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Research Papers

Assessing the Influence of Fourier Analysis Parameters on Short-Time Modal Parameter Extraction

[+] Author and Article Information
Matthew Lamb1

 Victoria University, P.O. Box 14428, MCMC 8001, Melbourne, AustraliaMatthew.Lamb@vu.edu.au

Vincent Rouillard

 Victoria University, P.O. Box 14428, MCMC 8001, Melbourne, AustraliaVincent.Rouillard@vu.edu.au

1

Corresponding author.

J. Vib. Acoust 134(3), 031002 (Apr 24, 2012) (12 pages) doi:10.1115/1.4005654 History: Received July 22, 2010; Revised September 18, 2011; Published April 23, 2012; Online April 24, 2012

It is sometimes necessary to determine the manner in which materials and structures deteriorate with respect to time when subjected to sustained random dynamic loads. In such cases a system’s fatigue characteristics can be obtained by continuously monitoring its modal parameters. This allows for any structural deterioration, often manifested as a loss in stiffness, to be detected. Many common structural integrity assessment techniques make use of Fourier analysis for modal parameter extraction. For continual modal parameter extraction, the Fourier transform requires that a compromise be made between the accuracy of the estimates and how frequently they can be obtained. The limitations brought forth by this compromise can be significantly reduced by selecting suitable values for the analysis parameters, mainly subrecord length and number of averages. Further improvements may also be possible by making use of spectral enhancement techniques, specifically overlapped averaging and zero padding. This paper uses the statistical analysis of results obtained from numerous physical and numerical experiments to evaluate the influence of the analysis parameters and spectral enhancement techniques on modal estimates obtained from limited data sets. This evaluation will assist analysts in selecting the most suitable inputs for parameter extraction purposes. The results presented in this paper show that when using the Fourier transform to extract modal characteristics, any variation in the parameters used for analysis can have a significant influence on the extraction of natural frequency estimates from systems subjected to random excitation. It was found that for records containing up to 10% noise, subrecord length; hence spectral resolution, has a more pronounced influence on the accuracy of modal estimates than the level of spectral averaging; therefore spectral uncertainty. It was also found that while zero padding may not increase the actual spectral resolution, it does allow for improved natural frequency estimates with the introduction of interpolated estimates at the nondescribed frequencies. Finally, it was found that for modal parameter extraction purposes (in this case natural frequency), increased amounts of overlapped averaging can significantly reduce the variance of the estimates obtained. This is particularly useful as it allows for increased precision without compromising temporal resolution.

Copyright © 2012 by American Society of Mechanical Engineers
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Figures

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Figure 8

Experiment 2—Influence of zero padding on the estimation of natural frequency—physical data

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Figure 9

FRF estimates and zero padding. Left; No zero padding. Right; Zero padding (Tsr × 16).

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Figure 10

Spectral resolution and uncertainty with zero padding (Tsr × 16)

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Figure 11

(a) FRF magnitude obtained using two independent averages, (b) FRF magnitude obtained using 50% overlap, resulting in three overlapped averages, and (c) FRF magnitude obtained using 99% overlap, resulting in 101 overlapped averages

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Figure 12

Experiment 3—Influence of overlapping on the estimation of natural frequency. (Maximum represents the case where all but one sample point were overlapped.)

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Figure 13

Experiment 3—Influence of overlapped averaging on natural frequency estimate variance (where x is the number of overlapped averages)

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Figure 14

Influence of overlapped averaging on the natural frequency estimate variance with zero-padding applied (Tsr × 16)

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Figure 15

Natural frequency estimate precision versus temporal resolution

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Figure 16

Influence of parameter selection on the analysis of a time variant system, physical data (steel cantilever)

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Figure 6

Experiment 2—Influence of zero padding on the estimation of natural frequency—uncontaminated numerical data (Nd is the number of averages and Tsr is the subrecord length)

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Figure 7

Experiment 2—Influence of zero padding on the estimation of natural frequency—numerical data containing 10% noise

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Figure 1

Schematic of spectral analysis identifying zero padding

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Figure 2

Schematic of spectral analysis identifying overlap

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Figure 3

Schematic of Simulink model for simulation of foundation displacement input/displacement response SDOF systems

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Figure 4

Schematic of physical experiment arrangement (inset: photograph of experimental rig)

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Figure 5

Experiment 1—Spectral resolution and uncertainty

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