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.
Issue Section:
Research Papers
References
1.
Paz
, M.
, and Leigh
, W.
, 2004
, Structural Dynamics: Theory and Computation
, 5th ed., Kluwer Academic
, Boston, MA/London
.2.
Clough
, R. W.
, and Penzien
, J.
, 1993
, Dynamics of Structures
, McGraw-Hill Book
, Singapore.3.
Worden
, K.
, and Tomlinson
, G. R.
, 2001
, Nonlinearity in Structural Dynamics: Detection, Identification and Modelling
, Institute of Physics Publishing
, Bristol, UK/Philadelphia, PA
.4.
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
.5.
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
.6.
Crawley
, E. F.
, and Aubert
, A. C.
, 1986
, “Identification of Nonlinear Structural Elements by Force-State Mapping
,” AIAA J.
, 24
(1
), pp. 155
–162
.7.
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
.8.
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
.9.
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
.10.
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
.11.
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
.12.
Billings
, S. A.
, 2013
, Nonlinear System Identification: Narmax Methods in the Time, Frequency, and Spatio-Temporal Domains
, Wiley
, Hoboken, NJ
.13.
Coca
, D.
, and Billings
, S. A.
, 2002
, “Identification of Finite Dimensional Models of Infinite Dimensional Dynamical Systems
,” Automatica
, 38
(11
), pp. 1851
–1865
.14.
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
.15.
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
.16.
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
.17.
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).18.
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
.19.
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
.20.
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
.21.
Chesher
, A.
, 1991
, “The Effect of Measurement Error
,” Biometrika
, 78
(3
), pp. 451
–462
.Copyright © 2016 by ASME
You do not currently have access to this content.