考虑多种误差的结构可靠度指标置信度研究
|
摘要
随着科技的进步与理论的深入，对结构可靠性研究的要求愈来愈高，结构可靠度指标计算精度的要求也不断提高。本文将按照结构可靠度指标的计算原理，总结寻找其影响因素和可能产生的误差，分析误差产生原理及作用方式，并提出合适的数学力学方法量化误差作用大小，对可靠度指标进行修正，以期获得对实际工程具有更好指导意义的结果。
很多实际工程，尤其是岩土工程，可靠性计算数据直接来源于现场测量结果。依据数理统计，同一性能指标的现场试验可看作抽样试验，测量结果则可看作样本。根据样本可以对性能指标进行参数估计，这些估计值是可靠度指标计算的基础。以样本参数估计母体参数，必然存在随机性，同一母体在不同子样下有不同的参数估计结果，导致可靠度指标将会在一定范围内产生随机波动，故依据子样得到的可靠度指标应该是一个随机变量，而目前可靠度研究中将其简化为一个固定的简单的数值。作为随机变量的可靠度指标要实现对工程的指导意义，必须进行置信区间研究，即可靠度指标真实值发生在某个数值区间内的概率大小。不论是传统的可靠度指标的取值，还是本文提出的随机变量的可靠度指标的置信区间都受到各种误差因素的影响，必须进行相关误差研究才能更好地应用于实践。本文将对相关误差因素进行逻辑分析与量化计算，具体分析过程如下：
首先，可靠度指标赖以计算的基础是测量数据，而在具体测量过程中误差不可避免。测量误差包括系统误差、随机误差和粗差，这些误差可以通过提高子样样本容量和严格按照数理统计理论处理数据得到有效控制。然而，在实际工程中，相应规范标准在数据采集时要求的测量次数很少，对数据的处理比较简单，在大多数情况下可以对数据进行有效处理，但是在某些情况下可能会出现数据处理的误差，导致可靠度计算的结果成为“空中楼阁”。本文通过实例数据说明土木工程规范在数据处理中存在的某些缺陷，同时测绘科学与技术中测量误差的相关理论与处理方法可以有效改善这些缺陷，这也说明测量误差理论在土木工程数据处理领域的应用可以有效提高结构可靠性分析结果自身的可靠性。
其次，结构可靠性理论分析中，正态分布应用较为广泛。其与很多随机变量的实际概型契合较高，且具有较好的数学优势，易于推导及变换。但是，理论与实际很难完全符合，随机变量只可能近似服从正态分布，特别是概率密度曲线尾部是否有界的问题，导致理论失效概率与实际失效概率之间存在偏差的尾部效应问题。随着可靠性研究精度要求的提高，必须考虑尾部效应，特别是在结构的系统可靠性问题中，偏差将会产生非线性累积。为消除尾部效应，本文提出了平截尾正态分布，该分布是对正态分布的修正，继承了正态分布的优点，并有效解决了尾部效应。本文完成了新分布的相关理论和应用研究，通过假设检验证明新分布可用于实际工程的理论分析模型，并深入讨论其与正态分布计算得到的失效概率的偏差，计算结果显示两者偏差在10%以上。
再次，任何结构在设计、制造、施工和管理使用等全过程的各个阶段都是由人进行相关操作，不可避免存在各种人因失误造成的影响。例如：设计图配筋失误、混凝土浇筑施工失误、使用超载失误等等。为保证可靠性研究结果对实际工程的指导意义，应该考虑人因失误因素。本文提出了AHP-THERP复合模型分析建筑结构全过程人因失误概率，继而量化人因失误对结构抗力总体水平的影响，使计算可靠度指标的结构抗力值能够真实反映结构实际承载能力。
最后，结构由若干构件组成，而构件安装后实际尺寸受生产控制技术、安装、使用环境等多种因素的影响不可能与设计尺寸完全相同，即结构存在几何误差。对于超静定结构，几何误差将会在杆件内部产生自内力，从而影响荷载在杆件中的分布。本文通过结构力学方法推导出的结构冗余分量矩阵，得到结构在几何误差下的自内力，得到其对结构可靠性的影响。
综上所述，为更加全面真实的研究结构可靠性状况，应该考虑各种因素对可靠度指标的影响。本文提出了可靠度指标计算的参数漂移模型，该模型能够量化各种误差因素对可靠度指标的影响，从而能够得到真实准确反映结构可靠性的可靠度指标。实例分析结果显示本文模型计算结果与传统计算结果差距超过10%，因此，实际工程有必要同时考虑本文模型于传统计算模型的分析结果。本文模型在可靠性研究中具有一定的实用意义和广泛的应用前景。
With the development of the structure reliability, the accuracy ofreliability index no longer demands with real engineering. This paper willlook for error factors in reliability calculating procedure. Then theinfluence of these error factors on reliability index is analyzed to makethe reliability index more significant.
The data for calculating the reliability index are from measuringresults. By probability theory, a measuring result is a test, and repeatedmeasuring results are specimen. Generally, the sample result is regardedas parameter estimation of the population. Then, different sample resultwill get different parameter of the same population. Therefore, thereliability index is a random variable, not a fixed value in classicalstructure reliability. As a random variable, the reliability index must beconsidered confidence interval when using in engineering. The influenceof error factors on the reliability index will be researched in this paper.
Firstly, the error in measuring process is inescapable. These errorscontain systematic error, random error and gross error. They can becontrolled by increasing the sample size and logical data processing. But,civil engineering standards and criterions demands are not strict and notagree with real engineering. Then, the calculated results of reliabilitywould be a castle in the air when standards and criterions do not work.Therefore, it is necessary to pay attention to data processing in structurereliability to prevent data processing error.
Secondly, the normal distribution is applied extensively in structurereliability. It has mathematics advantage and agrees with real distributionof engineering data in a large part. The difference between the normaldistribution and engineering distribution is at two tails of their probabilitydensity curves. It is named end effect and can produce nonlinearcumulative error in structural system reliability. A new distribution is putforward in this paper. It inherits the advantage of the normal distributionand avoids the end effect.
Thirdly, the whole process of a structure, which containing design, manufacturing and managing, is completed by human. Then, human erroris inevitable. An AHP-THERP model in created in this paper to analyzethe influence of human error on reliability index.
Finally, a structure is made up of many construction members. Themanufacture size of a member is not equal to its design size. Thisdifference is structural geometrical error. It can bring up internal forceand influences structure reliability.
In summary, a new calculating model of reliability index consideringall error factors is put forward in this paper. It is significant to structurereliability research.
