Detection and Quantification of the Influence of Time Variation in Frequency Response Function Measurements Using Arbitrary Excitations

This paper presents a nonparametric method for detecting and quantifying the influence of time variation in frequency response function measurements. The method is based on the estimation of the best linear time-invariant (BLTI) approximation of a linear time-variant (LTV) system from known input, noisy output data. The key idea consists in reformulating the single-input, single-output time-variant problem as a multiple-input, single-output time-invariant problem. In addition to the BLTI approximation of the LTV system, the contribution of the disturbing noise, the leakage error, and the time-varying effects at the output is also quantified. As such, the approximation error of the time-invariant framework is known.

[1]  W. Marsden.  I and J , 2012 .

[2]  S. Bittanti,et al.  Periodic Systems: Filtering and Control , 2008 .

[3]  Lotfi A. Zadeh,et al.  On Stability of Linear Varying‐Parameter Systems , 1951 .

[4]  J. Schoukens,et al.  Identification of linear systems in the presence of nonlinear distortions. A frequency domain approach. I. Non-parametric identification , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[5]  J. Schoukens,et al.  Estimation of nonparametric noise and FRF models for multivariable systems—Part II: Extensions, applications , 2010 .

[6]  Victor Solo,et al.  On the stability of slowly time-varying linear systems , 1994, Math. Control. Signals Syst..

[7]  R. Pintelon,et al.  Frequency-domain weighted non-linear least-squares estimation of continuous-time, time-varying systems , 2011 .

[8]  Pertti M. Mäkilä,et al.  LTI approximation of nonlinear systems via signal distribution theory , 2006, Autom..

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

[10]  Lotfi A. Zadeh,et al.  The Determination of the Impulsive Response of Variable Networks , 1950 .

[11]  D. Brillinger.  Time series - data analysis and theory , 1981, Classics in applied mathematics.

[12]  Lennart Ljung,et al.  Estimating Linear Time-invariant Models of Nonlinear Time-varying Systems , 2001, Eur. J. Control.

[13]  Rik Pintelon,et al.  Nonparametric Tracking of the Time-Varying Dynamics of Weakly Nonlinear Periodically Time-Varying Systems Using Periodic Inputs , 2012, IEEE Transactions on Instrumentation and Measurement.

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

[15]  L. Zadeh,et al.  Frequency Analysis of Variable Networks , 1950, Proceedings of the IRE.

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

[17]  Petre Stoica,et al.  Decentralized Control , 2018, The Control Systems Handbook.

[18]  Rik Pintelon,et al.  Identification of continuous-time systems using arbitrary signals , 1997, Autom..

[19]  Rik Pintelon,et al.  Detecting a Time-Varying Behavior in Frequency Response Function Measurements , 2012, IEEE Transactions on Instrumentation and Measurement.

[20]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[21]  Rik Pintelon,et al.  Non-parametric estimate of the system function of a time-varying system , 2012, Autom..

[22]  Donald L. Kreider,et al.  An introduction to linear analysis , 1966 .

[23]  J. Schoukens,et al.  Parametric and nonparametric identification of linear systems in the presence of nonlinear distortions-a frequency domain approach , 1998, IEEE Trans. Autom. Control..

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

[25]  J. Schoukens,et al.  Identification of linear systems in the presence of nonlinear distortions , 2000, Proceedings of the 17th IEEE Instrumentation and Measurement Technology Conference [Cat. No. 00CH37066].