频域模态参数识别研究及其软件实现
|
摘要
本文的主要内容包括频域内确定性及不确定性MIMO模态参数识别方法,环境激励下的模态参数识别方法,模态参数不确定性的计算以及算法的软件实现。
在确定性框架中,深入研究了基于频响函数右矩阵分式模型的模态参数识别方法,对s域、Z域中正交基函数的识别能力进行了比较,在Z域中研究了算法的快速实现。给出一种基于频响函数左矩阵分式模型的模态参数识别方法。
针对有限测量数据情况下频响函数不易准确估计的问题,研究了直接使用输入、输出数据DFT谱(IO谱)的模态参数识别方法。根据频响函数所采用参数模型,分别实现了基于公分母模型与基于左矩阵分式模型的两种识别方法。采用GARTEUR仿真算例对两种方法进行了验证,结果表明左矩阵分式模型识别方法要明显优于公分母模型识别方法,尤其是密集模态的识别。在不确定性框架中,实现了基于极大似然估计的模态参数识别方法。该方法采用离散时间域中频响函数右矩阵分式模型,使用噪声的协方差矩阵作为加权信息。在最小二乘估计的基础上,通过对极大似然函数进行迭代优化,得到精度更高的模态参数识别结果。根据Cramer-Rao下界不等式,在增加少量计算的情况下获得识别结果的统计信息,增加了模态参数识别的可靠性。采用GARTEUR仿真算例与汽车车架实测算例对算法进行了验证。
在模态参数识别中,测量噪声的干扰导致识别结果中存在不确定性,这种不确定性可以由模态参数的方差进行描述。通过对测量频响函数与模态参数之间进行一阶灵敏度分析,给出了CMIF、FDPR、polyLSCF这三种频域识别方法中模态参数方差的估计方法。Monte Carlo模拟结果表明:在噪声不高的情况下,一阶灵敏度分析已经具有较高的精度。
以半功率谱密度为基础,研究了环境激励下的模态参数识别。根据半功率谱密度与频响函数之间的相似数学表达式,因此将EMA方法用于环境激励下的模态参数识别。讨论了正时延相关函数点数、指数窗、响应信号长度对识别结果的影响。给出了工程应用中多组测量数据的处理方法。针对结构状态监测中对自动模态识别技术的需求,提出了一种基于模糊聚类的稳定图自动分析方法,实现了结构模态的自动选取。
在Visual C++平台下,实现了模态参数识别软件N-Broband。该软件以宽频带模态参数识别为特色,适用于EMA与OMA情况,并且能够与有限元软件分析结果进行相关分析。通过振动台夹具的模态试验对软件进行了一个完整应用。
The research in this dissertation is focused on frequency-domain modal parameters identification method for MIMO in deterministic and stochastic framework, operational modal analysis, uncertainty calculation of model parameters and software implementation of algorithm. The main work and conclusions include as follows.
Modal parameter identification method based on right matrix fraction description model is studied deeply in deterministic framework. The performance of orthogonal functions is compared in s and Z domain. Fast implementation methods are investigated in Z domain. A modal parameter identification method based on left matrix fraction description of FRF is proposed.
Owing to the fact that FRF cannot be estimated exactly when only a limited test data is available, a modal parameters identification method starting directly from IO spectra is studied. Two algorithms based on common denominator and left matrix fraction description are presented according to parametric model of FRF. A simulation case of GARTEUR model is employed to validate the algorithm. The results show that the algorithm based on left matrix fraction description can get better identification, especially for closely spaced mode.
A frequency-domain modal parameters identification method based on maximum likelihood estimation is investigated in stochastic framework. This method uses right matrix fraction description model of FRF in discrete time domain. The noise covariance matrix is adopted as weighting function. First, the least square estimation is implemented to get the initial value of modal parameters. Then, the iterative optimization of Newton-Gauss algorithm is carried out to get more precise identification result. According to the Cramer-Rao lower bounder inequality, statistical information of the modal parameters is obtained with increasing a little calculation. A simulation case of a GARTEUR model and an application case of an automobile chassis are employed to validate the method.
Due to the measurement noise, the uncertainty of model parameters is inevitable. The uncertainty can be described by using the variance of model parameters. For CMIF, FDPR and polyLSCF, the variance estimation procedure is proposed by first-order sensitivity analysis of the modal parameters to the perturbations of measured FRF. The Monte Carlo results show that first-order sensitivity analysis can reach to high accuracy under small noise.
Modal parameters identification approach based on positive power spectral density is studied for ambient excitation. According to the same expression between positive power spectral density and FRF, EMA algorithms can be applicable for ambient excitation. The positive time lag points, exponential window and response date length which have influence on the identification results are discussed. Processing methods for multi-setup measurement data are presents for engineering application. Focusing on the requirement of automatic modal analysis in condition monitoring, a method based on fuzzy clustering is proposed for the analysis of stabilization diagram. Automatic modal analysis is achieved by selecting the clusters grouped by physical poles.
A modal parameter identification software named as N-Broband is developed in VC++ platform. The software is suitable for EMA and OMA with broband identification feature. Correlation analysis between experiment and FEA can be performed in N-Broband. An application case of vibration table is carried by N-Broband.
在确定性框架中,深入研究了基于频响函数右矩阵分式模型的模态参数识别方法,对s域、Z域中正交基函数的识别能力进行了比较,在Z域中研究了算法的快速实现。给出一种基于频响函数左矩阵分式模型的模态参数识别方法。
针对有限测量数据情况下频响函数不易准确估计的问题,研究了直接使用输入、输出数据DFT谱(IO谱)的模态参数识别方法。根据频响函数所采用参数模型,分别实现了基于公分母模型与基于左矩阵分式模型的两种识别方法。采用GARTEUR仿真算例对两种方法进行了验证,结果表明左矩阵分式模型识别方法要明显优于公分母模型识别方法,尤其是密集模态的识别。在不确定性框架中,实现了基于极大似然估计的模态参数识别方法。该方法采用离散时间域中频响函数右矩阵分式模型,使用噪声的协方差矩阵作为加权信息。在最小二乘估计的基础上,通过对极大似然函数进行迭代优化,得到精度更高的模态参数识别结果。根据Cramer-Rao下界不等式,在增加少量计算的情况下获得识别结果的统计信息,增加了模态参数识别的可靠性。采用GARTEUR仿真算例与汽车车架实测算例对算法进行了验证。
在模态参数识别中,测量噪声的干扰导致识别结果中存在不确定性,这种不确定性可以由模态参数的方差进行描述。通过对测量频响函数与模态参数之间进行一阶灵敏度分析,给出了CMIF、FDPR、polyLSCF这三种频域识别方法中模态参数方差的估计方法。Monte Carlo模拟结果表明:在噪声不高的情况下,一阶灵敏度分析已经具有较高的精度。
以半功率谱密度为基础,研究了环境激励下的模态参数识别。根据半功率谱密度与频响函数之间的相似数学表达式,因此将EMA方法用于环境激励下的模态参数识别。讨论了正时延相关函数点数、指数窗、响应信号长度对识别结果的影响。给出了工程应用中多组测量数据的处理方法。针对结构状态监测中对自动模态识别技术的需求,提出了一种基于模糊聚类的稳定图自动分析方法,实现了结构模态的自动选取。
在Visual C++平台下,实现了模态参数识别软件N-Broband。该软件以宽频带模态参数识别为特色,适用于EMA与OMA情况,并且能够与有限元软件分析结果进行相关分析。通过振动台夹具的模态试验对软件进行了一个完整应用。
The research in this dissertation is focused on frequency-domain modal parameters identification method for MIMO in deterministic and stochastic framework, operational modal analysis, uncertainty calculation of model parameters and software implementation of algorithm. The main work and conclusions include as follows.
