Estimating Low-Bias Frequency Response Using Random Decrement Rune Brincker Aarhus School of Engineering, Aarhus University, Ny Munkegade 120, Building 1521, DK-8000 Aarhus C, Denmark Anders Brandt Department of Industrial and Civil Engineering, University of Southern Denmark, Niels Bohrs Allé 1, DK-5230 Odense M, Denmark NOMENCLATURE k t t, : Continuous, discrete time ( ), ( ) x t y t : Signals, stochastic processes ( ) h t : Impulse response function : Angular frequency ( ), ( ) X Y : Signal Fourier transforms ( ) ˆ ( ), ˆ YX XX G G : Spectral densities ( ) ( ), 2 1 H H : Frequency response functions ( ) : Coherence ( ) ( ), XY XX D D : Random decrement functions ( ) ˆ ( ), ˆ XY XX D D : Random decrement function estimates ABSTRACT It is well known that in order to minimize the influence of leakage bias in frequency response function (FRF) estimates, smooth windows should be applied in the FFT processing. It is also normal practice to use self windowing excitation signals whenever possible. However, in many cases FRFs have to be estimated on systems where the excitation signal cannot be altered. Since random data can be compressed in a random decrement function, and since this procedure introduces a natural window, using this technique significantly reduces the influence of leakage bias, and thus, can be used as an alternative to Welch based estimates in cases where the signals involved are random. This means that almost bias-free FRF estimates can be obtained from stationary random excitation. In the paper it is shown how the random decrement technique can be applied to process the time series, and the level of bias on the FRF is estimated and compared to normal Welch based FRF estimates. INTRODUCTION The way most vibration data acquisition systems are designed is based on the premises in the 1970’s when the first FFT analyzers became available. One restriction in those days was the price of memory, and thus the way the data processing was implemented was to reduce data as soon as possible after acquisition. The result became the frequency block averaging that is commonly used today, usually referred to as Welch averaging after [1]. This procedure is well investigated and a current discussion of its use can be found in [2]. T. Proulx (ed.), Modal Analysis Topics, Volume 3, Conference Proceedings of the Society for Experimental Mechanics Series 6, 497 DOI 10.1007/978-1-4419-9299-4_41, © The Society for Experimental Mechanics, Inc. 2011
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