Repeated exponential sine sweeps for the autonomous estimation of nonlinearities and bootstrap assessment of uncertainties

Measurements on vibrating structures has been a topic of interest for decades. Vibrating structures are however generally assumed to behave linearly and in a noise-free environment, which is not the case in practice. This paper provides a methodology that allows for the autonomous estimation of nonlinearities and assessment of uncertainties by bootstrap on a given vibrating structure. Nonlinearities are estimated by means of a block-oriented nonlinear model approach based on parallel Hammerstein models and on exponential sine sweeps. Estimation uncertainties are simultaneously assessed using repetitions of the input signal (multi-sine sweeps) as the input of a bootstrap procedure. Mathematical foundations and a practical implementation of the method are discussed using an experimental example. The experiment chosen here consists in exciting a steel plate under various boundary conditions with exponential sine sweeps and at different levels in order to assess the evolution of nonlinearities and uncertainties over a wide range of frequencies and input amplitudes.

[1]  Marc Rébillat,et al.  Identification of cascade of Hammerstein models for the description of nonlinearities in vibrating devices , 2011 .

[2]  E. Bai,et al.  Block Oriented Nonlinear System Identification , 2010 .

[3]  Leon O. Chua,et al.  Fading memory and the problem of approximating nonlinear operators with volterra series , 1985 .

[4]  F. Jacobsen,et al.  A new interpretation of distortion artifacts in sweep measurements , 2011 .

[5]  Cyril Touzé,et al.  ASYMMETRIC NON-LINEAR FORCED VIBRATIONS OF FREE-EDGE CIRCULAR PLATES. PART 1: THEORY , 2002 .

[6]  Yves Rolain,et al.  Structure discrimination in block-oriented models using linear approximations: A theoretic framework , 2015, Autom..

[7]  Laurent Simon,et al.  Nonlinear acoustic characterization of micro-damaged materials through higher harmonic resonance analysis , 2012 .

[8]  Swen Müller,et al.  Transfer-Function Measurement with Sweeps , 2001 .

[9]  P. Gallman,et al.  An iterative method for the identification of nonlinear systems using a Uryson model , 1975 .

[10]  Miomir Mijic,et al.  On the effects of nonlinearities in room impulse response measurements with exponential sweeps , 2013 .

[11]  R. Pearson.  Discrete-time Dynamic Models , 1999 .

[12]  Jérôme Antoni,et al.  Fast detection of system nonlinearity using nonstationary signals , 2010 .

[13]  Marc Rébillat,et al.  Nonlinear structural damage detection based on cascade of Hammerstein models , 2014 .

[14]  Peter Balazs,et al.  Multiple Exponential Sweep Method for Fast Measurement of Head-Related Transfer Functions , 2007 .

[15]  Hai-Wen Chen,et al.  Modeling and identification of parallel nonlinear systems: structural classification and parameter estimation methods , 1995, Proc. IEEE.

[16]  Guy-Bart Stan,et al.  Comparison of different impulse response measurement techniques , 2002 .

[17]  Marc Rébillat,et al.  A multi-sine sweep method for the characterization of weak non-linearities ; plant noise and variability estimation. , 2015 .

[18]  Angelo J. Canty.  Bootstrap Techniques for Signal Processing , 2007 .

[19]  Pierrick Lotton,et al.  Nonlinear System Identification Using Exponential Swept-Sine Signal , 2010, IEEE Transactions on Instrumentation and Measurement.

[20]  Andrzej Janczak.  Identification of Nonlinear Systems Using Neural Networks and Polynomial Models , 2005 .

[21]  Rik Pintelon,et al.  System Identification: A Frequency Domain Approach , 2012 .

[22]  A. Janczak,et al.  Identification of Nonlinear Systems Using Neural Networks and Polynomial Models: A Block-Oriented Approach , 2004 .

[23]  Kerem Ege,et al.  Vibroacoustics of the piano soundboard: (Non)linearity and modal properties in the low- and mid-frequency ranges , 2013 .

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