Modal parameter identification method based on right matrix fraction description model is studied deeply in deterministic framework. The performance of orthogonal functions is compared in s and Z domain. Fast implementation methods are investigated in Z domain. A modal parameter identification method based on left matrix fraction description of FRF is proposed.
Owing to the fact that FRF cannot be estimated exactly when only a limited test data is available, a modal parameters identification method starting directly from IO spectra is studied. Two algorithms based on common denominator and left matrix fraction description are presented according to parametric model of FRF. A simulation case of GARTEUR model is employed to validate the algorithm. The results show that the algorithm based on left matrix fraction description can get better identification, especially for closely spaced mode.
A frequency-domain modal parameters identification method based on maximum likelihood estimation is investigated in stochastic framework. This method uses right matrix fraction description model of FRF in discrete time domain. The noise covariance matrix is adopted as weighting function. First, the least square estimation is implemented to get the initial value of modal parameters. Then, the iterative optimization of Newton-Gauss algorithm is carried out to get more precise identification result. According to the Cramer-Rao lower bounder inequality, statistical information of the modal parameters is obtained with increasing a little calculation. A simulation case of a GARTEUR model and an application case of an automobile chassis are employed to validate the method.
Due to the measurement noise, the uncertainty of model parameters is inevitable. The uncertainty can be described by using the variance of model parameters. For CMIF, FDPR and polyLSCF, the variance estimation procedure is proposed by first-order sensitivity analysis of the modal parameters to the perturbations of measured FRF. The Monte Carlo results show that first-order sensitivity analysis can reach to high accuracy under small noise.
Modal parameters identification approach based on positive power spectral density is studied for ambient excitation. According to the same expression between positive power spectral density and FRF, EMA algorithms can be applicable for ambient excitation. The positive time lag points, exponential window and response date length which have influence on the identification results are discussed. Processing methods for multi-setup measurement data are presents for engineering application. Focusing on the requirement of automatic modal analysis in condition monitoring, a method based on fuzzy clustering is proposed for the analysis of stabilization diagram. Automatic modal analysis is achieved by selecting the clusters grouped by physical poles.
A modal parameter identification software named as N-Broband is developed in VC++ platform. The software is suitable for EMA and OMA with broband identification feature. Correlation analysis between experiment and FEA can be performed in N-Broband. An application case of vibration table is carried by N-Broband.
引文
[1]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,2002
[2]沃德·海伦,斯蒂芬·拉门兹,波尔·萨斯著.模态分析理论与实验[M].白化同,郭继忠,译.北京理工大学出版社, 2001
[3]曹树谦等.振动结构模态分析理论、实验与应用[M] .天津:天津大学出版社,2001
[4] Vold H, Kundrat J, Rocklin G. T, et al. A Multi-input Modal Estimation Algorithm for Mini-Computers[J], 1982, 91: 815~821
[5] Juang J N. and Pappa R. S, An Eigensystem Realization Algorithm (ERA) for Modal Parameter Identification and Model Reduction, Journal of Guidance[J], Control and Dynamics, 1985, 8(5):620~627
[6] Zhang L M. On the Two-Stage Time Domain Modal Identification[C]// Proc of the 21th International Modal Analysis Conference. Kissimmee, USA, February 2003.
[7] Moor B D , Vandewalle J, A Geometrical Strategy for the Identification of State Space Models of Linear Multivariable Systems with Singular Value Decomposition[C]//. Proc. of the 3rd International Symposium on Applications of Multivariable System Techniques,1987
[8] Verhaegen M, Westwick D. Identifying MIMO Hammerstein Systems in the Context of Subspace Model Identification Methods[J]. International Journal of Control, 1996, 63(2):331-349
[9] Overschee P V, Moor B D. N4SID-Subspace Algorithms for the Identification of Combined Deterministic-Stochastic Systems[J]. Automatica, 1994, 30(1):75-94
[10] Levy E C. Complex Curve Fitting[J]. IEEE Transaction on Automatic Control, 1959, 4(1):37-44
[11] Richardson M H, Formenti D L. Parameter Estimation from Frequency Response Measurements using Rational Fraction Polynomials[C] //Proceedings of the 1st International Modal Analysis Conference, Orlando. 1982:167-181.
[12] Richardson M H. Global Frequency & Damping Estimates from Frequency Response Measurements[C] //Proceedings of the 4td International Modal Analysis Conference, 1986
[13] van der Auweraer H, Leuridan J. Multiple Input Orthogonal Polynomial Parameter Estimation[J]. Mechanical Systems and Signal Processing, 1987, 1(3):259-27
[14] Shih C Y, Tsuei Y G, Allemang R J ,et al. A Frequency Domain Global Parameter Estimation Method for Multiple Reference Frequency Response Measurements[J]. Mechanical System and Signal Processing, 1988,2(4): 349-365
[15] Shih C Y, Tsuei Y G. Complex Mode Indication Function and its Applications to SpatialDomain Parameter Estimation[C]// Proceedings of the 7th International Modal Analysis Conference, 1989
[16] Zhang L M, Kanda H. Some Applications of Frequency Domain poly-Reference Modal Parameter Identification[C]//Proc of the 4th International Modal Analysis Conference, Los Angeles, USA, 1986:1237-1245
[17] Lembregts F, Leuridan J, van Brussel H. Frequency domain direct parameter identification for modal analysis: State space formulation[J].Mechanical Systems and Signal Processing, 1990,4(1): 65-75.
[18] Rolain Y, Pintelon R, Xu K Q, et al. On the Use of Orthogonal Polynomials In High Order Frequency Domain System Identification and Its Application to Modal Parameter Estimation.[C]//Proceedings of the 33rd IEEE Conference on Decision and Control,1994
[19] Rolain Y, Pintelon R, Xu K Q, et al. Best Conditioned Parametric Identification of Transfer Function Models in the Frequency Fomain[J]. IEEE Transactions on Automatic Control, 1995, 40 (11): 1954-1960
[20]杜永昌,管迪.多输入多输出频域模态识别算法的探讨[J].清华大学学报,1997,37(11):61-64
[21]陈怀海,许峰,彭江水.用幂基多项式拟合频响函数的几点技巧[J].振动工程学报, 2001,14(1),122-124
[22]焦群英,陈奎孚.整体正交多项式法识别模态参数的改进[J].中国农业大学学报, 2003, 8(2): 1-6.
