Research Progress on Time-domain Modal Parameter Estimation Methods for Linear Time-varying Structures

doi:10.3901/JME.2018.23.137

Abstract

Abstract: With the development of engineering applications, more and more time-varying structures are being used and their intrinsic time-varying characteristics are increasingly inevitable, which brings us many problems on time-varying structural dynamics. The research background of time-varying structural dynamics and the motivation of modal parameter estimation for time-varying structures are first introduced from the standpoint of inverse problems. The modal parameter estimation methods for linear time-varying structures are classified, and the procedures to obtain "frozen-time" modal parameters from parametric time-domain identified models are subsequently presented. By investigating state-of-the-art of time-domain modal parameter estimation methods for time-varying structures and the existing experimental verification systems, major issues and future research directions in this area are finally discussed.

Key words: linear time-varying structures, modal parameter estimation, time-domain

CLC Number:

MA Zhisai, DING Qian, LIU Li, ZHOU Sida. Research Progress on Time-domain Modal Parameter Estimation Methods for Linear Time-varying Structures[J]. Journal of Mechanical Engineering, 2018, 54(23): 137-159.

References

[1] CLOUGH R W,PENZIEN J. Dynamics of structures[M]. Berkeley:Computers & Structures Inc.,1995.
[2] 龚尧南. 结构力学[M]. 北京:北京航空航天大学出版社,2001. GONG Yaonan. Structural mechanics[M]. Beijing:Beihang University Press,2001.
[3] 龙驭球,包世华,匡文起,等. 结构力学教程[M]. 北京:高等教育出版社,2000. LONG Yuqiu,BAO Shihua,KUANG Wenqi,et al. Structural mechanics[M]. Beijing:Higher Education Press,2000.
[4] 马骏,曾庆华,张令弥. 时变参数识别方法研究[J]. 振动与冲击,1997,16(1):6-10,29. MA Jun,ZENG Qinghua,ZHANG Lingmi. Research of the time varying parameters identification methods[J]. Journal of Vibration and Shock,1997,16(1):6-10,29.
[5] 王光远. 论时变结构力学[J]. 土木工程学报,2000,33(6):105-108. WANG Guangyuan. On mechanics of time-varying structures[J]. China Civil Engineering Journal,2000,33(6):105-108.
[6] 邹经湘,于开平,杨炳渊. 时变结构的参数识别方法[J]. 力学进展,2000,30(3):370-377. ZOU Jingxiang,YU Kaiping,YANG Bingyuan. Methods of time-varying structural parameter identification[J]. Advances in Mechanics,2000,30(3):370-377.
[7] CHATTERJEE P K,DATTA T K,SURANA C S. Vibration of continuous bridges under moving vehicles[J]. Journal of Sound and Vibration,1994,169(5):619-632.
[8] AU F T K,JIANG R J,CHEUNG Y K. Parameter identification of vehicles moving on continuous bridges[J]. Journal of Sound and Vibration,2004,269(1-2):91-111.
[9] MARCHESIELLO S,BEDAOUI S,GARIBALDI L,et al. Time-dependent identification of a bridge-like structure with crossing loads[J]. Mechanical Systems and Signal Processing,2009,23(6):2019-2028.
[10] PEETERS B,VAN DER AUWERAER H,VANHOLLEBEKE F,et al. Operational modal analysis for estimating the dynamic properties of a stadium structure during a football game[J]. Shock and Vibration,2007,14(4):283-303.
[11] KOPMAZ O,ANDERSON K S. On the eigenfrequencies of a flexible arm driven by a flexible shaft[J]. Journal of Sound and Vibration,2001,240(4):679-704.
[12] CHANG P H,PARK H S. Time-varying input shaping technique applied to vibration reduction of an industrial robot[J]. Control Engineering Practice,2005,13(1):121-130.
[13] MOUSTAFA K A F,GAD E H,EL-MONEER A M A,et al. Modelling and control of overhead cranes with flexible variable-length cable by finite element method[J]. Transactions of the Institute of Measurement and Control,2005,27(1):1-20.
[14] MOUSTAFA K A F,TRABIA M B,ISMAIL M I S. Modelling and control of an overhead crane with a variable length flexible cable[J]. International Journal of Computer Applications in Technology,2009,34(3):216-228.
[15] ALLEN M S,SRACIC M W,CHAUHAN S,et al. Output-only modal analysis of linear time-periodic systems with application to wind turbine simulation data[J]. Mechanical Systems and Signal Processing,2011,25(4):1174-1191.
[16] AVENDANO-VALENCIA L D,FASSOIS S D. Stationary and non-stationary random vibration modelling and analysis for an operating wind turbine[J]. Mechanical Systems and Signal Processing,2014,47(1-2):263-285.
[17] JHINAOUI A,MEVEL L,MORLIER J. A new SSI algorithm for LPTV systems:application to a hinged-bladed helicopter[J]. Mechanical Systems and Signal Processing,2014,42(1-2):152-166.
[18] MEIROVITCH L. General motion of a variable-mass flexible rocket with internal flow[J]. Journal of Spacecraft and Rockets,1970,7(2):186-195.
[19] JOSHI A. Free vibration characteristics of variable mass rockets having large axial thrust/acceleration[J]. Journal of Sound and Vibration,1995,187(4):727-736.
[20] BANERJEE A K. Dynamics of a variable-mass,flexible-body system[J]. Journal of Guidance,Control,and Dynamics,2000,23(3):501-508.
[21] TOBBE P A,MATRAS A L,WILSON H E. Modeling and simulation of variable mass,flexible structures[C]//AIAA Modeling and Simulation Technologies Conference. Chicago,Illinois,2009:1-12.