很多实际工程，尤其是岩土工程，可靠性计算数据直接来源于现场测量结果。依据数理统计，同一性能指标的现场试验可看作抽样试验，测量结果则可看作样本。根据样本可以对性能指标进行参数估计，这些估计值是可靠度指标计算的基础。以样本参数估计母体参数，必然存在随机性，同一母体在不同子样下有不同的参数估计结果，导致可靠度指标将会在一定范围内产生随机波动，故依据子样得到的可靠度指标应该是一个随机变量，而目前可靠度研究中将其简化为一个固定的简单的数值。作为随机变量的可靠度指标要实现对工程的指导意义，必须进行置信区间研究，即可靠度指标真实值发生在某个数值区间内的概率大小。不论是传统的可靠度指标的取值，还是本文提出的随机变量的可靠度指标的置信区间都受到各种误差因素的影响，必须进行相关误差研究才能更好地应用于实践。本文将对相关误差因素进行逻辑分析与量化计算，具体分析过程如下：
首先，可靠度指标赖以计算的基础是测量数据，而在具体测量过程中误差不可避免。测量误差包括系统误差、随机误差和粗差，这些误差可以通过提高子样样本容量和严格按照数理统计理论处理数据得到有效控制。然而，在实际工程中，相应规范标准在数据采集时要求的测量次数很少，对数据的处理比较简单，在大多数情况下可以对数据进行有效处理，但是在某些情况下可能会出现数据处理的误差，导致可靠度计算的结果成为“空中楼阁”。本文通过实例数据说明土木工程规范在数据处理中存在的某些缺陷，同时测绘科学与技术中测量误差的相关理论与处理方法可以有效改善这些缺陷，这也说明测量误差理论在土木工程数据处理领域的应用可以有效提高结构可靠性分析结果自身的可靠性。
其次，结构可靠性理论分析中，正态分布应用较为广泛。其与很多随机变量的实际概型契合较高，且具有较好的数学优势，易于推导及变换。但是，理论与实际很难完全符合，随机变量只可能近似服从正态分布，特别是概率密度曲线尾部是否有界的问题，导致理论失效概率与实际失效概率之间存在偏差的尾部效应问题。随着可靠性研究精度要求的提高，必须考虑尾部效应，特别是在结构的系统可靠性问题中，偏差将会产生非线性累积。为消除尾部效应，本文提出了平截尾正态分布，该分布是对正态分布的修正，继承了正态分布的优点，并有效解决了尾部效应。本文完成了新分布的相关理论和应用研究，通过假设检验证明新分布可用于实际工程的理论分析模型，并深入讨论其与正态分布计算得到的失效概率的偏差，计算结果显示两者偏差在10%以上。
再次，任何结构在设计、制造、施工和管理使用等全过程的各个阶段都是由人进行相关操作，不可避免存在各种人因失误造成的影响。例如：设计图配筋失误、混凝土浇筑施工失误、使用超载失误等等。为保证可靠性研究结果对实际工程的指导意义，应该考虑人因失误因素。本文提出了AHP-THERP复合模型分析建筑结构全过程人因失误概率，继而量化人因失误对结构抗力总体水平的影响，使计算可靠度指标的结构抗力值能够真实反映结构实际承载能力。
最后，结构由若干构件组成，而构件安装后实际尺寸受生产控制技术、安装、使用环境等多种因素的影响不可能与设计尺寸完全相同，即结构存在几何误差。对于超静定结构，几何误差将会在杆件内部产生自内力，从而影响荷载在杆件中的分布。本文通过结构力学方法推导出的结构冗余分量矩阵，得到结构在几何误差下的自内力，得到其对结构可靠性的影响。
综上所述，为更加全面真实的研究结构可靠性状况，应该考虑各种因素对可靠度指标的影响。本文提出了可靠度指标计算的参数漂移模型，该模型能够量化各种误差因素对可靠度指标的影响，从而能够得到真实准确反映结构可靠性的可靠度指标。实例分析结果显示本文模型计算结果与传统计算结果差距超过10%，因此，实际工程有必要同时考虑本文模型于传统计算模型的分析结果。本文模型在可靠性研究中具有一定的实用意义和广泛的应用前景。
With the development of the structure reliability, the accuracy ofreliability index no longer demands with real engineering. This paper willlook for error factors in reliability calculating procedure. Then theinfluence of these error factors on reliability index is analyzed to makethe reliability index more significant.
The data for calculating the reliability index are from measuringresults. By probability theory, a measuring result is a test, and repeatedmeasuring results are specimen. Generally, the sample result is regardedas parameter estimation of the population. Then, different sample resultwill get different parameter of the same population. Therefore, thereliability index is a random variable, not a fixed value in classicalstructure reliability. As a random variable, the reliability index must beconsidered confidence interval when using in engineering. The influenceof error factors on the reliability index will be researched in this paper.
Firstly, the error in measuring process is inescapable. These errorscontain systematic error, random error and gross error. They can becontrolled by increasing the sample size and logical data processing. But,civil engineering standards and criterions demands are not strict and notagree with real engineering. Then, the calculated results of reliabilitywould be a castle in the air when standards and criterions do not work.Therefore, it is necessary to pay attention to data processing in structurereliability to prevent data processing error.
Secondly, the normal distribution is applied extensively in structurereliability. It has mathematics advantage and agrees with real distributionof engineering data in a large part. The difference between the normaldistribution and engineering distribution is at two tails of their probabilitydensity curves. It is named end effect and can produce nonlinearcumulative error in structural system reliability. A new distribution is putforward in this paper. It inherits the advantage of the normal distributionand avoids the end effect.
Thirdly, the whole process of a structure, which containing design, manufacturing and managing, is completed by human. Then, human erroris inevitable. An AHP-THERP model in created in this paper to analyzethe influence of human error on reliability index.
Finally, a structure is made up of many construction members. Themanufacture size of a member is not equal to its design size. Thisdifference is structural geometrical error. It can bring up internal forceand influences structure reliability.
In summary, a new calculating model of reliability index consideringall error factors is put forward in this paper. It is significant to structurereliability research.
引文
[1] Weibull W.. A statistical distribution function of wide applicability[J]. Journal of AppliedMechanics.1951,18(3):293-297.
[2] RehardE.Barlow. Mathematieal Theory of Reliability: A Historieal Pers Peetive[J]. IEEETrans.on Reliability.1984,33(l):16-20.
[3] Desieno C. F.,Stine L. L.. A probability method for determining the reliability of electric powersystems[J]. IEEE Transactions on Power Apparatus and Systems.1964, PAS-83(2):174-179.
[4] Kaufman A.. Introduction to the Theory of Fuzzy Subsets Volume1[M]. New York: AcademicPress.1975:235-243.
[5] Zadeh L. A.. Fuzzy sets[J]. Information and Control.1965,8(3):338-353.
[6] Onisawa T.. Fuzzy theory in reliability analysis[J]. Fuzzy Sets and Systems.1989,29(2):250-251.
[7] Cai K.,Wen C., Zhang M.. Posbist reliability behavior of fault-tolerant systems[J].Microelectronics and Reliability.1995,35(1):49-56.
[8] Cai K.,Wen C., Zhang M.. Posbist reliability behavior of typical system with two types offailures[J]. Fuzzy Sets and Systems.1991,43(1):17-32.
[9] Cai K.,Wen C., Zhang M.. Fuzzy states as a basis for a theory of fuzzy reliability[J].Microelectronics and Reliability.1993,33(15):2253-2263.
[10] Cai K.,Wen C., Zhang M.. Mixture models in profust reliability theory[J]. Microelectronicsand Reliability.1995,35(6):985-993.
[11] Billinton R., Sachdev M.. Direct current transmission system reliability evaluation[J]. Trans.CEA.1968,7(3):68-170.
[12] Billinton R., Prasad V.. Quantitative reliability analysis of HVDC transmission systems: Part Iand II[J]. IEEE Transactions on Power Apparatus and Systems.1971, PAS-90(3):1034-1054.
[13] Billinton R., Ahluwalia D. S.. Incorporation of A DC link in a composite system adequacyassessment-DC system modeling[J]. IEE Proceedings-C.1992,139(3):211-220.
[14]普罗尼科夫A. C.等著,李昌琪等译.数控机床的精度与可靠性[M].北京:机械工业出版社，1987.
[15] Vasilev V. S.. Cost efficiency approach to the selection of NC machine tool reliabilitystandards[J]. Soviet Engineering Research,1985,5(9):49-50.
[16] FreudenthalA. M.. The safety of structures[J]. Transation,ASCE, V112，1947.
[17] РжаницынA.P.. Строителъная промышленноств[J].No.8.1947.
[18] Стрелецкий Н.С.. Основы статистического учета коэфициента эапаса прочностисооружении[J]. Стройиэдат.1947.
[19] Cornell C. A.. A probability-based structural code [J]. J.ACI,1969,66(12):974-958.
