A nonlinear decomposition and regulation method for nonlinearity characterization

Nonlinearity detection and characterization for crack-/damage-related fault evaluation/detection is a hot engineering topic. This study investigates a novel and systematic nonlinear decomposition and regulation method for nonlinearity characterization. It is shown that, using the proposed output decomposition and regulation, the even-order nonlinearity and crack-incurred nonlinearity (not a simple even-order nonlinearity although at its initial stage) can all be effectively evaluated by the magnitude of the second-order harmonic response, and the latter is a linear function of the crack severity and can be accurately estimated with the proposed method. Theoretical analysis, example studies, finite element modeling, and experiment validation are provided to demonstrate the advantages and effectiveness of the proposed method in characterizing nonlinear dynamics incurred by initial crack or damage. The theory and methods of this study would provide a useful and alternative frequency-domain approach for nonlinear signal processing in crack/damage evaluation, nonlinearity detection and characterization, and can benefit a broad spectrum of engineering practice.

[1]  S. Billings,et al.  Output frequency properties of nonlinear systems , 2010 .

[2]  Xingjian Jing,et al.  Frequency domain analysis and design of nonlinear systems based on Volterra series expansion : a parametric characteristic approach , 2015 .

[3]  Xingjian Jing,et al.  Frequency domain analysis for suppression of output vibration from periodic disturbance using nonlinearities , 2008 .

[4]  Jay Lee,et al.  Prognostics and health management design for rotary machinery systems—Reviews, methodology and applications , 2014 .

[5]  D. Marshall,et al.  Review of progress in quantitative non-destructive evaluation: edited by D. O. Thompson and D. E. Chimenti; published by Plenum, New York, 1983; 1853 pp.; price, U.S. $225.00 , 1985 .

[6]  N. T. Khiem,et al.  Multi-crack detection for beam by the natural frequencies , 2004 .

[7]  Animesh Chatterjee,et al.  Structural damage assessment in a cantilever beam with a breathing crack using higher order frequency response functions , 2010 .

[8]  S. Billings,et al.  Mapping non-linear integro-differential equations into the frequency domain , 1990 .

[9]  Laurence J. Jacobs,et al.  Experimental characterization of fatigue damage in a nickel-base superalloy using nonlinear ultrasonic waves , 2006 .

[10]  Izzet Yilmaz Önel,et al.  Induction Motor Bearing Failure Detection and Diagnosis: Park and Concordia Transform Approaches Comparative Study , 2007 .

[11]  Jinping Ou,et al.  Structural Health Monitoring in mainland China: Review and Future Trends , 2010 .

[12]  Francois Leonard,et al.  FREE-VIBRATION BEHAVIOUR OF A CRACKED CANTILEVER BEAM AND CRACK DETECTION , 2001 .

[13]  Don-Ha Hwang,et al.  High-Resolution Parameter Estimation Method to Identify Broken Rotor Bar Faults in Induction Motors , 2013, IEEE Transactions on Industrial Electronics.

[14]  John E. T. Penny,et al.  Crack Modeling for Structural Health Monitoring , 2002 .

[15]  K. M. Liew,et al.  DETECTION OF DAMAGE LOCATIONS IN A BEAM USING THE WAVELET ANALYSIS , 2001 .

[16]  Haym Benaroya,et al.  Mechanical Vibration: Analysis, Uncertainties, and Control , 1997 .

[17]  A. Bovsunovsky,et al.  Crack Detection in Beams by Means of the Driving Force Parameters Variation at Non-Linear Resonance Vibrations , 2007 .

[18]  Pizhong Qiao,et al.  Vibration-based Damage Identification Methods: A Review and Comparative Study , 2011 .

[19]  Bimlesh Kumar,et al.  Identification of crack location and crack size in a simply supported beam by measurement of natural frequencies , 2012 .

[20]  Zhiwei Gao,et al.  From Model, Signal to Knowledge: A Data-Driven Perspective of Fault Detection and Diagnosis , 2013, IEEE Transactions on Industrial Informatics.

[21]  Stephen A. Billings,et al.  Mapping from parametric characteristics to generalized frequency response functions of non-linear systems , 2008, Int. J. Control.

[22]  Antonino Morassi,et al.  Identification of Two Cracks in a Simply Supported Beam from Minimal Frequency Measurements , 2001 .

[23]  O. S. Salawu.  Detection of structural damage through changes in frequency: a review , 1997 .

[24]  Charles R. Farrar,et al.  A summary review of vibration-based damage identification methods , 1998 .

[25]  T. D. Burton,et al.  Damage characterization by vibration test , 1994 .

[26]  Stephen A. Billings,et al.  Frequency domain analysis for non-linear Volterra systems with a general non-linear output function , 2008, Int. J. Control.

[27]  S. Billings,et al.  Non-linear systems in the frequency domain: Energy transfer filters , 2002 .

[28]  Michael I. Friswell,et al.  Crack modelling for structural health monitoring , 2002 .

[29]  Xingjian Jing,et al.  Frequency Domain Analysis and Design of Nonlinear Systems based on Volterra Series Expansion , 2015 .

[30]  Li Cheng,et al.  Computation of Parametric Convergence Bound and Parametric Convergence Margin for Volterra series expansion , 2013, 2013 9th Asian Control Conference (ASCC).

[31]  Norris Stubbs,et al.  Crack detection in beam-type structures using frequency data , 2003 .

[32]  Robert D. Adams,et al.  The location of defects in structures from measurements of natural frequencies , 1979 .

[33]  G. C. Sih,et al.  Mechanics of Nonlinear Crack Growth: Effects of Specimen Size and Loading Step , 1984 .

[34]  W. Rugh.  Nonlinear System Theory: The Volterra / Wiener Approach , 1981 .

[35]  Fabrizio Vestroni,et al.  Nonlinear Features in the Dynamic Response of a Cracked Beam Under Harmonic Forcing , 2005 .

[36]  L. K. Toan,et al.  A novel method for crack detection in beam-like structures by measurements of natural frequencies , 2014 .

[37]  David C. Swanson,et al.  PROGNOSTIC MODELLING OF CRACK GROWTH IN A TENSIONED STEEL BAND , 2000 .

[38]  S. Billings,et al.  The parametric characteristic of frequency response functions for nonlinear systems , 2006 .

[39]  Stephen A. Billings,et al.  Output frequency response function of nonlinear Volterra systems , 2006, Autom..

[40]  Xingjian Jing,et al.  Nonlinear Characteristic Output Spectrum for Nonlinear Analysis and Design , 2014, IEEE/ASME Transactions on Mechatronics.

[41]  Zhike Peng,et al.  A novel approach for nonlinearity detection in vibrating systems , 2008 .

[42]  Shaocheng Wang,et al.  Multisensor Wireless System for Eccentricity and Bearing Fault Detection in Induction Motors , 2014, IEEE/ASME Transactions on Mechatronics.

[43]  S. Billings,et al.  Output frequency response function-based analysis for nonlinear Volterra systems , 2008 .