[22] THORNTON E A,DECHAUMPHAI P. Coupled flow,thermal,and structural analysis of aerodynamically heated panels[J]. Journal of Aircraft,1992,25(11):1052-1059.
[23] MCNAMARA J J,FRIEDMANN P P. Flutter boundary identification for time-domain computational aeroelasticity[J]. AIAA Journal,2007,45(7):1546-1555.
[24] 吴大方,赵寿根,潘兵,等. 高速巡航导弹翼面结构热-振联合试验研究[J]. 航空学报,2012,33(9):1633-1642. WU Dafang,ZHAO Shougen,PAN Bing,et al. Research on thermal-vibration joint test for wing structure of high-speed cruise missile[J]. Acta Aeronautica et Astronautica Sinica,2012,33(9):1633-1642.
[25] 周思达,刘莉,李昱霖,等. 高速飞行器热结构工作时变模态参数辨识[J]. 航空学报,2015,36(1):373-380. ZHOU Sida,LIU Li,LI Yulin,et al. Operational identification of time-varying modal parameters for thermal structures of high-speed aerial vehicles[J]. Acta Aeronautica et Astronautica Sinica,2015,36(1):373-380.
[26] 刘浩,李晓东,杨文岐,等. 高速飞行器翼面结构热振动试验的TARMA模型方法[J]. 航空学报,2015,36(7):2225-2235. LIU Hao,LI Xiaodong,YANG Wenqi,et al. Thermal vibration test on wing structure of high-speed flight vehicle using TARMA model method[J]. Acta Aeronautica et Astronautica Sinica,2015,36(7):2225-2235.
[27] VERBOVEN P,CAUBERGHE B,GUILLAUME P,et al. Modal parameter estimation and monitoring for on-line flight flutter analysis[J]. Mechanical Systems and Signal Processing,2004,18(3):587-610.
[28] ERTVELDT J,LATAIRE J,PINTELON R,et al. Frequency-domain identification of time-varying systems for analysis and prediction of aeroelastic flutter[J]. Mechanical Systems and Signal Processing,2014,47(1-2):225-242.
[29] KRISHNAMURTHY K,CHAO M C. Active vibration control during deployment of space structures[J]. Journal of Sound and Vibration,1992,152(2):205-218.
[30] 朱桂东,王本利,邵成勋. 带梁式伸展附件航天器动力学分析[J]. 空间科学学报,1996,16(4):326-330. ZHU Guidong,WANG Benli,SHAO Chengxun. Dynamic property analysis for spacecraft with beam-like deploying appendages[J]. Chinese Journal of Space Science,1996,16(4):326-330.
[31] 宋宇,王本利,马兴瑞. 伸展柔性附件对简谐激励的响应分析[J]. 航空学报,1999,20(1):8-10. SONG Yu,WANG Benli,MA Xingrui. Dynamic response of flexible appendages to the harmonic excitation during extension[J]. Acta Aeronautica et Astronautica Sinica,1999,20(1):8-10.
[32] WIE B. Solar sail attitude control and dynamics,part two[J]. Journal of Guidance,Control,and Dynamics,2004,27(4):536-544.
[33] HAMADA Y,OHTANI T,KIDA T,et al. Synthesis of a linearly interpolated gain scheduling controller for large flexible spacecraft ETS-VⅢ[J]. Control Engineering Practice,2011,19(6):611-625.
[34] CHAKRAVARTHY A,GRANT D,LIND R. Time-varying dynamics of a micro air vehicle with variable-sweep morphing[J]. Journal of Guidance,Control,and Dynamics,2012,35(3):890-903.
[35] COOPER J E. Identification of time varying modal parameters[J]. Aeronautical Journal,1990,94(938):271-278.
[36] JANG J W,HALL R,BEDROSSIAN N,et al. Ares-I bending filter design using a constrained optimization approach[C]//AIAA Guidance,Navigation and Control Conference and Exhibit. Honolulu,Hawaii,2008:1-10.
[37] 吴燕生,何麟书. 新一代运载火箭姿态控制技术[J]. 北京航空航天大学学报,2009,35(11):1294-1297. WU Yansheng,HE Linshu. Attitude control technology of new-generation launch vehicles[J]. Journal of Beijing University of Aeronautics and Astronautics,2009,35(11):1294-1297.
[38] JOSHI A. Structure-control interactions in flexible aerospace vehicles[C]//The 51st AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics,and Materials Conference. Orlando,Florida,2010:1-13.
[39] 马道远,王其政,荣克林. 液体捆绑火箭POGO稳定性分析的闭环传递函数法[J]. 强度与环境,2010,37(1):1-7. MA Daoyuan,WANG Qizheng,RONG Kelin. Close-loop transfer function of POGO stability analysis for binding liquid-propellant rocket[J]. Structure & Environment Engineering,2010,37(1):1-7.
[40] 李家文. 大型捆绑火箭姿态控制系统的建模、设计与分析[D]. 长沙:国防科学技术大学,2011. LI Jiawen. Modeling, design and analysis of large strap-on launch vehicle's attitude control system[D]. Changsha:National University of Defense Technology,2011.
[41] 王庆伟,谭述君,吴志刚,等. 大型液体火箭姿控与跷振大回路耦合动力学建模与分析[J]. 力学学报,2015,47(5):789-798. WANG Qingwei,TAN Shujun,WU Zhigang,et al. Dynamic modeling and analysis of large-loop coupled by attitude control and POGO for large liquid rockets[J]. Chinese Journal of Theoretical and Applied Mechanics,2015,47(5):789-798.
[42] 曹树谦,张文德,萧龙翔. 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. CAO Shuqian,ZHANG Wende,XIAO Longxiang. Vibrational structure modal analysis:theory,testing and application[M]. Tianjin:Tianjin University Press,2001.
