结构可靠性的概率设计法综述
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摘要
综述了目前国际上结构可靠性设计法领域现有的概率设计法,如随机有限元法、一阶及二阶可靠性设计法、蒙特卡罗法及拉丁超立方采样法、随机过程及随机场。讨论了具有代表性的概率设计法,如多项式混沌扩展法及KL变换。基于随机过程概念的随机扩展法具有良好的分析收敛特性,直接采用随机扩展法进行随机分析是一种高效的可靠性解算方法。Karhunen和Loeve基于由协方差函数导出的正交坐标函数,分别对连续时间过程进行了描述,KL变换能有效减少相关数据集的维度。当协方差函数已知时,可采用KL扩展法表征不确定性系统的随机特征;而当结构响应的协方差函数未知时,可采用PCE代替KL扩展法来表示这种类型的不确定性。出于对工程系统性能的严格要求,安全及可靠性余量的进一步缩小,加之严酷的市场竞争等因素,结构可靠性的概率设计法将迅速在多学科设计领域中得到广泛应用并产生显著的工程及经济效益,有力地推动我国装备质量的跨越式发展。
The existing probabilistic design methods in the field of current international structure reliability design method are reviewed, such as stochastic finite element method, first order and second order reliability design method, Monte Carlo method and Latin hypercube sampling method, random processes and random fields. The representative probabilistic design methods are discussed, such as polynomial chaos expansion method and KL transform. Stochastic expansion method based on the concept of stochastic process has a good analytic convergence property, and stochastic analysis is an efficient method for reliability calculation. Karhunen and Loeve are derived from the covariance function based on the orthogonal coordinate function, the continuous time process is described respectively, and KL transform can effectively reduce the dimension of the data set. When the covariance function is known, the KL expansion of the stochastic characteristics of the method can be used to characterize the uncertainty system, and when the structural response of the covariance function is unknown, the PCE can instead of KL expansion method to represent this type of uncertainty. Considering the strict requirements of the performance of engineering system, safety and reliability margins are further narrowed, and coupled with the harsh market competition and other factors, the probability design method of structure reliability will be widely applied in the field of the multidisciplinary design and produce significant engineering and economic benefits, effectively promoting the great leap forward development of China's equipment quality.
The existing probabilistic design methods in the field of current international structure reliability design method are reviewed, such as stochastic finite element method, first order and second order reliability design method, Monte Carlo method and Latin hypercube sampling method, random processes and random fields. The representative probabilistic design methods are discussed, such as polynomial chaos expansion method and KL transform. Stochastic expansion method based on the concept of stochastic process has a good analytic convergence property, and stochastic analysis is an efficient method for reliability calculation. Karhunen and Loeve are derived from the covariance function based on the orthogonal coordinate function, the continuous time process is described respectively, and KL transform can effectively reduce the dimension of the data set. When the covariance function is known, the KL expansion of the stochastic characteristics of the method can be used to characterize the uncertainty system, and when the structural response of the covariance function is unknown, the PCE can instead of KL expansion method to represent this type of uncertainty. Considering the strict requirements of the performance of engineering system, safety and reliability margins are further narrowed, and coupled with the harsh market competition and other factors, the probability design method of structure reliability will be widely applied in the field of the multidisciplinary design and produce significant engineering and economic benefits, effectively promoting the great leap forward development of China's equipment quality.
引文
[1]程家军,李春枝,陈颖.舰载环境振动摇摆特性测试分析[J].装备环境工程,2015,12(1):114—119.CHENG Jia-jun,LI Chun-zhi,CHEN Ying.Testing Analysis of Vibration and Sway Characteristics in Shipboard Environment[J].Equipment Environmental Engineering,2015,12(1):114—119.
[2]李勘.装备研制项目可靠性风险预警技术研究[J].装备环境工程,2014,11(4):125—130.LI Kan.Research on Pre-warning Technology for Reliability Risk of Equipment Research Project[J].Equipment Environmental Engineering,2014,11(4):125—130.
