A Nonlinear Block Structure Identification Procedure Using Frequency Response Function Measurements

Based on simple frequency response function (FRF) measurements, we give the user some guidance in the selection of an appropriate nonlinear block structure for the system to be modeled. The method consists in measuring the FRF using a Gaussian-like input signal and varying in a first experiment the root-mean-square (rms) value of this signal while maintaining the coloring of the power spectrum. Next, in a second experiment, the coloring of the power spectrum is varied while keeping the rms value constant. Based on the resulting behavior of the FRF, an appropriate nonlinear block structure can be selected to approximate the real system. The identification of the selected block-oriented model itself is not addressed in this paper. A theoretical analysis and two practical applications of this structure identification method are presented for some nonlinear block structures.

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

[2]  J. Schoukens,et al.  Identification of Linear Systems with Nonlinear Distortions , 2003 .

[3]  Johan Schoukens,et al.  Fast identification of systems with nonlinear feedback , 2004 .

[4]  Heinz Unbehauen,et al.  Structure identification of nonlinear dynamic systems - A survey on input/output approaches , 1990, Autom..

[5]  Lennart Ljung,et al.  Linear approximations of nonlinear FIR systems for separable input processes , 2005, Autom..

[6]  M. Enqvist.  Linear models of nonlinear systems , 2005 .

[7]  David Rees,et al.  Nonlinear distortions and multisine signals. I. Measuring the best linear approximation , 2000, IEEE Trans. Instrum. Meas..

[8]  Rik Pintelon,et al.  Variance analysis of frequency response function measurements using periodic excitations , 2004, IMTC 2004.

[9]  Hsiao-Ping Huang,et al.  Structure Identification for Block-Oriented Nonlinear Models Using Relay Feedback Tests , 2001 .

[10]  Jan Swevers,et al.  Initial estimates for block structured nonlinear systems with feedback , 2005 .

[11]  Yves Rolain,et al.  Fast approximate identification of nonlinear systems , 2003, Autom..

[12]  H. Saunders.  Book Reviews : Engineering Applications of Correlatidn and Spectral Analysis: J.S. Bendat and A.G. Piersol John Wiley and Sons, New York, NY, 1980 , 1981 .

[13]  Yves Rolain,et al.  Identification of a Block-Structured Nonlinear Feedback System, Applied to a Microwave Crystal Detector , 2008, IEEE Transactions on Instrumentation and Measurement.

[14]  David Rees,et al.  Structure identification of block-oriented nonlinear systems using periodic test signals , 1996, Quality Measurement: The Indispensable Bridge between Theory and Reality (No Measurements? No Science! Joint Conference - 1996: IEEE Instrumentation and Measurement Technology Conference and IMEKO Tec.