[20] Lind N. C.. Consistent partial safety factors[J]. Struct. Div., ASCE,1971,97(6):1651-1669.
[21] Alfredo H-S.Ang and Wilson H.Tang. Probability Concepts in Engineering Planning andDesingn[M]. John Wiley&Sons, Volume I,1975, VolumeⅡ,1984.
[22] Rackwitz R. and Fiessler B.. An Algorithm for Calculation of Structural Reliability underCombined Loading[M]. Munchen,1977:36-45.
[23]宋笔锋等.飞行器可靠性工程[M].西安:西北工业大学出版社,2006,1-29.
[24]尹晓伟.基于贝叶斯网络的机械系统可靠性评估[D].东北大学博士学位论文,2008.1-12.
[25] Dorigo M., Maniezzo V., Colorni A.. The ant system:Optimization by a colony of cooperatingagents [J]. IEEE Transactions on Systems,Man and Cybernetics-PartB,1996,26(1):29-41.
[26] Dorigo M., Bonabeau E., Theraulaz G.. Ant algorithms and stigmergy [J]. FutureGeneration Computer Systems,2000,16:851-871.
[27] Kennedy J., Eberhart R. C., Shi Y. H.. Swarm Intelligence[M]. San Francisco: MorganKaufmann Publishers,2001.
[28]李晓磊.一种新型的智能优化方法—人工鱼群算法[D].浙江大学博士学位论文.2003,1-23.
[29]宋保维.系统可靠性设计与分析[M].西安:西北工业大学出版社,2008.43-58.
[30]邹天一.结构可靠度[M].北京:人民交通出版社,1998,1-1.
[31]交通部.公路预应力混凝土桥梁设计规范（试行）.北京:人民交通出版社,1978.
[32]铁道部.铁路工程设计规范第二篇桥涵.北京:人民铁道出版社,1975.
[33]全苏标准委员会建筑及建筑材料标准局.钢筋混凝土结构设计标准及技术规范（全苏标准OCT9003-38）,1938.
[34]赵国藩.钢筋混凝土结构按极限状态计算[M].北京:建筑工程出版社,1961.
[35]建设部.建筑结构可靠度设计统一标准[M].北京:中国建筑工业出版社,2002.
[36]常大民.江克斌.桥梁结构可靠性分析与设计[M].北京:中国铁道出版社.1995.
[37]吴世伟.结构可靠度分析[M].北京:人民交通出版社,1990.
[38]张建仁，刘扬，许福友等.结构可靠度理论及其在桥梁工程中的应用[M].北京:人民交通出版社,2003.
[39]董艳秋，田镜博.蒙特卡洛法结构可靠性分析[J].黑龙江工程学院学报（自然科学版），2010（3），V.24（1）：27-29.
[40] Andrzej S. Nowak, Kevin R. Collins. Reliability of Structures[M]. New York: McGraw-Hill.2000.
[41] Yaacob Ibrahim. Observations of applications of importance sampling in structural reliabilityanalysis[J]. Structural Safety.1991,10(4):269-281.
[42] Lieber D., Nemirovskii A., Rubinstein R. Y.. A fast Monte Carlo method for valuatingreliability indexes[J]. IEEE Trans on Reliability,1999,48(3):256-261.
[43] Pereira M. V. F., Maceira M. E. P., Oliveira G. C., et al. Combining analytical models andMonte Carlo techniques in probabilistic power system analysis[J]. IEEE Trans on PowerSystems,1992,7(1):265-272.
[44]王斌,赵渊,刘威.基于分裂最优乘子重要抽样的电网可靠性评估[J].电力系统自动化，2008,32(19):30-34.
[45] Melo A. C. G., Oliveira G. C., Morozowski FO. M., et al. Ahybrid algorithm for Monte Carloenumeration based composite reliability evaluation[C]. Proceedings of the3rd InternationalConference on Probabilistic Methods Applied to Electric Power Systems, July3-5，1991，London:UK:70-74.
[46] Ocnasu A. B., Besanger Y.. Distribution system availability assessment Monte Carlo andantithetic variants method[C]. Proceedings of the19th International Conference on ElectricityDistribution, May21-24,2007，Vienna, Austria:21-24.
[47]李云贵.工程结构可靠度分析方法研究[D].大连理工大学博士学位论文，1990.
[48]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: S1-S5.
[49]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,2000.21-64.
[50] Paloheimo E. H.. Structural design based on weighted fractiles[J]. Journal of the StructuralDivision.1974,100.
[51]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.
[52] Paloheimo E., Hannus H.. Structural based on weighted fractiles[J]. Journal of the StructuralDivision. ASCE,1974. Vol.100(ST7).
[53] Fiessler B., Rackwitz R., Neumann H.J.. Quadratic limit states in structural reliability[J].Journal of the Engineering Mechanics Division.1979,105(4):661-676.
[54] Der Kiureghian A., Lin H. Z., Hwuang S.T.. Second-order reliability approximation [J].Journal of Engineering Mechanics.1984,110(8):1208-1225.
[55] Tvedt L.. The distribution of quadratic forms in normal space-an application to structuralreliability[J]. Journal of Engineering Mechanics.1990,116(6):1183一1197.
[56] Breitung K.. Asymptotic approximation for multinomial integrals[J]. Journal of EngineeringMechanics.1984,110(3):357-366.
[57] Breitung K.. Asymptotic approximations for probability integrals[J]. ProbabilisticEngineering Mechanics.1989,4(4):187-190.
[58]李云贵，赵国藩，张保和.结构可靠度的渐进分析方法[J].大连理工大学学报,1994,34(4):442-447.
[59]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.
[60]赵国藩.工程结构可靠性理论与应用[M].大连理工大学出版社,1996.
[61]李伟.大跨度斜拉桥静东里可靠度分析[D].华南理工大学博士学位论文,2010.
[62]周林聪.钢筋混凝土结构非线性和可靠度分析方法研究[D].上海交通大学博士学位论文,2007.
[63]彭泽.结构可靠度Metamodel方法及其工程应用研究[D].中南大学硕士学位论文,2010.
[64]胡鸣.结构可靠度计算方法研究[D].华南理工大学硕士学位论文,2010.
[65]王文.基于能力谱方法的结构非概率可靠度[D].湖南大学硕士学位论文,2010.
[66]何木.基于传递系数法的边坡稳定性可靠度分析及应用[D].成都理工大学硕士学位论文,2010.
[67]孙宁.结构可靠度计算方法分析及其在系留机构中的应用[D].哈尔滨工程大学硕士学位论文,2008.
[68]杨会杰.预应力钢结构拉索的可靠度分析与设计指标研究[D].天津大学硕士学位论文,2007.
[69]柳颖臣.基于概率理论的预应力混凝土桥梁结构可靠度研究[D].长安大学硕士学位论文,2008.
[70]王嵩.已有砌体结构的抗震可靠度分析及实例应用[D].同济大学硕士学位论文,2007.
[71]孙思奥.结构可靠度分析方法及相关理论研究[D].清华大学硕士学位论文,2007.
[72]田英.结构可靠度估计理论及应用研究[D].西安建筑科技大学硕士学位论文,2007.
[73]史冀波.结构可靠度的反问题在桥梁工程中的应用研究[D].武汉理工大学硕士学位论文,2007.
[74]张宇.工程结构可靠度分析的若干问题研究[D].同济大学博士学位论文,2006.
[75]郑怡.既有结构构件可靠性研究及应用[D].大连理工大学博士学位论文,2009.
[76]李炜.边坡稳定可靠性分析[D].大连理工大学博士学位论文,2009.