[3]倪育才.实用测量不确定度评定[M].第4版.北京:中国质检出版社,2014:7—50.NI Yu-cai.Evaluation of the Uncertainty of Practical Measurement[M].Fourth Edition.Beijing:China Quality Inspection Press,2014:7—50.
[4]范义龙,吴飒,李琦.基于PLC的冷却系统自整定模糊控制研究[J].环境技术,2014(6):66—71.FAN Yi-long,WU Sa,LI Qi.Research of the PLC Based Parameter Self-tuning Fuzzy Control for Cooling System[J].Environmental Technology,2014(6):66—71.
[5]HORáLEK V.Analysis of Basic Probability Distributions,Their Properties and Use in Determining Type B Evaluation of Measurement Uncertainties[J].Measurement,2013,46(1):16—23.
[6]CHU-AGOR M L,MU?OZ-CARPENA R,KIKER G A,et al.Simulating the Fate of Florida Snowy Plovers with Sea-level rise:Exploring Research and Management Priorities with a Global Uncertainty and Sensitivity Analysis Perspective[J].Ecological Modelling,2012,224(1):33—47.
[7]SCHWABE O,SHEHAB E,ERKOYUNCU J.Uncertainty Quantification Metrics for Whole Product Life Cycle Cost Estimates in Aerospace Innovation[J].Progress in Aerospace Sciences,2015,77:1—24.
[8]DANOWSKY B P,CHRSTOS J R,KLYDE D H,et al.Evaluation of Aeroelastic Uncertainty Analysis Methods[J].Journal of Aircraft,2010,47(4):1266—1273.
[9]MIRZAEI M,GALAVI H,FAGHIH M,et al.Model Calibration and Uncertainty Analysis of Runoff in the Zayanderood River Basin Using Generalized Likelihood Uncertainty Estimation(GLUE)Method[J].Aqua,2013,62(5):309—320.
[10]WU Y,PAN X,KANG R,et al.Multi-parameters Uncertainty Analysis of Logistic Support Process Based on GERT[J].Journal of Systems Engineering&Electronics,2014,25(6):1011—1019.
[11]ZHAO Y,FAN F,WANG J,et al.Uncertainty Analysis for Bulk Power Systems Reliability Evaluation Using Taylor Series and Nonparametric Probability Density Estimation[J].International Journal of Electrical Power&Energy Systems,2015,64:804—814.
[12]MOON H J.Uncertainty Analysis in Mould Spore Transportation and Its Application in an Existing Building[J].Indoor&Built Environment,2010,19(19):355—365.
[13]CAMACHO R A,MARTIN J L,DIAZ-RAMIREZ J,et al.Uncertainty Analysis of Estuarine Hydrodynamic Models:An Evaluation of Input Data Uncertainty in the Weeks Bay Estuary,Alabama[J].Applied Ocean Research,2014,47(2):138—153.
[14]SHI F,LONG H,ZHAN M,et al.Uncertainty Analysis on Process Responses of Conventional Spinning Using Finite Element Method[J].Structural&Multidisciplinary Optimization,2014,49(5):839—850.
[15]朱庆鹏,孙宇,陈浩,等.基于区间层次分析法的高速送料机可靠性综合分配方法[J].锻压技术,2015(4):131—136.ZHU Qing-peng,SUN Yu,CHEN Hao,et.Comprehensive Reliability Allocation Method for High-speed Feeder Based on Interval Analytic Hierarchy Process[J].Forging&Stamping Technology,2015(4):131—136.
[16]赵远,焦健,赵廷弟.基于模糊理论的风险评价方法[J].系统工程与电子技术,2015(8):1825—1831.ZHAO Yuan,JIAO Jian,ZHAO Ting-di.Risk Assessment Method Based on Fuzzy Logic[J].Systems Engineering and Electronics,2015(08):1825—1831.
[17]严巍,赵川.可能性理论研究[J].数字通信,2014(5):24—27.YAN Wei,ZHAO Chuan.Brief Analysis of the Possibility Theory[J].Digital Communication,2014(5):24—27.