[23]胡彦超,陈章位.实验模态分析中一种改进的傅氏域离散正交多项式.振动工程学报.2008,21(1):43-47
[24] Chen K F, Wang J L. Generating Complex Orthogonal Polynomials. Integral Transforms and Special Functions.2008,19(1):59-64
[25] Chen K F, Jiao Q Y, Shen Y H. On the Frequency Mapping of Modal Parameters Identification[J]. Mechanical Systems and Signal Processing, 2007, 21(4): 1665-1673
[26] Tang W, Shi Z K, Chen J. Aircraft Flutter Modal Parameter Identification Using a Numerically Robust Least-Squares Estimator in Frequency Domain[J]. Chinese Journal of Aeronautics, 2008, 21(6): 550-558
[27] Guillaume P, Verboven P, Vanlanduit S. Frequency-Domain Maximum Likelihood Identification of Modal Parameters with Confidence Intervals[C]// Proceeding of ISMA 23, 1998
[28] Van der Auweraer H Verboven P, Verboven P. Application of a Fast-Stabilizing Frequency Domain Parameter Estimation Method [J]. Journal of Dynamic System, Measurement, and Control, 2001,123(4):651-659
[29] Auweraer H V, Peeters B. Discriminating Physical Poles from Mathematical Poles in HighOrder Systems: Use and Automation of the Stabilization Diagram [C]// Instrumentation and Measurement Technology Conference. Italy, May 2004. 2193 -2198
[30] Verboven P, Guillaume P, Cauberghe B, et al. Modal Parameter Estimation and Monitoring for On-line Flight Flutter Analysis[J]. Mechanical Systems and Signal Processing,2004,18: 587–610
[31] Verboven P, Cauberghe B, Parloo E. User-assisting Tools for a Fast Frequency-Domain Modal Parameter Estimation Method[J]. Mechanical Systems and Signal Processing, 2004,18: 759–780
[32] Verboven P, Cauberghe B, Guillaume P. Improved Total Least Squares Estimators for Modal Analysis[J]. Computers and Structures,2005, 83: 2077–2085
[33] Alessandro Fasana. Modal Parameters Estimation in the Z-domain[J]. Mechanical Systems and Signal Processing, 2009, 23(1):217-225
[34] Guillaume P, Verboven P, Vanlanduit S, et al. A Poly-Reference Implementation of the Least-Squares Complex Frequency Domain Estimator [C]// Proc of the 21th International Modal Analysis Conference. Kissimmee, USA, February 2003
[35] Cauberghe B. Applied Frequency-Domain System Identification In the Field of Experimental and Operational Modal Analysis[D]. Belgium: Vrije Universiteit Brussel, 2004
[36] Peeters B, Van der Auweraer H, Guillaume P, et al. The PolyMAX frequency-domain method: a new standard for modal parameter estimation [J]. Shock and Vibration, 2004, 11: 395-409
[37] Peeters B, Guillaume P. Automotive and Aerospace Applictions of the LMS PolyMAX Modal Parameter Estimation Method[C]// Proc of the 22th International Modal Analysis Conference, Dearborn, USA, January 2004.
[38]易伟建,周云.基于高阶局部模态的弹性地基上框架结构物理参数识别研究[J].地震工程与工程振动, 2007,27(1):414-423
[39]周云,易伟建.用PolyMAX方法进行弹性地基板的实验模态分析[J].振动与冲击,2007,26(7):139-144
[40] McKelvey T, Akcay H, Ljung L. Subspace-based Multivariable System Identification from Frequency Response Data[J]. IEEE Transactions on Automatic Control, 1996,41(7):960-979
[41] Overschee P V, Moor B D. Continuous-Time Frequency Domain Subspace System Identification, Signal Processing[J], 1996,52(2):179-194
[42] Overschee P V, Moor B D, Dehandschutter W. A Subspace Algorithm For the Identification of Discrete Time Frequency Domain Power Spectra[J]. Automatica,1997,33(12): 2147-2157
[43] McKelvey T. Frequency Domain Identification Methods[J]. Circuits Systems Signal, Processing, 2002, 21(1): 39–55.
[44] McKelvey T. Subspace Methods for Frequency Domain Data[C]// Proceeding of the 2004American Control Conference, 2004, Boston Massachusetts,USA
[45] Pintelon R. Frequeney-domain Subspace System Identification Using non-parametric Noise Models [J]. Automatica, 2002, 38:1295-1311
[46] Cauberghe B, Guillaume P, Pintelon R, et al. Frequency-Domain Subspace Identification using FRF Data From Arbitrary Signals[J]. 2006, 290(3):555-571
[47] Ak?ay H Frequency Domain subspace-based identification of discrete-time power spectra from nonuniformly spaced measurements[J]. Automatica, 2004,40(8): 1333-1347
[48] Pintelon R, Guillaume P, Rolain Y., and Schoukens J., Parametric Identification of Transfer Functions in the Frequency Domain––– A Survey, IEEE Transactions on Automatic Control, 1994,39(11): 2245-2260
[49]傅志方,陈旅乐.模态参数的一种统计识别方法一极大似然函数估计法[J].振动与冲击,1986,2:11-21
[50] Schoukens J, Pintelon R, Renneboog J. A Maximum Likelihood Estimator for Linear and Nonlinear Systems-a Practical Application of Estimation Techniques in Measurement Problem[J]. IEEE Transactions on Instrument and Measures, 1988, 37(1):10-17
[51] Guillaume P, Pintelon R, Schoukens J. Description of Parametric Maximum Likelihood Estimator in the Frequency Domain for Multi-Input, Multi-Output Systems and Its Application to Flutter Analysis[J]. 1990, 4(5):405-416
[52] Verboven P, Guillaume P, Cauberghe B, et al. Frequency-domain generalized total least-squares identification for modal analysis [J]. Journal of Sound and Vibration , 2004,278 :21–38
[53]唐炜.飞机颤振模态参数识别方法研究[D].西安:西北工业大学, 2006
[54] Guillaume P, Hermans L, Van Der Auweraer H. Maximum Likelihood Identification of Modal Parameters from Operational Data.[C]// Proc of the 17th International Modal Analysis Conference. Kissimmee, USA, February 1999 :1887-189
[55] Parloo E, Guillaume P, Cauberghe B. Maximum Likelihood Identification of Non-stationary Operational Data[J] .Journal of Sound and Vibration, 2003, 268 :971–991
[56] Pintelon R, Schoukens J. Frequency Domain Maximum Likelihood Estimation of Linear Dynamic Errors-In-Variables Models[J]. Automatica, 2007,43:621-630
