Transient suppression in FRF measurement: Comparison and analysis of four state-of-the-art methods

Abstract This paper compares four well selected methods for computing the non-parametric Frequency Response Function (FRF) of a periodically excited linear time invariant system. The suppression of the transient is mandatory when its influence in the data is large. Better suppression of the transient leads to a better non-parametric FRF estimate. A good non-parametric FRF estimate can be used to validate the parametric transfer function model in a second step. The suppression of the transient will be highlighted using the mean squared error of the non-parametric FRF estimate. Temperature transients caused by heat diffusion are used as example. The selected methods consist of two standard windowing methods and two methods based on the Local Polynomial Method (LPM). LPM was designed to find a non-parametric FRF estimate in the presence of nonlinearities. This paper will modify LPM to find a non-parametric FRF estimate for linear systems using a single experiment. The mean squared error of the four non-parametric FRF estimates will be compared and analyzed, based on a simulation and a measurement example.

[1]  F. Harris.  On the use of windows for harmonic analysis with the discrete Fourier transform , 1978, Proceedings of the IEEE.

[2]  G. Vandersteen,et al.  Transient suppression in non-parametric frequency response function estimates of heat diffusion phenomena , 2012, 2012 IEEE International Instrumentation and Measurement Technology Conference Proceedings.

[3]  Yves Rolain,et al.  Improved (non-)parametric identification of dynamic systems excited by periodic signals—The multivariate case , 2011 .

[4]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[5]  T. McKelvey,et al.  Non-parametric frequency response estimation using a local rational model , 2012 .

[6]  J. Schoukens,et al.  Estimation of nonparametric noise and FRF models for multivariable systems—Part I: Theory , 2010 .

[7]  S. Sakakibara.  Properties of Vibration with Fractional Derivative Damping of Order 1/2. , 1997 .

[8]  Julius S. Bendat,et al.  Engineering Applications of Correlation and Spectral Analysis , 1980 .

[9]  Johan Schoukens,et al.  The Transient Impulse Response Modeling Method and the Local Polynomial Method for Nonparametric System Identification , 2012 .

[10]  Per Eskilson.  Thermal analysis of heat extraction boreholes , 1987 .

[11]  Thierry Poinot,et al.  Fractional modelling and identification of thermal systems , 2011, Signal Process..

[12]  Rik Pintelon,et al.  Diffusion systems: stability, modeling, and identification , 2005, IEEE Transactions on Instrumentation and Measurement.

[13]  O. Agrawal,et al.  Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering , 2007 .

[14]  Yves Rolain,et al.  Analysis of windowing/leakage effects in frequency response function measurements , 2006, Autom..

[15]  Rik Pintelon,et al.  Welch Method Revisited: Nonparametric Power Spectrum Estimation Via Circular Overlap , 2010, IEEE Transactions on Signal Processing.

[16]  José António Tenreiro Machado,et al.  Control of a heat diffusion system through a fractional order nonlinear algorithm , 2010, Comput. Math. Appl..

[17]  Yves Rolain,et al.  User friendly Box-Jenkins identification using nonparametric noise models , 2011, IEEE Conference on Decision and Control and European Control Conference.

[18]  Håkan Hjalmarsson,et al.  Non-parametric Frequency Function Estimation using Transient Impulse Response Modelling , 2012 .

[19]  J. Schoukens,et al.  Study of the maximal interpolation errors of the local polynomial method for frequency response function measurements , 2012, 2012 IEEE International Instrumentation and Measurement Technology Conference Proceedings.