Journal
MECHANICAL SYSTEMS AND SIGNAL PROCESSING
Volume 38, Issue 2, Pages 460-481Publisher
ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ymssp.2013.02.007
Keywords
Reconstruction of displacement; Inverse problem; Minimization; Finite impulse response (FIR) filter; Target frequency; Target accuracy
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Funding
- Ministry of Land, Transport and Maritime of Korean government through the Core Research Institute at Seoul National University for Core Engineering Technology Development of Super Long Span Bridge RD Center [09CCTI-A052531-02-000000]
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This paper presents a displacement reconstruction scheme using acceleration measured at a high sampling rate and displacement measured at a considerably low sampling rate. The governing equation and the boundary conditions for the reconstruction are derived using the variational statement of an inverse problem to minimize the errors between measured and reconstructed responses. The transfer function of the governing equation is identically 1 over whole frequency domain, and the proposed scheme would not result in any reconstruction error. A finite impulse response filter (FIR filter) is formulated through the finite element discretization of the governing equation. The Hermitian shape function is adopted to interpolate the displacement in a finite element. The transfer functions of the FIR filter are derived, and their characteristics are thoroughly discussed. It is recommended that the displacement sampling rate should be higher than the Nyquist rate of the target frequency, which is the lowest physically meaningful frequency in measured acceleration. In case the displacement sampling rate is lower than the recommended rate, the use of a higher target accuracy, which is the predefined accuracy at the target frequency, is required. The reconstruction of velocity with the proposed scheme is also presented. The validity of the proposed scheme is demonstrated with a numerical simulation study and a field test on a simply-supported railway bridge. (C) 2013 Elsevier Ltd. All rights reserved.
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