基于响应面方法的复杂结构模型修正方法研究
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摘要
由于现场实测或模型试验的困难,在计算模型的基础上进行各种计算分析,是目前复杂结构设计、施工、维护过程中了解结构力学性能的重要手段。然而,由于计算模型隐含有各种假设,通常与实际结构存在差异,导致分析结果与实测结果不吻合。因此,要想获得符合实际的分析结果,首先要保证计算模型的正确性。工程领域的模型修正,就是指利用综合利用各种信息,使建立的结构分析模型与实际相吻合。
本文通过回顾结构动力模型修正技术的发展历程和研究现状,指出传统的基于数值模型的修正方法对问题的复杂性考虑不够,将解决办法限制在经典力学原理的范围内,最终陷入数值计算的麻烦。近年来发展起来的基于统计分析技术的模型修正方法虽然注意到问题的复杂性,认为应当使用数值分析的结果作为样本,通过试验设计获取典型样本,使拟合(或回归)得到的结构动力模型尽量与测试结果一致,但没有充分利用结构分析所获得的其他先验信息,过于依赖统计分析技术,而且修正模型的物理意义不明确。
本文认为,对于复杂结构,除了基本的经典力学原理外,还有复杂性规律在起作用,而复杂性规律隐藏在数据流中,使得问题变成面向数据的问题。在复杂结构的模型修正过程中,应当综合考虑数学物理关系、统计规律以及先(后)验信息,才有可能获得真实可信的修正结果。
本文的主要工作和创新点集中在以下几个方面：
(1)提出对复杂结构的动力修正问题应该针对于某一类具体结构进行,而不宜从一般意义上去寻找对任意结构都适用的动力修正技术,这样才能充分利用该类结构的先验信息,保证求解的可行性和稳定性。
(2)提出对复杂结构应当建立一个等价的快速运行参数模型来进行动力修正,而不应当直接对有限元模型的质量矩阵、刚度矩阵等进行修正,然后利用响应面方法予以实施。
(3)提出一种基于结构力学方程和量纲分析原理的响应面函数构造方法,用于改进传统响应面方法在复杂结构模型修正技术中的应用,力图利用先验信息指导响应面函数的选取,降低响应面回归的复杂度,并寻找响应与设计参数之间的机理模型。
(4)提出一种基于统计学习理论的复杂结构模型修正方法。将统计学习理论的最新成果—支持向量机应用于复杂结构模型修正过程中的参数计算,避免了传统模型修正的数值计算困难,也避免了神经网络方法的维数灾难和过学习问题。
(5)探索了支持向量机应用于复杂结构模型修正的可行性和途径,并在一个实际的复杂结构—抽水蓄能电站地下厂房结构模型修正过程中应用与实施。
Due to the difficulty of prototype test or model test for complex structures during the period of design, construction and maintenance, anaylysis based on computing model is a common alternate method to achieve the mechanical properties of the complex structures. But differences are offen found between the initial computing model, which is built based on the specifications and the experiences of the engineers, and the prototype because of the suppositions in the modeling process. The differences may lead to analysis errors. It indicates that the initial computing model must be modified or updated to fit the analysis request, or make the computing model corresponding to the real conditions.
Based on the review on the development and current research of structure dynamic model updating technology, the paper points out that traditional model based on numerical correction method did not take into account the complexity of the problem, limited solved method just in classical mechanics principle and finally entrapped in trouble of numerical calculation. Model updating based on statistical analysis has made a rapid progress in recent years. Although it has given into consideration the complexity of problem, obtained typical samples by means of experiment and employed analysis results as sample in order to make agreement between calculated results and actual ones, it did not make full use of prior infor-mation and excessively depended on analysis technology which leads to indefinite physical meaning of the modified model.
This paper argues that not only basic classical mechanics but also complexity play roles in solving complicated structure issue. Complexity hidden in the stream of data, which makes model updating technology face to. The authentic, reliable update results can be achieved only if the relationship between mathematical and physical principles, the laws of statistics and the prior (posterior) information should be given into account during the process of modification model for complicated structure.
(1) Put forward that dynamic correction for complex structures should be aimed at spe-cific structure rather than modification techniques which meet all structures, so as to make full use of prior information of this structure to reach and ensure solutions'feasibility and stability and ensure solution.
(2) Propose that complex structure should be established on an equivalent fast runnig parameter model for dynamic model modification and use response surface method rather than base on finite element model of the mass matrix, stiffness matrix.
(3) Come up with response surface methodology based on structure mechanics equa-tions and dimensional analysis principle to improve the application of traditional response surface method in model modification for complex structure and attempt to make the re-sponse surface function form closer to the real structure of the mechanism model.
(4) Propose that complex structure model modification method based on statistical learn- ing theory. Apply the latest results-support vector machine (SVM) model into parameter calculation in the process of complex structure modification and avoid numerical calculation difficulty in traditional model and the dimension disasters and over-fitting problems in neural network method as well.
(5) Explore the feasibility and approaches of support vector machine (SVM) in com-plex structure model modification. Apply and implement the theory into the model modifi-cation process of an actual complicated structure-an underground powerhouse structure in a pumped storage power station.
本文通过回顾结构动力模型修正技术的发展历程和研究现状,指出传统的基于数值模型的修正方法对问题的复杂性考虑不够,将解决办法限制在经典力学原理的范围内,最终陷入数值计算的麻烦。近年来发展起来的基于统计分析技术的模型修正方法虽然注意到问题的复杂性,认为应当使用数值分析的结果作为样本,通过试验设计获取典型样本,使拟合(或回归)得到的结构动力模型尽量与测试结果一致,但没有充分利用结构分析所获得的其他先验信息,过于依赖统计分析技术,而且修正模型的物理意义不明确。
本文认为,对于复杂结构,除了基本的经典力学原理外,还有复杂性规律在起作用,而复杂性规律隐藏在数据流中,使得问题变成面向数据的问题。在复杂结构的模型修正过程中,应当综合考虑数学物理关系、统计规律以及先(后)验信息,才有可能获得真实可信的修正结果。
本文的主要工作和创新点集中在以下几个方面：
(1)提出对复杂结构的动力修正问题应该针对于某一类具体结构进行,而不宜从一般意义上去寻找对任意结构都适用的动力修正技术,这样才能充分利用该类结构的先验信息,保证求解的可行性和稳定性。
(2)提出对复杂结构应当建立一个等价的快速运行参数模型来进行动力修正,而不应当直接对有限元模型的质量矩阵、刚度矩阵等进行修正,然后利用响应面方法予以实施。
(3)提出一种基于结构力学方程和量纲分析原理的响应面函数构造方法,用于改进传统响应面方法在复杂结构模型修正技术中的应用,力图利用先验信息指导响应面函数的选取,降低响应面回归的复杂度,并寻找响应与设计参数之间的机理模型。
(4)提出一种基于统计学习理论的复杂结构模型修正方法。将统计学习理论的最新成果—支持向量机应用于复杂结构模型修正过程中的参数计算,避免了传统模型修正的数值计算困难,也避免了神经网络方法的维数灾难和过学习问题。
(5)探索了支持向量机应用于复杂结构模型修正的可行性和途径,并在一个实际的复杂结构—抽水蓄能电站地下厂房结构模型修正过程中应用与实施。
Due to the difficulty of prototype test or model test for complex structures during the period of design, construction and maintenance, anaylysis based on computing model is a common alternate method to achieve the mechanical properties of the complex structures. But differences are offen found between the initial computing model, which is built based on the specifications and the experiences of the engineers, and the prototype because of the suppositions in the modeling process. The differences may lead to analysis errors. It indicates that the initial computing model must be modified or updated to fit the analysis request, or make the computing model corresponding to the real conditions.
Based on the review on the development and current research of structure dynamic model updating technology, the paper points out that traditional model based on numerical correction method did not take into account the complexity of the problem, limited solved method just in classical mechanics principle and finally entrapped in trouble of numerical calculation. Model updating based on statistical analysis has made a rapid progress in recent years. Although it has given into consideration the complexity of problem, obtained typical samples by means of experiment and employed analysis results as sample in order to make agreement between calculated results and actual ones, it did not make full use of prior infor-mation and excessively depended on analysis technology which leads to indefinite physical meaning of the modified model.
This paper argues that not only basic classical mechanics but also complexity play roles in solving complicated structure issue. Complexity hidden in the stream of data, which makes model updating technology face to. The authentic, reliable update results can be achieved only if the relationship between mathematical and physical principles, the laws of statistics and the prior (posterior) information should be given into account during the process of modification model for complicated structure.
(1) Put forward that dynamic correction for complex structures should be aimed at spe-cific structure rather than modification techniques which meet all structures, so as to make full use of prior information of this structure to reach and ensure solutions'feasibility and stability and ensure solution.
(2) Propose that complex structure should be established on an equivalent fast runnig parameter model for dynamic model modification and use response surface method rather than base on finite element model of the mass matrix, stiffness matrix.
(3) Come up with response surface methodology based on structure mechanics equa-tions and dimensional analysis principle to improve the application of traditional response surface method in model modification for complex structure and attempt to make the re-sponse surface function form closer to the real structure of the mechanism model.
