It should be mentioned that the large number of averages used for each realization in the MIMO case was made to obtain a low random error in the FRF estimate, to clearly see the difference in the time domain averaging based estimate compared to the frequency domain based estimate. In practice fewer averages may be able to be used if a larger random error can be tolerated. The necessary number of averages in the time domain averaging is dependent on the SNR around the resonances and antiresonances, which can be evaluated by observing the multiple coherence. CONCLUSIONS In this paper we have investigated the effects of suppressing contaminating noise on both the input and output signal in FRF estimation, by using periodic excitation signals and time domain averaging. It was shown that estimators for SISO as well as MIMO cases are asymptotically unbiased. A formula was also given in the SISO case for an “efficient coherence function” which is well-defined at frequencies where only one of the contaminating noise sources is present, such as around resonances and antiresonances. Fig. 3 FRF estimates from a simulation of a 2-input-1-output model excited by periodic random with frequency domain averaging (rings), and with time domain averaging (plus signs). In solid, the true FRF is shown. The FRF is zoomed in around the resonance in a) and around the antiresonance in b), similar to Fig. 2 d) and f). See text for details. REFERENCES [1] Bendat, J. & Piersol, A. G. Random Data: Analysis and Measurement Proceedures Wiley Interscience, 2010. [2] Wicks, A. & Vold, H. The Hs Frequency Response Estimator. Proc. 4th International Modal Analysis Conference, Los Angeles, CA, 1986. [3] Rocklin, G. T.; Crowley, J. & Vold, H. A Comparison of H1, H2, and Hv Frequency Response Functions. Proc. 3rd International Modal Analysis Conference, Orlando, FL, 1985. [4] White, P. R.; Tan, M. H. & Hammond, J. K. Analysis of the maximum likelihood, total least squares and principal component approaches for frequency response function estimation. Journal of Sound and Vibration, 290, pp. 676-689, 2006. [5] Antoni, J.; Wagstaff, P. & Henrio, J. C. H – A consistent estimator for frequency response functions with input and output noise. IEEE Transactions On Instrumentation And Measurement, 53, pp. 457-465, 2004. 304
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