Fractal-dimension-based signal processing has been extensively applied to various fields for nondestructive testing. The dynamic response signal can be utilized as an analytical tool to evaluate the structural health state without baseline data. The fractal features of the dynamic responses with fractal dimensions (FDs) were investigated using the Higuchi, Katz, and Sevcik methods. The waveform FD proposed by these methods was extracted from the measured frequency response function (FRF) data in the frequency domain. Damage was observed within this region, which resulted in an abrupt change in the curvature of the FD. The effectiveness of the methods was investigated via the results of a steel beam test and a numerical experiment to detect damage.

References

References
1.
Lee
,
U.
, and
Shin
,
J.
,
2002
, “
A Frequency Response Function-Based Structural Damage Identification Method
,”
Comput. Struct.
,
80
(
2
), pp.
117
132
.10.1016/S0045-7949(01)00170-5
2.
Higuchi
,
T.
,
1988
, “
Approach to an Irregular Time Series on the Basis of the Fractal Theory
,”
Phys. D
,
31
(
2
), pp.
277
283
.10.1016/0167-2789(88)90081-4
3.
Katz
,
M.
,
1988
, “
Fractals and the Analysis of Waveforms
,”
Comput. Biol. Med.
,
18
(
3
), pp.
145
156
.10.1016/0010-4825(88)90041-8
4.
Sevcik
,
C.
,
1998
, “
A Procedure to Estimate the Fractal Dimension of Waveforms
,”
Complexity Int.
,
5
, available at: http://www.complexity.org.au/ci/vol05/sevcik/sevcik.html
5.
Hadjileontiadis
,
L. J.
,
Douka
,
E.
, and
Trochidis
,
A.
,
2005
, “
Fractal Dimension Analysis for Crack Identification in Beam Structures
,”
Mech. Syst. Signal Process.
,
19
(
3
), pp.
659
674
.10.1016/j.ymssp.2004.03.005
6.
Qiao
,
P.
, and
Cao
,
M.
,
2008
, “
Waveform Fractal Dimension for Mode Shape-Based Damage Identification of Beam-Type Structures
,”
Int. J. Solids Struct.
,
45
(
22–23
), pp.
5946
5961
.10.1016/j.ijsolstr.2008.07.006
7.
Huang
,
Y.
,
Li
,
H.
, and
Ou
,
J.
,
2009
, “
Damage Detection on Beam Structures Based on Fractal Theory and Wavelet Packet Transform
,”
ICCES
,
12
(2), pp.
53
64
.
8.
Tao
,
D.
,
Li
,
H.
,
Huang
,
Y.
, and
Bao
,
Y.
,
2012
, “
Output Only Earthquake Damage Detection of Moment Resist Frame Using Wavelet Analysis and Fractal Dimension
,”
Proc. SPIE
,
8348
, p.
834820
.10.1117/12.915008
9.
Cao
,
M. S.
,
Ostachowicz
,
W.
,
Bai
,
R. B.
, and
Radzieski
,
M.
,
2013
, “
Fractal Mechanism for Characterizing Singularity of Mode Shape for Damage Detection
,”
Appl. Phys. Lett.
,
103
(22), p.
221906
.10.1063/1.4833837
10.
Farhidzadeh
,
A.
,
Dehghan-Niri
,
E.
,
Moustafa
,
A.
,
Salamone
,
S.
, and
Whittaker
,
A.
,
2013
, “
Damage Assessment of Reinforced Concrete Structures Using Fractal Analysis of Residual Crack Patterns
,”
Exp. Mech.
,
53
(
9
), pp.
1607
1619
.10.1007/s11340-013-9769-7
11.
Zhou
,
L.
,
Sun
,
H.
, and
He
,
Z. Q.
,
2013
, “
Fractal Dimension-Based Damage Imaging for Composites
,”
Shock Vib.
,
20
(
5
), pp.
979
998
.10.1155/2013/164539
12.
Bai
,
R.
,
Cao
,
M.
,
Su
,
Z.
,
Ostachowicz
,
W.
, and
Xu
,
H.
,
2012
, “
Fractal Dimension Analysis of Higher-Order Mode Shapes for Damage Identification of Beam Structures
,”
Math. Probl. Eng.
,
2012
, p. 454568.10.1155/2012/454568
13.
Cao
,
M. S.
, and
Qiao
,
P. Z.
,
2009
, “
On the Wavelet-Fractal Nonlinear Damage Diagnosis of Mechanical Systems
,”
Smart Mater. Struct.
,
18
(
8
), p.
085022
.10.1088/0964-1726/18/8/085022
You do not currently have access to this content.