[57] Smail M, Thomas M, ARMA Models for Modal Analysis: Effect of Model Orders and Sampling Frequency[J].Mechanical Systems and Signal Processing,1999,13(6):925-941
[58] Bodeux J B, Golinval J C, Modal Identification and Damage Detection Using the Data-Driven Stochastic Subspace and ARMAV Methods, Mechanical Systems and Signal Processing, 2003, 17(1):83-89
[59] James G. H., Extraction of Modal Parameter from an Operating HAWT using the NaturalExcitation Technique (NExT)[C]// The 13th ASME Wind Energy Symposium, 1994
[60] Overschee P V, Moor B. D. Identification for Linear Systems: Theory, Implementation, Application[M]. Kluwer Academic Publishers, 1996
[61] Peeters B. System Identification and Damage Detection in Civil Engineering [D]. Belgium: Katholieke Universiteit Leuven, 2000
[62] Reynders E, De Roeck. Reference-based Combined Deterministic-stochastic subspace identification for experimental and operational modal analysis[J]. Mechanical Systems and Signal Processing ,2008, 22(3) :617-637
[63] Brincker R, Zhang Lingmi, Andersen P. Modal Identification from Ambient Response using Frequency Domain Decomposition[C]//Proc of the 18th International Modal Analysis Conference, San Antonio, USA, 2000
[64]王彤.复杂结构多输入多输出频域模态参数识别研究及软件[D].南京:南京航空航天大学博士学位论文, 2003
[65]王彤,张令弥.运行模态分析的频域空间域分解法及其应用[J].航空学报, 2006,27(1):62-66
[66] Wang T, Zhang L M, Tamura Y. An operational modal analysis method in frequency and spatial domain. Earthquake Engineering and Engineering Vibration[J]. 2005,4(2):295-300
[67]申凡,郑敏,陈怀海等.采用频域多参考点模态识别法进行工作状态下的模态识别[J].航空学报, 2002, 23(4):294-297
[68] Cauberghe B, Guillaume P , Verboven P. Combined deterministic-stochastic Frequency Domain subspace for experimental and operational modal analysis[C]// Proc of 7th Biennial Conference on Engineering Systems Design and Analysis, Manchester, 2004
[69]于开平,邹经湘,庞世伟.结构系统模态参数识别方法研究进展[J],世界科技研究与发展, 2005, 26(6):22-30
[70] Pintelon R, Schoukens J. Robust Identification of Transfer Functions in the s-and Z-Domains[J]. IEEE Transactions on Instrumentation and Measurement,1990,39(4):565-573
[71] Pintelon R, Rolain Y, Bultheel A, et al, Numerically robust frequency domain identification of multivariable systems[C]//Proceedings of International Seminar on Modal Analysis (ISMA), Leuven, Belgium, 2002:1315–1321
[72] LMS International. LMS Test.Lab Structural Testing Rev 7A [EB/OL]. Leuven, Belgium, www.lmsintl.com, 2007
[73] Verboven P, Guillaume P, Cauberghe B, et al. A Comparison of Frequency-domain Transfer Function Model Estimator Formulations for Structural Dynamics Modeling[J]. Journal of Sound and Vibration , 2005,279 :775–798
[74]郑大钟.线性系统理论[M].北京:清华大学出版社, 2002
[75] Cauberghe B, Guillaume P, Verboven P, et al. On the Influence of the Parameter Constraint on the Stability of Poles[J]. Mechanical Systems and Signal Processing,2005,19(5): 989-1014
[76] Williams R, Crowley J, Vold H. the Multivariate Mode Indicator Function in Modal Analysis. [C]// Proc of the 3rd International Modal Analysis Conference. USA, February 1985
[77]柳重堪.正交函数及其应用[M].北京:国防工业出版社
[78] Li Z F, Hua H X. Extracting Modal Parameters From Structures Undergoing Ambient Excitation Excitation[J]. Journal of Shanghai Jiaotong University, 2001, 2, 117-122
[79] Schoukens J, Rolain Y, Gustafsson F, et al. Fast Calculation of Least-Squares Estimates for System Identification[C]// Proceedings of the37th IEEE Conference on Decision & Control ,Tampa, Florida USA .1998:3408-3410
[80]彭红涛,陈奎孚.应用FFT高精度快速计算瞬态响应.航空计算技术.1999,29(3):33~38
[81]王世一.数字信号处理[M].北京:北京理工大学出版社, 2001
[82] Allemang R J, Brown D L. A Unified Matrix Polynomial Approach to Modal Identification, Journal of Sound and Vibration, 1998, 211(3):301-322
[83]张令弥.振动测试与动态分析[M] .北京:航空工业出版社,1992
[84]吕志民,张武军,徐金梧.基于奇异谱的降噪方法及其在故障诊断技术中的应用[J].机械工程学报,1999,35(3):85-88
[85]杨文献,姜节胜.机械信号奇异熵研究[J].机械工程学报,2000,36(12):9-13
[86] Verboven P, Guillaume P, Cauberghe B, et al. Modal Parameter Estimation from Input–output Fourier Data using Frequency-domain Maximum Likelihood Identification[J]. Journal of Sound and Vibration, 2004, 276(22): 957-979
[87] Cauberghe B, Guillaume P. Frequency Response Function-based Parameter Identification from Short Data Sequences[J]. Mechanical Systems and Signal Processing, 2004 ,18: 1097-1116
[88] Cauberghe B, Guillaume P. Identification of Modal Parameters Including Unmeasured Forces and Transient Effects[J]. Journal of Sound and Vibration,2003,265: 609–625
[89] Pintelon R, Schoukens J, and Vandersteen G. Frequency Domain System Identification using Arbitrary Signals [J]. IEEE Transactions on Automatic Control, 1997,42(12):1717-1720
[90] Pintelon R, Schoukens J. Identification of Continuous-time System using Arbitrary Signals [J]. Automatica, 1997,33(5):991-994
[91] Link M, Friswell M. Working Group 1: Generation of Validated Structural Dynamic Models - Result s of a Benchmark Study Utilising the GARTEUR SM-AG19 Test-bed[J]. Mechanical System and Signal Processing , 2003, 17 (1): 9-20
[92]哥德温,潘恩著.动态系统辨识:试验设计与数据分析[M].北京:科学出版社,1983
[93]李鹏波,胡德文.系统辨识基础[M].北京:中国水利水电出版社, 2006
[94] Schoukens J, Rolain Y, Pintelon R. Analysis of Windowing/leakage Effects in Frequency Response Function Measurements[J]. Automatica, 2006,42:27-38
[95]贝达特,皮尔索著,令福根译.相关分析和谱分析的工程应用[M].北京:国防工业出版社,1983
[96]刘济科,彭林欣.一般矩阵小扰动的特征值近似计算[J].中山大学学报, 2000, 39(4): 23-26
[97]张义民,陈力奋,闻邦椿.振动系统特征值问题的矩阵灵敏度分析[J].振动、测试与诊断,2002,22(1):24-28
[98]戴华.矩阵论[M].北京:科学出版社, 2001.
