Abstract
The present study exploits the maximum likelihood identification framework for deriving statistically-optimal models of nonlinear mechanical systems. The identification problem is formulated in the frequency domain, and model parameters are calculated by minimising a weighted least-squares cost function. Initial values of the model parameters are obtained by means of a nonlinear subspace algorithm. The complete identification methodology is first demonstrated on a Duffing oscillator, prior to being applied to a full-scale aerospace structure.
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References
Ahlquist JR, Carreno JM, Climent H, de Diego R, de Alba J (2010) Assessment of nonlinear structural response in A400M GVT. In: Proceedings of the international modal analysis conference XXVIII, Jacksonville, FL
Link M, Boeswald M, Laborde S, Weiland M, Calvi A (2011) Non-linear experimental modal analysis and application to satellite vibration test data. In: Proceedings of the 3rd international conference on computational methods in structural dynamics and earthquake engineering, Corfu
Noël JP, Renson L, Kerschen G, Peeters B, Manzato S, Debille J (2013) Nonlinear dynamics analysis of an F-16 aircraft using GVT data. In: Proceedings of the international forum on aeroelasticity and structural dynamics, Bristol
Kerschen G, Worden K, Vakakis AF, Golinval JC (2006) Past, present and future of nonlinear system identification in structural dynamics. Mech Syst Signal Process 20:505–592
Noël JP, Kerschen G (2013) Frequency-domain subspace identification for nonlinear mechanical systems. Mech Syst Signal Process 40: 701–717
Noël JP, Marchesiello S, Kerschen G (2014) Subspace-based identification of a nonlinear spacecraft in the time and frequency domains. Mech Syst Signal Process 43:217–236
Noël JP, Kerschen G, Foltête E, Cogan S (2013) Frequency-domain subspace identification of nonlinear mechanical systems - application to a solar array structure. In: Proceedings of the international modal analysis conference XXXI, Garden Grove, CA
Pintelon R, Schoukens J (2001) System identification: a frequency domain approach, 1st edn. IEEE Press, New York
Paduart J, Lauwers L, Swevers J, Smolders K, Schoukens J, Pintelon R (2010) Identification of nonlinear systems using polynomial nonlinear state space models. Automatica 46:647–656
Adams DE, Allemang RJ (2000) A frequency domain method for estimating the parameters of a non-linear structural dynamic model through feedback. Mech Syst Signal Process 14(4):637–656
Schetzen M (1980) The Volterra and Wiener theories of nonlinear systems, 1st edn. Wiley, New York
Schoukens J, Pintelon R, Rolain Y, Dobrowiecki T (2001) Frequency response function measurements in the presence of nonlinear distortions. Automatica 37:939–946
Van Overschee P, De Moor B (1996) Continuous-time frequency domain subspace system identification. Signal Process 52:179–194
Yang ZJ, Sanada S (2000) Frequency domain subspace identification with the aid of the w-operator. Electr Eng Jpn 132(1):46–56
Marchesiello S, Garibaldi L (2008) A time domain approach for identifying nonlinear vibrating structures by subspace methods. Mech Syst Signal Process 22:81–101
Ljung L (1999) System identification: theory for the user, 2nd edn. Prentice-Hall, Upper Saddle River
Schoukens J, Renneboog J (1986) Modeling of noise influence of the Fourier coefficients after a discrete Fourier transform. IEEE Trans Instrum Meas 35(3):278–286
Sracic MW, Allen MS, Sumali H (2012) Identifying the modal properties of nonlinear structures using measured free response time histories from a scanning last Doppler vibrometer. In: Proceedings of the international modal analysis conference XIX, Jacksonville, FL
Giuliani P, Di Maio D, Schwingshackl CW, Martarelli M, Ewins DJ (2013) Six degrees of freedom measurement with continuous scanning laser doppler vibrometer. Mech Syst Signal Process 20(2):367–383
Russell AG (2000) Thick skin, faceted, CFRP, monocoque tube structure for smallsats. In: Proceedings of the European conference on spacecraft structures, materials and mechanical testing, Noordwijk
Camarasa P, Kiryenko S (2009) Shock attenuation system for spacecraft and adaptor (SASSA). In: Proceedings of the European conference on spacecraft structures, materials and mechanical testing, Toulouse
Noël JP, Renson L, Kerschen G (2013) Experimental identification of the complex dynamics of a strongly nonlinear spacecraft structure. In: Proceedings of the ASME international design engineering technical conferences, Portland, OR
Vacher P, Jacquier B, Bucharles A (2010) Extension of the MAC criterion to complex modes. In: Proceedings of the international conference on noise and vibration engineering, Leuven
Acknowledgements
The author J.P. Noël is a Research Fellow (FRIA fellowship) of the Fonds de la Recherche Scientifique—FNRS which is gratefully acknowledged.
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© 2014 The Society for Experimental Mechanics, Inc.
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Noël, J.P., Schoukens, J., Kerschen, G. (2014). A Stochastic Framework for Subspace Identification of a Strongly Nonlinear Aerospace Structure. In: Kerschen, G. (eds) Nonlinear Dynamics, Volume 2. Conference Proceedings of the Society for Experimental Mechanics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-04522-1_16
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DOI: https://doi.org/10.1007/978-3-319-04522-1_16
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