(4) Propose that complex structure model modification method based on statistical learn- ing theory. Apply the latest results-support vector machine (SVM) model into parameter calculation in the process of complex structure modification and avoid numerical calculation difficulty in traditional model and the dimension disasters and over-fitting problems in neural network method as well.
(5) Explore the feasibility and approaches of support vector machine (SVM) in com-plex structure model modification. Apply and implement the theory into the model modifi-cation process of an actual complicated structure-an underground powerhouse structure in a pumped storage power station.
引文
[1]张德文,魏阜旋.模型修正与破损诊断[M].北京：科学出版社,1999
[2]王博,吕正勋,何伟.结构动力模型修正方法研究与进展[J].水利与建筑工程学报,2009,7(1)：16-19
[3]王春岩.结构有限元模型修正算法研究综述[J],黑龙江科技信息,2009,19：58
[4]李辉,丁桦.结构动力模型修正方法研究进展[J],力学进展,2005,(2)：170-180
[5]荣见华.结构动力修改及优化设计[M].北京：人民交通出版社,2003
[6]邓方林,廖守亿,孙新利.复杂工程系统建模与仿真[M].北京：国防工业出版社,2009
[7]黄欣荣.复杂性科学的方法论研究[M].重庆：重庆大学出版社,2006
[8]黄欣荣.复杂性科学与哲学[M].北京：中央编译出版社,2007
[9]吴彤.科学哲学视野中的客观复杂性[J].系统辩证学学报,2001,(4)：44-47
[10]隋允康,宇慧平.响应面方法的改进及其对工程优化的应用[M].北京：科学出版社,2011
[11]张哲,李生勇,石磊.结构可靠度分析中的改进响应面法及其应用[J].工程力学,2007,(8)：111-115
[12]朱跃,张令弥.结基于确定性计算响应面的复杂工程结构不确定性建模研究[J].计算力学学报,2011,(3)：412-416
[13]郭勤涛,张令弥,费庆国.用于确定性计算仿真的响应面法及其试验设计研究[J].航空学报,2006,(1)：55-61
[14]韩芳.复杂结构模型修正技术研究[D].武汉：武汉大学博士学位论文,2008
[15]王勖成.有限单元法[M].北京：清华大学出版社,2003
[16]Mottershead J E, Friswell M I. Model Updating in Structural Dynamics:a Survey [J]. Journal of Sound and Vibration,1993,167(2):347-375
[17]张之沧,科学技术哲学[M],南京：南京师范大学出版社,2009
[18]Goodwin G C, Payne R L. Dynamic System Identification:Experiment Design and Data Analysis [M], Academic Press, New York,1977
[19]Berman A. System Identification of Structural Dynamic Models Theoretical and Prac-tical Bounds [C], Structures, Structural Dynamics and Materials Conference,25th, Palm Springs, CA; United States; 14-16 May 1984. pp.123-129.1984
[20]Berman A. Nonunique Structural Identification [C], Proc. Of the 7th MAC,1989, 355-359
[21]Astrom K J, Wittenmark B. Adaptive Control [M],2nd ed, Addison Wesley,1995
[22]Berman A. Mass Matrix Correction from Incomplete Set of Measured Modes[J]. AIAA Journal,1979,17(10):1147-1148
[23]Wei F S. Stiffness Matrix Correction from Incomplete Test Data [J]. AIAA Journal, 1980,18(10):1274-1275
[24]Berman A, Wei F S, Rao V. Improvement of Analytical Dynamic Models Using Modal Test Data [C]. Proc. of the AIAA 21st SDM Conf.,1980,809-814
[25]Berman A, Wei F S. Automated Dynamic Analytical Model Improvement [R]. NASA CR-3452,1981
[26]Berman A, Nagy E J. Improvement of a Large Dynamic Analytical Model Using Ground Vibration Test Data [C]. Structures, Structural Dynamics and Materials Con-ference,23rd, New Orleans, LA; United States; 10-12 May 1982. pp.301-306.1982
[27]Baruch M. Optimal Corrrection of Mass and Stiffness Matrices Using Mearsured Modes [J]. AIAA Journal,1982,20(11):1623-1626
[28]Zhang D W, Zhang L. The Matrix Transform Method for Updating Dynamic Model [J]. AIAA Journal,1992,30(5):1440-1443
[29]Zhang Q, Lallement et al. A Complete Procedure for the Adjustment of a Mathemat-ical Model from the Identified Complex Modes [C]. Proc. of the 5th IMAC,1987, 1183-1189
[30]侯吉林,欧进萍.基于局部模态的约束子结构模型修正法[J].力学学报,2009,(5)：748-756
[31]Kabe A M. Stiffness Matrix Adjustment Using Mode Data [J]. AIAA Journal,1985, 23(9):1431-1436
[32]Zhang O, Zerva A, Zhang D W. Stiffness Matrix Adjustment Using Incomplete Mea-sured Modes [J]. AIAA Journal,1997,35(5):1431-1436
[33]张德文,魏阜旋.关于质量阵之元素修正法的改进[J].应用力学学报,1992,(1)：129-133
[34]郭杏林,高海洋.一种基于振型正交化的元素型模型修正方法[J].振动与冲击,2011,(6)：5-9
[35]张德文,魏阜旋,张欧.实用完备空间模态空间中的相容修正模型[J].振动工程学报,1989,2(4)：33-40
[36]张德文,魏阜旋.完备模态空间技术的短评和注记[J].振动与冲击,1991,(3)：14-19
[37]Gravitz S I. An Analytical Procedure for Orthogonalization of Experimentally Mea-sured Modes [J]. Journal of the Aero/Space Sciences,1958,25(11):721-722
[38]Rodden W P. A Method for Deriving Structural Influence Coefficients from Ground Vibration Tests [J]. AIAA Journal,1967,5(5):991-1000
[39]Mc-Grew J. Orthogonalization of Measured Modes and Calculation of Influence Co-efficients [J]. AIAA Journal,1969,7(4):774-776
[40]费庆国,韩晓林,苏鹤玲.响应面有限元模型修正的实现与应用[J].振动,测试与诊断,2010,(2)：132-134页
[41]费庆国,张令弥,李爱群等.基于统计分析技术的有限元模型修正研究[J].振动与冲击,2005,(3)：23-26
[42]Baruch M, Itzhack Y B. Optimal Weighted Orthogonalization of Measured Modes [J]. AIAA Journal,1978,16(4):346-351
[43]Berman A, Nagy E J. Improvement of a Large Dynamic Analytical Model Using Test Data [J]. AIAA Journal,1983,21(8):1168-1173
[44]Smith S W, Beattie C A. Secant-method Adjustment for Structural Models [J]. AIAA Journal,1991,29(1):119-126
[45]Janter T, Sas P. Uniqueness Aspect of Model-updating Procedures [J]. AIAA Journal, 1990,28(3):538-543
[46]Roy N A, Girard A, Bugeat L P, et al. A Survey of Finite Element Model Updating Methods [C]. Environmental Testing for Space Programmes Test:Facilities and Meth-ods, Proceedings of an International Symposium held in Noordwijk, The Netherlands, June 26-29 1990. Paris:European Space Agency (ESA),1990, (304):333-349
[47]Caesar B. Updating System Matrices Using Modal Test Data [C]. Proc.5th IMAC. 1987:453-459
[48]魏来生.结构有限元动态模型修正方法综述[J].振动与冲击,1998,17(3)：43-48
[49]Bugeat L, Fillod R, Lallemend G, et al. Adjustment of a Conservative Non Gyroscopic Mathematical from Measurement [J]. Shock & Vibration Bullstin,1978, Proc.48, pt.3: 71-81
[50]张德文,李应明.一种普遍性的元素型修正法—排列方程法[J].强度与环境,1989,(6)：9-15
[51]张德文,魏阜旋.关于质量阵之元素修正法的改进[J].应用力学学报,1992,(1)：129-133
[52]张德文,Wei S F,李应明.修正动力分析模型的最优元素型摄动法[J].振动工程学报,1988,(4)：97-105
[53]韩芳,钟冬望,汪君.基于径向基神经网络的有限元模型修正研究[J].武汉科技大学学报,2011,(2)：115-118
[54]鲁峰,黄金泉.基于遗传算法的航空发动机机载模型支持向量机修正方法[J].航空动力学报,2009,(4)：880-885
[55]华宏星,傅志方.模糊数学在有限元模型修正中的应用[J].振动工程学报,1997,(4)
[56]刘继承,周传荣.一个基于优化的有限元模型修正方法[J].振动与冲击,2003,22(2)：33-34
[57]王乐,杨智春,李斌等.基于固有频率向量的模型修正方法[J].西北工业大学学报,2008,26(1)：93-98
[58]杨智春,王乐,丁燕等.基于附加已知刚度的动力学模型修正方法[J].工程力学,2009,(5)：19-24