[43] 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. FU Zhifang,HUA Hongxing. Modal analysis theory and application[M]. Shanghai:Shanghai Jiao Tong University Press,2000.
[44] HEYLEN W,LAMMENS S,SAS P. Modal analysis theory and testing[M]. Leuven:Katholieke Universiteit Leuven,2007.
[45] EWINS D J. Modal testing:theory,practice and application[M]. Baldock:Research Studies Press LTD.,2001.
[46] 周思达. 线性时变结构时频域模态参数辨识理论及实验研究[D]. 北京:北京理工大学,2012. ZHOU Sida. Study on theory and experiment of time-frequency-domain modal parameter estimation for linear time-varying mechanical structures[D]. Beijing:Beijing Institute of Technology,2012.
[47] 周思达,刘莉,杨武,等. 基于矩阵分式多项式时变结构模态参数最小二乘辨识[J]. 振动与冲击,2014,33(6):118-123. ZHOU Sida,LIU Li,YANG Wu,et al. Matrix fraction polynomial model-based least square estimation of modal parameters for linear time-varying structures[J]. Journal of Vibration and Shock,2014,33(6):118-123.
[48] 马志赛. 线性时变结构模态参数仅输出递推辨识方法研究[D]. 北京:北京理工大学,2017. MA Zhisai. Output-only modal parameter recursive estimation for linear time-varying structures[D]. Beijing:Beijing Institute of Technology,2017.
[49] GARIBALDI L,FASSOIS S. MSSP special issue on the identification of time varying structures and systems[J]. Mechanical Systems and Signal Processing,2014,47(1-2):1-2.
[50] SPIRIDONAKOS M D,FASSOIS S D. Non-stationary random vibration modelling and analysis via functional series time-dependent ARMA (FS-TARMA) models-a critical survey[J]. Mechanical Systems and Signal Processing,2014,47(1-2):175-224.
[51] MA Z,LIU L,ZHOU S,et al. Dynamic stability analysis of linear time-varying systems via an extended modal identification approach[J]. Chinese Journal of Mechanical Engineering,2017,30(2):459-471.
[52] 刘豹,唐万生. 现代控制理论[M]. 北京:机械工业出版社,2006. LIU Bao,TANG Wansheng. Modern control theory[M]. Beijing:China Machine Press,2006.
[53] LIU K. Identification of linear time-varying systems[J]. Journal of Sound and Vibration,1997,206(4):487-505.
[54] LIU K. Extension of modal analysis to linear time-varying systems[J]. Journal of Sound and Vibration,1999,226(1):149-167.
[55] 杨叔子,吴雅,轩建平. 时间序列分析的工程应用[M].2版.武汉:华中科技大学出版社,2007. YANG Shuzi,WU Ya,XUAN Jianping. Time series analysis in engineering application[M].2nd ed.Wuhan:Huazhong University of Science & Technology Press,2007.
[56] POULIMENOS A G,FASSOIS S D. Non-stationary random vibration modelling and analysis via functional series TARMAX models[C]//ISMA 2004 International Conference on Noise and Vibration Engineering. Leuven,2004:2475-2489.
[57] POULIMENOS A G,FASSOIS S D. Parametric time-domain methods for non-stationary random vibration modelling and analysis-a critical survey and comparison[J]. Mechanical Systems and Signal Processing,2006,20(4):763-816.
[58] YANG W,LIU L,ZHOU S D,et al. Moving Kriging shape function modeling of vector TARMA models for modal identification of linear time-varying structural systems[J]. Journal of Sound and Vibration,2015,354:254-277.
[59] ANDERSEN P,BRINCKER R,KIRKEGAARD P H. Theory of covariance equivalent ARMAV models of civil engineering structures[C]//The 14th IMAC,International Modal Analysis Conference. Detroit,Michigan,1996:518-524.
[60] BODEUX J B,GOLINVAL J C. Application of ARMAV models to the identification and damage detection of mechanical and civil engineering structures[J]. Smart Materials & Structures,2001,10(3):479-489.
[61] BERTHA M,GOLINVAL J C. Identification of non-stationary dynamical systems using multivariate ARMA models[J]. Mechanical Systems and Signal Processing,2017,88:166-179.
[62] HO B,KALMAN R. Efficient construction of linear state variable models from input/output functions[J]. Regelungstechnik,1966,14(1):545-548.
[63] 于开平,庞世伟,赵婕. 时变线性/非线性结构参数识别及系统辨识方法研究进展[J]. 科学通报,2009,54(20):3147-3156. YU Kaiping,PANG Shiwei,ZHAO Jie. Advances in method of time-varying linear/nonlinear structural system identification and parameter estimate[J]. Chinese Science Bulletin,2009,54(20):3147-3156.
[64] VAN OVERSCHEE P,DE MOOR B. Subspace identification for linear systems:theory-implementation-applications[M]. Boston/London/Dordrecht:Kluwer Academic Publishers,1996.
[65] LIU K,DENG L. Experimental verification of an algorithm for identification of linear time-varying systems[J]. Journal of Sound and Vibration,2005,279(3-5):1170-1180.
[66] LIU K,DENG L. Identification of pseudo-natural frequencies of an axially moving cantilever beam using a subspace-based algorithm[J]. Mechanical Systems and Signal Processing,2006,20(1):94-113.
[67] SHOKOOHI S,SILVERMAN L M. Identification and model reduction of time-varying discrete-time systems[J]. Automatica,1987,23(4):509-521.
[68] MACNEIL J B,KEARNEY R E,HUNTER I W. Identification of time-varying biological systems from ensemble data[J]. IEEE Transactions on Biomedical Engineering,1992,39(12):1213-1225.
[69] VERHAEGEN M,YU X. A class of subspace model identification algorithms to identify periodically and arbitrarily time-varying systems[J]. Automatica,1995,31(2):201-216.
