Bias errors due to leakage effects when estimating frequency response functions
Blekinge Institute of Technology, School of Engineering, Department of Mechanical Engineering2012 (English)In: Shock and Vibration, ISSN 1070-9622, E-ISSN 1875-9203, Vol. 19, no 6, 1257-1266 p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
IOS Press , 2012. Vol. 19, no 6, 1257-1266 p.
Frequency response functions, bias error, leakage effects, Welch's method
Signal Processing Applied Mechanics
IdentifiersURN: urn:nbn:se:bth-6939DOI: 10.3233/SAV-2012-0668ISI: 000312153500008Local ID: oai:bth.se:forskinfo1F7DBAB903C0C929C12579C9004526D5OAI: oai:DiVA.org:bth-6939DiVA: diva2:834494