[77] Ditlevsen O., Madsen H. O.. Proposal for a code for the direct use of reliability methods instructural design[J]. In: Working Document of Joint Committee on Structural Safety,1989.
[78]王光远.工程软设计原理[M].北京:科学出版社.1992:253-258,153-159.
[79] Moses F.. System reliability developments in structural engineering[J]. Structural Safety.1982,1:3-13.
[80] Moses F.. New directions and research needs in system reliability research[J]. StructuralSafety,1990,7:93-100.
[81] Feng Y. S.. Enumerating significant failure modes of a structural system by using criterionmethods[J]. Computers and Structures,1988,30(5):1153-1157.
[82]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.
[83]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.
[84]董聪,杨庆雄.冗余析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.
[85]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.
[86]冯元生.飞机结构的分析与先进设计原理[M].西安:西北工业大学出版社.1991,1-10.
[87]杨庆雄.自动矩阵力法及扩大算题规模的措施.[D]西北工业大学论文选,1979,177-188.
[88]姚卫星,顾怡.用自动矩阵力法枚举结构的主要模式[C].中国航空学会结构设计专业委员会第一届学术交流大会论文.
[89]姚卫星,顾怡.用自动矩阵力法枚举结构的主要模式[J].计算结构力学及其应用,1996,13(1):62-66.
[90] Reashedi M. R., Moses F.. Application of linear programming to structural systemreliability[J]. Comput&Struct,1986,24(3):375-384.
[91]张云阁,姚卫星.结构系统主要失效模式的枚举[J].强度与环境，1997(1),1-11.
[92] Murotsu Y., Okada H., Niwa K., et al. Reliability analysis of truss structures by using Matrixmethod[J]. Transactions of theASME，Journal of Mechanical Design.1980,102(4):749-756.
[93] Murotsu Y., Okada H., Yonezawa M., et al. Automatic generation of stochastically dominantmodes of structural failure in framestructure[J]. Structural Safety,1984,28(2):17-25.
[94]蔡荫林,安伟光,陈卫东.空间彬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,广州,1992(12).
[95]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.
[96] Melcher R. E. and Tang T. K.. Dominant failure modes in stochastic structural systems[J].Structural safety.1984(2):127-143.
[97] Thoft-Christensen P., Sorensen J. D.. Reliability of structural systems with correlatedelements[J]. Applied Mathematical Modeling,1982,6:171-178.
[98] Thoft-Christensen P., Baker M. J.. Structural reliability theory and its applications[J].Spring-Verlag, Berlin, Heidelberg, New York,1982.
[99] Thoft-Christensen P., Murotsu Y.. Application of structural systems reliability theory[J].Spring-Verlag, Berlin, Heidelberg, New York, Tokyo,1986.
[100] Thoft-christensen. Reliability of structural system[J]. Strudies in Apllied Mechanics,24:Advances in the theory of plates and shells，Elsevier science publishers B U,1990.
[101] Ranganathan R., Deshpande A. G.. Reliability analysis of reinforced concrete frame[J].J.Struct Eng, ASCE,1987,113(6):1315-1328.
[102]刘扬,张建仁.混凝土斜拉桥施工阶段的体系可靠度[J].中国公路学报.2006,9.Vol19（5）:53-58.
[103] Cornell C. A.. Bounds on the reliability of structural systems[J]. Journal of StructuralDivision, ASCE1967,93(st1).
[104] Ditlevsen O.. Nallow reliability bounds for structural system[J]. Journal of StructuralMechanics,1979,7(4):453-472.
[105] Feng Y. S.. A method of computing structural system reliability with high accuracy[J].Computers and Structures,1989,33(1):1-5.
[106]董聪.结构系统可靠性分析与优化[D].西北工业大学硕士学位论文,1990.
[107] Zhang Y. C.. Derivative fitting procedure for computing bivariate normal distribution andsome applications[J]. Structural Safety,1994,14(3):173-183.
[108]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.
[109]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.
[110] Stevenson L., Moses F.. Reliability analysis of frame structures. Journal of StructuralDivision[J].ASCE, ST11,96.1970.
[111] Gorman M. R. and Moses F.. Reliability of structural systems[C]. Report No.79-2, CaseWestern Reserve University,1979.
[112] Ang H-S, Ma H. F.. On the reliability of structural systems[C]. Proceedings of InternationalConference on Structural Safety and Reliability. Trondheim,1981.
[113] Ma H. F,, Ang H-S. Reliability analysis of redundant ductile structural systems[C].University of Illinois at Urbana-Champaign, August1981.
[114] Ditlevsen O.. Taylor expansion of series reliability[J]. Journal of Engineering Mechanics,1984,110(2):293-307.
[115] Hohenbichler M., Rackwitz R.. First-order concepts in system reliability[J]. StructuralSafety,1983,1(3):177-188.
[116] Tang L. K., Melchers R. E.. Improved approximation for multinormal integral[J]. StructuralSafety,1987,4(2):81-93.
[117] Tallis G. M.. The moment generating function of the truncated multi-normal distribution[J]. JRoyal Statistical Society, Series B1961,23:223-229.
[118] Terada S., Takahashi T.. Failure-conditioned reliability index[J]. Journal of StructuralEngineering, ASCE1988,114(4):943-952.
[119] Pandey M. D.. An effective approximation to evaluate multi-normal integrals[J]. StructuralSafety,1998,20:51-67.
[120]何嘉年.基于体系可靠度的半刚性钢框架结构优化设计研究[D].汕头大学博士学位论文,2010.
[121]赵文争.基于响应面法索弯顶结构的可靠度研究[D].浙江大学硕士学位论文,2011.
[122]许林.基于可靠度的结构优化研究[D].大连理工大学博士学位论文,2004.
[123]张小庆.结构体系可靠度分析方法研究[D].大连理工大学博士学位论文,2003.
[124]安海.析架结构系统可靠性分析方法的研究[D].哈尔滨工程大学博士学位论文,2009.
[125]姜封国.结构系统基于可靠性的优化设计研究[D].哈尔滨工程大学博士学位论文,2009.
[126] Matousek M.. Outcome of a servey on800construction failure[C]. IABSE Clloquium onInspection and Quality Control Institute of Structural Engineering. Zurich Swiss Federal Instituteof Technology,1977.
[127] Ellongwood B.. Design and construction error effect on structural reliability[J]. Journal ofStructural Engeering, ASCE,1987,113(2):409-422.
[128Smith D. W.. Why do bridges fail[J]. Civil Engineering,1977,47:58-62.
[129]贾桐,卢文良,杨明虎,张文雨.考虑人误影响的桥梁施工阶段可靠性分析[C].第20届全国结构工程学术会议论文集（第Ⅱ册）,2011:163-167.
[130]杨伟军,陈劲飙.土木工程施工过程中人为差错的博弈分析[J].长沙交通学院学报,2005,21(2):46~49.
[131] Stewart M. A., Melchers R. E.. Simulation of human error in design loading task[J].Structural Safety,1988,5(4):285-297.
[132] Stewart M. A., Melchers R. E.. Error control in member design[J]. Structural Safety,1989,6(1):11-24.
[133] Schneider J.. Introduction to safety and reliability of structures[C]. Zurich, Switzerland:International Association for Bridge and Structural Engineering.1997.
[134] Schneider J.. Quality assurance within the building process[J]. Proceedings, IABSEWorkshop, Vol.47, Rigi, Switzerland.
[135]周详.考虑人为错误的结构模糊随机可靠度分析模型[J].武汉工业大学学报,1996,18（2）:38-40.
[136]张铟,陈孝珍,程旭东.考虑人为错误影响的结构可靠度实用计算[J].水电能源科学,2004,32(2):73~76.
[137]俞然刚,于述强,程旭东等.水工结构考虑施工过程中人为错误影响的模糊随机可靠度分析[J].建筑技术开发,2005,32（5）4-6.
