Measurement of Multivariable Frequency Response Functions in the Presence of Non-Linear Distortions – Some Practical Aspects

Nele Dedene, Rik Pintelon, Philippe Lataire, Ieee Instrumentation (Editor), Measurment Society (Editor)

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


The aim of this paper is the design of optimal multi-input periodic excitations (i.e., sets of multisines) that allow accurate calculation of a nonparametric multivariable frequency response function (MFRF) of a multiple input multiple output (MIMO) system in the presence of nonlinear distortions. Dur to the presence of nonlinear distortions, it is essential that the different experiments necessary to determine the MFRF are performed at the same operating point/region. It will be shown that, in order to reduce the noise on the measured MFRF, one has to consider the class of excitation signals for whcih the matrix formed by the input Fourier vectors used in the different experiments has a condition number close to one for all the considered frequencies (modified E-optimality). Within this selected class of excitations with condition number close to one, the uncertainty on the measured MFRFs can further be minimized by maximizing the determinant of the Fisher information matrix. This is achieved by using crest factor optimized excitation signals. The theoretical results are experimentally verified in the field of electric machinery. Finally, a precompensation technique is proposed that further improves the signal-to-noise ratio (SNR) of the measurements.
Original languageEnglish
Pages (from-to)577-582
Number of pages6
JournalIEEE Transactions on Instrumentation and Measurement
Issue numberAugust 2002
Publication statusPublished - 1 Aug 2002

Bibliographical note

IEEE Transactions on Instrumentation and Measurement, Vol. 51, No. 4, August 2002, pp. 577-582
Series editor: IEEE Instrumentation and measurment society


  • Frequency response
  • multivariable systems
  • nonlinear distortions
  • nonparametric identification
  • optimal excitations


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