.
[145]董聪,结构系统可靠性分析与优化[D],西北工业大学,1990.
[146]董聪,杨庆雄.冗余桁架结构系统可靠性分析理论与算法[J].计算结构力学及其应用,1992,9(4)：393-398.
[147]蔡迎建,孙炔纯.结构失效模式的快速识别方法[J].大连理工大学学报,1999,39(4)：489-493.
[148]Duunett C. W, Sobel M. Approximation to the probability of integral and certain percentage points of a multivariate analogue of student's distribution[J]. Biometrika, 1955,42 (1-2):258-260.
[149]Johnson N, Kotz S. Distributions in statistics:continuous multivariate distributions. New York, NY:John Wiley & Sons Inc.,1972.
[150]何水清,王善.结构可靠性分析与设计.北京：国防工业出版社,1993.
[151]Cornell CA. Bounds on the reliability of structural systems [J]. Journal of Structural Division,ASCE,1967,93 (ST1).
[152]Kounias EG. Bounds for the probability of a union with applications. Annuals of Mathematical Statistics,1968,39 (6):2154-2158.
[153]Ditlevsen O. Nallow reliability bounds for structural system[J]. Journal of Structural Mechanics,1979,7 (4):453-472.
[154]Thoft-Christensen P. Murotsu Y. Application of structural systems reliability theory. Spring-Verlag, Berlin, Heidelberg, New York, Tokyo,1986.
[155]Feng YS. A Method of computing structural system reliability with high accuracy[J]. Computers and Structures,1989,33 (1):1-5.
[156]Zhang YC. Derivative fitting procedure for computing bivariate normal distribution and some applications [J]. Structural Safety,1994,14 (3):173-183.
[157]贡金鑫,赵国藩.二维正态分布函数值的一个近似算法[J].计算结构力学及其应用,1996,13(4)：494-499.
[158]姚继涛,赵国藩,浦聿修.二维标准正态联合概率的计算[J].建筑结构学报,1996,17(4)：10-19.
[159]吕震宙,冯元生.结构安全概率方法评述[J].机械强度.1993.12.15(4)：1-5.
[160]Ditlevsen 0, Bjerager P. Methods of structural systems reliability[J]. Structural Safety,1986,3 (3-4):195-229.
[161]Ang H-S, Ma HF. On the reliability of structural systems. In:Proceedings of International Conference on Structural Safety and Reliability, Trondheim,1981.
[162]Hohenbichler M, Rackwitz R. First-order concepts in system reliability[J]. Structural Safety,1983,1 (3):177-188.
[163]Tang L. K, Melchers R. E. Improved approximation for multinormal integral[J]. Structural Safety,1986,4 (2):81-93.
[164]Birnbaum ZW. Effect of linear truncation on a multinormal population[J]. The Annals of Mathematical Statistics,1950,21 (2):272-279.
[165]Tallis GM. The moment generating function of the truncated multi-normal distribution[J]. Journal of the Royal Statistical Society, Series B (Methodological),1961,23 (1):223-229.
[166]Terada S, Takahashi T. Failure-conditioned reliability index[J]. Journal of Structural Engineering,1988,114 (4):942-952.
[167]Pandey M. D. An effective approximation to evaluate multinormal integrals[J]. Structural Safety,1998,20 (1):51-67.
[168]Pandey MD, Sarkar A. Comparison of a simple approximation for multinormal integration with an importance sampling-based simulation method[J]. Probabilistic Engineering Mehanics,2002,17 (2):215-218.
[169]X.-X. Yuan, M. D. Pandey. Analysis of approximations for multinormal integration in system reliability computation[J]. Structural Safety,2006,28 (4):361-377.
[170]S. Gollwitzer, R. Rackwitz, Equivalent components in first-order system reliability [J], Reliability Engineering,1983,5 (2):99-115.
[171]贡金鑫.结构体系可靠度计算的逐步当量平面法.水工结构理论与实践,大连：大连海运学院出版社,1993：97-104.
[172]张小庆,康海贵,王复明.改进的微分等价地归算法[J].土木工程学报,2004,37(1)：31-38.
[173]张小庆,康海贵,王复明.一种新的体系可靠度的近似计算方法[J].工程力学.2004,21(1)：93-97.
[174]Vanmarcke E H. Matrix formulation of reliability analysis and reliability based design[J].Computers & Structures,1973.3 (4):757-770.
[175]Tichy M, Vorlica K. Safety of reinforced concrete framed structure, in Mech. Of Reinforcd Concrete. In:Proc of the ASCE ACI Int Sm.1974:171-179.
[176]李云贵,赵国藩.结构体系可靠度的近似计算方法[J].土木工程学报,1993,26(5)：70-76.
[177]郭书祥.结构体系失效概率计算的一种快速有效方法[J].计算力学学报,2007,24(1)：107-110.
[178]Thoft-Christensen P, Sorensen J. D. Reliability of structural systems with correlated elements[J]. Applied Mathematical Modeling,1982,6 (3):171-178.
[179]Ditlevsen O. Taylor expansion of series system reliability[J]. Journal of Engineering Mechanics,1984,110 (2):293-307.
[180]贡金鑫,赵国藩.串联结构体系可靠度的二元泰勒级数展开[J].计算力学学报,1997,14(1)：78-84.
[181]贡金鑫.一类多维正态积分的近似解法[J].西安建筑科技大学学报,1996,28(1)：52-56.
[182]贡金鑫,赵国藩.并联结构体系可靠度计算的二次二阶矩法[J].工程力学(增刊),1996：548-553.
[183]姚继涛,赵国藩,蒲聿修.结构体系失效概率的快速半数值积分方法.中国土木工程学会桥梁及结构工程学会结构可靠度委员会工程结构可靠性第四届全国学术交流会论文集.北京：地震出版社,1996.
[184]侯钢领,欧进萍.结构可靠指标矢量及其计算与应用[J].计算力学学报,2002,19(2)：143-147.
[185]CB271单井平台结构分析报告(No.海工-03038/计)[R].中国石化胜利油田有限公司规划设计研究院,2003.
[186]Mori Y, Kato T. Multinormal integrals by importance sampling for series system reliability[J]. Structural Safety 2003;25 (4):363-378.
[187]Sudret B, Kiureghian AD. Comparison of Finite Element Reliability Methods[J], Probabilistic Engineering Mechanics,2002,17 (4):337-348.
[188]吴恒立.拱式体系的稳定计算.北京：人民交通出版社,1979.31-32.