[70] 于开平,谢礼立,樊久铭,等. 移动质量-简支梁系统的参数辩识[J]. 地震工程与工程振动,2002,22(5):14-17. YU Kaiping,XIE Lili,FAN Jiuming,et al. A parameter identification of simply supported beams system carrying a moving mass[J]. Earthquake Engineering and Engineering Vibration,2002,22(5):14-17.
[71] 庞世伟,于开平,邹经湘. 识别时变结构模态参数的改进子空间方法[J]. 应用力学学报,2005,22(2):184-188,332. PANG Shiwei,YU Kaiping,ZOU Jingxiang. Improved subspace method with application in linear time-varying structural modal parameter identification[J]. Chinese Journal of Applied Mechanics,2005,22(2):184-188,332.
[72] JUANG J N,PAPPA R S. An eigensystem realization algorithm for modal parameter identification and model reduction[J]. Journal of Guidance,Control,and Dynamics,1985,8(5):620-627.
[73] JUANG J N. Applied system identification[M]. Englewood Cliffs,New Jersey:Prentice Hall,1994.
[74] MAJJI M. System identification:time varying and nonlinear methods[D]. Texas:Texas A&M University,2009.
[75] MAJJI M,JUANG J N,JUNKINS J L. Time-varying eigensystem realization algorithm[J]. Journal of Guidance,Control,and Dynamics,2010,33(1):13-28.
[76] MAJJI M,JUANG J N,JUNKINS J L. Observer/Kalman-filter time-varying system identification[J]. Journal of Guidance,Control,and Dynamics,2010,33(3):887-900.
[77] MAJJI M,JUANG J N,JUNKINS J L. Time-varying deadbeat controller design[J]. Journal of Guidance,Control,and Dynamics,2012,35(1):284-295.
[78] PEETERS B,ROECK G D. Stochastic system identification for operational modal analysis:a review[J]. Journal of Dynamic Systems,Measurement,and Control,2001,123(4):659-667.
[79] VERHAEGEN M,DEPRETTERE E. A fast recursive MIMO state space model identification algorithm[C]//The 30th Conference on Decision and Control. Brighton,England,1991:1349-1354.
[80] LOVERA M,GUSTAFSSON T,VERHAEGEN M. Recursive subspace identification of linear and non-linear wiener state-space models[J]. Automatica,2000,36(1):1639-1650.
[81] YANG B. Projection approximation subspace tracking[J]. IEEE Transactions on Signal Processing,1995,43(1):95-107.
[82] YANG B. Asymptotic convergence analysis of the projection approximation subspace tracking algorithms[J]. Signal Processing,1996,50(1):123-136.
[83] GUSTAFSSON T. Instrumental variable subspace tracking using projection approximation[J]. IEEE Transactions on Signal Processing,1998,46(3):669-681.
[84] CHO Y M,XU G,KAILATH T. Fast recursive identification of state space models via exploitation of displacement structure[J]. Automatica,1994,30(1):45-59.
[85] OKU H,KIMURA H. Recursive 4SID algorithms using gradient type subspace tracking[J]. Automatica,2002,38(1):1035-1043.
[86] MERCERE G,LECOEUCHE S,LOVERA M. Recursive subspace identification based on instrumental variable unconstrained quadratic optimization[J]. International Journal of Adaptive Control & Signal Processing,2004,18(1):771-797.
[87] MERCERE G,BAKO L,LECOEUCHE S. Propagator-based methods for recursive subspace model identification[J]. Signal Processing,2008,88(3):468-491.
[88] TASKER F,BOSSE A,FISHER S. Real-time modal parameter estimation using subspace methods:theory[J]. Mechanical Systems and Signal Processing,1998,12(6):797-808.
[89] BOSSE A,TASKER F,FISHER S. Real-time modal parameter estimation using subspace methods:applications[J]. Mechanical Systems and Signal Processing,1998,12(6):809-823.
[90] 吴日强,于开平,邹经湘. 改进的子空间方法及其在时变结构参数辨识中的应用[J]. 工程力学,2002,19(4):67-70+89. WU Riqiang,YU Kaiping,ZOU Jingxiang. An improved subspace method and its application to parameter identification of time-varying structures[J]. Engineering Mechanics,2002,19(4):67-70+89.
[91] 庞世伟,于开平,邹经湘. 用于时变结构模态参数识别的投影估计递推子空间方法[J]. 工程力学,2005,22(5):115-119. PANG Shiwei,YU Kaiping,ZOU Jingxiang. A projection approximation recursive subspace method for identification of modal parameters of time-varying structures[J]. Engineering Mechanics,2005,22(5):115-119.
[92] 庞世伟,于开平,邹经湘. 用于时变系统辨识的自由响应递推子空间方法[J]. 振动工程学报,2005,18(2):233-237. PANG Shiwei,YU Kaiping,ZOU Jingxiang. Time-varying system identification using recursive subspace method based on free response data[J]. Journal of Vibration Engineering,2005,18(2):233-237.
[93] 庞世伟,于开平,邹经湘. 用于线性时变系统辨识的固定长度平移窗投影估计递推子空间方法[J]. 机械工程学报,2005,41(10):117-122. PANG Shiwei,YU Kaiping,ZOU Jingxiang. Using recursive subspace method based on projection approximation with moving window to estimate parameters of linear time-varying structure[J]. Journal of Mechanical Engineering,2005,41(10):117-122.
[94] 杨利芳,于开平,庞世伟,等. 用于线性时变结构系统辨识的子空间方法比较研究[J]. 振动与冲击,2007,26(3):8-12,153. YANG Lifang,YU Kaiping,PANG Shiwei,et al. Comparison study on identification methods applied to linear time-varying structures[J]. Journal of Vibration and Shock,2007,26(3):8-12,153.