[18]唐和生,邓立新,胡长远,等.基于证据理论和微分演化的结构不确定分析[J].同济大学学报(自然科学版),2014(3):325—330.TANG He-sheng,DENG Li-xin,HU Chang-yuan,et al.Evidence Theory and Differential Evolution for Uncertainty Quantification of Structures[J].Journal of Tongji University(Natural Science),2014(3):325—330.
[19]洪兴福,胡祥涛,邹满玲.基于随机有限元方法的地面雷达支耳连接结构可靠性评估[J].机械设计与研究,2014(6):59—61.HONG Xing-fu,HU Xiang-tao,ZOU Man-ling.Reliability Assessment for Radar Supporting Structure Based on Stochastic Finite Element Method[J].Mechanical Design and Research,2014(6):59—61.
[20]郭彪,顾德华,董玉革,等.可靠性分析的FORM和SORM组合法[J].合肥工业大学学报(自然科学版),2014(1):30—33.GUO Biao,GU De-hua,DONG Yu-ji,et al.Combination of FORM and SORM for Reliability Analysis[J].Journal of Hefei University of Technology(Natural Science),2014(1):30—33.
[21]伍国军,陈卫忠,谭贤君,等.基于拉丁超立方抽样的有限元可靠度程序开发及应用[J].岩土力学,2015(2):550—554.WU Guo-jun,CHEN Wei-zhong,TAN Xian-jun,et al.Program Development of Finite Element Reliability Method and Its Application Based on Latin Hypercube Sampling[J].Rock and Soil Mechanics,2015(2):550—554.
[22]王涛,周国庆,阴琪翔,等.岩土参数随机场离散的三角形单元局部平均法[J].岩土力学,2014(5):1482—1488.WANG Tao,ZHOU Guo-qing,YIN Qi-xiang,et al.Local Average Method of Triangular Elements for Discretization of Random Field of Geotechnical Parameters[J].Rock and Soil Mechanics,2014(5):1482—1488.
[23]DAERYONG P,ROESNER L A.Evaluation of Pollutant Loads from Stormwater BMPs to Receiving Water Using Load Frequency Curves with Uncertainty Analysis[J].Water Research,2012,46(20):6881—6890.
[24]MANDAL T K,GHOSH S,PUJARI N N.Seismic Fragility Analysis of a Typical Indian PHWR Containment:Comparison of Fragility Models[J].Structural Safety,2015,58:11—19.
[25]BERNUZZI C,GABBIANELLI G,GOBETTI A,et al.Beam Design for Steel Storage Racks[J].Journal of Constructional Steel Research,2016,116(1):156—172.
[26]BECK A T,áVILA DA SILVA C R J.Strategies for Finding the Design Point under Bounded Random Variables[J].Structural Safety,2016,58:79—93.
[27]FREEMAN R R.Simplified Uncertainty Analysis of Layer of Protection Analysis Results[J].Process Safety Progress,2013,32(4):351—360.
[28]李鹏,李传日,李桃.基于可靠性分配的整机加速因子计算方法研究[J].装备环境工程,2015,12(3):53—57.LI Peng,LI Chuan-ri,LI Tao.Research on the Calculation Method of Overall Acceleration Factor Based on Reliability Allocation[J].Equipment Environmental Engineering,2015,12(3):53—57.
[29]向树红.“航天器环境新技术研究”专题序言[J].装备环境工程,2015,12(3):3—4.XIANG Shu-hong.The Introduction of the New Technology Research of Spacecraft Environment[J].Equipment Environmental Engineering,2015,12(3):3—4.
[30]杨云峰,汤鹏杰.服务器集群网络中纠缠疑似攻击检测技术研究[J].计算机仿真,2015,32(5):315—317.TANG Peng-jie,YANG Yun-feng.Research on Detection Technology for Entanglement Suspected Attack in Server Cluster Network[J].Computer Simulation,2015,32(5):315—317.
[31]王红,王希诚,李克秋.混合Kriging代理模型的高维参数估计优化算法[J].大连理工大学学报.2015(2):215—222.WANG Hong,WANG Xi-cheng,LI Ke-qiu.Hybrid Kriging Surrogate Model Optimization Algorithm for High-dimension Parameter Estimation[J].Journal of Dalian University of Technology,2015(2):215—222.
