In this paper, modified transfer entropy theory is combined with a surrogate data algorithm to produce a new method in order to identify nonlinearity in the vibration data of a damaged cylindrical shell. The proposed identification method can eliminate the necessity of acquiring baseline statistics by comparing the transfer entropy of original vibration data and that of surrogate data. Moreover, a new index ξ is established to reflect the degree of nonlinearity by quantifying the discreteness of the entropy of each group of surrogate data. Vibration tests are conducted and experimental data are analyzed to confirm the effectiveness of this method. Then, a semi-analytical method based on a Galerkin method and the classic shell theory is used to precisely predict the linear and nonlinear vibration response of a cylindrical shell under different damage circumstances. The corresponding results show that the proposed method can not only identify the structural damage but also be further applied to the evaluation of such damage for cylindrical shells. In addition, the influence of different load pressures and degrees of damage on the effectiveness of the identification method is analyzed and discussed. As verified, the proposed methodology can be potentially used for structural damage identification and evaluation in areas such as civil engineering, mechanical engineering, and ocean engineering.

References

References
1.
Achenbach
,
J. D.
,
2009
, “
Structural Health Monitoring-What Is the Prescription
,”
Mech. Res. Com.
,
36
(
2
), pp.
137
142
.
2.
Zembaty
,
Z.
,
Kowalski
,
M.
, and
Pospisil
,
S.
,
2006
, “
Dynamic Identification of a Reinforced Concrete Frame in Progressive States of Damage
,”
Eng. Struct.
,
28
(
5
), pp.
668
681
.
3.
Zou
,
Y.
,
Tong
,
L.
, and
Steven
,
G. P.
,
2000
, “
Vibration-Based Model-Dependent Damage (Delamination) Identification and Health Monitoring for Composite Structures—A Review
,”
J. Sound Vib.
,
230
(
2
), pp.
357
378
.
4.
Bagchi
,
A.
,
Humar
,
J.
, and
Xu
,
H. P.
,
2010
, “
Model-Based Damage Identification in a Continuous Bridge Using Vibration Data
,”
J. Perform. Constr. Fac.
,
24
(
2
), pp.
148
158
.
5.
Schreiber
,
T.
,
2000
, “
Measuring Information Transfer Entropy
,”
Phys. Rev. Lett.
,
85
(
2
), pp.
461
464
.
6.
Overbey
,
L. A.
, and
Todd
,
M. D.
,
2009
, “
Dynamic System Change Detection Using a Modification of the Transfer Entropy
,”
J. Sound Vib.
,
322
(
1–2
), pp.
438
453
.
7.
Overbey
,
L. A.
, and
Todd
,
M. D.
,
2009
, “
Effects of Noise on Transfer Entropy Estimation for Damage Detection
,”
Mech. Syst. Signal Process
,
23
(
7
), pp.
2178
2191
.
8.
Gotoda
,
H.
,
Asano
,
Y.
, and
Chuah
,
K. H.
,
2010
, “
Dynamic Behavior of Buoyancy-Induced Flame Oscillation Under Swirling Flow by a Use of Nonlinear Time Series Analysis in Combination With Surrogates Method
,”
Combust. Sci. Technol.
,
182
(
11–12
), pp.
1820
1840
.
9.
Yin
,
Y.
, and
Shang
,
P. J.
,
2015
, “
Modified Cross Sample Entropy and Surrogates Analysis Method for Financial Time Series
,”
Phys. A
,
433
(
3
), pp.
17
25
.
10.
Gan
,
M.
,
Huang
,
Y. Z.
,
Ding
,
M.
,
Dong
X. P.
, and
Peng
,
J. B.
,
2012
, “
Testing for Nonlinearity in Solar Radiation Time Series by a Fast Surrogates Test Method
,”
Sol. Energy
,
86
(
9
), pp.
2893
2896
.
11.
Nichols
,
J. M.
,
Seaver
,
M.
, and
Trickey
,
S. T.
,
2006
, “
A Method for Detecting Damage-Induced Nonlinearities in Structures Using Information Theory
,”
J. Sound Vib.
,
297
(
1–2
), pp.
1
16
.
12.
Nichols
,
J. M.
,
Seaver
,
M.
,
Trickey
,
S. T.
,
Todd
,
M. D.
,
Olson
,
C.
, and
Overbey
,
L.
,
2005
, “
Detecting Nonlinearity in Structural Systems Using the Transfer Entropy
,”
Phys. Rev. E
,
72
(
4
), pp.
1
11
.
13.
Shi
,
Z. Y.
,
Law
,
S. S.
, and
Zhang
,
L. M.
,
2000
, “
Damage Localization by Directly Using Incomplete Mode Shapes
,”
J. Eng. Mech.
,
126
(
6
), pp.
656
660
.
14.
Schreiber
,
T.
, and
Schmitz
,
A.
,
1996
, “
Improved Surrogates for Nonlinearity Tests
,”
Phys. Rev. Lett.
,
77
(
4
), pp.
635
638
.
15.
Prichard
,
D.
, and
Theiler
,
J.
,
1994
, “
Generating Surrogates for Time Series With Several Simultaneously Measured Variables
,”
Phys. Rev. Lett.
,
73
(
7
), pp.
951
954
.
16.
Theiler
,
J.
,
Eubank
,
S.
,
Longtin
,
A.
,
Galdrikian
,
B.
, and
Farmer
,
J. D.
,
1992
, “
Testing for Nonlinearity in Time Series: The Method of Surrogates
,”
Phys. Rev D
,
58
(
1–4
), pp.
77
94
.
17.
Girish
,
J.
, and
Ramachandra
,
L. S.
,
2005
, “
Thermal Postbuckled Vibrations of Symmetrically Laminated Composite Plates With Initial Geometric Imperfections
,”
J. Sound Vib.
,
282
(
3–5
), pp.
1137
1153
.
18.
Lopatin
,
A. V.
, and
Morozov
,
E. V.
,
2013
, “
Buckling of the Composite Orthotropic Clamped-Clamped Cylindrical Shell Loaded by Transverse Inertia Forces
,”
Comp. Struct.
,
95
, pp.
471
478
.
19.
Wang
,
T. L.
, and
Tang
,
W. Y.
,
2005
, “
The Semi-Analytical Method to Solve Dynamic Response of Composite Cylindrical Shell
,”
J. Shanghai Jiaotong Univ.(Sci.)
,
39
(
3
), pp.
1851
1857
.http://link.springer.com/article/10.1007%2Fs11741-007-0306-1
20.
Nguyen
,
D.
, and
Pham
,
T.
,
2015
, “
Nonlinear Dynamic Response and Vibration of Shear Deformable Imperfect Eccentrically Stiffened S-FGM Circular Cylindrical Shells Surrounded on Elastic Foundations
,”
Aero. Sci. Technol.
,
40
(
8
), pp.
115
127
.
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