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.

References

References
1.
Cannon
,
J.
, and
Dostrovsky
,
S.
, 1981,
The Evolution of Dynamics: Vibration Theory 1687 to 1742
,
Springer
,
New York
.
2.
Rao
,
S.
, 2005,
Mechanical Vibrations
,
SI ed., Prentice Hall
,
Englewood Cliffs, NJ
, pp.
5
239
.
3.
University of St. Andrews 2008, “
Jean Baptiste Joseph Fourier
,” (http://www-groups.dcs.st-and.ac.uk/∼history/Printonly/Fourier.html); (Accessed 7 August 2008).
4.
Burke-Hubbard
,
B.
, 1998,
The World According to Wavelets
,
A. K.
Peters
,
Natick
, pp.
4
208
.
5.
Crandall
,
S.
, 1958,
Mechanical Random Vibrations
,
Wiley
,
London
, pp.
5
15
.
6.
Bendat
,
J.
, and
Piersol
,
A.
, 2000,
Random Data: Analysis and Measurement Procedures
,
3rd ed.
,
John Wiley
,
New York
, pp.
9
505
.
7.
Randall
,
R. B.
, 1987,
Frequency Analysis
,
3rd ed.
,
Brüel & Kjaer, K Larson & Son
,
Denmark
, pp.
20
250
.
8.
Huang
,
N.
,
Shen
,
J.
,
Long
,
S.
,
Wu
,
M.
,
Shih
,
H.
,
Zheng
,
Q.
,
Yen
,
N.
,
Tung
,
C.
, and
Liu
,
H.
, 1998, “
The Empirical Mode Decomposition and the Hilbert Spectrum for Non-linear and Non-Stationary Time Series Analysis
,”
Proceedings of the Royal Society
,
The Royal Society
,
London
, p.
907
.
9.
Newland
,
D. E.
, 1993,
An Introduction to Random Vibrations, Spectral and Wavelet Analysis
,
3rd ed.
,
Longman Scientific & Technical
,
New York
, pp.
137
295
.
10.
Gabor
,
D.
, 1946, “
Theory of Communication
,”
J. Inst. Electr. Eng., 1889–1948, Part 3
,
93
, pp.
429
411
.
11.
Ewins
,
D.
, 1995,
Modal Testing Theory and Practice
,
Research Studies Press
,
Taunton
, pp.
178
995
.
12.
Avitabile
,
P.
, 2006, “
101 Ways to Extract Modal Parameters—Which one is for me?
,”
Experimental Techniques
,
Society for Experimental Mechanics
,
Bethel, CT
.
13.
Iglesias
,
A.
, 2000, “
Investigating Various Modal Analysis Extraction Techniques to Estimate Damping Ratio
,” Mechanical Engineering Thesis, Virginia Polytechnic Institute and State University.
14.
Garcia-Romeu-Martinez
,
M. A.
,
Rouillard
,
V.
,
Sek
,
M.
, and
Cloquell-Ballester
,
V. A.
, 2007, “
Monitoring the Evolution of Fatigue in Corrugated Paperboard Under Random Loads
,”
Proceedings of the 5th BSSM International Conference on Advances in Experimental Mechanics
,
British Society for Strain Measurement
,
Manchester
.
15.
Rouillard
,
V.
,
Lamb
,
M.
, and
Sek
,
M.
, 2007, “
Determining Fatigue Progression in Corrugated Paperboard Containers Subjected to Dynamic Compression
,”
Proceedings of the 5th Australasian Congress on Applied Mechanics
,
ACAM 2007, The Institute of Engineers Australia
,
Brisbane
, Vol.
1
, pp.
331
336
.
16.
Sek
,
M.
, 2007, “
Numerical Simulation of Impacts Involving a Collapsible Nonlinear Multilayer Structure
,”
Proceedings of the World Conference of Engineering
,
London
, pp.
1367
1372
.
17.
Harris
,
F.
, 1978, “
On the Use of Windows for Harmonic Analysis With the Discrete Fourier Transform
,”
Proc. IEEE
,
66
(
1
), pp.
51
83
.
18.
Kay
,
S.
, 1988, “
Spectral Estimation
,” in
Advanced Topics in Signal Processing
, edited by
J.
Lim
and
A.
Oppenheim
,
Prentice Hall
,
Englewood Cliffs, NJ
, pp.
78
79
.
19.
Weeks
,
M.
, 2007,
Digital Signal Processing Using Matlab and Wavelets
,
Infinity Science Press
,
Hingham
, pp.
202
203
.
20.
Lyons
,
R.
, 2004,
Understanding Digital Signal Processing
,
2nd ed.
,
Prentice Hall
,
Upper Saddle River, NJ
, p.
87
.
21.
Manolakis
,
D.
,
Ingle
,
V.
, and
Kogon
,
S.
, 2005,
Statistical and Adaptive Signal Processing: Spectral Estimation, Signal Modeling, Adaptive Filtering, and Array Processing
,
Artech House
,
Boston
, p.
202
.
22.
Andreas
,
A.
, 2006,
Digital Signal Processing: Signals, Systems, and Filters
,
McGraw-Hill
,
New York
, p.
328
.
23.
Roberts
,
M.
, 2004,
Signals and Systems: Analysis Using Transform Methods and MATLAB
,
McGraw-Hill
,
London
, pp.
541
542
.
24.
Baher
,
H.
, 1990,
Analog & Digital Signal Processing
,
Wiley
,
Chichester
, pp.
365
367
.
25.
Douglas
,
E.
, 1987,
Handbook of Digital Signal Processing
,
Elsevier Academic
,
New York
, pp.
722
723
.
26.
Semmlow
,
J.
, 2005,
Circuits, Signals and Systems for Bioengineers: A Matlab Based Introduction
,
Academic
,
New York
, pp.
96
97
.
27.
Naidu
,
P.
, 1996,
Modern Spectrum Analysis of Time Series: Fast Algorithms and Error Control Techniques
,
CRC Press
,
Boca Raton, FL
, pp.
173
192
.
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