[59]朱凼凼,冯咬齐,宋海丰.一种基于加速度频响函数的动力学模型修正方法[J].固体力学学报,2005,26(3)：329-332
[60]朱凼凼,冯咬齐.应用位移频响函数进行模型修正[J].宇航学报,2006,(2)：201-204
[61]Xia Y, Lin R. A New Iterative Order Reduction (IOR) Method for Eigensolutions of Large Structures [J]. International Journal for Numerical Methods in Engineering, 2004, (59):153-172
[62]周睿,陈力奋.基于可测点信息的模型参数修正方法[J].振动与冲击,2007,26(6)：70-73
[63]张连振；黄侨；郑一峰.桥梁结构损伤识别理论的研究进展[J].哈尔滨工业大学学报,2005,(10)：1415-1418
[64]张坤,段忠东,刘洋.连续刚构桥动力特性参数识别与有限元模型修正[J].公路交通科技,2008,(9)：67-72
[65]张纯,宋固全,吴光宇.实测模态和结构模型同步修正的结构损伤识别方法[J].振动与冲击,2010,(9)：1-4
[66]卢菊洪,陈志平.基于有限元模型修正的损伤识别方法研究[J].机械设计,2010,(5)：25-27
[67]张保强,郭勤涛,陈国平.基基于复模态模型修正方法的磁悬浮轴承支承参数识别[J].南京航空航天大学学报,2010,(6)：748-752
[68]郭杏林,高海洋.一种基于振型正交化的元素型模型修正方法[J].振动与冲击,2011,(6)：5-9
[69]周传荣,Link M.修正结构有限元模型的一种方法[J].振动工程学报,1989,2(4)：70-75
[70]罗漳平,向锦武.结构动力学模型修正的一种参数型方法[J].北京航空航天大学学报,2004,(7)：648-651
[71]郭勤涛,张令弥,费庆国.结构动力学有限元模型修正的发展—模型确认[J].力学进展,2006,(1)：36-42
[72]Friswell M I, Mottershead J E. Model Updating in Structural Dynamics [M]. London: Kluwer Academic Publisher,1995
[73]Schedlinski C. Computational Model Updating of Large Scale Finite Element Models [C]. Proc. SPIE Vol.4062, Proceedings of IMAC-ⅩⅧ:A Conference on Structural Dynamics.2000,476-482
[74]Zhang Q W, Chang T Y P, Chang C C. Finite-Element Model Updating for the Kap Shui Mun Cable-Stayed Bridge [J]. Journal of Bridge Engineering,2001,6(4):285-293
[75]夏品奇, Brown J M W.斜拉桥有限元建模与模型修正[J].振动工程学报,2003,16(2)：220-223
[76]丁幼亮,李爱群,韩晓林.润扬大桥斜拉桥结构安全评估的有限元建模与修正[J].东南大学学报(自然科学版),2006,(1)：92-96
[77]程霄翔,费庆国,何顶顶等.基于响应面的大型输电塔结构有限元模型动力修正[J].振动与冲击,2011,(5)：116-122
[78]Weber B, Paultre P. Damage Identification in a Truss Tower by Regularized Model Updating [J]. Journal of Structural Engineering,2010,136(3):307-316
[79]王万中.试验的设计与分析[M].北京：高等教育出版社,2004
[80]蒙哥马利.试验的设计与分析[M].北京：人民邮电出版社,2009
[81]滕军,朱焰煌,卢云军.基于多输出支持向量回归机的有限元模型修正[J].振动与冲击,2010,(3)：9-12
[82]任丕顺.基于支持向量机的响应面模型及其工程应用[J].湖南农业大学学报(自然科学版),2009,(6)：702-704
[83]Box G E P, Wilson K B. On the Experimental Attainment of Optimum Conditions [J]. Journal of Ryal Statistical Society,1951, B(13):1-45
[84]Box G E P, Draper K B. A Basis for the Selection of a Response Surface Design [J]. Journal of American Statistical Association,1959, (54):622-654
[85]Hill W J, Hunter W G. A Review of Response Surface Methodology:Literaure Review [J]. Technometrics,1966,8:571-590
[86]Mead R, Pike D J. A Review of Response Surface Methodology from a Biometrics Viewpoint [J]. Biometrics,1975,31(12):803-851
[87]Myers R H, Khuri A I, Carter W H. Response Surface Methdology:1966-1988 [J]. Technometrics,1989,31(2):137-157
[88]Myers R H, Montgomery D C. Response Surface Methdology [M]. New York:Wiley & Sons,1995
[89]Myers R H. Response Surface Methodology-Current Status and Future Directions [J]. Journal of Quality Technology,1999,31(1):30-44
[90]Wujeff C F, Hamada M. Experiments Planning, Analysis, and Parameter Design Op-timization [J]. New York:John Wiley & Sons,1978
[91]Taguchi G. Introduction to Quality Engineering. White Plains [M]. New York: UNIPUB/Kraus International,1991
[92]Taguchi G. System of Experimental Design:Engineering Methods to Optimize Qual-ity and Minimise Cost. White Plains [M]. New York:UNIPUB/Kraus International, 1987
[93]Box G E P. Signal-to-Noise, Performance Criteria, and Transformations [J]. Techno-metrics,1988,30:1-17
[94]Miller A. Analysis of Parameter Design Experiments for Signal-Response Systems [J]. Journal of Quality Technology,2002,34(2):139-151
[95]Vining G, Myers R. Combining Taguchi and response surface philosophies-A dual response approach [J]. Journal of Quality Technology.1990,22(1):38-45
[96]Lind E E, Goldin J, Hickman J B. Fitting Yeild and Cost Rsponse Surface [J]. Chemi-cal Engineering Process,1960,56:62-68
[97]Ankenman B E, Bisgaard S. Standard Errors for the Eigenvalues in Second-Order Response Surface Models [J]. Thecnometrics,1996,38(2):238-246
[98]Derringer G C, Suich R. Simultaneous Optimization of Several Response Variables [J]. Journal of Quality Technology,1980,12(1):214-219
[99]Myers R H, Montgomery D C, Ving G G. Generalized Linear Models with Application in Engineering and the Sciences [M]. New York:John Wiley& Sons,2002
[100]Vining G G, Bohn L L. Response Surface for the Mean and Variance Using a Non-parametric Approach [J]. Journal of Quality Technology,1998,30(3):282-291
[101]何曙光,齐二石,何桢.神经网络在响应曲面分析中的应用[J].系统工程理论与实践,2001(12)：130-133
[102]黄小光,许金泉.基于ANN响应面法和Monte Carlo法的海洋平台可靠度分析[J].中国海洋平台,2010,(2)：45-49
[103]Jansson T, Nilsson L. Optimizing Sheet Metal Forming Processes Using a Design Hierarchy and Response Surface Methodology [J]. Journal of Materials Processing Technology,2006,178(1):218-233
[104]Macodiyo D, Soyama O, et al. Optimization of Cavitation Peening Parameters for Fatigue Performance of Carburized Steel Using Taguchi Methods [J]. Journal of Ma-terials Processing Technology,2006,178(1):234-240
[105]Beal V E, Erasenthiran P, Hopkinson N, et al. Optimisation of Processing Parameters in Laser Fused H13/Cu Materials Using Response Surface Method (RSM) [J]. Journal of Materials Processing Technology,2006,174(1-3):145-154
[106]Forsberg J, Nilsson L. Evaluation of Response Surface Methodologies Used in Crash-worthiness Optimization [J]. International Journal of Impact Engineering International Symposium on the Crashworthiness of Light-weight Automotive Structures,2006, 32(5):759-777
[107]Dong C J. Development of a Process Model for the Vacuum Assisted Resin Trans-fer Molding Simulation by the Response Surface Method [J]. Composites:Part A, Applied Science& Manufacturing,2006,37(9):1316-1324
[108]袁人炜,陈明,曲征洪.响应曲面法预测铣削力模型及影响因素的分析[J].上海交通大学学报,2001,(7)：1040-1044
[109]胡峪,李为吉.飞机多学科设计中的协同优化算法[J].西北工业大学学报,2001,(3)：357-360
[110]王海亮,林忠钦,金先龙.基于响应面模型的薄壁构件耐撞性优化设计[J].应用力学学报,2003,(3)：61-65
[111]张科施,李为吉,李响.飞机概念设计的多学科综合优化技术[J].西北工业大学学报,2005,(1)：102-106
[112]瞿伟廉,陈伟,李秋胜.基于神经网络技术的复杂框架结构节点损伤的两步诊断法[J].土木工程学报,2003,36(5)：3745