[95] 杨凯,于开平,刘荣贺,等. 两种新的基于子空间跟踪的时变模态参数快速辨识算法[J]. 工程力学,2012,29(10):294-300. YANG Kai,YU Kaiping,LIU Ronghe,et al. Two new fast identification algorithms of time-varying modal parameters based on subspace tracking[J]. Engineering Mechanics,2012,29(10):294-300.
[96] 倪智宇,谭述君,吴志刚. 改进的TW-API方法及其在时变模态参数辨识中的应用[J]. 振动工程学报,2015,28(5):721-729. NI Zhiyu,TAN Shujun,WU Zhigang. An improved TW-API recursive method and its application on time-varying modal parameters identification[J]. Journal of Vibration Engineering,2015,28(5):721-729.
[97] 倪智宇,邬树楠,吴志刚,等. 利用改进TW-API方法在轨辨识挠性航天器时变模态参数[J]. 宇航学报,2015,36(7):769-776. NI Zhiyu,WU Shunan,WU Zhigang,et al. On-orbit identification of time-varying modal parameters of flexible spacecraft by an improved TW-API method[J]. Journal of Astronautics,2015,36(7):769-776.
[98] 倪智宇,吴志刚. 线性时变系统的状态空间模型递推辨识研究[J]. 振动与冲击,2016,35(4):8-14. NI Zhiyu,WU Zhigang. Recursive identification for state space model of a linear time-varying system[J]. Journal of Vibration and Shock,2016,35(4):8-14.
[99] 倪智宇,谭述君,吴志刚. 线性时变反馈系统的状态空间模型和模态参数递推辨识[J]. 控制与决策,2016,31(2):324-330. NI Zhiyu,TAN Shujun,WU Zhigang. Recursive identification of state space model and modal parameter of linear time-varying feedback system[J]. Control and Decision,2016,31(2):324-330.
[100] 李会娜,史治宇. 基于自由响应数据的时变系统物理参数识别[J]. 振动工程学报,2007,20(4):348-352. LI Huina,SHI Zhiyu. Physical parameter identification of time-varying system based on free response data[J]. Journal of Vibration Engineering,2007,20(4):348-352.
[101] 李会娜,史治宇. 基于随机激励响应的时变系统物理参数子空间识别方法研究[J]. 工程力学,2008,25(9):46-51. LI Huina,SHI Zhiyu. Subspace-based physical parameter identification of time-varying system using random excitation response[J]. Engineering Mechanics,2008,25(9):46-51.
[102] 静大海,刘晓平. 基于子空间法与子结构法时变结构连接处的物理参数在线辨识[J]. 振动与冲击,2007,26(11):59-63,183. JING Dahai,LIU Xiaoping. On-line identification of physical parameters at joint in time-varying structure system based on subspace and substructure method[J]. Journal of Vibration and Shock,2007,26(11):59-63,183.
[103] VAN OVERSCHEE P,DE MOOR B. Subspace algorithms for the stochastic identification problem[C]//The 30th IEEE Conference on Decision and Control. Brighton,England,1991:1321-1326.
[104] VAN OVERSCHEE P,DE MOOR B. Subspace algorithms for the stochastic identification problem[J]. Automatica,1993,29(3):649-660.
[105] PEETERS B,DE ROECK G,POLLET T,et al. Stochastic subspace techniques applied to parameter identification of civil engineering structures[C]//New Advances in Modal Synthesis of Large Structures:Non-Linear,Damped and Non-Deterministic Cases. Lyon,France,1995:151-162.
[106] PEETERS B,DE ROECK G. Reference-based stochastic subspace identification for output-only modal analysis[J]. Mechanical Systems and Signal Processing,1999,13(6):855-878.
[107] PEETERS B. System identification and damage detection in civil engineering[D]. Leuven:Katholieke Universiteit Leuven,2000.
[108] CHANG C C,LI Z. Recursive stochastic subspace identification for structural parameter estimation[C]//Proceedings of SPIE,Sensors and Smart Structures Technologies for Civil,Mechanical,and Aerospace Systems. San Diego,California,2009:1-9.
[109] LI Z,CHANG C C,ASCE M. Tracking of structural dynamic characteristics using recursive stochastic subspace identification and instrumental variable technique[J]. Journal of Engineering Mechanics,2012,138(6):591-600.
[110] 张家滨,陈国平. 基于随机子空间的递推在线模态识别算法[J]. 振动与冲击,2009,28(8):42-45. ZHANG Jiabin,CHEN Guoping. Stochastic subspace based on-line recursive modal identification method[J]. Journal of Vibration and Shock,2009,28(8):42-45.
[111] 张家滨,陈国平. 利用响应数据识别模态参数的子空间在线递推算法[J]. 振动工程学报,2009,22(1):26-30. ZHANG Jiabin,CHEN Guoping. An online subspace recursive method for modal identification using output data[J]. Journal of Vibration Engineering,2009,22(1):26-30.
[112] BELLINO A,GARIBALDI L,MARCHESIELLO S. Time-varying output-only identification of a cracked beam[J]. Key Engineering Materials,2009,413-414:643-650.
[113] BELLINO A,FASANA A,GANDINO E,et al. A time-varying inertia pendulum:analytical modelling and experimental identification[J]. Mechanical Systems and Signal Processing,2014,47(1-2):120-138.
[114] GOURSAT M,BASSEVILLE M,BENVENISTE A,et al. Output-only modal analysis of Ariane 5 launcher[C]//The 19th IMAC,International Modal Analysis Conference. Kissimmee,Florida,2001:1483-1489.
[115] GOETHALS I,MEVEL L,BENVENISTE A,et al. Recursive output only subspace identification for in-flight flutter monitoring[C]//The 22nd IMAC,International Modal Analysis Conference. Dearborn,Michigan,2004:1-8.