[32]苏盈盈,李太福,易军,等.基于KICA子空间虚假邻点判别的软传感器变量选择方法[J].机械工程学报,2015(4):15—21.SU Ying-ying,LI Tai-fu,YI Jun,et al.Variable Selection for Nonlinear Soft Sensor Based on False Nearest Neighbors in KICA Space[J].Journal of Mechanical Engineering,2015(4):15—21.
[33]MELCHERS R E.Structural Reliability Analysis and Prediction[M].UK:Ellis Horwood Limited,1987.
[34]仲伟君,李德胜,崔亮.一种制导弹药电子部件可靠性预计方法[J].装备环境工程,2014,11(2):103—105.ZHONG Wei-jun,LI De-sheng,CUI Liang.A Method for the Reliability Prediction of Electronic Components in Guided Munitions[J].Equipment Environmental Engineering,2014,11(2):103—105.
[35]CAMERON R H,MARTIN W T.The Orthogonal Development of Nonlinear Functionals in Series of Fourier-Hermite Functionals[J].Annals of Mathematics,1947,48:385—392.
[36]GHANEM R G,SPANOS P D.Stochastic Finite Elements:A Spectral Approach[M].NY:Springer,1991.
[37]TATANG M A.Direct Incorporation of Uncertainty in Chemical and Environmental Engineering Systems[D].Cambrigde,MA:Massachusetts Institute of Technology,1995.
[38]ISUKAPALLI S S.Uncertainty Analysis of TransportTransformation Models[D].New Brunswick,NJ:the State University of New Jersey,1999.
[39]XIU D,KARNIADAKIS G.The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations[J].SIAM Journal of Scientific Computing,2002,24(2):619—644.
[40]XIU D,LUCOR D,SU C,et al.Stochastic Modeling of Flow-structure Interactions Using Generalized Polynomial Chaos[J].Journal of Fluids Engineering,Transactions of the ASME,2002,24(51):51—59.
[41]BABUSKA I,TEMPONE R,ZOURARIS G E.Galerkin Finite Element Approximations of Stochastic Elliptic Differential Equations[J].SIAM Journal on Numerical Analysis,2004,42:800—825.
[42]HOTELLING H.Analysis of a Complex of Statistical Variables into Principal Components[J].Journal of Educational Psychology,1933,24:498—520.
[43]U S Department of Transportation,Federal Aviation Administration.Advisory Circular 33.70-1:Guidance Material for Aircraft Engine-Life-Limited Parts Requirements[R].Washington DC:FAA,AC33 70-1,2009:30—50.
[44]VITTAL S,HAJELA P,JOSHI A.Review of Approaches to Gas Turbine Life Management[R].AIAA-2004-4372,2004.
[45]王卫国.轮盘低循环疲劳寿命预测模型和试验评估方法研究[D].南京:南京航空航天大学,2006.WANG Wei-guo.Disc LCF Life Prediction Models and Experiment Assessment Methodologies[D].Nanjing:Nanjing University of Aeronautics&Astronautics,2006.
[46]丁水汀,张弓,蔚夺魁,等.航空发动机适航概率风险评估方法研究综述[J].航空动力学报,2011,26(7):1142—1143.DING Shui-ting,ZHANG Gong,WEI Duo-kui,et al.Review of Probabilistic Risk Assessment on Aero-engine Airworthiness[J].Journal of Aerospace Power,2011,26(7):1142—1143.
[47]MIL-HDBK-1783B,Engine Structural Integrity Program[S].
[48]MCCLUNG R C,LEVERANT G R,ENRIGHT M P.Turbine Rotor Material Design-Phase II[R].Washington,DC:FAA Grant 99-G-016,2008:50—55.
[2]李勘.装备研制项目可靠性风险预警技术研究[J].装备环境工程,2014,11(4):125—130.LI Kan.Research on Pre-warning Technology for Reliability Risk of Equipment Research Project[J].Equipment Environmental Engineering,2014,11(4):125—130.
