Identification of non-stationary dynamical systems using multivariate ARMA models

Bertha, Mathieu; Golinval, Jean-Claude

doi:10.1016/j.ymssp.2016.11.024

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Identification of non-stationary dynamical systems using multivariate ARMA models

Bertha, Mathieu; Golinval, Jean-Claude

2017 • In Mechanical Systems and Signal Processing, 88, p. 166-179

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https://hdl.handle.net/2268/203829

DOI
10.1016/j.ymssp.2016.11.024

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Keywords :

Time-varying systems; modal identification; vector auto-regressive moving average modeling; basis functions; moving mass problem

Abstract :

[en] This paper is concerned by the modal identification of time-varying mechanical systems. Based on previous works about autoregressive moving average models in vector form (ARMAV) for the modal identification of linear time invariant systems, and time-varying autoregressive moving average models (TV-ARMA) for the identification of nonstationary systems, a time-varying ARMAV (TV-ARMAV) model is presented for the multivariate identification of time-varying systems. It results in the identification of not only the time-varying poles of the system but also of its respective time-varying mode shapes. The method is applied on a time-varying structure composed of a beam on which a mass is moving.

Disciplines :

Aerospace & aeronautics engineering
Mechanical engineering

Author, co-author :

Bertha, Mathieu ; Université de Liège > Département d'aérospatiale et mécanique > LTAS - Vibrations et identification des structures

Golinval, Jean-Claude ; Université de Liège > Département d'aérospatiale et mécanique > LTAS - Vibrations et identification des structures

Language :

English

Title :

Identification of non-stationary dynamical systems using multivariate ARMA models

Publication date :

01 May 2017

Journal title :

Mechanical Systems and Signal Processing

ISSN :

0888-3270

eISSN :

1096-1216

Publisher :

Elsevier, Atlanta, Georgia

Volume :

Pages :

