0
Research Papers

A New Efficient System Identification Method for Nonlinear Multiple Degree-of-Freedom Structural Dynamic Systems

[+] Author and Article Information
Yuzhu Guo

Department of Automatic Control
and Systems Engineering,
University of Sheffield,
Mappin Street,
Sheffield S1 3JD, UK
e-mail: yuzhu.guo@shef.ac.uk

L. Z. Guo

Department of Automatic Control
and Systems Engineering,
University of Sheffield,
Mappin Street,
Sheffield S1 3JD, UK
e-mail: l.guo@shef.ac.uk

S. A. Billings

Department of Automatic Control
and Systems Engineering,
University of Sheffield,
Mappin Street,
Sheffield S1 3JD, UK
e-mail: s.billings@shef.ac.uk

Z. Q. Lang

Department of Automatic Control
and Systems Engineering,
University of Sheffield,
Mappin Street,
Sheffield S1 3JD, UK
e-mail: z.lang @ sheffield.ac.uk

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 26, 2013; final manuscript received August 18, 2015; published online October 1, 2015. Assoc. Editor: Corina Sandu.

J. Comput. Nonlinear Dynam 11(2), 021012 (Oct 01, 2015) (8 pages) Paper No: CND-13-1229; doi: 10.1115/1.4031488 History: Received September 26, 2013; Revised August 18, 2015

A new efficient system identification method is introduced to determine the model structure and parameter estimates of an unknown structural system to produce a multi-input multi-output (MIMO) model. No a priori knowledge is assumed regarding the nonlinearities. When the system involves lumped masses, all the information about the locations, types, and coefficients of both linear and nonlinear links which connect the lumped masses in the system can be determined in one efficient procedure. The new algorithm yields a parsimonious continuous time model which is useful for the interpretation of the system in practical applications. An illustrative example demonstrates the efficiency of the new method.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Paz, M. , and Leigh, W. , 2004, Structural Dynamics: Theory and Computation, 5th ed., Kluwer Academic, Boston, MA/London.
Clough, R. W. , and Penzien, J. , 1993, Dynamics of Structures, McGraw-Hill Book, Singapore.
Worden, K. , and Tomlinson, G. R. , 2001, Nonlinearity in Structural Dynamics: Detection, Identification and Modelling, Institute of Physics Publishing, Bristol, UK/Philadelphia, PA.
Van Der Auweraer, H. , 2001, “ Structural Dynamics Modeling Using Modal Analysis: Applications, Trends and Challenges,” Instrumentation and Measurement Technology Conference (IMTC 2001), Budapest, Hungary, May 21–23, Vol. 3, pp. 1502–1509.
Masri, S. F. , and Caughey, T. K. , 1979, “ A Nonparametric Identification Technique for Nonlinear Dynamic Problems,” ASME J. Appl. Mech., 46(2), pp. 433–447. [CrossRef]
Crawley, E. F. , and Aubert, A. C. , 1986, “ Identification of Nonlinear Structural Elements by Force-State Mapping,” AIAA J., 24(1), pp. 155–162. [CrossRef]
Masri, S. F. , Bekey, G. A. , Sassi, H. , and Caughey, T. K. , 1982, “ Non-Parametric Identification of a Class of Nonlinear Multidegree Dynamic Systems,” Earthquake Eng. Struct. Dyn., 10(1), pp. 1–30. [CrossRef]
Mohammad, K. S. , Worden, K. , and Tomlinson, G. R. , 1992, “ Direct Parameter Estimation for Linear and Non-Linear Structures,” J. Sound Vib., 152(3), pp. 471–499. [CrossRef]
Ajjan Al-Hadid, M. , and Wright, J. R. , 1989, “ Developments in the Force-State Mapping Technique for Non-Linear Systems and the Extension to the Location of Non-Linear Elements in a Lumped-Parameter System,” Mech. Syst. Signal Process., 3(3), pp. 269–290. [CrossRef]
Rice, H. J. , and Fitzpatrick, J. A. , 1988, “ A Generalised Technique for Spectral Analysis of Non-Linear Systems,” Mech. Syst. Signal Process., 2(2), pp. 195–207. [CrossRef]
Richards, C. M. , and Singh, R. , 1998, “ Identification of Multi Degree of Freedom Nonlinear System Under Random Excitations by the Reverse Path Spectral Method,” J. Sound Vib., 213(4), pp. 673–708. [CrossRef]
Billings, S. A. , 2013, Nonlinear System Identification: Narmax Methods in the Time, Frequency, and Spatio-Temporal Domains, Wiley, Hoboken, NJ.
Coca, D. , and Billings, S. A. , 2002, “ Identification of Finite Dimensional Models of Infinite Dimensional Dynamical Systems,” Automatica, 38(11), pp. 1851–1865. [CrossRef]
Kerschen, G. , Worden, K. , Vakakis, A. F. , and Golinval, J.-C. , 2006, “ Past, Present and Future of Nonlinear System Identification in Structural Dynamics,” Mech. Syst. Signal Process., 20(3), pp. 505–592. [CrossRef]
Setio, S. , Setio, H. D. , and Jezequel, L. , 1992, “ Modal Analysis of Nonlinear Multi-Degree-of-Freedom Structure,” Int. J. Anal. Exp. Modal Anal., 7(2), pp. 75–93.
Preisig, H. A. , and Rippin, D. W. T. , 1993, “ Theory and Application of the Modulating Function Method—I. Review and Theory of the Method and Theory of the Spline-Type Modulating Functions,” Comput. Chem. Eng., 17(1), pp. 1–16. [CrossRef]
Guo, Y. , Guo, L. Z. , Billings, S. A. , and Wei, H.-L. , “ Identification of Continuous-Time Models for Nonlinear Dynamic Systems From Discrete Data,” Int. J. Syst. Sci. (in press).
Billings, S. A. , Chen, S. , and Korenberg, M. J. , 1989, “ Identification of MIMO Non-Linear Systems Using a Forward-Regression Orthogonal Estimator,” Int. J. Control, 49(6), pp. 2157–2189. [CrossRef]
Chen, S. , Billings, S. A. , and Luo, W. , 1989, “ Orthogonal Least Squares Methods and Their Application to Non-Linear System Identification,” Int. J. Control, 50(5), pp. 1873–1896. [CrossRef]
Worden, K. , 1990, “ Data Processing and Experiment Design for the Restoring Force Surface Method, Part I: Integration and Differentiation of Measured Time Data,” Mech. Syst. Signal Process., 4(4), pp. 295–319. [CrossRef]
Chesher, A. , 1991, “ The Effect of Measurement Error,” Biometrika, 78(3), pp. 451–462. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

An example of system with two nonlinear links

Grahic Jump Location
Fig. 2

An MDOF structural system

Grahic Jump Location
Fig. 3

Approximation of the nonlinearity nl3 between m2 and m4 : (a) ninth-order approximation of cube-root nonlinearities in subsystem 2 and 4 and (b) approximation of the cube-root nonlinearity by different orders of polynomials

Grahic Jump Location
Fig. 4

Responses of the original system and identified model to a harmonic input applied on m3 :—output of the real system and – output of the identified model

Grahic Jump Location
Fig. 5

Phase portraits of the response of the original system and the model predicted output of the identified model: (a) original system and (b) identified model

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In