[116] COCK K D,MERCERE G,MOOR B D. Recursive subspace identification for in-flight modal analysis of airplanes[C]//ISMA 2006 International Conference on Noise and Vibration Engineering. Leuven,2006:1563-1577.
[117] BASSEVILLE M,BENVENISTE A,GOURSAT M,et al. In-flight vibration monitoring of aeronautical structures[J]. IEEE Control Systems Magazine,2007,27(5):27-42.
[118] LIU Y C,LOH C H,NI Y Q. Stochastic subspace identification for output-only modal analysis:application to super high-rise tower under abnormal loading condition[J]. Earthquake Engineering & Structural Dynamics,2013,42(4):477-498.
[119] NIKOLAKOPOULOS G,TZES A. Application of adaptive lattice filters for modal parameter tracking of a single flexible link carrying a shifting payload[J]. Mechanical Systems and Signal Processing,2010,24(1):1338-1348.
[120] ZGHAL M,MEVEL L,DEL MORAL P. Modal parameter estimation using interacting Kalman filter[J]. Mechanical Systems and Signal Processing,2014,47(1-2):139-150.
[121] YULE G U. On a method of investigating periodicities in disturbed series,with special reference to wolfer's sunspot numbers[J]. Philosophical Transactions of the Royal Society of London,1927,226(636-646):267-298.
[122] BOX G E P,JENKINS G M. Time series analysis:forecasting and control[M]. San Francisco:Holden-Day,1976.
[123] DAHLHAUS R. Fitting time series models to nonstationary processes[J]. Annals of Statistics,1997,25(1):1-37.
[124] OZAKI T,TONG H. On the fitting of non-stationary autoregressive models in time series analysis[C]//The 8th Hawaii Conference on System Science. Hawaii,1975:224-226.
[125] KITAGAWA G,AKAIKE H. A procedure of the modeling of nonstationary time series[J]. Annals of the Institute of Statistical Mathematics,1978,30(B):351-363.
[126] GERSH W,BROTHERTON T. Estimation of stationary structural system parameters from non-stationary random vibration data:a locally stationary model[J]. Journal of Sound and Vibration,1982,81(1):215-227.
[127] LIN C C,SOONG T T,NATKE H G. Real-time system identification of degrading structures[J]. Journal of Engineering Mechanics,1990,116(10):2258-2274.
[128] 于开平. 时变结构动力学数值方法及其模态参数识别方法研究[D]. 哈尔滨:哈尔滨工业大学,2000. YU Kaiping. Study on time-varying structural dynamics numerical algorithm and modal parameter identification method[D]. Harbin:Harbin Institute of Technology,2000.
[129] OWEN J S,ECCLES B J,CHOO B S,et al. The application of auto-regressive time series modelling for the time-frequency analysis of civil engineering structures[J]. Engineering Structures,2001,23(1):521-536.
[130] MOBARAKEH A A,ROFOOEI F R,AHMADI G. Simulation of earthquake records using time-varying ARMA(2,1) model[J]. Probabilistic Engineering Mechanics,2002,17(1):15-34.
[131] LJUNG L,SODERSTROM T. Theory and practice of recursive identification[M]. Cambridge,Massachusetts:MIT Press,1983.
[132] LJUNG L. System identification-theory for the user (second edition)[M]. Upper Saddle River,New Jersey:Prentice Hall,1999.
[133] KULHAVY R. Restricted exponential forgetting in real-time identification[J]. Automatica,1987,23(5):589-600.
[134] COOPER J E,WORDEN K. Adaptive forgetting factors for on-line identification[C]//The 11st IMAC,International Modal Analysis Conference. Orlando,Florida,1993:132-137.
[135] COOPER J E,WORDEN K. On-line physical parameter estimation with adaptive forgetting factors[J]. Mechanical Systems and Signal Processing,2000,14(5):705-730.
[136] 梁艳春,王在申. 振动系统时变参数识别分析[J]. 吉林大学自然科学学报,1993(4):17-22. LIANG Yanchun,WANG Zaishen. Identification analysis of the time varying parameters of vibration systems[J]. Acta Scientiarum Naturalium Universitatis Jilinensis,1993(4):17-22.
[137] 梁艳春,王在申. 遗忘因子选取对于时变参数识别结果的影响[J]. 宇航学报,1996,17(1):75-80. LIANG Yanchun,WANG Zaishen. Effect of forgetting factors on estimated results of time varying parameters[J]. Journal of Astronautics,1996,17(1):75-80.
[138] SPIRIDONAKOS M D,FASSOIS S D. Parametric identification of a time-varying structure based on vector vibration response measurements[J]. Mechanical Systems and Signal Processing,2009,23(6):2029-2048.
[139] JIANG J,COOK R. Fast parameter tracking RLS algorithm with high noise immunity[J]. Electron Letter,1992,28(22):2042-2045.
[140] CHOI B Y,BIEN Z. Sliding-windowed weighted recursive least-squares method for parameter estimation[J]. Electron Letter,1989,25(20):1381-1382.
[141] KITAGAWA G. Changing spectrum estimation[J]. Journal of Sound and Vibration,1983, 89(1):433-445.
[142] GERSCH W,KITAGAWA G. A time varying AR coefficient model for modelling and simulating earthquake ground motion[J]. Earthquake Engineering & Structural Dynamics,1985,13(1):243-254.
[143] KITAGAWA G,GERSCH W. A smoothness priors time-varying AR coefficient modeling of nonstationary covariance time series[J]. IEEE Transactions on Automatic Control,1985,30(1):48-56.
[144] JIANG X Q,KITAGAWA G. A time varying coefficient vector AR modeling of nonstationary covariance time series[J]. Signal Processing,1993,33:315-331.