[113]Piggio T, Vetter T. Recognition and Structure from one 2D Model View:Obsevations on Prototypes, Ogject Classes, and Symmetries [R]. A. I. Memo No.1347. Artifical Intelligence Laboratory, Massachusetts Institute of Technology,1992
[114]于旭,杨静,谢志强.虚拟样本生成技术研究[J].计算机科学,2011,38(3)：16-19
[115]洪东跑,赵宇,温玉全.基于虚拟样本的火工品可靠性评估[J].爆炸与冲击,2009,29(6)：669-672
[116]Niyogi P, Girosi F, Poggio T. Incorporating Prior Information on Machine Learning by Creating Virtual Examples [C]. Proceedings of the IEEE.1998,86:2196-2209
[117]马林.六西格玛管理[M].北京：中国人民大学出版社,2004
[118]张德丰,周燕.详解Matlab在统计与工程数据分析中的应用[M].北京：电子工业出版社,2010
[119]Link M, Friswell M. Generation of Validated Structural Dynamic Models-result of a Benchmark Study Utilizing the GARTEUR SM-AG19 Test-bed [J]. Mechanical Sys-tems and Signal Processing.2003,17(1):9-20
[120]谢多夫.力学中的相似方法与量纲理论[M].北京：科学出版社,1982
[121]谈庆明.量纲分析[M].合肥：中国科学技术大学出版社,2005
[122]崔庆安,何桢,崔楠.基于SVM的RSM模型拟合方法研究[J].管理科学学报,2008,11(1)：31-41
[123]谭东宁,谭东汉.小样本机器学习理论：统计学习理论[J].南京理工大学学报,2001,(1)：108-112
[124]方瑞明,支持向量机理论及其应用分析[M].北京：中国电力出版社,2007
[125]谭锋奇,李洪奇,孟照旭等.数据挖掘方法在石油勘探开发中的应用研究[J],石油地球物理勘探,2010,45(1)：85-91
[126]Mitshell T M. Machine Learning [M], New York:McGraw-Hill Companies, Inc., 1997
[127]边肇祺,张学工.模式识别[M],北京：清华大学出版社,2000
[128]Vapnik V N. The Nature of Statistical Learning Theory (2nd Edit) [M]. Berlin: Springer,1999
[129]瓦普尼克.统计学习理论[M].北京：电子工业出版社,2009
[130]苏展,徐立霞.基于贝叶斯理论的支持向量机综述[J].计算机应用与软件,2010,(5)：179-181
[131]张学工译.统计学习理论的本质[M].北京：清华大学出版社,2000
[132]白鹏,张喜斌,张斌等.支持向量机理论及工程应用实例[M].西安：西安电子科技大学出版社,2008
[133]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1)：32-42
[134]邓乃扬,田英杰.数据挖掘中的新方法—支持向量机[M],北京：科学出版社,2004
[135]Cristianini N, Shawe-Taylor J. An Introduction to Support Vector Machines and Othr Kernel-based Learning Methods [M]. Cambridge:Cambridge University Press,2000
[136]Cherkassky V, Ma Y. Selection of Meta-parameters for Support Vector Regression [C]. Proceedings of International Conference on Artificial Neural Networks (ICANN), Madrid, Spain,2002
[137]Scholkopf B, Sung K K, Burges C J, et al. Comparing Support Vector Machine with Gaussian Kernels to Radial Basis Function Classifiers [J]. IEEE Transaction on Signal Processing,1997,45(11):2758-2765
[138]Chapelle O, Vapnik V, Bousquet O, et al. Choosing Multiple Parameters for Support Vector Machines [J]. Machine Learning,2002,46(1):131-159
[139]Cherkassky V, Ma Y. Comparision of Model Selection for Regression [J]. Neural Computation,2003,15(7):1691-1714
[140]Soares C, Brazdil P B, Kuba P. A Meta-learning Method to Select the Kernel Width in Support Vector Regression [J]. Machine Learning,2004,54(3):195-209
[141]Scholkopf B, Smola A, Bartlett P. New Support Vector Algorithms [J]. Neural Com-putation,2000, (12):1207-1245 Putation,20(X),12:1207-1245
[142]Mangasarian O L. Generalized Support Vector Machines [C]. In Smola A, Bartlett P, Scholkopf B, and Schuurmans D, editors, Advances in Large Margin Classifiers, MIT Press,2000:135-146
[143]Takuya I, Shigeo A. Fuzzy Support Vector Machines for Pattern Classification [C]. In Proceeding of Internatioanl Joint Conference on Neural Networks,2001, (2):1449-1454
[144]Lin C F, Wang S D. Fuzzy Support Vector Machines [J]. IEEE Transactions on Neural Networks,2002,13(2):464-471
[145]Suykens J A K, Vandewalle J. Least Squares Support Vector Machines Classifiers [J]. Neural Processing Letters,1999,9(3):293-300
[146]Chew H G, Crisp D, Bogner R E, et al. Target Detection in Radar Imagery Using Support Vector machines with Training Size Biasing [C]. In Proceedings of the 6th International Conference on Control, Automation, Robotics and Vision, Singapore, 2000
[147]Osuna E, Freund R, Girosi F. An Improved Training Algorithm for Support Vector Machines [C]. IEEE Workshop on Neural Networks and Signal Processing, Amelia Island,1997,276-285
[148]Joachims T. Making Large-scale Support Vector Machine Practical [C]. In Advances in Kernel Methods-Support Vector Learning, Cambridge, Massachusetts:The MIT Press,1999,169-184
[149]Platt J. Sequential minimal optimization:A fast algorithm for training support vector machines [J]. Advances in Kernel Methods-Support Vector Learning,1999,208:98-112
[150]Cauwenberghs G, Poggio T. Incremental and Decremental Support Vector Machine Learning [C]. In Advances in neural information processing systems, Cambridge, MA: The MIT Press,2001,13:426-433
[151]Amari S, Wu S. Improving Support Vector Machine Classifiers by Modifying Kernel Functions [J]. Neural Networks,1999, (12):783-789
[152]吴涛,贺汉根,贺明科.基于插值的核函数构造[J].计算机学报,2003,26(8)：990-996
[153]张莉,周伟达,焦李成.用于一维图像识别的支撑矢量机方法[J].红外与毫米波学报,2002,(2)：119-123
[154]胡丹,肖建,车畅.尺度核支持向量机及在动态系统辨识中的应用[J].西南交通大学学报,2006,(4)：460-465
[155]武方方,赵银亮.最小二乘Littlewood-Paley小波支持向量机[J].信息与控制,2005,34(5)：604-609
[156]Ustun B, Meissen W J, Buydens L M C. Facilitating the Application of Support Vector Regression by Using a Universal Pearson VII Function Based Kernel[J]. Chemomet-rics and Intelligent Laboratory Systems,2006,81(1):29-40
[157]Chapelle O, Vapnik V, Bousquet O. Choosing Multiple Parameters for Support Vector Machines [J]. Machine Learning,2002,46(1):131-159
[158]刘琼荪,范瑞雅.确定高斯核参数的聚类方法[J].计算机工程与应用,2011,(3)：38-40
[159]万家强,王越,刘羽.一种组合核支持向量机建模的方案[J].计算机工程与应用,2011,(19)：35-38
[160]冯汉中,陈永义,成永勤.双流机场低能见度天气预报方法研究[J].应用气象学报,2006,(1)：94-99
[161]胡中辉,李烨,蔡云泽.基于属性约简及支持向量机的医疗诊断决策研究[J].计算机工程与应用,2005,(13)：183-185
[162]王志明,谭显胜,周玮.基于支持向量回归的生物测定数据分析[J].昆虫学报,2010,(12)：1436-1441
[163]宗朝霞,汤宏胜,贺曼.基于遗传算法的支持向量机预测含能材料密度的研究[J].计算机与应用化学,2009,(12)：1529-1533
[164]马迎坤,张希农.多维传感器标定的支持向量机复合式方法[J].航空动力学报,2011,(6)：1274-1281
[165]王嗣平,沈海斌,严晓浪.一种可伸缩的支持向量机的硬件实现方法[J].浙江大学学报(理学版),2009,(3)：282-287
[166]刘亚娟,张晓芹.基于支持向量机的旋转机械故障诊断[J].计算机工程与设计,2005,(12)：3436-3438
[167]董泽,李鹏,王学厚.基于粗糙集和支持向量机的汽轮机组故障诊断[J].华北电力大学学报(自然科学版),2008,(2)：79-82
[168]刘德庆,唐贵基,张超.改进的支持向量机在旋转机械故障诊断中的应用[J].噪声与振动控制,2011,(1)：114-118
[169]王快妮,钟萍,赵耀红.鲁棒SVR 金融时间序列预测中的应用[J].计算机工程,2011,(15)：155-157
[170]Drezet P M L, Harrison R F. Support Vector Machines for System Identification [C]. UKACC International Conference on Control,1998, (1):688-692
