Improvements in modal parameter extraction through post-processing frequency response function estimates

Frequency response functions are the primary means of experimentally evaluating the structural characteristics of dynamic systems. These response functions, which are frequently utilized in vibration and modal analysis, are estimated through the periodograms of measurements. Some form of averaging of the periodograms is necessary to eliminate the effects of unavoidable estimation and measurement noise. In the last decade, wavelet domain denoising methods have emerged as powerful means of estimating functions from noisy data. As an application of these methods in structural dynamics, wavelet domain denoising methods and their variants have recently been proposed as a post processor step for reducing the number of averaging operations required in frequency response function estimation. In this paper, the improvements in modal parameter estimates resulting from median interpolating transform post-processing of periodograms are investigated through an analytical test case. It is shown that the number of required averages can significantly be reduced when periodograms and the median interpolating pyramid transform are implemented together. The improvements in modal parameter estimates for a fixed number of averages are quantified in terms of bias and variance.