[145] GERSCH W,KITAGAWA G. Smoothness priors in time series,in J.C. Spall(ed.),Bayesian analysis of time series and dynamic models[M]. New York:Marcel Dekker Inc.,1988:
[146] KITAGAWA G,GERSCH W. Smoothness priors analysis of time series[M]. Berlin:Springer,1996.
[147] NIEDZWIECKI M. Identification of nonstationary stochastic systems using parallel estimation schemes[J]. IEEE Transactions on Automatic Control,1990,35(3):329-334.
[148] NIEDZWIECKI M. Identification of time-varying processes[M]. New York:John Wiley & Sons,2000.
[149] CHEN L. Vector time-varying autoregressive (TVAR) models and their application to downburst wind speeds[D]. Texas:Texas Tech University,2005.
[150] OMENZETTER P,BROWNJOHN J M W. Application of time series analysis for bridge monitoring[J]. Smart Materials & Structures,2006,15(1):129-138.
[151] ZHAN Y M,JARDINE A K S. Adaptive autoregressive modeling of non-stationary vibration signals under distinct gear states. part 1:modeling[J]. Journal of Sound and Vibration,2005,286(3):429-450.
[152] ZHAN Y M,JARDINE A K S. Adaptive autoregressive modeling of non-stationary vibration signals under distinct gear states. part 2:experimental analysis[J]. Journal of Sound and Vibration,2005,286(3):451-476.
[153] AVENDANO-VALENCIA L D,FASSOIS S D. In-operation identification of wind turbine non-stationary dynamics:a comparison of various methods[C]//IOMAC 2013 International Operational Modal Analysis Conference. Guimaraes,Portugal,2013:1-8.
[154] AVENDANO-VALENCIA L D,FASSOIS S D. Generalized stochastic constraint TARMA models for in-operation identification of wind turbine non-stationary dynamics[J]. Key Engineering Materials,2013,570:587-594.
[155] AVENDANO-VALENCIA L D,FASSOIS S D. Decoupled estimation of the parameters and hyperparameters of generalized stochastic constraint TARMA models[C]//The 6th International Symposium on Communications,Control and Signal Processing. Athens,Greece,2014:429-432.
[156] AVENDANO-VALENCIA L D,FASSOIS S D. Markov Chain Monte Carlo estimation of non-stationary GSC-TARMA models:application to random vibration modelling and analysis for an operating wind turbine[C]//ISMA 2016 International Conference on Noise and Vibration Engineering. Leuven,2016:4153-4167.
[157] RAO T S. The fitting of non-stationary time-series models with time-dependent parameters[J]. Journal of the Royal Statistical Society,1970,32(2):312-322.
[158] MENDEL J M. Discrete techniques of parameter estimation:the equation error formulation[M]. New York:Marcel Dekker Inc.,1973.
[159] KOZIN F. Estimation and modeling of nonstationary time series[C]//Symposium of Applications of Computer Method in Engineering. Los Angeles,California,1977:603-612.
[160] GRENIER Y. Time-dependent ARMA modeling of nonstationary signals[J]. IEEE Transactions on Acoustics,Speech,and Signal Processing,1983,31(4):899-911.
[161] GRENIER Y. Estimation of non-stationary moving average models[C]//IEEE International Conference on Acoustics,Speech,and Signal Processing. Boston,Massachusetts,1983:268-271.
[162] GRENIER Y. Time-frequency analysis using time-dependent ARMA models[C]//IEEE International Conference on Acoustics,Speech,and Signal Processing. San Diego,California,1984:270-273.
[163] CHEVALIER M,CHOLLET C,GRENIER Y. Speech analysis and restitution using time-dependent autoregressive models[C]//IEEE International Conference on Acoustics,Speech,and Signal Processing. Tampa,Florida,1985:501-504.
[164] GRENIER Y. Nonstationary ARMA models via simultaneous AR and MA estimation[C]//IEEE International Conference on Acoustics,Speech,and Signal Processing. Tokyo,Japan,1986:2339-2342.
[165] NIEDZWIECKI M. Functional series modeling approach to identification of nonstationary stochastic systems[J]. IEEE Transactions on Automatic Control,1988,33(10):955-961.
[166] NIEDZWIECKI M. Recursive functional series modeling estimators for identification of time-varying plants-more bad news than good?[J]. IEEE Transactions on Automatic Control,1990,35(5):610-616.
[167] TSATSANIS M K,GIANNAKIS G B. Time-varying system identification and model validation using wavelets[J]. IEEE Transactions on Signal Processing,1993,41(12):3512-3523.
[168] TSATSANIS M K,GIANNAKIS G B. Modelling and equalization of rapidly fading channels[J]. International Journal of Adaptive Control and Signal Processing,1996,10(2-3):159-176.
[169] GERSH W,KITAGAWA G. A time-varying multivariate autoregressive modeling of econometric time series[C]//The Business and Statics ASA Annual Meeting. Toronto,1983:399-404.
[170] SATO J R,MORETTIN P A,ARANTES P R,et al. Wavelet based time-varying vector autoregressive modelling[J]. Computational Statistics & Data Analysis,2007,51:5847-5866.
[171] SPIRIDONAKOS M D,FASSOIS S D. Adaptable functional series TARMA models for non-stationary signal representation and their application to mechanical random vibration modeling[J]. Signal Processing,2014,96(1):63-79.
[172] 杨武. 时变结构模态参数的时域辨识方法及在线辨识技术研究[D]. 北京:北京理工大学,2015. YANG Wu. Study on modal parameter estimation and on-line identification technology for linear time-varying structures in time-domain[D]. Beijing:Beijing Institute of Technology,2015.