[171]王群京,鲍晓华,倪有源.基于支持向量机和遗传算法的爪极发电机建模及参数优化[J].电工技术学报,2006,(4)：57-61
[172]赵吉文,刘永斌,孔凡让.基于SVM和遗传算法的新型直线电机结构参数优化[J].光学精密工程,2006,(5)：870-875
[173]Gretton A, Doucet A, Herbrich R. Support vector regression for black-box system identification [C]. Proceedings of the 11th IEEE Signal Processing Workshop on Sta-tistical Signal Processing,2001
[174]Suykens J A K. Vandewalle J, Moor B D. Optimal Control by Least Squares Support Vector Machines [J]. Neural Networks,2001, (14):23-35
[175]Salat R, Osowski S. Accurate fault location in the power transmission line using sup-port vector machine approach [J]. IEEE Transactions on Power Systems,2004,19(2): 979-986
[176]Rojo-Alvarez J L, Martinez-Ramon M, Prado-Cumplido M, et al. Support vector method for robust ARMA system identification [J]. IEEE Transactions on Signal Pro-cessing,2004,52(1):155-164
[177]Chang M W, Lin C J. Leave-one-out Bounds for Support Vector Regression Model Selection [J]. Neural Computation,2005,17(5):1188-1222
[178]MuUer K R, Mika S, Ratsch G, et al. An Introduction to Keraal-based Learning Algo-rithms [J]. IEEE Transactions of Neural Networks,2001,12(2):181-201
[179]谭冬梅,瞿伟廉,王锦文.基于小波包和支持向量机的结构有限元模型修正[J].华中科技大学学报(自然科学版),2009,(6)：104-107
[180]秦玉灵,孔宪仁,罗文波.多铺层碳纤维蜂窝板模型修正[J].航空学报,2011,(4)：636-648
[181]秦玉灵,孔宪仁,罗文波.基于响应面方法的碳纤维蜂窝板有限元模型修正[J].振动与冲击,2011,(7)：71-76
[182]邓苗毅,任伟新,王复明.基于静力响应面的结构有限元模型修正方法[J].实验力学,2008,(2)：103-109
[183]赵瑞安,吴方.非线性最优化理论和方法[M].杭州：浙江科学技术出版社,1992
[184]赵凤治,尉继英.约束最优化计算方法[M].北京：科学出版社,1991
[185]Evetitt B S. Cluster Analysis (3rd Edit) [M]. London:Edward Arnold,1993
[186]崔庆安.基于支持向量回归机的复杂过程响应曲面法研究[D].天津：天津大学博士论文,2006
[187]McKay M D, Beckman R J, Conover W J. A Comparison on Three Methods for Se-lecting Values of Input Variables in the Analysis of Output from a Computer Code [J]. Thecnometrics,1979,21(2):239-245
[188]方开泰.正交与均匀试验设计[M].北京：科学出版社,2001
[189]方开泰.均匀实验设计的理论、方法和应用—历史回顾[J].数理统计与管理,2004,23(3)：69-80
[190]中国水力发电工程学会电网调峰与抽水蓄能专业委员会组.抽水蓄能电站工程建设文集2011[C].北京：中国电力出版社,2011
[191]邱彬如,刘连希.抽水蓄能电站工程技术[M].北京：中国电力出版社,2008
[192]张克诚.抽水蓄能电站水能设计[M.北京：中国水利水电出版社,2007
[193]张春生,姜忠见.天荒坪抽水蓄能电站技术总结[C].北京：中国电力出版社,2007
[194]邱彬如.世界抽水蓄能电站新发展[M].北京：中国电力出版社,2006
[195]梅祖彦,赵士和.抽水蓄能电站百问[M].北京：中国电力出版社,2002
[196]中国抽水蓄能网.http://www.psp.org.cn[OL]
[197]马震岳,董毓新.水电站机组及厂房振动的研究与治理[M].北京：中国水利水电出版社,2004
[198]陈婧,马震岳,戚海峰等.宜兴抽水蓄能电站厂房结构水力振动反应分析[J].水力发电学报,2009,(5)：195-199
[199]刘玉斌,林恺.惠州抽水蓄能机组振动在线监测系统[J].水力发电,2010,(9)：76-78
[200]熊卫,史仁杰,毛文然.回龙抽水蓄能电站地下厂房整体结构振动研究[J].人民黄河,2004,(7)：40-41
[201]吴秋芳,戴跃华,陈晓铭.惠州抽水蓄能电站厂房结构振动分析与研究[J].广东水利水电,2008,(7)：49-53
[202]李俊.广州抽水蓄能电站球阀动水关闭振动原因分析[J].水力发电,1997,(10)：45-46
[203]魏炳漳.广蓄二期工程抽水蓄能机组的振动评估[J].水力发电,2001,(11)：48-51
[204]王俊红,黄勇.广蓄二期工程地下厂房结构振动研究及减振措施[J].水力发电,2001,(11)：30-34
[205]朱以文,蔡元奇,吴春秋,黄克戬.抽水蓄能电站厂房结构振动分析报告研究[R].武汉：武汉大学,2004.
[206]朱以文,蔡元奇,吴春秋,徐晗.桐柏抽水蓄能电站地下厂房动静力分析报告[R].武汉：武汉大学,2005
[207]朱以文,蔡元奇,徐晗,韩芳.泰安电站地下厂房动静力分析报告[R].武汉：武汉大学,2005
[208]朱以文,蔡元奇,徐晗,韩芳.琅琊山抽水蓄能电站地下厂房机组动力分析报告[R].武汉：武汉大学,2005
[209]朱以文,曾又林,蔡元奇,徐晗.江苏宜兴抽水蓄能电站地下厂房结构静动力分析[R].武汉：武汉大学,2005
[210]傅志方,华宏星.模态分析理论与应用[M].上海：上海交通大学出版社,2000
[211]Grandhi R. Structural optimization with frequency constraints-a review [J]. AIAA Journal.1993,31(12):22962303
[212]广州大学工程抗震研究中心.广州蓄能水电厂A厂振动测试分析报告[R].广州：广州大学,2010
[213]ANSYS Inc. http://www.ansys.com/[OL],2011
[214]丁毓峰.ANSYS12.0有限元分析完全手册[M],北京：电子工业出版社,2011
[215]王金龙.ANSYS 12.0土木工程应用实例解析[M],北京：机械工业出版社,2011
[2]王博,吕正勋,何伟.结构动力模型修正方法研究与进展[J].水利与建筑工程学报,2009,7(1)：16-19
[3]王春岩.结构有限元模型修正算法研究综述[J],黑龙江科技信息,2009,19：58
[4]李辉,丁桦.结构动力模型修正方法研究进展[J],力学进展,2005,(2)：170-180
[5]荣见华.结构动力修改及优化设计[M].北京：人民交通出版社,2003
[6]邓方林,廖守亿,孙新利.复杂工程系统建模与仿真[M].北京：国防工业出版社,2009
[7]黄欣荣.复杂性科学的方法论研究[M].重庆：重庆大学出版社,2006
[8]黄欣荣.复杂性科学与哲学[M].北京：中央编译出版社,2007
[9]吴彤.科学哲学视野中的客观复杂性[J].系统辩证学学报,2001,(4)：44-47
[10]隋允康,宇慧平.响应面方法的改进及其对工程优化的应用[M].北京：科学出版社,2011
[11]张哲,李生勇,石磊.结构可靠度分析中的改进响应面法及其应用[J].工程力学,2007,(8)：111-115
[12]朱跃,张令弥.结基于确定性计算响应面的复杂工程结构不确定性建模研究[J].计算力学学报,2011,(3)：412-416
[13]郭勤涛,张令弥,费庆国.用于确定性计算仿真的响应面法及其试验设计研究[J].航空学报,2006,(1)：55-61
[14]韩芳.复杂结构模型修正技术研究[D].武汉：武汉大学博士学位论文,2008
[15]王勖成.有限单元法[M].北京：清华大学出版社,2003
[16]Mottershead J E, Friswell M I. Model Updating in Structural Dynamics:a Survey [J]. Journal of Sound and Vibration,1993,167(2):347-375
[17]张之沧,科学技术哲学[M],南京：南京师范大学出版社,2009
[18]Goodwin G C, Payne R L. Dynamic System Identification:Experiment Design and Data Analysis [M], Academic Press, New York,1977
[19]Berman A. System Identification of Structural Dynamic Models Theoretical and Prac-tical Bounds [C], Structures, Structural Dynamics and Materials Conference,25th, Palm Springs, CA; United States; 14-16 May 1984. pp.123-129.1984
[20]Berman A. Nonunique Structural Identification [C], Proc. Of the 7th MAC,1989, 355-359
[21]Astrom K J, Wittenmark B. Adaptive Control [M],2nd ed, Addison Wesley,1995
[22]Berman A. Mass Matrix Correction from Incomplete Set of Measured Modes[J]. AIAA Journal,1979,17(10):1147-1148
[23]Wei F S. Stiffness Matrix Correction from Incomplete Test Data [J]. AIAA Journal, 1980,18(10):1274-1275
[24]Berman A, Wei F S, Rao V. Improvement of Analytical Dynamic Models Using Modal Test Data [C]. Proc. of the AIAA 21st SDM Conf.,1980,809-814
[25]Berman A, Wei F S. Automated Dynamic Analytical Model Improvement [R]. NASA CR-3452,1981
[26]Berman A, Nagy E J. Improvement of a Large Dynamic Analytical Model Using Ground Vibration Test Data [C]. Structures, Structural Dynamics and Materials Con-ference,23rd, New Orleans, LA; United States; 10-12 May 1982. pp.301-306.1982
[27]Baruch M. Optimal Corrrection of Mass and Stiffness Matrices Using Mearsured Modes [J]. AIAA Journal,1982,20(11):1623-1626
[28]Zhang D W, Zhang L. The Matrix Transform Method for Updating Dynamic Model [J]. AIAA Journal,1992,30(5):1440-1443
[29]Zhang Q, Lallement et al. A Complete Procedure for the Adjustment of a Mathemat-ical Model from the Identified Complex Modes [C]. Proc. of the 5th IMAC,1987, 1183-1189
[30]侯吉林,欧进萍.基于局部模态的约束子结构模型修正法[J].力学学报,2009,(5)：748-756
