Nonlinear System Identification in Structural Dynamics: Current Status and Future Directions

Nonlinear system identification aims at developing high-fidelity mathematical models in the presence of nonlinearity from input and output measurements performed on the real structure. The present paper is a discussion of the recent developments in this research field. Three of the latest approaches are presented, and application examples are considered to illustrate their fundamental concepts, advantages and limitations. Another objective of this paper is to identify future research needs, which would make the identification of structures with a high modal density in a broad frequency range viable.

[1]  John Crowley,et al.  THE MULTIVARIATE MODE INDICATOR FUNCTION IN MODAL ANALYSIS , 1985 .

[2]  Oleg Gendelman,et al.  Energy Pumping in Nonlinear Mechanical Oscillators: Part II—Resonance Capture , 2001 .

[3]  Brian F. Feeny,et al.  On the Proper Orthogonal Modes and Normal Modes of Continuous Vibration Systems , 2002 .

[4]  Rajendra Singh,et al.  IDENTIFICATION OF MULTI-DEGREE-OF-FREEDOM NON-LINEAR SYSTEMS UNDER RANDOM EXCITATIONS BY THE “REVERSE PATH” SPECTRAL METHOD , 1998 .

[5]  S. Wiggins Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

[6]  G. Kerschen,et al.  PHYSICAL INTERPRETATION OF THE PROPER ORTHOGONAL MODES USING THE SINGULAR VALUE DECOMPOSITION , 2002 .

[7]  John E. Mottershead,et al.  Results Obtained by Minimising Natural-Frequency Errors and Using Physical Reasoning , 2003 .

[8]  D. Ewins,et al.  Analytical model improvement using frequency response functions , 1994 .

[9]  David J. Ewins,et al.  Modal Testing: Theory, Practice, And Application , 2000 .

[10]  B. Feeny,et al.  On the physical interpretation of proper orthogonal modes in vibrations , 1998 .

[11]  Alexander F. Vakakis,et al.  Nonlinear System Identification in Structural Dynamics: A Short (and Biased) History , 2007 .

[12]  C. M. Richards,et al.  COMPARISON OF TWO NON-LINEAR SYSTEM IDENTIFICATION APPROACHES DERIVED FROM “REVERSE PATH” SPECTRAL ANALYSIS , 2000 .

[13]  Rajendra Singh,et al.  CHARACTERIZATION OF RUBBER ISOLATOR NONLINEARITIES IN THE CONTEXT OF SINGLE- AND MULTI-DEGREE-OF-FREEDOM EXPERIMENTAL SYSTEMS , 2001 .

[14]  P. Spanos,et al.  SPECTRAL IDENTIFICATION OF NONLINEAR STRUCTURAL SYSTEMS , 1998 .

[15]  Alex Berman,et al.  Theory of Incomplete Models of Dynamic Structures , 1971 .

[16]  COMMENTS ON “IDENTIFICATION OF MULTI-DEGREE-OF-FREEDOM NON-LINEAR SYSTEMS UNDER RANDOM EXCITATIONS BY THE ‘REVERSE PATH’ SPECTRAL METHOD” , 2000 .

[17]  Y. Songa,et al.  Simulation of dynamics of beam structures with bolted joints using adjusted Iwan beam elements , 2004 .

[18]  J. Angeles,et al.  Vibration of Strongly Nonlinear Discontinuous Systems. Foundations of Engineering Mechanics , 2002 .

[19]  Gaëtan Kerschen,et al.  "European Cost action F3 on structural dynamics. WG3: identification of non-linear systems.Activities and Results" , 2002 .

[20]  G. Kerschen,et al.  The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview , 2005 .

[21]  Sami F. Masri,et al.  A Nonparametric Identification Technique for Nonlinear Dynamic Problems , 1979 .

[22]  D. Dane Quinn,et al.  Resonance Capture in a Three Degree-of-Freedom Mechanical System , 1997 .

[23]  P. Ibáñez,et al.  Identification of dynamic parameters of linear and non-linear structural models from experimental data , 1973 .

[24]  Jann N. Yang,et al.  On-line identification of non-linear hysteretic structures using an adaptive tracking technique , 2004 .

[25]  Henry J. Rice,et al.  A generalised technique for spectral analysis of non-linear systems , 1988 .

[26]  P. Holmes,et al.  Turbulence, Coherent Structures, Dynamical Systems and Symmetry , 1996 .

[27]  M. Link,et al.  Updating of Analytical Models — Basic Procedures and Extensions , 1999 .

[28]  Identification of Certain Polynomial Nonlinear Structures by Adaptive Selectively-Sensitive Excitation , 1993 .

[29]  Gaëtan Kerschen,et al.  A model updating strategy of non‐linear vibrating structures , 2004 .

