A method for non-parametric identification of non-linear vibration systems with asymmetric restoring forces from a resonant decay response

Abstract A method for non-parametric identification of systems with asymmetric non-linear restoring forces is proposed in this paper. The method, named the zero-crossing method for systems with asymmetric restoring forces (ZCA), is an extension of zero-crossing methods and allows identification of backbones, damping curves and restoring elastic and dissipative forces from a resonant decay response. The validity of the proposed method is firstly demonstrated on three simulated resonant decay responses of the systems with off-centre clearance, bilinear and quadratic stiffness. Then, the method is applied to experimental data from a micro-electro-mechanical resonator in order to quantify its non-linear damping and stiffness effects. Throughout the paper the proposed method is also compared with the Hilbert vibration decomposition to demonstrate that the ZCA yields more accurate results with much less effort.

[1]  W. Staszewski.  IDENTIFICATION OF NON-LINEAR SYSTEMS USING MULTI-SCALE RIDGES AND SKELETONS OF THE WAVELET TRANSFORM , 1998 .

[2]  Jonathan J. Stickel,et al.  Data smoothing and numerical differentiation by a regularization method , 2010, Comput. Chem. Eng..

[4]  S. Billings.  Nonlinear System Identification: NARMAX Methods in the Time, Frequency, and Spatio-Temporal Domains , 2013 .

[5]  Michael Feldman,et al.  Hilbert Transform Applications in Mechanical Vibration: Feldman/Hilbert Transform Applications in Mechanical Vibration , 2011 .

[6]  Michael Feldman,et al.  Decomposition of non-stationary signals into varying time scales: Some aspects of the EMD and HVD methods , 2011 .

[7]  N. Huang,et al.  The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis , 1998, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[8]  Michael Feldman,et al.  Nonparametric identification of asymmetric nonlinear vibration systems with the Hilbert transform , 2012 .

[9]  Gaëtan Kerschen,et al.  Modal testing of nonlinear vibrating structures based on nonlinear normal modes: Experimental demonstration , 2011 .

[10]  K. Worden,et al.  Past, present and future of nonlinear system identification in structural dynamics , 2006 .

[11]  Michael Feldman,et al.  Time-varying vibration decomposition and analysis based on the Hilbert transform , 2006 .

[12]  Christoph W. Schwingshackl,et al.  Comparison of Nonlinear System Identification Methods for Free Decay Measurements with Application to MEMS Devices , 2017 .

[13]  Yi Liu,et al.  Hilbert-Huang Transform and the Application , 2020, 2020 IEEE International Conference on Artificial Intelligence and Information Systems (ICAIIS).

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

[15]  Pavel M. Polunin,et al.  Nonlinearities and noise in micromechanical resonators: From understanding to characterization and design tools , 2016 .

[16]  M. Feldman.  Hilbert transform in vibration analysis , 2011 .

[17]  Matthew S. Allen,et al.  Measurement of nonlinear normal modes using multi-harmonic stepped force appropriation and free decay , 2016 .

[18]  P. Frank Pai,et al.  Time–frequency characterization of nonlinear normal modes and challenges in nonlinearity identification of dynamical systems , 2011 .

[19]  James Hensman,et al.  Natural computing for mechanical systems research: A tutorial overview , 2011 .

[20]  T. Kenny,et al.  Characterization of MEMS Resonator Nonlinearities Using the Ringdown Response , 2016, Journal of Microelectromechanical Systems.

[21]  Michael Feldman,et al.  Non-linear system vibration analysis using Hilbert transform--I. Free vibration analysis method 'Freevib' , 1994 .

[22]  Norden E. Huang,et al.  On Instantaneous Frequency , 2009, Adv. Data Sci. Adapt. Anal..

[23]  P. Eilers,et al.  Evaluating the effectiveness of smoothing algorithms in the absence of ground reference measurements , 2011 .

[24]  Jin-Song Pei,et al.  Solving Dynamical Systems Involving Piecewise Restoring Force Using State Event Location , 2012 .

[25]  Jonathan E. Cooper,et al.  Identification of backbone curves of nonlinear systems from resonance decay responses , 2015 .

[26]  P. D. McFadden,et al.  A review of time-frequency methods for structural vibration analysis , 2003 .

[27]  P. Eilers.  A perfect smoother. , 2003, Analytical chemistry.

[28]  M. Feldman.  Theoretical analysis and comparison of the Hilbert transform decomposition methods , 2008 .

[29]  P. Frank Pai,et al.  Time-frequency analysis for parametric and non-parametric identification of nonlinear dynamical systems , 2013 .