[31]Kabe A M. Stiffness Matrix Adjustment Using Mode Data [J]. AIAA Journal,1985, 23(9):1431-1436
[32]Zhang O, Zerva A, Zhang D W. Stiffness Matrix Adjustment Using Incomplete Mea-sured Modes [J]. AIAA Journal,1997,35(5):1431-1436
[33]张德文,魏阜旋.关于质量阵之元素修正法的改进[J].应用力学学报,1992,(1)：129-133
[34]郭杏林,高海洋.一种基于振型正交化的元素型模型修正方法[J].振动与冲击,2011,(6)：5-9
[35]张德文,魏阜旋,张欧.实用完备空间模态空间中的相容修正模型[J].振动工程学报,1989,2(4)：33-40
[36]张德文,魏阜旋.完备模态空间技术的短评和注记[J].振动与冲击,1991,(3)：14-19
[37]Gravitz S I. An Analytical Procedure for Orthogonalization of Experimentally Mea-sured Modes [J]. Journal of the Aero/Space Sciences,1958,25(11):721-722
[38]Rodden W P. A Method for Deriving Structural Influence Coefficients from Ground Vibration Tests [J]. AIAA Journal,1967,5(5):991-1000
[39]Mc-Grew J. Orthogonalization of Measured Modes and Calculation of Influence Co-efficients [J]. AIAA Journal,1969,7(4):774-776
[40]费庆国,韩晓林,苏鹤玲.响应面有限元模型修正的实现与应用[J].振动,测试与诊断,2010,(2)：132-134页
[41]费庆国,张令弥,李爱群等.基于统计分析技术的有限元模型修正研究[J].振动与冲击,2005,(3)：23-26
[42]Baruch M, Itzhack Y B. Optimal Weighted Orthogonalization of Measured Modes [J]. AIAA Journal,1978,16(4):346-351
[43]Berman A, Nagy E J. Improvement of a Large Dynamic Analytical Model Using Test Data [J]. AIAA Journal,1983,21(8):1168-1173
[44]Smith S W, Beattie C A. Secant-method Adjustment for Structural Models [J]. AIAA Journal,1991,29(1):119-126
[45]Janter T, Sas P. Uniqueness Aspect of Model-updating Procedures [J]. AIAA Journal, 1990,28(3):538-543
[46]Roy N A, Girard A, Bugeat L P, et al. A Survey of Finite Element Model Updating Methods [C]. Environmental Testing for Space Programmes Test:Facilities and Meth-ods, Proceedings of an International Symposium held in Noordwijk, The Netherlands, June 26-29 1990. Paris:European Space Agency (ESA),1990, (304):333-349
[47]Caesar B. Updating System Matrices Using Modal Test Data [C]. Proc.5th IMAC. 1987:453-459
[48]魏来生.结构有限元动态模型修正方法综述[J].振动与冲击,1998,17(3)：43-48
[49]Bugeat L, Fillod R, Lallemend G, et al. Adjustment of a Conservative Non Gyroscopic Mathematical from Measurement [J]. Shock & Vibration Bullstin,1978, Proc.48, pt.3: 71-81
[50]张德文,李应明.一种普遍性的元素型修正法—排列方程法[J].强度与环境,1989,(6)：9-15
[51]张德文,魏阜旋.关于质量阵之元素修正法的改进[J].应用力学学报,1992,(1)：129-133
[52]张德文,Wei S F,李应明.修正动力分析模型的最优元素型摄动法[J].振动工程学报,1988,(4)：97-105
[53]韩芳,钟冬望,汪君.基于径向基神经网络的有限元模型修正研究[J].武汉科技大学学报,2011,(2)：115-118
[54]鲁峰,黄金泉.基于遗传算法的航空发动机机载模型支持向量机修正方法[J].航空动力学报,2009,(4)：880-885
[55]华宏星,傅志方.模糊数学在有限元模型修正中的应用[J].振动工程学报,1997,(4)
[56]刘继承,周传荣.一个基于优化的有限元模型修正方法[J].振动与冲击,2003,22(2)：33-34
[57]王乐,杨智春,李斌等.基于固有频率向量的模型修正方法[J].西北工业大学学报,2008,26(1)：93-98
[58]杨智春,王乐,丁燕等.基于附加已知刚度的动力学模型修正方法[J].工程力学,2009,(5)：19-24
[59]朱凼凼,冯咬齐,宋海丰.一种基于加速度频响函数的动力学模型修正方法[J].固体力学学报,2005,26(3)：329-332
[60]朱凼凼,冯咬齐.应用位移频响函数进行模型修正[J].宇航学报,2006,(2)：201-204
[61]Xia Y, Lin R. A New Iterative Order Reduction (IOR) Method for Eigensolutions of Large Structures [J]. International Journal for Numerical Methods in Engineering, 2004, (59):153-172
[62]周睿,陈力奋.基于可测点信息的模型参数修正方法[J].振动与冲击,2007,26(6)：70-73
[63]张连振；黄侨；郑一峰.桥梁结构损伤识别理论的研究进展[J].哈尔滨工业大学学报,2005,(10)：1415-1418
[64]张坤,段忠东,刘洋.连续刚构桥动力特性参数识别与有限元模型修正[J].公路交通科技,2008,(9)：67-72
[65]张纯,宋固全,吴光宇.实测模态和结构模型同步修正的结构损伤识别方法[J].振动与冲击,2010,(9)：1-4
[66]卢菊洪,陈志平.基于有限元模型修正的损伤识别方法研究[J].机械设计,2010,(5)：25-27
[67]张保强,郭勤涛,陈国平.基基于复模态模型修正方法的磁悬浮轴承支承参数识别[J].南京航空航天大学学报,2010,(6)：748-752
[68]郭杏林,高海洋.一种基于振型正交化的元素型模型修正方法[J].振动与冲击,2011,(6)：5-9
[69]周传荣,Link M.修正结构有限元模型的一种方法[J].振动工程学报,1989,2(4)：70-75
[70]罗漳平,向锦武.结构动力学模型修正的一种参数型方法[J].北京航空航天大学学报,2004,(7)：648-651
[71]郭勤涛,张令弥,费庆国.结构动力学有限元模型修正的发展—模型确认[J].力学进展,2006,(1)：36-42
[72]Friswell M I, Mottershead J E. Model Updating in Structural Dynamics [M]. London: Kluwer Academic Publisher,1995
[73]Schedlinski C. Computational Model Updating of Large Scale Finite Element Models [C]. Proc. SPIE Vol.4062, Proceedings of IMAC-ⅩⅧ:A Conference on Structural Dynamics.2000,476-482
[74]Zhang Q W, Chang T Y P, Chang C C. Finite-Element Model Updating for the Kap Shui Mun Cable-Stayed Bridge [J]. Journal of Bridge Engineering,2001,6(4):285-293
[75]夏品奇, Brown J M W.斜拉桥有限元建模与模型修正[J].振动工程学报,2003,16(2)：220-223
[76]丁幼亮,李爱群,韩晓林.润扬大桥斜拉桥结构安全评估的有限元建模与修正[J].东南大学学报(自然科学版),2006,(1)：92-96
[77]程霄翔,费庆国,何顶顶等.基于响应面的大型输电塔结构有限元模型动力修正[J].振动与冲击,2011,(5)：116-122
[78]Weber B, Paultre P. Damage Identification in a Truss Tower by Regularized Model Updating [J]. Journal of Structural Engineering,2010,136(3):307-316
[79]王万中.试验的设计与分析[M].北京：高等教育出版社,2004
[80]蒙哥马利.试验的设计与分析[M].北京：人民邮电出版社,2009
[81]滕军,朱焰煌,卢云军.基于多输出支持向量回归机的有限元模型修正[J].振动与冲击,2010,(3)：9-12
[82]任丕顺.基于支持向量机的响应面模型及其工程应用[J].湖南农业大学学报(自然科学版),2009,(6)：702-704
[83]Box G E P, Wilson K B. On the Experimental Attainment of Optimum Conditions [J]. Journal of Ryal Statistical Society,1951, B(13):1-45
[84]Box G E P, Draper K B. A Basis for the Selection of a Response Surface Design [J]. Journal of American Statistical Association,1959, (54):622-654
[85]Hill W J, Hunter W G. A Review of Response Surface Methodology:Literaure Review [J]. Technometrics,1966,8:571-590
[86]Mead R, Pike D J. A Review of Response Surface Methodology from a Biometrics Viewpoint [J]. Biometrics,1975,31(12):803-851
[87]Myers R H, Khuri A I, Carter W H. Response Surface Methdology:1966-1988 [J]. Technometrics,1989,31(2):137-157
[88]Myers R H, Montgomery D C. Response Surface Methdology [M]. New York:Wiley & Sons,1995
[89]Myers R H. Response Surface Methodology-Current Status and Future Directions [J]. Journal of Quality Technology,1999,31(1):30-44
[90]Wujeff C F, Hamada M. Experiments Planning, Analysis, and Parameter Design Op-timization [J]. New York:John Wiley & Sons,1978
[91]Taguchi G. Introduction to Quality Engineering. White Plains [M]. New York: UNIPUB/Kraus International,1991
[92]Taguchi G. System of Experimental Design:Engineering Methods to Optimize Qual-ity and Minimise Cost. White Plains [M]. New York:UNIPUB/Kraus International, 1987
[93]Box G E P. Signal-to-Noise, Performance Criteria, and Transformations [J]. Techno-metrics,1988,30:1-17