[30]  Michael Link,et al.  WORKING GROUP 1: GENERATION OF VALIDATED STRUCTURAL DYNAMIC MODELS—RESULTS OF A BENCHMARK STUDY UTILISING THE GARTEUR SM-AG19 TEST-BED , 2003 .

[31]  Gaëtan Kerschen,et al.  Identification of a continuous structure with a geometrical non-linearity. Part I: Conditioned reverse path method , 2003 .

[32]  José Roberto de França Arruda,et al.  Mechanical joint parameter estimation using frequency response functions and component mode synthesis , 1993 .

[33]  Randall J. Allemang,et al.  A FREQUENCY DOMAIN METHOD FOR ESTIMATING THE PARAMETERS OF A NON-LINEAR STRUCTURAL DYNAMIC MODEL THROUGH FEEDBACK , 2000 .

[34]  Nuno M. M. Maia,et al.  Theoretical and Experimental Modal Analysis , 1997 .

[35]  François M. Hemez,et al.  Info-gap robustness for the correlation of tests and simulations of a non-linear transient , 2004 .

[36]  James L. Beck,et al.  Updating Properties of Nonlinear Dynamical Systems with Uncertain Input , 2003 .

[37]  K. D. Dippery,et al.  An optimal control approach to nonlinear system identification , 1998 .

[38]  D. M. McFarland,et al.  Experimental study of non-linear effects in a typical shear lap joint configuration , 2004 .

[39]  Henry J. Rice,et al.  A procedure for the identification of linear and non-linear multi-degree-of-freedom systems , 1991 .

[40]  Douglas E. Adams,et al.  A time and frequency domain approach for identifying nonlinear mechanical system models in the absence of an input measurement , 2005 .

[41]  L. Gaul,et al.  Nonlinear dynamics of structures assembled by bolted joints , 1997 .

[42]  Reinhard Schmidt Updating non-linear components , 1994 .

[43]  Gaëtan Kerschen,et al.  A Frequency Domain Versus a Time Domain Identification Technique for Nonlinear Parameters Applied to Wire Rope Isolators , 2001 .

[44]  R. M. Rosenberg,et al.  On Nonlinear Vibrations of Systems with Many Degrees of Freedom , 1966 .

[45]  Julius S. Bendat,et al.  Nonlinear System Techniques And Applications , 1990 .

[46]  Wilfred D. Iwan,et al.  A generalization of the concept of equivalent linearization , 1973 .

[47]  Christophe Pierre,et al.  Normal Modes for Non-Linear Vibratory Systems , 1993 .

[48]  M. Baruch Optimization Procedure to Correct Stiffness and Flexibility Matrices Using Vibration Tests , 1978 .

[49]  Richard H. Rand,et al.  A direct method for non-linear normal modes , 1974 .

[50]  Etienne Balms,et al.  A FINITE ELEMENT UPDATING PROCEDURE USING FREQUENCY RESPONSE FUNCTIONS. APPLICATIONS TO THE MlT/SERC INTERFEROMETER TESTBED , 2001 .

[51]  Hans Günther Natke,et al.  Einführung in Theorie und Praxis der Zeitreihen- und Modalanalyse , 1983 .

[52]  R C.M.,et al.  FEASIBILITY OF IDENTIFYING NON-LINEAR VIBRATORY SYSTEMS CONSISTING OF UNKNOWN POLYNOMIAL FORMS , 1999 .

[53]  T. K. Caughey,et al.  Free and forced oscillations of a dynamic system with “linear hysteretic damping” (non-linear theory) , 1970 .

[54]  R. M. Rosenberg,et al.  The Normal Modes of Nonlinear n-Degree-of-Freedom Systems , 1962 .

[55]  Robert N. Coppolino,et al.  Identification of physical parameters with memory in non-linear systems , 1995 .

[56]  Julius S. Bendat,et al.  Los Angeles, CA 90049 Spectral Techniques for Nonlinear System Analysis and Identification , 1993 .

[57]  Christophe Pierre,et al.  Accurate reduced-order models for a simple rotor blade model using nonlinear normal modes , 2001 .

[58]  T. K. Hasselman,et al.  Principal components analysis for nonlinear model correlation, updating and uncertainty evaluation , 1998 .

[59]  Winson Taam,et al.  Nonlinear System Analysis and Identification From Random Data , 1991 .

[60]  Keith Worden,et al.  IDENTIFICATION OF HYSTERETIC SYSTEMS USING THE DIFFERENTIAL EVOLUTION ALGORITHM , 2001 .

[61]  Keith Worden,et al.  An extension of force appropriation to the identification of non-linear multi-degree of freedom systems , 2000 .

[62]  Alexander F. Vakakis,et al.  Normal modes and localization in nonlinear systems , 1996 .

[63]  F. Hemez,et al.  Title : Inversion of Structural Dynamics Simulations : State-ofthe-art and Orientations of the Research , 2000 .