[3]倪育才.实用测量不确定度评定[M].第4版.北京:中国质检出版社,2014:7—50.NI Yu-cai.Evaluation of the Uncertainty of Practical Measurement[M].Fourth Edition.Beijing:China Quality Inspection Press,2014:7—50.
[4]范义龙,吴飒,李琦.基于PLC的冷却系统自整定模糊控制研究[J].环境技术,2014(6):66—71.FAN Yi-long,WU Sa,LI Qi.Research of the PLC Based Parameter Self-tuning Fuzzy Control for Cooling System[J].Environmental Technology,2014(6):66—71.
[5]HORáLEK V.Analysis of Basic Probability Distributions,Their Properties and Use in Determining Type B Evaluation of Measurement Uncertainties[J].Measurement,2013,46(1):16—23.
[6]CHU-AGOR M L,MU?OZ-CARPENA R,KIKER G A,et al.Simulating the Fate of Florida Snowy Plovers with Sea-level rise:Exploring Research and Management Priorities with a Global Uncertainty and Sensitivity Analysis Perspective[J].Ecological Modelling,2012,224(1):33—47.
[7]SCHWABE O,SHEHAB E,ERKOYUNCU J.Uncertainty Quantification Metrics for Whole Product Life Cycle Cost Estimates in Aerospace Innovation[J].Progress in Aerospace Sciences,2015,77:1—24.
[8]DANOWSKY B P,CHRSTOS J R,KLYDE D H,et al.Evaluation of Aeroelastic Uncertainty Analysis Methods[J].Journal of Aircraft,2010,47(4):1266—1273.
[9]MIRZAEI M,GALAVI H,FAGHIH M,et al.Model Calibration and Uncertainty Analysis of Runoff in the Zayanderood River Basin Using Generalized Likelihood Uncertainty Estimation(GLUE)Method[J].Aqua,2013,62(5):309—320.
[10]WU Y,PAN X,KANG R,et al.Multi-parameters Uncertainty Analysis of Logistic Support Process Based on GERT[J].Journal of Systems Engineering&Electronics,2014,25(6):1011—1019.
[11]ZHAO Y,FAN F,WANG J,et al.Uncertainty Analysis for Bulk Power Systems Reliability Evaluation Using Taylor Series and Nonparametric Probability Density Estimation[J].International Journal of Electrical Power&Energy Systems,2015,64:804—814.
[12]MOON H J.Uncertainty Analysis in Mould Spore Transportation and Its Application in an Existing Building[J].Indoor&Built Environment,2010,19(19):355—365.
[13]CAMACHO R A,MARTIN J L,DIAZ-RAMIREZ J,et al.Uncertainty Analysis of Estuarine Hydrodynamic Models:An Evaluation of Input Data Uncertainty in the Weeks Bay Estuary,Alabama[J].Applied Ocean Research,2014,47(2):138—153.
[14]SHI F,LONG H,ZHAN M,et al.Uncertainty Analysis on Process Responses of Conventional Spinning Using Finite Element Method[J].Structural&Multidisciplinary Optimization,2014,49(5):839—850.
[15]朱庆鹏,孙宇,陈浩,等.基于区间层次分析法的高速送料机可靠性综合分配方法[J].锻压技术,2015(4):131—136.ZHU Qing-peng,SUN Yu,CHEN Hao,et.Comprehensive Reliability Allocation Method for High-speed Feeder Based on Interval Analytic Hierarchy Process[J].Forging&Stamping Technology,2015(4):131—136.
[16]赵远,焦健,赵廷弟.基于模糊理论的风险评价方法[J].系统工程与电子技术,2015(8):1825—1831.ZHAO Yuan,JIAO Jian,ZHAO Ting-di.Risk Assessment Method Based on Fuzzy Logic[J].Systems Engineering and Electronics,2015(08):1825—1831.