[99] Verboven P, Cauberghe B. User-assisting tools for a fast frequency-domain modal parameter estimation method. Mechanical Systems and Signal Processing, 2004, 18(4): 759-780
[100]易伟建,吴高烈,徐丽.模态参数不确定性分析的贝叶斯方法研究[J].计算力学学报,2006,23(6):700-705
[101] Xu L, Yi W J, Yi Z H. Uncertainty Analysis of Strain Modal Parameters by Bayesian Method using Frequency Response Function. Earthquake Engineering and Engineering Vibration, 2007,6(2): 183-189
[102] Gao W. Natural Frequency and Mode Shape Analysis of Atructures with Uncertainty[J]. Mechanical Systems and Signal Processing, 2007, 21(1):24-39
[103]邱志平,王靖.不确定参数结构特征值问题的概率统计方法和区间分析方法的比较[J].航空学报, 2007,28(3):590-592
[104] Longman R W, Juang J N. Variance Based Confidence Criterion for ERA Identification Modal Parameters. AAS 87-454:581-601
[105] Paez T L , Hunter N F. Statistcal series : part25 :Fundamental Concepts of the Bootstrap for Statistical Analysis of Mechanical Systems [J]. Experimental Techniques,1998,22 (3) :3523
[106] Reynders E, Pintelon R, Roecka G. Uncertainty Bounds on Modal Parameters Obtained From Stochastic Subspace Identification[J]. Mechanical Systems and Signal Processing, 2008, 22(4):948-969
[107] Carden E P, Mita A. Challenges in Developing Confidence Intervals on Modal Parameters Estimated for Large Civil Infrastructure with Stochastic Subspace Identification[J]. Structural Control and Health Monitoring, 2009, 23(1):217-225
[108] Guillaume P, Schoukens J, Pintelon R, Sensitivity of Roots to Errors in the Coefficients of Polynomials Obtained by Frequency Domain Estimation Methods[J] IEEE Transactions on Instrumentation and Measurement 1989, 38 (6):1050–1056
[109] Pintelon R, Guillaume P, Schoukens J. Uncertainty calculation in (operational) modal analysis [J]. Mechanical Systems and Signal Processing, 2007,21(6): 2359-2373
[110] Troyer T, Guillaume P, Steenackers G. Fast variance calculation of polyreference least-squares frequency-domain estimates [J]. Mechanical Systems and Signal Processing, 2009,23(5): 1423-1433
[111] Troyer T, Guillaume P, Pintelon R, et al. Fast calculation of confidence intervals on parameter estimates of least-squares frequency-domain estimators [J]. Mechanical Systems and Signal Processing, 2009,23(2): 261-273
[112] Zhang L M, Sun X H, Wang T. Narrow-band, Select-band vs Broadband Modal Identification: their Features and Comparisons. Proc of the 26th International Modal Analysis Conference. USA, February 2009.
[113] Verboven P, Parloo E, Cauberghe B, et al. Improved modal parameter estimation for lowly damped systems using non-parametric exponential windowing techniques [J]. Mechanical Systems and Signal Processing, 2005 ,19: 675-699
[114]陈常松.大跨度混凝土斜拉桥模态试验技术研究.土木工程学报, 2005, 38(10):72-76
[115] Andersen P. Theory of Covariance Equivalent ARMAV Models of Civil Engineering Structures[C]//Proceedings of the 14th International Modal Analysis Conference, 1996
[116]樊可清,倪一清,高赞明.改进随机子空间系统辨识方法及其在桥梁状态监测中的应用[J].中国公路学报, 2004, 17(4):70-73
[117] Qin Q, Li H B, Qian L Z. Modal identification of Ting Ma Bridge by using improved eigen system realization algorithm [J]. Journal of Sound and Vibration, 2001, 247 (2): 325 -341
[118] Lanslots J P, Peeters B. Automated pole-selection: proof-of-concept & validation [C]//proc of ISMA 2004. leuven, Belgium, 2004.
[119] Lau J, Lanslots J, Bart Peeters, etal. Automatic modal analysis: reality or myth?[C]// Proceedings of the 25th International Modal Analysis Conference, Orlando, Fl, USA, 2007
[120]高新波.模糊聚类分析及应用[M].西安:西安电子科技大学出版社,2004.
[121]朱剑英.智能系统非经典数学方法[M].武汉:华中科技大学出版社.2001
[122]林俊杰.Visual C++2005程序设计[M].北京:清华大学出版社,2006
[123]宛延凯.C++语言和面向对象程序设计[M].北京:清华大学出版社, 1998
[124] Matrix Template Library Programmer's Reference.2005
[125] Math Kernel Library Reference Manual(V9.0),2007
[126] MathTools Function Reference Guide(V4.5),1999
[127]张志涌,徐彦琴.MatLab教程――基于6.x版本.北京:北京航空航天大学出版社,2001
[128] BCGControlBar Library (v. 9.56) User Maunual.2007
[129]王彤.模态测试与分软件中的通用文件读写接口设计[J].振动与冲击, 2006, 25(6):147~149
[130]阎锋欣,侯增选等. Open Inventor从入门到精通[M] .北京:清华大学出版社, 2007
[2]沃德·海伦,斯蒂芬·拉门兹,波尔·萨斯著.模态分析理论与实验[M].白化同,郭继忠,译.北京理工大学出版社, 2001
[3]曹树谦等.振动结构模态分析理论、实验与应用[M] .天津:天津大学出版社,2001
[4] Vold H, Kundrat J, Rocklin G. T, et al. A Multi-input Modal Estimation Algorithm for Mini-Computers[J], 1982, 91: 815~821
[5] Juang J N. and Pappa R. S, An Eigensystem Realization Algorithm (ERA) for Modal Parameter Identification and Model Reduction, Journal of Guidance[J], Control and Dynamics, 1985, 8(5):620~627
[6] Zhang L M. On the Two-Stage Time Domain Modal Identification[C]// Proc of the 21th International Modal Analysis Conference. Kissimmee, USA, February 2003.
[7] Moor B D , Vandewalle J, A Geometrical Strategy for the Identification of State Space Models of Linear Multivariable Systems with Singular Value Decomposition[C]//. Proc. of the 3rd International Symposium on Applications of Multivariable System Techniques,1987
[8] Verhaegen M, Westwick D. Identifying MIMO Hammerstein Systems in the Context of Subspace Model Identification Methods[J]. International Journal of Control, 1996, 63(2):331-349
[9] Overschee P V, Moor B D. N4SID-Subspace Algorithms for the Identification of Combined Deterministic-Stochastic Systems[J]. Automatica, 1994, 30(1):75-94
[10] Levy E C. Complex Curve Fitting[J]. IEEE Transaction on Automatic Control, 1959, 4(1):37-44
[11] Richardson M H, Formenti D L. Parameter Estimation from Frequency Response Measurements using Rational Fraction Polynomials[C] //Proceedings of the 1st International Modal Analysis Conference, Orlando. 1982:167-181.