[64]  Ali H. Nayfeh,et al.  A Plethora of Nonlinear Dynamics Phenomena Observed in a Simple Cantilever Plate , 2003 .

[65]  Michael Link,et al.  Modelling and updating of local non-linearities using frequency response residuals , 2003 .

[66]  F. Hemez,et al.  REVIEW AND ASSESSMENT OF MODEL UPDATING FOR NON-LINEAR, TRANSIENT DYNAMICS , 2001 .

[67]  H. Voss,et al.  Non-parametric identification of non-linear oscillating systems , 2003 .

[68]  S. Masri,et al.  Robust Adaptive Neural Estimation of Restoring Forces in Nonlinear Structures , 2001 .

[69]  P. J. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[70]  Rakesh K. Kapania,et al.  Parametric identification of nonlinear structural dynamic systems using time finite element method , 1997 .

[71]  Jan R. Wright,et al.  Identification of Multi-Degree of Freedom Weakly Non-linear Systems , 2001 .

[72]  Christophe Pierre,et al.  Nonlinear Modal Analysis of Structural Systems Using Multi-Mode Invariant Manifolds , 2001 .

[73]  Jonathan E. Cooper,et al.  NORMAL-MODE FORCE APPROPRIATION—THEORY AND APPLICATION , 1999 .

[74]  F. Verhulst Nonlinear Differential Equations and Dynamical Systems , 1989 .

[75]  Gaëtan Kerschen,et al.  Feature extraction using auto-associative neural networks , 2004 .

[76]  Christophe Pierre,et al.  Finite-Element-Based Nonlinear Modal Reduction of a Rotating Beam with Large-Amplitude Motion , 2003 .

[77]  Gaëtan Kerschen,et al.  Generation of Accurate Finite Element Models of Nonlinear Systems – Application to an Aeroplane-Like Structure , 2005 .

[78]  Elias B. Kosmatopoulos,et al.  Development of adaptive modeling techniques for non-linear hysteretic systems , 2002 .

[79]  L. Garibaldi APPLICATION OF THE CONDITIONED REVERSE PATH METHOD , 2003 .

[80]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[81]  M. Kramer Nonlinear principal component analysis using autoassociative neural networks , 1991 .

[82]  David C. Zimmerman,et al.  Approximation and Calibration of Nonlinear Structural Dynamics , 2005 .

[83]  Jonathan E. Cooper,et al.  Identification of Multi-Degree of Freedom Systems With Nonproportional Damping Using the Resonant Decay Method , 2004 .

[84]  John E. Mottershead,et al.  Finite Element Model Updating in Structural Dynamics , 1995 .

[85]  Andrew W. Smyth,et al.  A Re-Configurable Test Apparatus for Complex Nonlinear Dynamic Systems , 2004 .

[86]  Gaëtan Kerschen,et al.  PROPER ORTHOGONAL DECOMPOSITION FOR MODEL UPDATING OF NON-LINEAR MECHANICAL SYSTEMS , 2001 .

[87]  J. Bendat,et al.  Random Data: Analysis and Measurement Procedures , 1987 .

[88]  C. Pierre,et al.  A NEW GALERKIN-BASED APPROACH FOR ACCURATE NON-LINEAR NORMAL MODES THROUGH INVARIANT MANIFOLDS , 2002 .

[89]  C. James Li,et al.  Non-linear system identification using lumped parameter models with embedded feedforward neural networks , 2002 .

[90]  J. Tinsley Oden,et al.  Verification and validation in computational engineering and science: basic concepts , 2004 .

[91]  Patrick J. Roache,et al.  Verification and Validation in Computational Science and Engineering , 1998 .

[92]  Gaëtan Kerschen,et al.  Identification of a continuous structure with a geometrical non-linearity. Part II: Proper orthogonal decomposition , 2003 .

[93]  D. Inman Nonlinearity in Structural Dynamics: Detection, Identification and Modelling , 2002 .

[94]  Christophe Pierre,et al.  Modal Reduction of a Nonlinear Rotating Beam Through Nonlinear Normal Modes , 2002 .

[95]  Alexander F. Vakakis,et al.  Karhunen-Loève decomposition of the transient dynamics of a multibay truss , 1999 .

[96]  Anil K. Bajaj,et al.  Identification of Nonlinear and Viscoelastic Properties of Flexible Polyurethane Foam , 2003 .

[97]  Hoon Sohn,et al.  Statistical model updating and validation applied to nonlinear transient structural dynamics , 2000 .

[98]  J. Z. Zhu,et al.  The finite element method , 1977 .

[99]  Henry J. Rice,et al.  The Measurement of Nonlinear Damping in Single-Degree-of-Freedom Systems , 1991 .

[100]  D. Dane Quinn,et al.  The dynamics of resonant capture , 1995 .

[101]  Gaëtan Kerschen,et al.  On the Model Validation in Nonlinear structural Dynamics , 2002 .