Bias errors due to leakage effects when estimating frequency response functions

Document type: Journal Articles
Article type: Original article
Peer reviewed: Yes
Author(s): Andreas Josefsson, Kjell Ahlin, Göran Broman
Title: Bias errors due to leakage effects when estimating frequency response functions
Journal: Shock and Vibration
Year: 2012
Volume: 19
Issue: 6
Pagination: 1257-1266
ISSN: 1070-9622
Publisher: IOS Press
URI/DOI: 10.3233/SAV-2012-0668
ISI number: 000312153500008
Organization: Blekinge Institute of Technology
Department: School of Engineering - Dept. of Mechanical Engineering (Sektionen för ingenjörsvetenskap - avd. för maskinteknik)
School of Engineering S- 371 79 Karlskrona
+46 455 38 50 00
Authors e-mail:
Language: English
Abstract: Frequency response functions are often utilized to characterize a system's dynamic response. For a wide range of engineering applications, it is desirable to determine frequency response functions for a system under stochastic excitation. In practice, the measurement data is contaminated by noise and some form of averaging is needed in order to obtain a consistent estimator. With Welch's method, the discrete Fourier transform is used and the data is segmented into smaller blocks so that averaging can be performed when estimating the spectrum. However, this segmentation introduces leakage effects. As a result, the estimated frequency response function suffers from both systematic (bias) and random errors due to leakage. In this paper the bias error in the H_1 and H_2-estimate is studied and a new method is proposed to derive an approximate expression for the relative bias error at the resonance frequency with different window functions. The method is based on using a sum of real exponentials to describe the window's deterministic autocorrelation function. Simple expressions are derived for a rectangular window and a Hanning window. The theoretical expressions are verified with numerical simulations and a very good agreement is found between the results from the proposed bias expressions and the empirical results.
Subject: Mechanical Engineering\Structural Dynamics
Signal Processing\General
Keywords: Frequency response functions, bias error, leakage effects, Welch's method