Fast Precise Algorithm of Computing FRF by Considering Initial Response

  • J. M. Liu
  • W. D. Zhu
  • M. Ying
  • S. Shen
Conference paper
Part of the Conference Proceedings of the Society for Experimental Mechanics Series book series (CPSEMS)


At present, the common algorithm of computing FRF is averaging method in frequency domain. This algorithm is precise method for impact exciting or burst random exciting, but not for continuous exciting, for the initial response cannot be considered. In continuous exciting test, increasing data length which permits increasing averaging times is needed to alleviate the error of FRF caused by the initial response. The initial response is caused by the previous frame of exciting force. Thus, in this work an algorithm model is put forward by considering the initial response. For each averaging computation in frequency domain, the data of two frames force and one frame response, aligned in right end, are used. The initial response is caused by the first frame force. When the FRFs of MISO are known, the IRFs (Impulse Response Function) are obtained by IFFT transform of FRFs. The theoretical response of this point except the first frame can be computed out by the convolution of forces and IRFs. The RMS of error series between theoretical response and measured response, divided by the RMS of measured response, reflects the preciseness of FRF. The smaller is the value, the better. The speed of common averaging method in frequency domain is fast, but with bad FRF preciseness when data is short. The FRF preciseness of least square devolution method in time domain is best, but with the slowest computation speed and unpractical. The preciseness of FRF with new algorithm is very near to the devolution method but the computation time can be shortened greatly. Applying the new algorithm in continuous exciting MIMO test, the test time can be greatly shortened. The new algorithm can also be applied to impact MIMO test, with multi impacts acting in different points at the same time. In the paper, real test and simulating data are used to verify the new algorithm, and the new algorithm is also compared with the time domain iteration method which is put forwarded before.


FRF Preciseness Iteration algorithm Frequency domain IRF 


  1. 1.
    Fladung W, Rost R (1997)Application and correction of the exponential window for frequency response functions. Mech Syst Signal Process 11(1):23–36Google Scholar
  2. 2.
    Liu JM, Zhu WD, Lu QH, Ren GX (2011) An efficient iterative algorithm for accurately calculating impulse response functions in modal testing. J Vib Acoust 133(6). doi:10.1115/1.4005221Google Scholar
  3. 3.
    Heylen W, Lammens S, Sas P (1998) Modal analysis theory and testing. Katholieke Universiteit Leuven, LeuvenGoogle Scholar
  4. 4.
    Napolitano KL, Yoder NC, Brillhart RD (2012) A comparison of multiple impact testing methods. In: Proceeding of the SEM IMAC XXX conference, Jacksonville, FL, 30 Jan –2 Feb 2012Google Scholar

Copyright information

© The Society for Experimental Mechanics 2014

Authors and Affiliations

  1. 1.China Orient Institute of Noise & VibrationBeijingChina
  2. 2.University of MarylandBaltimoreUSA

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