166-179

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 28 November 2016

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Bibliography

[1] Garibaldi, L., Fassois, S., MSSP special issue on the identification of time varying structures and systems. Mech. Syst. Signal Process. 47:1–2 (2014), 1–2.
[2] Marchesiello, S., Bedaoui, S., Garibaldi, L., Argoul, P., Time-dependent identification of a bridge-like structure with crossing loads. Mech. Syst. Signal Process. 23:6 (2009), 2019–2028.
[3] M. Goursat, M. Döhler, L. Mevel, P. Andersen, Crystal Clear SSI for Operational Modal Analysis of Aerospace Vehicles, in: Proceedings of the IMAC-XXVIII, 2010, pp. 1421–1430.
[4] Basu, B., Nagarajaiah, S., Chakraborty, A., Online identification of linear time-varying stiffness of structural systems by wavelet analysis. Struct. Health Monit. 7 (2008), 21–36.
[5] Xu, X., Shi, Z., You, Q., Identification of linear time-varying systems using a wavelet-based state-space method. Mech. Syst. Signal Process. 26 (2012), 91–103.
[6] Staszewski, W.J., Wallace, D.M., wavelet-based frequency response function for time-variant systems - an exploratory study. Mech. Syst. Signal Process. 47:1–2 (2014), 35–49.
[7] N.E. Huang, S.S. Shen, Hilbert-Huang Transform and its Applications, Vol. 5 of Interdisciplinary Mathematical Sciences, World Scientific Publishing Co. Pte. Ltd., 2005.
[8] Feldman, M., Hilbert Transform Applications in Mechanical Vibration. 2011, John Wiley & Sons, Ltd, Chichester, UK.
[9] Shi, Z., Law, S., Xu, X., Identification of linear time-varying MDOF dynamic systems from forced excitation using Hilbert transform and EMD method. J. Sound Vib. 321:3–5 (2009), 572–589.
[10] M. Bertha, J.-C. Golinval, Experimental modal analysis of a beam travelled by a moving mass using Hilbert Vibration Decomposition, in: Proceedings of Eurodyn IX, Porto, 2014.
[11] M. Bertha, J.-C. Golinval, Modal identification of time-varying systems using Hilbert transform and signal decomposition, in: Proceedings of the International Conference on Noise and Vibration Engineering, ISMA 2014, Leuven, 2014, pp. 2409–2419.
[12] Liu, K., Identification of linear time-varying systems. J. Sound Vib. 206:4 (1997), 487–505.
[13] Liu, K., Extension of modal analysis to linear time-varying systems. J. Sound Vib. 226:1 (1999), 149–167.
[14] Liu, K., Deng, L., Identification of pseudo-natural frequencies of an axially moving cantilever beam using a subspace-based algorithm. Mech. Syst. Signal Process. 20:1 (2006), 94–113.
[15] Grenier, Y., Time-dependent ARMA modeling of nonstationary signals. IEEE Trans. Acoust., Speech, Signal Process. 31:4 (1983), 899–911.
[16] Grenier, Y., Modèles ARMAà coefficients dépendant du temps estimateurs et applications. Traitement du signal 3 (1986), 219–233.
[17] Rao, T.S., The fitting of non-stationary time-series models with time-dependent parameters. J. R. Stat. Soc. Ser. B (Stat. Methodol.) 32:2 (1970), 312–322.
[18] Spiridonakos, M., Poulimenos, A., Fassois, S., Output-only identification and dynamic analysis of time-varying mechanical structures under random excitation: a comparative assessment of parametric methods. J. Sound Vib. 329:7 (2010), 768–785.
[19] Spiridonakos, M., Fassois, S., Non-stationary random vibration modelling and analysis via functional series time-dependent ARMA (FS-TARMA) models - A critical survey. Mech. Syst. Signal Process. 47:1–2 (2013), 1–50.
[20] Spiridonakos, M.D., Fassois, S.D., Parametric identification of a time-varying structure based on vector vibration response measurements. Mech. Syst. Signal Process. 23:6 (2009), 2029–2048.
[21] P. Andersen, Identification of civil engineering structures using vector ARMA models, (Ph.D. thesis), 1997.
[22] Bodeux, J.-B., Golinval, J.-C., Application of ARMAV models to the identification and damage detection of mechanical and civil engineering structures. Smart Mater. Struct. 10:3 (2001), 479–489.
[23] B. Piombo, E. Giorcelli, L. Garibaldi, A. Fasana, Structures Identification Using ARMAV Models, in: Society for Experimental Mechanics (Ed.), IMAC 11, International Modal Analysis Conference, Orlando, 1993, pp. 588–592.
[24] P. Andersen, R. Brincker, P.H. Kirkegaard, Theory of covariance equivalent ARMAV models of civil engineering structures, in: IMAC XIV - Proceedings of the 14th International Modal Analysis Conference, Vol. 71, 1995.
[25] L. Ljung, System Identification: Theory for the User, 1999.
[26] Zadeh, L.A., Frequency analysis of variable networks. Proc. IRE 27:3 (1950), 170–177.
[27] K. Zenger, R. Ylinen, Poles and Zeros of Multivariable Lienar Time-Varying Systems, Proceedings of the 15th IFAC World Congress.
[28] Zhou, S.-D., Heylen, W., Sas, P., Liu, L., Parametric modal identification of time-varying structures and the validation approach of modal parameters. Mech. Syst. Signal Process. 47:1–2 (2014), 94–119.
[29] B. Peeters, H. Van der Auweraer, PolyMAX: A revolution in operational modal analysis, in: Proceedings of the 1st International Operational Modal Analysis Conference, Copenhagen, 2005.
[30] Niedzwiecki, M., Identification of Time-Varying Processes. 2000, John Wiley & Sons, Inc., New York, NY, USA.
[31] A. Beex, P. Shan, A time-varying Prony method for instantaneous frequency estimation at low SNR, in: ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349), Vol. 3, 1999, pp. 5–8.
[32] Rixen, D., Geradin, M., Mechanical Vibrations: Theory and Application to Structural Dynamics. 2nd edition, 1997, John Wiley & Sons, Ltd.
[33] Friswell, M., Mottershead, J.E., Finite Element Model Updating in Structural Dynamics. 1995, Springer.
[34] N.A.J. Lieven, D.J. Ewins, Spatial correlation of mode shapes: the coordinate modal assurance criterion (COMAC), in: Proceedings of the 6th International Modal Analysis Conference (IMAC), 1988, pp. 690–695.
[35] D.L. Hunt, Application of an enhanced Coordinate Modal Assurance Criterion, in: Proceedings of the 10th International Modal Analysis Conference, San Diego, 1992, pp. 66–71.
[36] J. O′Callahan, P. Avitabile, R. Riemer, System Equivalent Reduction Expansion Process (SEREP), in: Proceedings of the Seventh International Modal Analysis Conference, Las Vegas, 1989.