[138]巩春领.桥梁施工期间的人因可靠性分析[J].桥梁工程.2008,4(4):38～44.
[139]金福安,章勇武,马国丰,许伟.基于人为错误可靠度的深基坑工程灾害防治[J].地下空间与工程学报,2007,3(3):568～573.
[140]史文秀.钢结构施工阶段人为失误研究[D].西安建筑科技大学硕士学位论文,2009.
[141]陈金永.建造阶段考虑人为错误影响的钢结构模糊可靠度分析[D].太原理工大学硕士学位论文,2005.
[142]陈劲飚.建筑施工过程中人为差错控制及人的可靠性研究分析[D].长沙理工大学硕士学位论文,2004.
[143]陈劲飙,胡强.建筑施工中人为失误因素的敏感性分析[J].中国安全科学学报,2007,17（5）:9～16.
[144]周冲.基于污染分布模型下的结构可靠度分析[D].上海交通大学博士学位论文.2010.
[145]高佳,黄祥瑞.人的失误与人因工程学在核电厂安全性应用[J].中国安全科学学报.1994,4（2）:23-28
[146]张力.概率安全评价中人因可靠性分析技术[M].北京:原子能出版社.2006.
[147]严春风,刘东燕,张建辉等.岩土工程可靠度关于强度参数分布函数概型的敏感度分析.岩石力学与工程学报,1999,18(1):36-39.
[148]余俊.杆系结构的重要性和相关性研究[D].上海交通大学硕士学位论文,2005.
[149]陈晓龙,施庆生,邓晓卫.概率论与数理统计[M].南京:东南大学出版社.2011.
[150]中华人民共和国建设部. GB50007-2002.建筑地基基础设计规范.北京:中国建筑工业出版社.2002.
[151]中华人民共和国建设部. JGJ106-2003.建筑桩基检测技术规程.北京:中国建筑工业出版社.2003.
[152]中华人民共和国建设部. JGJ79-2002、J220-2002.建筑地基处理技术规范.北京:中国建筑工业出版社.2002.
[153]中华人民共和国建设部. GB50009-2001(2006版).建筑结构荷载规范（条文说明）.北京:中国建筑工业出版社.2006.
[154] P.索夫特-克里斯坦森, M.J.贝克.结构可靠性理论及其应用[M].北京:科学出版社.1988.
[155]中华人民共和国建设部. GB50068-2002.建筑结构可靠度设计统一标准.北京:中国建筑工业出版社.2002.
[156] Маликов М. Ф.. Основы Метрологни[M]. Коммерприбор.1944.
[157]沙定国.实用误差理论与数据处理[M].北京:北京理工大学出版社.1993.
[158]钟继贵.误差理论与数据处理[M].北京:水利电力出版社.1993.
[159]张崇立.截尾正态分布在地形变异变识别中的初步应用[J].地壳形变与地震.1991,11(1):75-84.
[160]王宝山.截尾正态分布与Robust估计[J].焦作矿业学院学报.1994,13(3):52-58.
[161]孙志礼,张风和,何雪宏,蔡春源.两端截尾分布的应力-强度干涉模型[J].东北大学学报（自然科学版）.1998,19(3):309-311.
[162]张玉,王丹,张风和,孙志礼,丁津原.断裂韧性的两端截尾分布概率法设计[J].机械设计与制造.1999,06:1-2.
[163]姜礼平,张国清.截尾正态分布的最小后验风险Bayes推断[J].运筹与管理.2005,14(1):47-51.
[164]丁德馨,毕忠伟,綦春明.两端截尾概率分布下围岩可靠度研究[J].中国安全科学学报.2008,18(4):111-115.
[165]赵瑞学,钱林芳,陈龙淼,石海军.基于双侧截尾正态分布的机构运动可靠度研究[J].计算机仿真.2011,28(2):248-251.
[166]潘继斌,胡宏昌.数理统计教程[M].武汉:湖北科技出版社.2009.
[167]李继华,夏正中,陈国兴.钢结构轴心受压构件可靠度分析[J].建筑结构学报.1985,01:2-17.
[168] Williams H. L.. Reliability Evaluation of The Man Component in Man-machine Systems[M].Elect. Manufacturing.1958.
[169] CSNI. Assessing Human Reliability in nuclear power plants[C]. CSNI Report No.75.1983.
[170] Swain A. D.. Guttmann, H.E. Handbook of Human Reliability Analysis with Emphasis onNuclear Power Plant Application[M]. NUREG/CR1278.1983.
[171] Erik Hollnagel. Cognitive Reliability and Error Analysis Method[M]. Elsevier Science Ltd.1998:122-130.
[172] Williams J. C.. A data-based method for assessing and reducing human error to improveoperational performance[J]. In: Proceedings of IEEE4th Conference on Human Factor in PowerPlants. Monterey, California. Institute of Electronic and Electrical Engineers. New York(USA).1988.
[173] Bello G. C., Colombari V.. The human factors in risk analysis of process plants: The controlroom operator model, TESRO[J]. Reliability Engineering,1980(1):3-14.
[174] Humphreys E.. Human Reliability Assessors Guide. RTS88/89Q, NCSR, UKAEA,Warrington.1988.
[175] Embrey D. E., Humphreys P., Rosa E. A., Kirwan B., Rea K.. LIM-MAUD: An approach toassessing human error probabilities using structured expert judgment, Vol. Ⅰ: Overview ofSLIM-MAUD, Vol. Ⅱ: Detailed Analyses of the Technical Issues. NUREG/CR-3518.Washington DC(USA).1984.
[176] IAEA. Models and Data Requirements for Human Reliability Analysis. IAEA-TECDOC-499. Vienna.1989.
[177] Saaty, T. L.. TheAnalytic Hierarchy Process[M]. NewYork: McGraw-Hill Inc;1980.
[178]王雪华.两种层次结构化决策方法的理论与应用研究[D].大连理工大学博士学位论文,2000.
[179]武广.我国风险投资项目评估模型的探究——层次分析法的借鉴及修正[D].华东师范大学博士学位论文,2008.
[180]焦树峰.AHP法中平均随机一致性指标的算法及Matlab实现[J].太原师范学院学报（自然科学版）,2006,5(4):45-47.
[181]雷宏刚.钢结构事故分析与处理[M].北京:中国建筑工业出版社.2003.
[2] RehardE.Barlow. Mathematieal Theory of Reliability: A Historieal Pers Peetive[J]. IEEETrans.on Reliability.1984,33(l):16-20.
[3] Desieno C. F.,Stine L. L.. A probability method for determining the reliability of electric powersystems[J]. IEEE Transactions on Power Apparatus and Systems.1964, PAS-83(2):174-179.
[4] Kaufman A.. Introduction to the Theory of Fuzzy Subsets Volume1[M]. New York: AcademicPress.1975:235-243.
[5] Zadeh L. A.. Fuzzy sets[J]. Information and Control.1965,8(3):338-353.
[6] Onisawa T.. Fuzzy theory in reliability analysis[J]. Fuzzy Sets and Systems.1989,29(2):250-251.
[7] Cai K.,Wen C., Zhang M.. Posbist reliability behavior of fault-tolerant systems[J].Microelectronics and Reliability.1995,35(1):49-56.
[8] Cai K.,Wen C., Zhang M.. Posbist reliability behavior of typical system with two types offailures[J]. Fuzzy Sets and Systems.1991,43(1):17-32.
[9] Cai K.,Wen C., Zhang M.. Fuzzy states as a basis for a theory of fuzzy reliability[J].Microelectronics and Reliability.1993,33(15):2253-2263.
