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A lower bound for the variance of frequency and damping ratio identified from noisy vibration measurements
Author(s) -
Hernandez Eric M.,
Polanco Néstor R.
Publication year - 2016
Publication title -
structural control and health monitoring
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.587
H-Index - 62
eISSN - 1545-2263
pISSN - 1545-2255
DOI - 10.1002/stc.1757
Subject(s) - damping ratio , estimator , vibration , modal , upper and lower bounds , cramér–rao bound , gaussian , mathematics , variance (accounting) , white noise , zero (linguistics) , noise (video) , modal testing , bias of an estimator , control theory (sociology) , modal analysis , statistics , mathematical analysis , minimum variance unbiased estimator , acoustics , physics , computer science , materials science , philosophy , artificial intelligence , business , image (mathematics) , linguistics , quantum mechanics , polymer chemistry , control (management) , accounting
Summary This paper derives exact expressions to compute the lowest achievable variance by any unbiased estimator of modal frequency and damping ratio from free vibration and forced vibration signals contaminated by additive zero‐mean Gaussian white noise. These limits are found through the Cramer–Rao lower bound theory. The paper presents simulated system identification results that confirm the applicability of the derived expressions. Copyright © 2015 John Wiley & Sons, Ltd.