Modal Parameter Estimation of Time-varying Structures Using GSC-TARMA Models Based on Vector Vibration Response Measurements

doi:10.3901/JME.2019.15.183

Abstract

Abstract: The problem of output-only identification of time-varying structures based on vector vibration response measurements is considered. A generalized stochastic constraints vector time-dependent auto-regressive moving average (GSC-VTARMA) model is presented, which is an extension form of the generalized stochastic constraints time-dependent ARMA (GSC-TARMA) model. In order to reduce computation complexity, an improved generalized stochastic constraints vector time-dependent auto-regressive moving average (GSC-TARMA^*) model is subsequently proposed. The proposed model is validated by non-stationary vibration signals of a numerical system with time-varying stiffness and a laboratory time-varying structure consisting of a simply supported beam and a moving mass. The results indicate that the proposed GSC-VTARMA^* model achieves same identification accuracy but less computation complexity to the GSC-VTARMA model, and achieves better identification robustness and higher data utilization to the GSC-TARMA model. Furthermore, the proposed model shows a similar identification accuracy and lower computational cost than the traditional FS-VTARMA model. Due to the recursive algorithm used by the GSC-VTARMA^* model, its enhanced online identification capability has also been demonstrated.

Key words: BPMN, Coupling relationship, Dynamic characteristics, energy units, CNC Machining tools, generalized stochastic constraints, modal parameter estimation, time-varying structures, vector vibration responses

CLC Number:

TP391
TH113

YU Lei, LIU Li, MA Zhisai, KANG Jie. Modal Parameter Estimation of Time-varying Structures Using GSC-TARMA Models Based on Vector Vibration Response Measurements[J]. Journal of Mechanical Engineering, 2019, 55(15): 183-192.

References

[1] AU F T K,IANG R J,CHEUNG Y K. Parameter identification of vehicles moving on continuous bridges[J]. Journal of Sound and Vibration,2004,269(1):91-111.
[2] KOPMAZ O,ANDERSON K S. On the eigenfrequencies of a flexible arm driven by a flexible shaft[J]. Journal of Sound & Vibration,2001,240(4):679-704.
[3] 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):263-285.
[4] WIE B. Solar sail attitude control and dynamics,Part 1[J]. Journal of Guidance Control & Dynamics,2004,27(4):536-544.
[5] 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.
[6] 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.
[7] 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 & Signal Processing,2006,20(4):763-816.
[8] NIEDŹWIECKI M. Identification of time-varying processes[M]. Hoboken:John Wiley & Sons,LTD,2000.
[9] KITAGAWA G,GERSCH W. Smoothness priors analysis of time series[M]. Berlin:Springer,1996.
[10] XU Xiuzhong,ZHANG Zhiyi,HUA Hongxing,et al. Identification of time-variant modal parameters by a time-varying parametric approach[J]. Acta Aeronautica Et Astronautica Sinica,2003,24(3):230-233.
[11] 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.
[12] 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):175-224.
[13] FLORAKIS A,FASSOIS S D,HEMEZ F M. MIMO LMS-ARMAX identification of vibrating structures-Part Ⅱ:A critical assessment[J]. Mechanical Systems & Signal Processing,2001,15(4):737-758.
[14] 马志赛,丁千,刘莉,等. 线性时变结构模态参数时域辨识方法的研究进展[J]. 机械工程学报,2018,54(23):137-159. MA Zhisai,DING Qian,LIU Li,et al. Reaearch progress on time-domain modal parameter estimation methods for linear time-varying structures[J]. Journal of Mechanical Engineering,2018,54(23):137-159.
[15] YANG J N,LIN S. Identification of parametric variations of structures based on least squares estimation and adaptive tracking technique[J]. Journal of Engineering Mechanics,2005,131(3):290-298.
[16] YANG J N,PAN S,LIN S. Least-squares estimation with unknown excitations for damage identification of structures[J]. Journal of Engineering Mechanics,2007,133(1):12-21.
[17] GOETHALS I,MEVEL L,BENVENISTE A,et al. Recursive output only subspace identification for in-flight flutter[C]//Proceedings of the 22nd International Modal Analysis Conference,Dearborn,Michigan,2004.
[18] MEVEL L,BASSEVILLE M,BENVENISTE A. Fast in-flight detection of flutter onset:A statistical approach[J]. Journal of Guidance Control & Dynamics,2003,28(3):431-438.
[19] LIU K,DENG L. Identification of pseudo-natural frequencies of an axially moving cantilever beam using a subspace-based algorithm[J]. Mechanical Systems & Signal Processing,2006,20(1):94-113.
[20] GERSCH W,KITAGAWA G. A time varying multivariate autoregressive modeling of econometric time series[C]//Proceedings of the Business and Statistics ASA Annual Meeting,Toronto,1983,399-404.
[21] 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(12):5847-5866.
[22] KITAGAWA G. Changing spectrum estimation[J]. Journal of Sound and Vibration,1983,89(3):433-445.
[23] 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.
[24] GERSCH W,KITAGAWA G. A time varying AR coefficient model for modelling and simulating earthquake ground motion[J]. Earthquake Engineering and Structural Dynamics,1985,13(1):243-254.
[25] CHEN L. Vector time-varying autoregressive (TVAR) models and their application to downburst wind speeds[D]. Texas:Texas Tech University,2005.
[26] 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.
[27] YANG Wu,LIU Li,ZHOU Sida,et al. Moving kriging shape function modeling of vector TARMA models for modal identification of linear time-varying structural systems[J]. Journal of Sound & Vibration,2015,354:254-277.
[28] 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]//Proceedings of the International Conference on Noise and Vibration Engineering,Leuven,2016.
[29] DAN S. Optimal state estimation:Kalman,H∞,and nonlinear approaches[M]. New York:Wiley-Interscience,2006.
[30] 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.
[31] 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. MA Zhisai,LIU Li,ZHOU Sida,et al. Modelling and experimental design of the coupled moving-mass and simply supported beam time-varying system[J]. Journal of Vibration Measurement and Dagnosis,2015,35(5):913-920.