[10] Cai K.,Wen C., Zhang M.. Mixture models in profust reliability theory[J]. Microelectronicsand Reliability.1995,35(6):985-993.
[11] Billinton R., Sachdev M.. Direct current transmission system reliability evaluation[J]. Trans.CEA.1968,7(3):68-170.
[12] Billinton R., Prasad V.. Quantitative reliability analysis of HVDC transmission systems: Part Iand II[J]. IEEE Transactions on Power Apparatus and Systems.1971, PAS-90(3):1034-1054.
[13] Billinton R., Ahluwalia D. S.. Incorporation of A DC link in a composite system adequacyassessment-DC system modeling[J]. IEE Proceedings-C.1992,139(3):211-220.
[14]普罗尼科夫A. C.等著,李昌琪等译.数控机床的精度与可靠性[M].北京:机械工业出版社，1987.
[15] Vasilev V. S.. Cost efficiency approach to the selection of NC machine tool reliabilitystandards[J]. Soviet Engineering Research,1985,5(9):49-50.
[16] FreudenthalA. M.. The safety of structures[J]. Transation,ASCE, V112，1947.
[17] РжаницынA.P.. Строителъная промышленноств[J].No.8.1947.
[18] Стрелецкий Н.С.. Основы статистического учета коэфициента эапаса прочностисооружении[J]. Стройиэдат.1947.
[19] Cornell C. A.. A probability-based structural code [J]. J.ACI,1969,66(12):974-958.
[20] Lind N. C.. Consistent partial safety factors[J]. Struct. Div., ASCE,1971,97(6):1651-1669.
[21] Alfredo H-S.Ang and Wilson H.Tang. Probability Concepts in Engineering Planning andDesingn[M]. John Wiley&Sons, Volume I,1975, VolumeⅡ,1984.
[22] Rackwitz R. and Fiessler B.. An Algorithm for Calculation of Structural Reliability underCombined Loading[M]. Munchen,1977:36-45.
[23]宋笔锋等.飞行器可靠性工程[M].西安:西北工业大学出版社,2006,1-29.
[24]尹晓伟.基于贝叶斯网络的机械系统可靠性评估[D].东北大学博士学位论文,2008.1-12.
[25] Dorigo M., Maniezzo V., Colorni A.. The ant system:Optimization by a colony of cooperatingagents [J]. IEEE Transactions on Systems,Man and Cybernetics-PartB,1996,26(1):29-41.
[26] Dorigo M., Bonabeau E., Theraulaz G.. Ant algorithms and stigmergy [J]. FutureGeneration Computer Systems,2000,16:851-871.
[27] Kennedy J., Eberhart R. C., Shi Y. H.. Swarm Intelligence[M]. San Francisco: MorganKaufmann Publishers,2001.
[28]李晓磊.一种新型的智能优化方法—人工鱼群算法[D].浙江大学博士学位论文.2003,1-23.
[29]宋保维.系统可靠性设计与分析[M].西安:西北工业大学出版社,2008.43-58.
[30]邹天一.结构可靠度[M].北京:人民交通出版社,1998,1-1.
[31]交通部.公路预应力混凝土桥梁设计规范（试行）.北京:人民交通出版社,1978.
[32]铁道部.铁路工程设计规范第二篇桥涵.北京:人民铁道出版社,1975.
[33]全苏标准委员会建筑及建筑材料标准局.钢筋混凝土结构设计标准及技术规范（全苏标准OCT9003-38）,1938.
[34]赵国藩.钢筋混凝土结构按极限状态计算[M].北京:建筑工程出版社,1961.
[35]建设部.建筑结构可靠度设计统一标准[M].北京:中国建筑工业出版社,2002.
[36]常大民.江克斌.桥梁结构可靠性分析与设计[M].北京:中国铁道出版社.1995.
[37]吴世伟.结构可靠度分析[M].北京:人民交通出版社,1990.
[38]张建仁，刘扬，许福友等.结构可靠度理论及其在桥梁工程中的应用[M].北京:人民交通出版社,2003.
[39]董艳秋，田镜博.蒙特卡洛法结构可靠性分析[J].黑龙江工程学院学报（自然科学版），2010（3），V.24（1）：27-29.
[40] Andrzej S. Nowak, Kevin R. Collins. Reliability of Structures[M]. New York: McGraw-Hill.2000.
[41] Yaacob Ibrahim. Observations of applications of importance sampling in structural reliabilityanalysis[J]. Structural Safety.1991,10(4):269-281.
[42] Lieber D., Nemirovskii A., Rubinstein R. Y.. A fast Monte Carlo method for valuatingreliability indexes[J]. IEEE Trans on Reliability,1999,48(3):256-261.
[43] Pereira M. V. F., Maceira M. E. P., Oliveira G. C., et al. Combining analytical models andMonte Carlo techniques in probabilistic power system analysis[J]. IEEE Trans on PowerSystems,1992,7(1):265-272.
[44]王斌,赵渊,刘威.基于分裂最优乘子重要抽样的电网可靠性评估[J].电力系统自动化，2008,32(19):30-34.
[45] Melo A. C. G., Oliveira G. C., Morozowski FO. M., et al. Ahybrid algorithm for Monte Carloenumeration based composite reliability evaluation[C]. Proceedings of the3rd InternationalConference on Probabilistic Methods Applied to Electric Power Systems, July3-5，1991，London:UK:70-74.
[46] Ocnasu A. B., Besanger Y.. Distribution system availability assessment Monte Carlo andantithetic variants method[C]. Proceedings of the19th International Conference on ElectricityDistribution, May21-24,2007，Vienna, Austria:21-24.
[47]李云贵.工程结构可靠度分析方法研究[D].大连理工大学博士学位论文，1990.
[48]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: S1-S5.
[49]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,2000.21-64.
[50] Paloheimo E. H.. Structural design based on weighted fractiles[J]. Journal of the StructuralDivision.1974,100.
[51]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.
[52] Paloheimo E., Hannus H.. Structural based on weighted fractiles[J]. Journal of the StructuralDivision. ASCE,1974. Vol.100(ST7).
[53] Fiessler B., Rackwitz R., Neumann H.J.. Quadratic limit states in structural reliability[J].Journal of the Engineering Mechanics Division.1979,105(4):661-676.
[54] Der Kiureghian A., Lin H. Z., Hwuang S.T.. Second-order reliability approximation [J].Journal of Engineering Mechanics.1984,110(8):1208-1225.
[55] Tvedt L.. The distribution of quadratic forms in normal space-an application to structuralreliability[J]. Journal of Engineering Mechanics.1990,116(6):1183一1197.
[56] Breitung K.. Asymptotic approximation for multinomial integrals[J]. Journal of EngineeringMechanics.1984,110(3):357-366.
[57] Breitung K.. Asymptotic approximations for probability integrals[J]. ProbabilisticEngineering Mechanics.1989,4(4):187-190.
[58]李云贵，赵国藩，张保和.结构可靠度的渐进分析方法[J].大连理工大学学报,1994,34(4):442-447.
[59]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.
[60]赵国藩.工程结构可靠性理论与应用[M].大连理工大学出版社,1996.
[61]李伟.大跨度斜拉桥静东里可靠度分析[D].华南理工大学博士学位论文,2010.
[62]周林聪.钢筋混凝土结构非线性和可靠度分析方法研究[D].上海交通大学博士学位论文,2007.
[63]彭泽.结构可靠度Metamodel方法及其工程应用研究[D].中南大学硕士学位论文,2010.
[64]胡鸣.结构可靠度计算方法研究[D].华南理工大学硕士学位论文,2010.
[65]王文.基于能力谱方法的结构非概率可靠度[D].湖南大学硕士学位论文,2010.