[12] Richardson M H. Global Frequency & Damping Estimates from Frequency Response Measurements[C] //Proceedings of the 4td International Modal Analysis Conference, 1986
[13] van der Auweraer H, Leuridan J. Multiple Input Orthogonal Polynomial Parameter Estimation[J]. Mechanical Systems and Signal Processing, 1987, 1(3):259-27
[14] Shih C Y, Tsuei Y G, Allemang R J ,et al. A Frequency Domain Global Parameter Estimation Method for Multiple Reference Frequency Response Measurements[J]. Mechanical System and Signal Processing, 1988,2(4): 349-365
[15] Shih C Y, Tsuei Y G. Complex Mode Indication Function and its Applications to SpatialDomain Parameter Estimation[C]// Proceedings of the 7th International Modal Analysis Conference, 1989
[16] Zhang L M, Kanda H. Some Applications of Frequency Domain poly-Reference Modal Parameter Identification[C]//Proc of the 4th International Modal Analysis Conference, Los Angeles, USA, 1986:1237-1245
[17] Lembregts F, Leuridan J, van Brussel H. Frequency domain direct parameter identification for modal analysis: State space formulation[J].Mechanical Systems and Signal Processing, 1990,4(1): 65-75.
[18] Rolain Y, Pintelon R, Xu K Q, et al. On the Use of Orthogonal Polynomials In High Order Frequency Domain System Identification and Its Application to Modal Parameter Estimation.[C]//Proceedings of the 33rd IEEE Conference on Decision and Control,1994
[19] Rolain Y, Pintelon R, Xu K Q, et al. Best Conditioned Parametric Identification of Transfer Function Models in the Frequency Fomain[J]. IEEE Transactions on Automatic Control, 1995, 40 (11): 1954-1960
[20]杜永昌,管迪.多输入多输出频域模态识别算法的探讨[J].清华大学学报,1997,37(11):61-64
[21]陈怀海,许峰,彭江水.用幂基多项式拟合频响函数的几点技巧[J].振动工程学报, 2001,14(1),122-124
[22]焦群英,陈奎孚.整体正交多项式法识别模态参数的改进[J].中国农业大学学报, 2003, 8(2): 1-6.
[23]胡彦超,陈章位.实验模态分析中一种改进的傅氏域离散正交多项式.振动工程学报.2008,21(1):43-47
[24] Chen K F, Wang J L. Generating Complex Orthogonal Polynomials. Integral Transforms and Special Functions.2008,19(1):59-64
[25] Chen K F, Jiao Q Y, Shen Y H. On the Frequency Mapping of Modal Parameters Identification[J]. Mechanical Systems and Signal Processing, 2007, 21(4): 1665-1673
[26] Tang W, Shi Z K, Chen J. Aircraft Flutter Modal Parameter Identification Using a Numerically Robust Least-Squares Estimator in Frequency Domain[J]. Chinese Journal of Aeronautics, 2008, 21(6): 550-558
[27] Guillaume P, Verboven P, Vanlanduit S. Frequency-Domain Maximum Likelihood Identification of Modal Parameters with Confidence Intervals[C]// Proceeding of ISMA 23, 1998
[28] Van der Auweraer H Verboven P, Verboven P. Application of a Fast-Stabilizing Frequency Domain Parameter Estimation Method [J]. Journal of Dynamic System, Measurement, and Control, 2001,123(4):651-659
[29] Auweraer H V, Peeters B. Discriminating Physical Poles from Mathematical Poles in HighOrder Systems: Use and Automation of the Stabilization Diagram [C]// Instrumentation and Measurement Technology Conference. Italy, May 2004. 2193 -2198
[30] Verboven P, Guillaume P, Cauberghe B, et al. Modal Parameter Estimation and Monitoring for On-line Flight Flutter Analysis[J]. Mechanical Systems and Signal Processing,2004,18: 587–610
[31] Verboven P, Cauberghe B, Parloo E. User-assisting Tools for a Fast Frequency-Domain Modal Parameter Estimation Method[J]. Mechanical Systems and Signal Processing, 2004,18: 759–780
[32] Verboven P, Cauberghe B, Guillaume P. Improved Total Least Squares Estimators for Modal Analysis[J]. Computers and Structures,2005, 83: 2077–2085
[33] Alessandro Fasana. Modal Parameters Estimation in the Z-domain[J]. Mechanical Systems and Signal Processing, 2009, 23(1):217-225
[34] Guillaume P, Verboven P, Vanlanduit S, et al. A Poly-Reference Implementation of the Least-Squares Complex Frequency Domain Estimator [C]// Proc of the 21th International Modal Analysis Conference. Kissimmee, USA, February 2003
[35] Cauberghe B. Applied Frequency-Domain System Identification In the Field of Experimental and Operational Modal Analysis[D]. Belgium: Vrije Universiteit Brussel, 2004
[36] Peeters B, Van der Auweraer H, Guillaume P, et al. The PolyMAX frequency-domain method: a new standard for modal parameter estimation [J]. Shock and Vibration, 2004, 11: 395-409
[37] Peeters B, Guillaume P. Automotive and Aerospace Applictions of the LMS PolyMAX Modal Parameter Estimation Method[C]// Proc of the 22th International Modal Analysis Conference, Dearborn, USA, January 2004.
[38]易伟建,周云.基于高阶局部模态的弹性地基上框架结构物理参数识别研究[J].地震工程与工程振动, 2007,27(1):414-423
[39]周云,易伟建.用PolyMAX方法进行弹性地基板的实验模态分析[J].振动与冲击,2007,26(7):139-144
[40] McKelvey T, Akcay H, Ljung L. Subspace-based Multivariable System Identification from Frequency Response Data[J]. IEEE Transactions on Automatic Control, 1996,41(7):960-979
[41] Overschee P V, Moor B D. Continuous-Time Frequency Domain Subspace System Identification, Signal Processing[J], 1996,52(2):179-194
[42] Overschee P V, Moor B D, Dehandschutter W. A Subspace Algorithm For the Identification of Discrete Time Frequency Domain Power Spectra[J]. Automatica,1997,33(12): 2147-2157
[43] McKelvey T. Frequency Domain Identification Methods[J]. Circuits Systems Signal, Processing, 2002, 21(1): 39–55.
