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Technical Briefs

An Efficient Iterative Algorithm for Accurately Calculating Impulse Response Functions in Modal Testing

[+] Author and Article Information
J. M. Liu, Q. H. Lu, G. X. Ren

Department of Mechanics,  Tsinghua University, Beijing 100084, China

W. D. Zhu1

Department of Mechanical Engineering,  University of Maryland, Baltimore County, Baltimore, MD 21250wzhu@umbc.edu

1

Corresponding author.

J. Vib. Acoust 133(6), 064505 (Nov 28, 2011) (9 pages) doi:10.1115/1.4005221 History: Received April 05, 2011; Revised September 16, 2011; Accepted September 25, 2011; Published November 28, 2011; Online November 28, 2011

Impulse response functions (IRFs) and frequency response functions (FRFs) are bases for modal parameter identification of single-input, single-output (SISO) and multiple-input, multiple-out (MIMO) systems, and the two functions can be transformed from each other using the fast Fourier transform and the inverse fast Fourier transform. An efficient iterative algorithm is developed in this work to directly and accurately calculate the IRFs of SISO and MIMO systems in the time domain using relatively short input and output data series. The iterative algorithm can avoid the time-consuming inversion of a large matrix in the conventional least-square method for calculating an IRF, greatly reducing the computation time. In addition, a fitting index and an error energy decreasing coefficient are introduced to evaluate the accuracy in calculating an IRF and to provide the termination criterion for the iterative algorithm. A new coherence function is also introduced to evaluate the accuracy of calculated IRFs and FRFs at different spectral lines. Two examples are given to illustrate the effectiveness and efficiency of the methodology.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 6

Relation between the fitting index and the calculation time for the iterative algorithm

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Figure 7

The first four identified mode shapes, natural frequencies, and damping ratios using the calculated IRFs from the current method

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Figure 8

A MIMO simulation example with two (top) or four (bottom) inputs

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Figure 9

The error energy decreasing coefficient versus the iteration loop number for output point 1 with four inputs

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Figure 10

The first four identified mode shapes using the calculated IRFs

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Figure 1

(a) A model bridge frame excited a horizontal shaker, and (b) the measurement setup

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Figure 2

The measured amplitude (top) and phase (middle) of the FRF using the frequency averaging method with the measured response at point 7, and the corresponding conventional (dotted line) and new (solid line) coherence functions (bottom)

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Figure 3

The measured amplitude (top) and phase (middle) of the FRF using the FFT of the IRF calculated by the current method, and the corresponding new coherence function (bottom)

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Figure 4

The error energy decreasing coefficient versus the iteration loop number

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Figure 5

The measured amplitude (top) and phase (middle) of the FRF using the FFT of the IRF calculated by the least-square method, and the corresponding new coherence function (bottom)

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