[94]Miller A. Analysis of Parameter Design Experiments for Signal-Response Systems [J]. Journal of Quality Technology,2002,34(2):139-151
[95]Vining G, Myers R. Combining Taguchi and response surface philosophies-A dual response approach [J]. Journal of Quality Technology.1990,22(1):38-45
[96]Lind E E, Goldin J, Hickman J B. Fitting Yeild and Cost Rsponse Surface [J]. Chemi-cal Engineering Process,1960,56:62-68
[97]Ankenman B E, Bisgaard S. Standard Errors for the Eigenvalues in Second-Order Response Surface Models [J]. Thecnometrics,1996,38(2):238-246
[98]Derringer G C, Suich R. Simultaneous Optimization of Several Response Variables [J]. Journal of Quality Technology,1980,12(1):214-219
[99]Myers R H, Montgomery D C, Ving G G. Generalized Linear Models with Application in Engineering and the Sciences [M]. New York:John Wiley& Sons,2002
[100]Vining G G, Bohn L L. Response Surface for the Mean and Variance Using a Non-parametric Approach [J]. Journal of Quality Technology,1998,30(3):282-291
[101]何曙光,齐二石,何桢.神经网络在响应曲面分析中的应用[J].系统工程理论与实践,2001(12)：130-133
[102]黄小光,许金泉.基于ANN响应面法和Monte Carlo法的海洋平台可靠度分析[J].中国海洋平台,2010,(2)：45-49
[103]Jansson T, Nilsson L. Optimizing Sheet Metal Forming Processes Using a Design Hierarchy and Response Surface Methodology [J]. Journal of Materials Processing Technology,2006,178(1):218-233
[104]Macodiyo D, Soyama O, et al. Optimization of Cavitation Peening Parameters for Fatigue Performance of Carburized Steel Using Taguchi Methods [J]. Journal of Ma-terials Processing Technology,2006,178(1):234-240
[105]Beal V E, Erasenthiran P, Hopkinson N, et al. Optimisation of Processing Parameters in Laser Fused H13/Cu Materials Using Response Surface Method (RSM) [J]. Journal of Materials Processing Technology,2006,174(1-3):145-154
[106]Forsberg J, Nilsson L. Evaluation of Response Surface Methodologies Used in Crash-worthiness Optimization [J]. International Journal of Impact Engineering International Symposium on the Crashworthiness of Light-weight Automotive Structures,2006, 32(5):759-777
[107]Dong C J. Development of a Process Model for the Vacuum Assisted Resin Trans-fer Molding Simulation by the Response Surface Method [J]. Composites:Part A, Applied Science& Manufacturing,2006,37(9):1316-1324
[108]袁人炜,陈明,曲征洪.响应曲面法预测铣削力模型及影响因素的分析[J].上海交通大学学报,2001,(7)：1040-1044
[109]胡峪,李为吉.飞机多学科设计中的协同优化算法[J].西北工业大学学报,2001,(3)：357-360
[110]王海亮,林忠钦,金先龙.基于响应面模型的薄壁构件耐撞性优化设计[J].应用力学学报,2003,(3)：61-65
[111]张科施,李为吉,李响.飞机概念设计的多学科综合优化技术[J].西北工业大学学报,2005,(1)：102-106
[112]瞿伟廉,陈伟,李秋胜.基于神经网络技术的复杂框架结构节点损伤的两步诊断法[J].土木工程学报,2003,36(5)：3745
[113]Piggio T, Vetter T. Recognition and Structure from one 2D Model View:Obsevations on Prototypes, Ogject Classes, and Symmetries [R]. A. I. Memo No.1347. Artifical Intelligence Laboratory, Massachusetts Institute of Technology,1992
[114]于旭,杨静,谢志强.虚拟样本生成技术研究[J].计算机科学,2011,38(3)：16-19
[115]洪东跑,赵宇,温玉全.基于虚拟样本的火工品可靠性评估[J].爆炸与冲击,2009,29(6)：669-672
[116]Niyogi P, Girosi F, Poggio T. Incorporating Prior Information on Machine Learning by Creating Virtual Examples [C]. Proceedings of the IEEE.1998,86:2196-2209
[117]马林.六西格玛管理[M].北京：中国人民大学出版社,2004
[118]张德丰,周燕.详解Matlab在统计与工程数据分析中的应用[M].北京：电子工业出版社,2010
[119]Link M, Friswell M. Generation of Validated Structural Dynamic Models-result of a Benchmark Study Utilizing the GARTEUR SM-AG19 Test-bed [J]. Mechanical Sys-tems and Signal Processing.2003,17(1):9-20
[120]谢多夫.力学中的相似方法与量纲理论[M].北京：科学出版社,1982
[121]谈庆明.量纲分析[M].合肥：中国科学技术大学出版社,2005
[122]崔庆安,何桢,崔楠.基于SVM的RSM模型拟合方法研究[J].管理科学学报,2008,11(1)：31-41
[123]谭东宁,谭东汉.小样本机器学习理论：统计学习理论[J].南京理工大学学报,2001,(1)：108-112
[124]方瑞明,支持向量机理论及其应用分析[M].北京：中国电力出版社,2007
[125]谭锋奇,李洪奇,孟照旭等.数据挖掘方法在石油勘探开发中的应用研究[J],石油地球物理勘探,2010,45(1)：85-91
[126]Mitshell T M. Machine Learning [M], New York:McGraw-Hill Companies, Inc., 1997
[127]边肇祺,张学工.模式识别[M],北京：清华大学出版社,2000
[128]Vapnik V N. The Nature of Statistical Learning Theory (2nd Edit) [M]. Berlin: Springer,1999
[129]瓦普尼克.统计学习理论[M].北京：电子工业出版社,2009
[130]苏展,徐立霞.基于贝叶斯理论的支持向量机综述[J].计算机应用与软件,2010,(5)：179-181
[131]张学工译.统计学习理论的本质[M].北京：清华大学出版社,2000
[132]白鹏,张喜斌,张斌等.支持向量机理论及工程应用实例[M].西安：西安电子科技大学出版社,2008
[133]张学工.关于统计学习理论与支持向量机[J].自动化学报,2000,26(1)：32-42
[134]邓乃扬,田英杰.数据挖掘中的新方法—支持向量机[M],北京：科学出版社,2004
[135]Cristianini N, Shawe-Taylor J. An Introduction to Support Vector Machines and Othr Kernel-based Learning Methods [M]. Cambridge:Cambridge University Press,2000
[136]Cherkassky V, Ma Y. Selection of Meta-parameters for Support Vector Regression [C]. Proceedings of International Conference on Artificial Neural Networks (ICANN), Madrid, Spain,2002
[137]Scholkopf B, Sung K K, Burges C J, et al. Comparing Support Vector Machine with Gaussian Kernels to Radial Basis Function Classifiers [J]. IEEE Transaction on Signal Processing,1997,45(11):2758-2765
[138]Chapelle O, Vapnik V, Bousquet O, et al. Choosing Multiple Parameters for Support Vector Machines [J]. Machine Learning,2002,46(1):131-159
[139]Cherkassky V, Ma Y. Comparision of Model Selection for Regression [J]. Neural Computation,2003,15(7):1691-1714
[140]Soares C, Brazdil P B, Kuba P. A Meta-learning Method to Select the Kernel Width in Support Vector Regression [J]. Machine Learning,2004,54(3):195-209
[141]Scholkopf B, Smola A, Bartlett P. New Support Vector Algorithms [J]. Neural Com-putation,2000, (12):1207-1245 Putation,20(X),12:1207-1245
[142]Mangasarian O L. Generalized Support Vector Machines [C]. In Smola A, Bartlett P, Scholkopf B, and Schuurmans D, editors, Advances in Large Margin Classifiers, MIT Press,2000:135-146
[143]Takuya I, Shigeo A. Fuzzy Support Vector Machines for Pattern Classification [C]. In Proceeding of Internatioanl Joint Conference on Neural Networks,2001, (2):1449-1454
[144]Lin C F, Wang S D. Fuzzy Support Vector Machines [J]. IEEE Transactions on Neural Networks,2002,13(2):464-471
[145]Suykens J A K, Vandewalle J. Least Squares Support Vector Machines Classifiers [J]. Neural Processing Letters,1999,9(3):293-300