[66]何木.基于传递系数法的边坡稳定性可靠度分析及应用[D].成都理工大学硕士学位论文,2010.
[67]孙宁.结构可靠度计算方法分析及其在系留机构中的应用[D].哈尔滨工程大学硕士学位论文,2008.
[68]杨会杰.预应力钢结构拉索的可靠度分析与设计指标研究[D].天津大学硕士学位论文,2007.
[69]柳颖臣.基于概率理论的预应力混凝土桥梁结构可靠度研究[D].长安大学硕士学位论文,2008.
[70]王嵩.已有砌体结构的抗震可靠度分析及实例应用[D].同济大学硕士学位论文,2007.
[71]孙思奥.结构可靠度分析方法及相关理论研究[D].清华大学硕士学位论文,2007.
[72]田英.结构可靠度估计理论及应用研究[D].西安建筑科技大学硕士学位论文,2007.
[73]史冀波.结构可靠度的反问题在桥梁工程中的应用研究[D].武汉理工大学硕士学位论文,2007.
[74]张宇.工程结构可靠度分析的若干问题研究[D].同济大学博士学位论文,2006.
[75]郑怡.既有结构构件可靠性研究及应用[D].大连理工大学博士学位论文,2009.
[76]李炜.边坡稳定可靠性分析[D].大连理工大学博士学位论文,2009.
[77] Ditlevsen O., Madsen H. O.. Proposal for a code for the direct use of reliability methods instructural design[J]. In: Working Document of Joint Committee on Structural Safety,1989.
[78]王光远.工程软设计原理[M].北京:科学出版社.1992:253-258,153-159.
[79] Moses F.. System reliability developments in structural engineering[J]. Structural Safety.1982,1:3-13.
[80] Moses F.. New directions and research needs in system reliability research[J]. StructuralSafety,1990,7:93-100.
[81] Feng Y. S.. Enumerating significant failure modes of a structural system by using criterionmethods[J]. Computers and Structures,1988,30(5):1153-1157.
[82]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.
[83]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.
[84]董聪,杨庆雄.冗余析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.
[85]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.
[86]冯元生.飞机结构的分析与先进设计原理[M].西安:西北工业大学出版社.1991,1-10.
[87]杨庆雄.自动矩阵力法及扩大算题规模的措施.[D]西北工业大学论文选,1979,177-188.
[88]姚卫星,顾怡.用自动矩阵力法枚举结构的主要模式[C].中国航空学会结构设计专业委员会第一届学术交流大会论文.
[89]姚卫星,顾怡.用自动矩阵力法枚举结构的主要模式[J].计算结构力学及其应用,1996,13(1):62-66.
[90] Reashedi M. R., Moses F.. Application of linear programming to structural systemreliability[J]. Comput&Struct,1986,24(3):375-384.
[91]张云阁,姚卫星.结构系统主要失效模式的枚举[J].强度与环境，1997(1),1-11.
[92] Murotsu Y., Okada H., Niwa K., et al. Reliability analysis of truss structures by using Matrixmethod[J]. Transactions of theASME，Journal of Mechanical Design.1980,102(4):749-756.
[93] Murotsu Y., Okada H., Yonezawa M., et al. Automatic generation of stochastically dominantmodes of structural failure in framestructure[J]. Structural Safety,1984,28(2):17-25.
[94]蔡荫林,安伟光,陈卫东.空间彬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,广州,1992(12).
[95]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.
[96] Melcher R. E. and Tang T. K.. Dominant failure modes in stochastic structural systems[J].Structural safety.1984(2):127-143.
[97] Thoft-Christensen P., Sorensen J. D.. Reliability of structural systems with correlatedelements[J]. Applied Mathematical Modeling,1982,6:171-178.
[98] Thoft-Christensen P., Baker M. J.. Structural reliability theory and its applications[J].Spring-Verlag, Berlin, Heidelberg, New York,1982.
[99] Thoft-Christensen P., Murotsu Y.. Application of structural systems reliability theory[J].Spring-Verlag, Berlin, Heidelberg, New York, Tokyo,1986.
[100] Thoft-christensen. Reliability of structural system[J]. Strudies in Apllied Mechanics,24:Advances in the theory of plates and shells，Elsevier science publishers B U,1990.
[101] Ranganathan R., Deshpande A. G.. Reliability analysis of reinforced concrete frame[J].J.Struct Eng, ASCE,1987,113(6):1315-1328.
[102]刘扬,张建仁.混凝土斜拉桥施工阶段的体系可靠度[J].中国公路学报.2006,9.Vol19（5）:53-58.
[103] Cornell C. A.. Bounds on the reliability of structural systems[J]. Journal of StructuralDivision, ASCE1967,93(st1).
[104] Ditlevsen O.. Nallow reliability bounds for structural system[J]. Journal of StructuralMechanics,1979,7(4):453-472.
[105] Feng Y. S.. A method of computing structural system reliability with high accuracy[J].Computers and Structures,1989,33(1):1-5.
[106]董聪.结构系统可靠性分析与优化[D].西北工业大学硕士学位论文,1990.
[107] Zhang Y. C.. Derivative fitting procedure for computing bivariate normal distribution andsome applications[J]. Structural Safety,1994,14(3):173-183.
[108]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.
[109]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.
[110] Stevenson L., Moses F.. Reliability analysis of frame structures. Journal of StructuralDivision[J].ASCE, ST11,96.1970.
[111] Gorman M. R. and Moses F.. Reliability of structural systems[C]. Report No.79-2, CaseWestern Reserve University,1979.
[112] Ang H-S, Ma H. F.. On the reliability of structural systems[C]. Proceedings of InternationalConference on Structural Safety and Reliability. Trondheim,1981.
[113] Ma H. F,, Ang H-S. Reliability analysis of redundant ductile structural systems[C].University of Illinois at Urbana-Champaign, August1981.
[114] Ditlevsen O.. Taylor expansion of series reliability[J]. Journal of Engineering Mechanics,1984,110(2):293-307.
[115] Hohenbichler M., Rackwitz R.. First-order concepts in system reliability[J]. StructuralSafety,1983,1(3):177-188.
[116] Tang L. K., Melchers R. E.. Improved approximation for multinormal integral[J]. StructuralSafety,1987,4(2):81-93.
[117] Tallis G. M.. The moment generating function of the truncated multi-normal distribution[J]. JRoyal Statistical Society, Series B1961,23:223-229.
[118] Terada S., Takahashi T.. Failure-conditioned reliability index[J]. Journal of StructuralEngineering, ASCE1988,114(4):943-952.
[119] Pandey M. D.. An effective approximation to evaluate multi-normal integrals[J]. StructuralSafety,1998,20:51-67.
[120]何嘉年.基于体系可靠度的半刚性钢框架结构优化设计研究[D].汕头大学博士学位论文,2010.
[121]赵文争.基于响应面法索弯顶结构的可靠度研究[D].浙江大学硕士学位论文,2011.
[122]许林.基于可靠度的结构优化研究[D].大连理工大学博士学位论文,2004.
[123]张小庆.结构体系可靠度分析方法研究[D].大连理工大学博士学位论文,2003.
[124]安海.析架结构系统可靠性分析方法的研究[D].哈尔滨工程大学博士学位论文,2009.
[125]姜封国.结构系统基于可靠性的优化设计研究[D].哈尔滨工程大学博士学位论文,2009.
[126] Matousek M.. Outcome of a servey on800construction failure[C]. IABSE Clloquium onInspection and Quality Control Institute of Structural Engineering. Zurich Swiss Federal Instituteof Technology,1977.
[127] Ellongwood B.. Design and construction error effect on structural reliability[J]. Journal ofStructural Engeering, ASCE,1987,113(2):409-422.
[128Smith D. W.. Why do bridges fail[J]. Civil Engineering,1977,47:58-62.