[17]严巍,赵川.可能性理论研究[J].数字通信,2014(5):24—27.YAN Wei,ZHAO Chuan.Brief Analysis of the Possibility Theory[J].Digital Communication,2014(5):24—27.
[18]唐和生,邓立新,胡长远,等.基于证据理论和微分演化的结构不确定分析[J].同济大学学报(自然科学版),2014(3):325—330.TANG He-sheng,DENG Li-xin,HU Chang-yuan,et al.Evidence Theory and Differential Evolution for Uncertainty Quantification of Structures[J].Journal of Tongji University(Natural Science),2014(3):325—330.
[19]洪兴福,胡祥涛,邹满玲.基于随机有限元方法的地面雷达支耳连接结构可靠性评估[J].机械设计与研究,2014(6):59—61.HONG Xing-fu,HU Xiang-tao,ZOU Man-ling.Reliability Assessment for Radar Supporting Structure Based on Stochastic Finite Element Method[J].Mechanical Design and Research,2014(6):59—61.
[20]郭彪,顾德华,董玉革,等.可靠性分析的FORM和SORM组合法[J].合肥工业大学学报(自然科学版),2014(1):30—33.GUO Biao,GU De-hua,DONG Yu-ji,et al.Combination of FORM and SORM for Reliability Analysis[J].Journal of Hefei University of Technology(Natural Science),2014(1):30—33.
[21]伍国军,陈卫忠,谭贤君,等.基于拉丁超立方抽样的有限元可靠度程序开发及应用[J].岩土力学,2015(2):550—554.WU Guo-jun,CHEN Wei-zhong,TAN Xian-jun,et al.Program Development of Finite Element Reliability Method and Its Application Based on Latin Hypercube Sampling[J].Rock and Soil Mechanics,2015(2):550—554.
[22]王涛,周国庆,阴琪翔,等.岩土参数随机场离散的三角形单元局部平均法[J].岩土力学,2014(5):1482—1488.WANG Tao,ZHOU Guo-qing,YIN Qi-xiang,et al.Local Average Method of Triangular Elements for Discretization of Random Field of Geotechnical Parameters[J].Rock and Soil Mechanics,2014(5):1482—1488.
[23]DAERYONG P,ROESNER L A.Evaluation of Pollutant Loads from Stormwater BMPs to Receiving Water Using Load Frequency Curves with Uncertainty Analysis[J].Water Research,2012,46(20):6881—6890.
[24]MANDAL T K,GHOSH S,PUJARI N N.Seismic Fragility Analysis of a Typical Indian PHWR Containment:Comparison of Fragility Models[J].Structural Safety,2015,58:11—19.
[25]BERNUZZI C,GABBIANELLI G,GOBETTI A,et al.Beam Design for Steel Storage Racks[J].Journal of Constructional Steel Research,2016,116(1):156—172.
[26]BECK A T,áVILA DA SILVA C R J.Strategies for Finding the Design Point under Bounded Random Variables[J].Structural Safety,2016,58:79—93.
[27]FREEMAN R R.Simplified Uncertainty Analysis of Layer of Protection Analysis Results[J].Process Safety Progress,2013,32(4):351—360.
[28]李鹏,李传日,李桃.基于可靠性分配的整机加速因子计算方法研究[J].装备环境工程,2015,12(3):53—57.LI Peng,LI Chuan-ri,LI Tao.Research on the Calculation Method of Overall Acceleration Factor Based on Reliability Allocation[J].Equipment Environmental Engineering,2015,12(3):53—57.
[29]向树红.“航天器环境新技术研究”专题序言[J].装备环境工程,2015,12(3):3—4.XIANG Shu-hong.The Introduction of the New Technology Research of Spacecraft Environment[J].Equipment Environmental Engineering,2015,12(3):3—4.
[30]杨云峰,汤鹏杰.服务器集群网络中纠缠疑似攻击检测技术研究[J].计算机仿真,2015,32(5):315—317.TANG Peng-jie,YANG Yun-feng.Research on Detection Technology for Entanglement Suspected Attack in Server Cluster Network[J].Computer Simulation,2015,32(5):315—317.