[146]Chew H G, Crisp D, Bogner R E, et al. Target Detection in Radar Imagery Using Support Vector machines with Training Size Biasing [C]. In Proceedings of the 6th International Conference on Control, Automation, Robotics and Vision, Singapore, 2000
[147]Osuna E, Freund R, Girosi F. An Improved Training Algorithm for Support Vector Machines [C]. IEEE Workshop on Neural Networks and Signal Processing, Amelia Island,1997,276-285
[148]Joachims T. Making Large-scale Support Vector Machine Practical [C]. In Advances in Kernel Methods-Support Vector Learning, Cambridge, Massachusetts:The MIT Press,1999,169-184
[149]Platt J. Sequential minimal optimization:A fast algorithm for training support vector machines [J]. Advances in Kernel Methods-Support Vector Learning,1999,208:98-112
[150]Cauwenberghs G, Poggio T. Incremental and Decremental Support Vector Machine Learning [C]. In Advances in neural information processing systems, Cambridge, MA: The MIT Press,2001,13:426-433
[151]Amari S, Wu S. Improving Support Vector Machine Classifiers by Modifying Kernel Functions [J]. Neural Networks,1999, (12):783-789
[152]吴涛,贺汉根,贺明科.基于插值的核函数构造[J].计算机学报,2003,26(8)：990-996
[153]张莉,周伟达,焦李成.用于一维图像识别的支撑矢量机方法[J].红外与毫米波学报,2002,(2)：119-123
[154]胡丹,肖建,车畅.尺度核支持向量机及在动态系统辨识中的应用[J].西南交通大学学报,2006,(4)：460-465
[155]武方方,赵银亮.最小二乘Littlewood-Paley小波支持向量机[J].信息与控制,2005,34(5)：604-609
[156]Ustun B, Meissen W J, Buydens L M C. Facilitating the Application of Support Vector Regression by Using a Universal Pearson VII Function Based Kernel[J]. Chemomet-rics and Intelligent Laboratory Systems,2006,81(1):29-40
[157]Chapelle O, Vapnik V, Bousquet O. Choosing Multiple Parameters for Support Vector Machines [J]. Machine Learning,2002,46(1):131-159
[158]刘琼荪,范瑞雅.确定高斯核参数的聚类方法[J].计算机工程与应用,2011,(3)：38-40
[159]万家强,王越,刘羽.一种组合核支持向量机建模的方案[J].计算机工程与应用,2011,(19)：35-38
[160]冯汉中,陈永义,成永勤.双流机场低能见度天气预报方法研究[J].应用气象学报,2006,(1)：94-99
[161]胡中辉,李烨,蔡云泽.基于属性约简及支持向量机的医疗诊断决策研究[J].计算机工程与应用,2005,(13)：183-185
[162]王志明,谭显胜,周玮.基于支持向量回归的生物测定数据分析[J].昆虫学报,2010,(12)：1436-1441
[163]宗朝霞,汤宏胜,贺曼.基于遗传算法的支持向量机预测含能材料密度的研究[J].计算机与应用化学,2009,(12)：1529-1533
[164]马迎坤,张希农.多维传感器标定的支持向量机复合式方法[J].航空动力学报,2011,(6)：1274-1281
[165]王嗣平,沈海斌,严晓浪.一种可伸缩的支持向量机的硬件实现方法[J].浙江大学学报(理学版),2009,(3)：282-287
[166]刘亚娟,张晓芹.基于支持向量机的旋转机械故障诊断[J].计算机工程与设计,2005,(12)：3436-3438
[167]董泽,李鹏,王学厚.基于粗糙集和支持向量机的汽轮机组故障诊断[J].华北电力大学学报(自然科学版),2008,(2)：79-82
[168]刘德庆,唐贵基,张超.改进的支持向量机在旋转机械故障诊断中的应用[J].噪声与振动控制,2011,(1)：114-118
[169]王快妮,钟萍,赵耀红.鲁棒SVR 金融时间序列预测中的应用[J].计算机工程,2011,(15)：155-157
[170]Drezet P M L, Harrison R F. Support Vector Machines for System Identification [C]. UKACC International Conference on Control,1998, (1):688-692
[171]王群京,鲍晓华,倪有源.基于支持向量机和遗传算法的爪极发电机建模及参数优化[J].电工技术学报,2006,(4)：57-61
[172]赵吉文,刘永斌,孔凡让.基于SVM和遗传算法的新型直线电机结构参数优化[J].光学精密工程,2006,(5)：870-875
[173]Gretton A, Doucet A, Herbrich R. Support vector regression for black-box system identification [C]. Proceedings of the 11th IEEE Signal Processing Workshop on Sta-tistical Signal Processing,2001
[174]Suykens J A K. Vandewalle J, Moor B D. Optimal Control by Least Squares Support Vector Machines [J]. Neural Networks,2001, (14):23-35
[175]Salat R, Osowski S. Accurate fault location in the power transmission line using sup-port vector machine approach [J]. IEEE Transactions on Power Systems,2004,19(2): 979-986
[176]Rojo-Alvarez J L, Martinez-Ramon M, Prado-Cumplido M, et al. Support vector method for robust ARMA system identification [J]. IEEE Transactions on Signal Pro-cessing,2004,52(1):155-164
[177]Chang M W, Lin C J. Leave-one-out Bounds for Support Vector Regression Model Selection [J]. Neural Computation,2005,17(5):1188-1222
[178]MuUer K R, Mika S, Ratsch G, et al. An Introduction to Keraal-based Learning Algo-rithms [J]. IEEE Transactions of Neural Networks,2001,12(2):181-201
[179]谭冬梅,瞿伟廉,王锦文.基于小波包和支持向量机的结构有限元模型修正[J].华中科技大学学报(自然科学版),2009,(6)：104-107
[180]秦玉灵,孔宪仁,罗文波.多铺层碳纤维蜂窝板模型修正[J].航空学报,2011,(4)：636-648
[181]秦玉灵,孔宪仁,罗文波.基于响应面方法的碳纤维蜂窝板有限元模型修正[J].振动与冲击,2011,(7)：71-76
[182]邓苗毅,任伟新,王复明.基于静力响应面的结构有限元模型修正方法[J].实验力学,2008,(2)：103-109
[183]赵瑞安,吴方.非线性最优化理论和方法[M].杭州：浙江科学技术出版社,1992
[184]赵凤治,尉继英.约束最优化计算方法[M].北京：科学出版社,1991
[185]Evetitt B S. Cluster Analysis (3rd Edit) [M]. London:Edward Arnold,1993
[186]崔庆安.基于支持向量回归机的复杂过程响应曲面法研究[D].天津：天津大学博士论文,2006
[187]McKay M D, Beckman R J, Conover W J. A Comparison on Three Methods for Se-lecting Values of Input Variables in the Analysis of Output from a Computer Code [J]. Thecnometrics,1979,21(2):239-245
[188]方开泰.正交与均匀试验设计[M].北京：科学出版社,2001
[189]方开泰.均匀实验设计的理论、方法和应用—历史回顾[J].数理统计与管理,2004,23(3)：69-80
[190]中国水力发电工程学会电网调峰与抽水蓄能专业委员会组.抽水蓄能电站工程建设文集2011[C].北京：中国电力出版社,2011
[191]邱彬如,刘连希.抽水蓄能电站工程技术[M].北京：中国电力出版社,2008
[192]张克诚.抽水蓄能电站水能设计[M.北京：中国水利水电出版社,2007
[193]张春生,姜忠见.天荒坪抽水蓄能电站技术总结[C].北京：中国电力出版社,2007
[194]邱彬如.世界抽水蓄能电站新发展[M].北京：中国电力出版社,2006
[195]梅祖彦,赵士和.抽水蓄能电站百问[M].北京：中国电力出版社,2002
[196]中国抽水蓄能网.http://www.psp.org.cn[OL]
[197]马震岳,董毓新.水电站机组及厂房振动的研究与治理[M].北京：中国水利水电出版社,2004
[198]陈婧,马震岳,戚海峰等.宜兴抽水蓄能电站厂房结构水力振动反应分析[J].水力发电学报,2009,(5)：195-199
[199]刘玉斌,林恺.惠州抽水蓄能机组振动在线监测系统[J].水力发电,2010,(9)：76-78
[200]熊卫,史仁杰,毛文然.回龙抽水蓄能电站地下厂房整体结构振动研究[J].人民黄河,2004,(7)：40-41
[201]吴秋芳,戴跃华,陈晓铭.惠州抽水蓄能电站厂房结构振动分析与研究[J].广东水利水电,2008,(7)：49-53
[202]李俊.广州抽水蓄能电站球阀动水关闭振动原因分析[J].水力发电,1997,(10)：45-46
[203]魏炳漳.广蓄二期工程抽水蓄能机组的振动评估[J].水力发电,2001,(11)：48-51
[204]王俊红,黄勇.广蓄二期工程地下厂房结构振动研究及减振措施[J].水力发电,2001,(11)：30-34
[205]朱以文,蔡元奇,吴春秋,黄克戬.抽水蓄能电站厂房结构振动分析报告研究[R].武汉：武汉大学,2004.
[206]朱以文,蔡元奇,吴春秋,徐晗.桐柏抽水蓄能电站地下厂房动静力分析报告[R].武汉：武汉大学,2005
[207]朱以文,蔡元奇,徐晗,韩芳.泰安电站地下厂房动静力分析报告[R].武汉：武汉大学,2005
[208]朱以文,蔡元奇,徐晗,韩芳.琅琊山抽水蓄能电站地下厂房机组动力分析报告[R].武汉：武汉大学,2005
[209]朱以文,曾又林,蔡元奇,徐晗.江苏宜兴抽水蓄能电站地下厂房结构静动力分析[R].武汉：武汉大学,2005
[210]傅志方,华宏星.模态分析理论与应用[M].上海：上海交通大学出版社,2000
[211]Grandhi R. Structural optimization with frequency constraints-a review [J]. AIAA Journal.1993,31(12):22962303
[212]广州大学工程抗震研究中心.广州蓄能水电厂A厂振动测试分析报告[R].广州：广州大学,2010
[213]ANSYS Inc. http://www.ansys.com/[OL],2011
[214]丁毓峰.ANSYS12.0有限元分析完全手册[M],北京：电子工业出版社,2011
[215]王金龙.ANSYS 12.0土木工程应用实例解析[M],北京：机械工业出版社,2011