[44] McKelvey T. Subspace Methods for Frequency Domain Data[C]// Proceeding of the 2004American Control Conference, 2004, Boston Massachusetts,USA
[45] Pintelon R. Frequeney-domain Subspace System Identification Using non-parametric Noise Models [J]. Automatica, 2002, 38:1295-1311
[46] Cauberghe B, Guillaume P, Pintelon R, et al. Frequency-Domain Subspace Identification using FRF Data From Arbitrary Signals[J]. 2006, 290(3):555-571
[47] Ak?ay H Frequency Domain subspace-based identification of discrete-time power spectra from nonuniformly spaced measurements[J]. Automatica, 2004,40(8): 1333-1347
[48] Pintelon R, Guillaume P, Rolain Y., and Schoukens J., Parametric Identification of Transfer Functions in the Frequency Domain––– A Survey, IEEE Transactions on Automatic Control, 1994,39(11): 2245-2260
[49]傅志方,陈旅乐.模态参数的一种统计识别方法一极大似然函数估计法[J].振动与冲击,1986,2:11-21
[50] Schoukens J, Pintelon R, Renneboog J. A Maximum Likelihood Estimator for Linear and Nonlinear Systems-a Practical Application of Estimation Techniques in Measurement Problem[J]. IEEE Transactions on Instrument and Measures, 1988, 37(1):10-17
[51] Guillaume P, Pintelon R, Schoukens J. Description of Parametric Maximum Likelihood Estimator in the Frequency Domain for Multi-Input, Multi-Output Systems and Its Application to Flutter Analysis[J]. 1990, 4(5):405-416
[52] Verboven P, Guillaume P, Cauberghe B, et al. Frequency-domain generalized total least-squares identification for modal analysis [J]. Journal of Sound and Vibration , 2004,278 :21–38
[53]唐炜.飞机颤振模态参数识别方法研究[D].西安:西北工业大学, 2006
[54] Guillaume P, Hermans L, Van Der Auweraer H. Maximum Likelihood Identification of Modal Parameters from Operational Data.[C]// Proc of the 17th International Modal Analysis Conference. Kissimmee, USA, February 1999 :1887-189
[55] Parloo E, Guillaume P, Cauberghe B. Maximum Likelihood Identification of Non-stationary Operational Data[J] .Journal of Sound and Vibration, 2003, 268 :971–991
[56] Pintelon R, Schoukens J. Frequency Domain Maximum Likelihood Estimation of Linear Dynamic Errors-In-Variables Models[J]. Automatica, 2007,43:621-630
[57] Smail M, Thomas M, ARMA Models for Modal Analysis: Effect of Model Orders and Sampling Frequency[J].Mechanical Systems and Signal Processing,1999,13(6):925-941
[58] Bodeux J B, Golinval J C, Modal Identification and Damage Detection Using the Data-Driven Stochastic Subspace and ARMAV Methods, Mechanical Systems and Signal Processing, 2003, 17(1):83-89
[59] James G. H., Extraction of Modal Parameter from an Operating HAWT using the NaturalExcitation Technique (NExT)[C]// The 13th ASME Wind Energy Symposium, 1994
[60] Overschee P V, Moor B. D. Identification for Linear Systems: Theory, Implementation, Application[M]. Kluwer Academic Publishers, 1996
[61] Peeters B. System Identification and Damage Detection in Civil Engineering [D]. Belgium: Katholieke Universiteit Leuven, 2000
[62] Reynders E, De Roeck. Reference-based Combined Deterministic-stochastic subspace identification for experimental and operational modal analysis[J]. Mechanical Systems and Signal Processing ,2008, 22(3) :617-637
[63] Brincker R, Zhang Lingmi, Andersen P. Modal Identification from Ambient Response using Frequency Domain Decomposition[C]//Proc of the 18th International Modal Analysis Conference, San Antonio, USA, 2000
[64]王彤.复杂结构多输入多输出频域模态参数识别研究及软件[D].南京:南京航空航天大学博士学位论文, 2003
[65]王彤,张令弥.运行模态分析的频域空间域分解法及其应用[J].航空学报, 2006,27(1):62-66
[66] Wang T, Zhang L M, Tamura Y. An operational modal analysis method in frequency and spatial domain. Earthquake Engineering and Engineering Vibration[J]. 2005,4(2):295-300
[67]申凡,郑敏,陈怀海等.采用频域多参考点模态识别法进行工作状态下的模态识别[J].航空学报, 2002, 23(4):294-297
[68] Cauberghe B, Guillaume P , Verboven P. Combined deterministic-stochastic Frequency Domain subspace for experimental and operational modal analysis[C]// Proc of 7th Biennial Conference on Engineering Systems Design and Analysis, Manchester, 2004
[69]于开平,邹经湘,庞世伟.结构系统模态参数识别方法研究进展[J],世界科技研究与发展, 2005, 26(6):22-30
[70] Pintelon R, Schoukens J. Robust Identification of Transfer Functions in the s-and Z-Domains[J]. IEEE Transactions on Instrumentation and Measurement,1990,39(4):565-573
[71] Pintelon R, Rolain Y, Bultheel A, et al, Numerically robust frequency domain identification of multivariable systems[C]//Proceedings of International Seminar on Modal Analysis (ISMA), Leuven, Belgium, 2002:1315–1321
[72] LMS International. LMS Test.Lab Structural Testing Rev 7A [EB/OL]. Leuven, Belgium, www.lmsintl.com, 2007
[73] Verboven P, Guillaume P, Cauberghe B, et al. A Comparison of Frequency-domain Transfer Function Model Estimator Formulations for Structural Dynamics Modeling[J]. Journal of Sound and Vibration , 2005,279 :775–798
[74]郑大钟.线性系统理论[M].北京:清华大学出版社, 2002
[75] Cauberghe B, Guillaume P, Verboven P, et al. On the Influence of the Parameter Constraint on the Stability of Poles[J]. Mechanical Systems and Signal Processing,2005,19(5): 989-1014
[76] Williams R, Crowley J, Vold H. the Multivariate Mode Indicator Function in Modal Analysis. [C]// Proc of the 3rd International Modal Analysis Conference. USA, February 1985
[77]柳重堪.正交函数及其应用[M].北京:国防工业出版社
[78] Li Z F, Hua H X. Extracting Modal Parameters From Structures Undergoing Ambient Excitation Excitation[J]. Journal of Shanghai Jiaotong University, 2001, 2, 117-122
[79] Schoukens J, Rolain Y, Gustafsson F, et al. Fast Calculation of Least-Squares Estimates for System Identification[C]// Proceedings of the37th IEEE Conference on Decision & Control ,Tampa, Florida USA .1998:3408-3410
[80]彭红涛,陈奎孚.应用FFT高精度快速计算瞬态响应.航空计算技术.1999,29(3):33~38
[81]王世一.数字信号处理[M].北京:北京理工大学出版社, 2001
[82] Allemang R J, Brown D L. A Unified Matrix Polynomial Approach to Modal Identification, Journal of Sound and Vibration, 1998, 211(3):301-322
[83]张令弥.振动测试与动态分析[M] .北京:航空工业出版社,1992
[84]吕志民,张武军,徐金梧.基于奇异谱的降噪方法及其在故障诊断技术中的应用[J].机械工程学报,1999,35(3):85-88
[85]杨文献,姜节胜.机械信号奇异熵研究[J].机械工程学报,2000,36(12):9-13
[86] Verboven P, Guillaume P, Cauberghe B, et al. Modal Parameter Estimation from Input–output Fourier Data using Frequency-domain Maximum Likelihood Identification[J]. Journal of Sound and Vibration, 2004, 276(22): 957-979
[87] Cauberghe B, Guillaume P. Frequency Response Function-based Parameter Identification from Short Data Sequences[J]. Mechanical Systems and Signal Processing, 2004 ,18: 1097-1116
[88] Cauberghe B, Guillaume P. Identification of Modal Parameters Including Unmeasured Forces and Transient Effects[J]. Journal of Sound and Vibration,2003,265: 609–625
[89] Pintelon R, Schoukens J, and Vandersteen G. Frequency Domain System Identification using Arbitrary Signals [J]. IEEE Transactions on Automatic Control, 1997,42(12):1717-1720
[90] Pintelon R, Schoukens J. Identification of Continuous-time System using Arbitrary Signals [J]. Automatica, 1997,33(5):991-994
[91] Link M, Friswell M. Working Group 1: Generation of Validated Structural Dynamic Models - Result s of a Benchmark Study Utilising the GARTEUR SM-AG19 Test-bed[J]. Mechanical System and Signal Processing , 2003, 17 (1): 9-20
[92]哥德温,潘恩著.动态系统辨识:试验设计与数据分析[M].北京:科学出版社,1983
[93]李鹏波,胡德文.系统辨识基础[M].北京:中国水利水电出版社, 2006
[94] Schoukens J, Rolain Y, Pintelon R. Analysis of Windowing/leakage Effects in Frequency Response Function Measurements[J]. Automatica, 2006,42:27-38
[95]贝达特,皮尔索著,令福根译.相关分析和谱分析的工程应用[M].北京:国防工业出版社,1983
[96]刘济科,彭林欣.一般矩阵小扰动的特征值近似计算[J].中山大学学报, 2000, 39(4): 23-26
[97]张义民,陈力奋,闻邦椿.振动系统特征值问题的矩阵灵敏度分析[J].振动、测试与诊断,2002,22(1):24-28
[98]戴华.矩阵论[M].北京:科学出版社, 2001.