[31]王红,王希诚,李克秋.混合Kriging代理模型的高维参数估计优化算法[J].大连理工大学学报.2015(2):215—222.WANG Hong,WANG Xi-cheng,LI Ke-qiu.Hybrid Kriging Surrogate Model Optimization Algorithm for High-dimension Parameter Estimation[J].Journal of Dalian University of Technology,2015(2):215—222.
[32]苏盈盈,李太福,易军,等.基于KICA子空间虚假邻点判别的软传感器变量选择方法[J].机械工程学报,2015(4):15—21.SU Ying-ying,LI Tai-fu,YI Jun,et al.Variable Selection for Nonlinear Soft Sensor Based on False Nearest Neighbors in KICA Space[J].Journal of Mechanical Engineering,2015(4):15—21.
[33]MELCHERS R E.Structural Reliability Analysis and Prediction[M].UK:Ellis Horwood Limited,1987.
[34]仲伟君,李德胜,崔亮.一种制导弹药电子部件可靠性预计方法[J].装备环境工程,2014,11(2):103—105.ZHONG Wei-jun,LI De-sheng,CUI Liang.A Method for the Reliability Prediction of Electronic Components in Guided Munitions[J].Equipment Environmental Engineering,2014,11(2):103—105.
[35]CAMERON R H,MARTIN W T.The Orthogonal Development of Nonlinear Functionals in Series of Fourier-Hermite Functionals[J].Annals of Mathematics,1947,48:385—392.
[36]GHANEM R G,SPANOS P D.Stochastic Finite Elements:A Spectral Approach[M].NY:Springer,1991.
[37]TATANG M A.Direct Incorporation of Uncertainty in Chemical and Environmental Engineering Systems[D].Cambrigde,MA:Massachusetts Institute of Technology,1995.
[38]ISUKAPALLI S S.Uncertainty Analysis of TransportTransformation Models[D].New Brunswick,NJ:the State University of New Jersey,1999.
[39]XIU D,KARNIADAKIS G.The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations[J].SIAM Journal of Scientific Computing,2002,24(2):619—644.
[40]XIU D,LUCOR D,SU C,et al.Stochastic Modeling of Flow-structure Interactions Using Generalized Polynomial Chaos[J].Journal of Fluids Engineering,Transactions of the ASME,2002,24(51):51—59.
[41]BABUSKA I,TEMPONE R,ZOURARIS G E.Galerkin Finite Element Approximations of Stochastic Elliptic Differential Equations[J].SIAM Journal on Numerical Analysis,2004,42:800—825.
[42]HOTELLING H.Analysis of a Complex of Statistical Variables into Principal Components[J].Journal of Educational Psychology,1933,24:498—520.
[43]U S Department of Transportation,Federal Aviation Administration.Advisory Circular 33.70-1:Guidance Material for Aircraft Engine-Life-Limited Parts Requirements[R].Washington DC:FAA,AC33 70-1,2009:30—50.
[44]VITTAL S,HAJELA P,JOSHI A.Review of Approaches to Gas Turbine Life Management[R].AIAA-2004-4372,2004.
[45]王卫国.轮盘低循环疲劳寿命预测模型和试验评估方法研究[D].南京:南京航空航天大学,2006.WANG Wei-guo.Disc LCF Life Prediction Models and Experiment Assessment Methodologies[D].Nanjing:Nanjing University of Aeronautics&Astronautics,2006.
[46]丁水汀,张弓,蔚夺魁,等.航空发动机适航概率风险评估方法研究综述[J].航空动力学报,2011,26(7):1142—1143.DING Shui-ting,ZHANG Gong,WEI Duo-kui,et al.Review of Probabilistic Risk Assessment on Aero-engine Airworthiness[J].Journal of Aerospace Power,2011,26(7):1142—1143.
[47]MIL-HDBK-1783B,Engine Structural Integrity Program[S].
[48]MCCLUNG R C,LEVERANT G R,ENRIGHT M P.Turbine Rotor Material Design-Phase II[R].Washington,DC:FAA Grant 99-G-016,2008:50—55.
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