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Design of an FIR filter for the displacement reconstruction using measured acceleration in low‐frequency dominant structures
Author(s) -
Lee Hae Sung,
Hong Yun Hwa,
Park Hyun Woo
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2769
Subject(s) - acceleration , tikhonov regularization , displacement (psychology) , mathematics , filter (signal processing) , mathematical analysis , algorithm , inverse problem , physics , computer science , classical mechanics , psychology , computer vision , psychotherapist
This paper presents a new class of displacement reconstruction scheme using only acceleration measured from a structure. For a given set of acceleration data, the reconstruction problem is formulated as a boundary value problem in which the acceleration is approximated by the second‐order central finite difference of displacement. The displacement is reconstructed by minimizing the least‐squared errors between measured and approximated acceleration within a finite time interval. An overlapping time window is introduced to improve the accuracy of the reconstructed displacement. The displacement reconstruction problem becomes ill‐posed because the boundary conditions at both ends of each time window are not known a priori . Furthermore, random noise in measured acceleration causes physically inadmissible errors in the reconstructed displacement. A Tikhonov regularization scheme is adopted to alleviate the ill‐posedness. It is shown that the proposed method is equivalent to an FIR filter designed in the time domain. The fundamental characteristics of the proposed method are presented in the frequency domain using the transfer function and the accuracy function. The validity of the proposed method is demonstrated by a numerical example, a laboratory experiment and a field test. Copyright © 2009 John Wiley & Sons, Ltd.