[129]贾桐,卢文良,杨明虎,张文雨.考虑人误影响的桥梁施工阶段可靠性分析[C].第20届全国结构工程学术会议论文集（第Ⅱ册）,2011:163-167.
[130]杨伟军,陈劲飙.土木工程施工过程中人为差错的博弈分析[J].长沙交通学院学报,2005,21(2):46~49.
[131] Stewart M. A., Melchers R. E.. Simulation of human error in design loading task[J].Structural Safety,1988,5(4):285-297.
[132] Stewart M. A., Melchers R. E.. Error control in member design[J]. Structural Safety,1989,6(1):11-24.
[133] Schneider J.. Introduction to safety and reliability of structures[C]. Zurich, Switzerland:International Association for Bridge and Structural Engineering.1997.
[134] Schneider J.. Quality assurance within the building process[J]. Proceedings, IABSEWorkshop, Vol.47, Rigi, Switzerland.
[135]周详.考虑人为错误的结构模糊随机可靠度分析模型[J].武汉工业大学学报,1996,18（2）:38-40.
[136]张铟,陈孝珍,程旭东.考虑人为错误影响的结构可靠度实用计算[J].水电能源科学,2004,32(2):73~76.
[137]俞然刚,于述强,程旭东等.水工结构考虑施工过程中人为错误影响的模糊随机可靠度分析[J].建筑技术开发,2005,32（5）4-6.
[138]巩春领.桥梁施工期间的人因可靠性分析[J].桥梁工程.2008,4(4):38～44.
[139]金福安,章勇武,马国丰,许伟.基于人为错误可靠度的深基坑工程灾害防治[J].地下空间与工程学报,2007,3(3):568～573.
[140]史文秀.钢结构施工阶段人为失误研究[D].西安建筑科技大学硕士学位论文,2009.
[141]陈金永.建造阶段考虑人为错误影响的钢结构模糊可靠度分析[D].太原理工大学硕士学位论文,2005.
[142]陈劲飚.建筑施工过程中人为差错控制及人的可靠性研究分析[D].长沙理工大学硕士学位论文,2004.
[143]陈劲飙,胡强.建筑施工中人为失误因素的敏感性分析[J].中国安全科学学报,2007,17（5）:9～16.
[144]周冲.基于污染分布模型下的结构可靠度分析[D].上海交通大学博士学位论文.2010.
[145]高佳,黄祥瑞.人的失误与人因工程学在核电厂安全性应用[J].中国安全科学学报.1994,4（2）:23-28
[146]张力.概率安全评价中人因可靠性分析技术[M].北京:原子能出版社.2006.
[147]严春风,刘东燕,张建辉等.岩土工程可靠度关于强度参数分布函数概型的敏感度分析.岩石力学与工程学报,1999,18(1):36-39.
[148]余俊.杆系结构的重要性和相关性研究[D].上海交通大学硕士学位论文,2005.
[149]陈晓龙,施庆生,邓晓卫.概率论与数理统计[M].南京:东南大学出版社.2011.
[150]中华人民共和国建设部. GB50007-2002.建筑地基基础设计规范.北京:中国建筑工业出版社.2002.
[151]中华人民共和国建设部. JGJ106-2003.建筑桩基检测技术规程.北京:中国建筑工业出版社.2003.
[152]中华人民共和国建设部. JGJ79-2002、J220-2002.建筑地基处理技术规范.北京:中国建筑工业出版社.2002.
[153]中华人民共和国建设部. GB50009-2001(2006版).建筑结构荷载规范（条文说明）.北京:中国建筑工业出版社.2006.
[154] P.索夫特-克里斯坦森, M.J.贝克.结构可靠性理论及其应用[M].北京:科学出版社.1988.
[155]中华人民共和国建设部. GB50068-2002.建筑结构可靠度设计统一标准.北京:中国建筑工业出版社.2002.
[156] Маликов М. Ф.. Основы Метрологни[M]. Коммерприбор.1944.
[157]沙定国.实用误差理论与数据处理[M].北京:北京理工大学出版社.1993.
[158]钟继贵.误差理论与数据处理[M].北京:水利电力出版社.1993.
[159]张崇立.截尾正态分布在地形变异变识别中的初步应用[J].地壳形变与地震.1991,11(1):75-84.
[160]王宝山.截尾正态分布与Robust估计[J].焦作矿业学院学报.1994,13(3):52-58.
[161]孙志礼,张风和,何雪宏,蔡春源.两端截尾分布的应力-强度干涉模型[J].东北大学学报（自然科学版）.1998,19(3):309-311.
[162]张玉,王丹,张风和,孙志礼,丁津原.断裂韧性的两端截尾分布概率法设计[J].机械设计与制造.1999,06:1-2.
[163]姜礼平,张国清.截尾正态分布的最小后验风险Bayes推断[J].运筹与管理.2005,14(1):47-51.
[164]丁德馨,毕忠伟,綦春明.两端截尾概率分布下围岩可靠度研究[J].中国安全科学学报.2008,18(4):111-115.
[165]赵瑞学,钱林芳,陈龙淼,石海军.基于双侧截尾正态分布的机构运动可靠度研究[J].计算机仿真.2011,28(2):248-251.
[166]潘继斌,胡宏昌.数理统计教程[M].武汉:湖北科技出版社.2009.
[167]李继华,夏正中,陈国兴.钢结构轴心受压构件可靠度分析[J].建筑结构学报.1985,01:2-17.
[168] Williams H. L.. Reliability Evaluation of The Man Component in Man-machine Systems[M].Elect. Manufacturing.1958.
[169] CSNI. Assessing Human Reliability in nuclear power plants[C]. CSNI Report No.75.1983.
[170] Swain A. D.. Guttmann, H.E. Handbook of Human Reliability Analysis with Emphasis onNuclear Power Plant Application[M]. NUREG/CR1278.1983.
[171] Erik Hollnagel. Cognitive Reliability and Error Analysis Method[M]. Elsevier Science Ltd.1998:122-130.
[172] Williams J. C.. A data-based method for assessing and reducing human error to improveoperational performance[J]. In: Proceedings of IEEE4th Conference on Human Factor in PowerPlants. Monterey, California. Institute of Electronic and Electrical Engineers. New York(USA).1988.
[173] Bello G. C., Colombari V.. The human factors in risk analysis of process plants: The controlroom operator model, TESRO[J]. Reliability Engineering,1980(1):3-14.
[174] Humphreys E.. Human Reliability Assessors Guide. RTS88/89Q, NCSR, UKAEA,Warrington.1988.
[175] Embrey D. E., Humphreys P., Rosa E. A., Kirwan B., Rea K.. LIM-MAUD: An approach toassessing human error probabilities using structured expert judgment, Vol. Ⅰ: Overview ofSLIM-MAUD, Vol. Ⅱ: Detailed Analyses of the Technical Issues. NUREG/CR-3518.Washington DC(USA).1984.
[176] IAEA. Models and Data Requirements for Human Reliability Analysis. IAEA-TECDOC-499. Vienna.1989.
[177] Saaty, T. L.. TheAnalytic Hierarchy Process[M]. NewYork: McGraw-Hill Inc;1980.
[178]王雪华.两种层次结构化决策方法的理论与应用研究[D].大连理工大学博士学位论文,2000.
[179]武广.我国风险投资项目评估模型的探究——层次分析法的借鉴及修正[D].华东师范大学博士学位论文,2008.
[180]焦树峰.AHP法中平均随机一致性指标的算法及Matlab实现[J].太原师范学院学报（自然科学版）,2006,5(4):45-47.
[181]雷宏刚.钢结构事故分析与处理[M].北京:中国建筑工业出版社.2003.