[173] 杨武,刘莉,周思达,等. 前后向时间序列模型联合估计的时变结构模态参数辨识[J]. 振动与冲击,2015,34(3):129-135. YANG Wu,LIU Li,ZHOU Sida,et al. Modal parameter identification of time-varying structures using a forward-backward time series model based on joint estimation[J]. Journal of Vibration and Shock,2015,34(3):129-135.
[174] 杨武,刘莉,周思达,等. 基于Kriging形函数的线性时变结构模态参数辨识[J]. 航空学报,2015,36(4):1169-1176. YANG Wu,LIU Li,ZHOU Sida,et al. Modal parameter identification of linear time-varying structures using Kriging shape function[J]. Acta Aeronautica et Astronautica Sinica,2015,36(4):1169-1176.
[175] 杨武,刘莉,周思达,等. 移动最小二乘法的时变结构模态参数辨识[J]. 机械工程学报,2016,52(3):79-85. YANG Wu,LIU Li,ZHOU Sida,et al. Modal parameter identification of time-varying structures via moving least square method[J]. Journal of Mechanical Engineering,2016,52(3):79-85.
[176] ZHOU S D,MA Y C,LIU L,et al. Output-only modal parameter estimator of linear time-varying structural systems based on vector TAR model and least squares support vector machine[J]. Mechanical Systems and Signal Processing,2018,98:722-755.
[177] XIE X,EVANS R J. Discrete time stochastic adaptive control for time-varying systems[J]. IEEE Transactions on Automatic Control,1984,29(7):638-640.
[178] LI Z. Discrete-time adaptive control of deterministic fast time-varying systems[J]. IEEE Transactions on Automatic Control,1987,32(5):444-447.
[179] NIEDZWIECKI M,KLAPUT T. Fast recursive basis function estimators for identification of time-varying processes[J]. IEEE Transactions on Signal Processing,2002,50(8):1925-1934.
[180] NIEDZWIECKI M,KLAPUT T. Fast algorithms for identification of periodically varying systems[J]. IEEE Transactions on Signal Processing,2003,51(12):3270-3279.
[181] JOENSEN A,MADSEN H,NIELSEN H A,et al. Tracking time-varying parameters with local regression[J]. Automatica,2000, 36(1):1199-1204.
[182] MA Z S,LIU L,ZHOU S D,et al. Parametric output-only identification of time-varying structures using a kernel recursive extended least squares TARMA approach[J]. Mechanical Systems and Signal Processing,2018,98:684-701.
[183] MA Z S,LIU L,ZHOU S D,et al. Output-only recursive identification of time-varying structures using a gaussian process regression TARMA approach[C]//ISMA2016 International Conference on Noise and Vibration Engineering. Leuven,2016:2859-2872.
[184] MA Z S,LIU L,ZHOU S D,et al. Output-only modal parameter recursive estimation of time-varying structures via a kernel ridge regression FS-TARMA approach[J]. Shock and Vibration,2017,2017(ID8176593):1-14.
[185] BAO C,HAO H,LI Z X,et al. Time-varying system identification using a newly improved HHT algorithm[J]. Computers & Structures,2009,87(23-24):1611-1623.
[186] POULIMENOS A G,FASSOIS S D. Output-only stochastic identification of a time-varying structure via functional series TARMA models[J]. Mechanical Systems and Signal Processing,2009,23(4):1180-1204.
[187] SPIRIDONAKOS M D,FASSOIS S D. Output-only identification of time-varying structures via a complete FS-TARMA model approach[C]//IOMAC2011 International Operational Modal Analysis Conference. Istanbul,Turkey,2011:1-8.
[188] SPIRIDONAKOS M D,FASSOIS S D. An FS-TAR based method for vibration-response-based fault diagnosis in stochastic time-varying structures:experimental application to a pick-and-place mechanism[J]. Mechanical Systems and Signal Processing,2013,38(1):206-222.
[189] 李雷. 工况模态分析在时变航天器结构中的应用[D]. 上海:复旦大学,2011. LI Lei. Application of operational modal analysis for time-varying aerospace structures[D]. Shanghai:Fudan University,2011.
[190] ZHOU S D,HEYLEN W,SAS P,et al. Parametric modal identification of time-varying structures and the validation approach of modal parameters[J]. Mechanical Systems and Signal Processing,2014,47(1-2):94-119.
[191] 马志赛,刘莉,周思达,等. 移动质量简支梁耦合时变系统建模与实验设计[J]. 振动、测试与诊断,2015,35(5):913-920+993. MA Zhisai,LIU Li,ZHOU Sida,et al. Modeling and experimental design of the coupled moving-mass and simply supported beam time-varying system[J]. Journal of Vibration,Measurement & Diagnosis,2015,35(5):913-920,993.
[192] WORDEN K,TOMLINSON G R. Nonlinearity in structural dynamics:detection,identification and modelling[M]. Bristol:Institute of Physics Publishing,2000.
[193] 续秀忠. 时变线性结构模态参数识别的理论及实验研究[D]. 上海:上海交通大学,2003. XU Xiuzhong. Theoretic and experimental study of modal parameter identification of time-varying linear structures[D]. Shanghai:Shanghai Jiao Tong University,2003.
[194] 王学敏. 基于Hilbert-Huang变换的桥梁监测信号分析与处理和时变模态参数识别[D]. 长沙:中南大学,2008. WANG Xuemin. Monitoring signal analysis & processing and time-varying modal parameter identification for bridges by using Hilbert-Huang transform[D]. Changsha:Central South University,2008.
[195] 李赞澄. 时变系统模态参数识别的研究[D]. 南京:南京航空航天大学,2010. LI Zancheng. Study on modal parameters identification of time-varying system[D]. Nanjing:Nanjing University of Aeronautics and Astronautics,2010.