[99] Verboven P, Cauberghe B. User-assisting tools for a fast frequency-domain modal parameter estimation method. Mechanical Systems and Signal Processing, 2004, 18(4): 759-780
[100]易伟建,吴高烈,徐丽.模态参数不确定性分析的贝叶斯方法研究[J].计算力学学报,2006,23(6):700-705
[101] Xu L, Yi W J, Yi Z H. Uncertainty Analysis of Strain Modal Parameters by Bayesian Method using Frequency Response Function. Earthquake Engineering and Engineering Vibration, 2007,6(2): 183-189
[102] Gao W. Natural Frequency and Mode Shape Analysis of Atructures with Uncertainty[J]. Mechanical Systems and Signal Processing, 2007, 21(1):24-39
[103]邱志平,王靖.不确定参数结构特征值问题的概率统计方法和区间分析方法的比较[J].航空学报, 2007,28(3):590-592
[104] Longman R W, Juang J N. Variance Based Confidence Criterion for ERA Identification Modal Parameters. AAS 87-454:581-601
[105] Paez T L , Hunter N F. Statistcal series : part25 :Fundamental Concepts of the Bootstrap for Statistical Analysis of Mechanical Systems [J]. Experimental Techniques,1998,22 (3) :3523
[106] Reynders E, Pintelon R, Roecka G. Uncertainty Bounds on Modal Parameters Obtained From Stochastic Subspace Identification[J]. Mechanical Systems and Signal Processing, 2008, 22(4):948-969
[107] Carden E P, Mita A. Challenges in Developing Confidence Intervals on Modal Parameters Estimated for Large Civil Infrastructure with Stochastic Subspace Identification[J]. Structural Control and Health Monitoring, 2009, 23(1):217-225
[108] Guillaume P, Schoukens J, Pintelon R, Sensitivity of Roots to Errors in the Coefficients of Polynomials Obtained by Frequency Domain Estimation Methods[J] IEEE Transactions on Instrumentation and Measurement 1989, 38 (6):1050–1056
[109] Pintelon R, Guillaume P, Schoukens J. Uncertainty calculation in (operational) modal analysis [J]. Mechanical Systems and Signal Processing, 2007,21(6): 2359-2373
[110] Troyer T, Guillaume P, Steenackers G. Fast variance calculation of polyreference least-squares frequency-domain estimates [J]. Mechanical Systems and Signal Processing, 2009,23(5): 1423-1433
[111] Troyer T, Guillaume P, Pintelon R, et al. Fast calculation of confidence intervals on parameter estimates of least-squares frequency-domain estimators [J]. Mechanical Systems and Signal Processing, 2009,23(2): 261-273
[112] Zhang L M, Sun X H, Wang T. Narrow-band, Select-band vs Broadband Modal Identification: their Features and Comparisons. Proc of the 26th International Modal Analysis Conference. USA, February 2009.
[113] Verboven P, Parloo E, Cauberghe B, et al. Improved modal parameter estimation for lowly damped systems using non-parametric exponential windowing techniques [J]. Mechanical Systems and Signal Processing, 2005 ,19: 675-699
[114]陈常松.大跨度混凝土斜拉桥模态试验技术研究.土木工程学报, 2005, 38(10):72-76
[115] Andersen P. Theory of Covariance Equivalent ARMAV Models of Civil Engineering Structures[C]//Proceedings of the 14th International Modal Analysis Conference, 1996
[116]樊可清,倪一清,高赞明.改进随机子空间系统辨识方法及其在桥梁状态监测中的应用[J].中国公路学报, 2004, 17(4):70-73
[117] Qin Q, Li H B, Qian L Z. Modal identification of Ting Ma Bridge by using improved eigen system realization algorithm [J]. Journal of Sound and Vibration, 2001, 247 (2): 325 -341
[118] Lanslots J P, Peeters B. Automated pole-selection: proof-of-concept & validation [C]//proc of ISMA 2004. leuven, Belgium, 2004.
[119] Lau J, Lanslots J, Bart Peeters, etal. Automatic modal analysis: reality or myth?[C]// Proceedings of the 25th International Modal Analysis Conference, Orlando, Fl, USA, 2007
[120]高新波.模糊聚类分析及应用[M].西安:西安电子科技大学出版社,2004.
[121]朱剑英.智能系统非经典数学方法[M].武汉:华中科技大学出版社.2001
[122]林俊杰.Visual C++2005程序设计[M].北京:清华大学出版社,2006
[123]宛延凯.C++语言和面向对象程序设计[M].北京:清华大学出版社, 1998
[124] Matrix Template Library Programmer's Reference.2005
[125] Math Kernel Library Reference Manual(V9.0),2007
[126] MathTools Function Reference Guide(V4.5),1999
[127]张志涌,徐彦琴.MatLab教程――基于6.x版本.北京:北京航空航天大学出版社,2001
[128] BCGControlBar Library (v. 9.56) User Maunual.2007
[129]王彤.模态测试与分软件中的通用文件读写接口设计[J].振动与冲击, 2006, 25(6):147~149
[130]阎锋欣,侯增选等. Open Inventor从入门到精通[M] .北京:清华大学出版社, 2007
© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号 地址：北京市海淀区学院路29号 邮编：100083 电话：办公室：(+86 10)66554848；文献借阅、咨询服务、科技查新：66554700 |