Based on the measured static displacements, an improved interval analysis technique was proposed for the structural damage identification. Due to the scarcity of uncertain information, the uncertainties were considered as interval numbers in this paper. Via the first-order Taylor series expansion, the interval bounds of the elemental stiffness parameters of undamaged and damaged structures are respectively obtained. The structural damage was detected by the quantitative measure of the possibility of damage existence in elements, which was more reasonable than the probability of damage existence in the condition of less sample points for the measurement data. Furthermore, the classic interval analysis method was improved by adopting the membership-set identification and two-step model updating procedure to make identification results more accurate. An uncertain truss structure was employed for damage identification, the damage identification results obtained by interval analysis method and probabilistic method, respectively, were compared. Moreover, the effects on the detection results of the damage level and uncertainty level subjected to single or multiple load cases were studied as well. The numerical example shows that the wide intervals resulting from the interval operation can be narrowed by the improved nonprobabilistic approach, and the feasibility and effectiveness of the present method were validated.

References

References
1.
Alvandi
,
A.
, and
Cremona
,
C.
, 2006, “
Assessment of Vibration-Based Damage Identification Techniques
,”
J. Sound Vib.
,
292
, pp.
179
202
.
2.
Sanayei
,
M.
, and
Onipede
,
O.
, 1991, “
Damage Assessment of Structures Using Static Test Data
,”
AIAA J.
,
29
, pp.
1174
1179
.
3.
Abe
,
M.
, 1996, “
Structural Damage Detection by Natural Frequencies,” AIAA/ASME/ASCE/AHS/ASC Structures
,
Structural Dynamics and Materials Conference and Exhibit, 37th. American Institute of Aeronautics and Astronautics Paper
, Salt Lake City, pp.
1064
1069
.
4.
Cawley
,
P.
, and
Adams
,
R. D.
, 1979, “
The Locations of Defects in Structures From Measurements of Natural Frequencies
,”
J. Strain Anal.
,
14
, pp.
49
57
.
5.
Kaouk
,
M.
, and
Zimmerman
,
D. C.
, “
Structural Damage Assessment Using a Generalized Minimum Rank Perturbation Theory
,”
AIAA J.
,
32
, pp.
836
842
.
6.
Parloo
,
E.
,
Guillaume
,
P.
, and
Overmeire
,
M. V.
, 2003, “
Damage Assessment Using Mode Shape Sensitivities
,”
Mech. Syst. Signal Process.
,
17
, pp.
499
518
.
7.
Lee
,
U.
, and
Shin
,
J.
, 2002, “
A Structural Damage Identification Method for Plate Structures
,”
Eng. Struct.
,
24
, pp.
1177
1188
.
8.
Pandey
,
A. K.
,
Biswas
,
M.
, and
Samman
,
M. M.
, 1991, “
Damage Detection From Changes in Curvature Mode Shapes
,”
J. Sound Vib.
,
145
, pp.
321
332
.
9.
Robinson
,
N. A.
,
Peterson
,
L. D.
, and
James
,
G. H.
, 1996, “
Health Monitoring of Aircraft Structures Using Experimental Flexibility Matrices
,”
AIAA/ASME/AHS Adaptive Structures Forum, American Institute of Aeronautics and Astronautics Paper
, Salt Lake City, pp.
328
337
.
10.
Caddemi
,
S.
, and
Greco
,
A.
, 2006, “
The Influence of Instrumental Error on the Static Identification of Damage Parameters for Elastic Beams
,”
Comput. Struct.
,
84
, pp.
1696
1708
.
11.
Sanayei
,
M.
, and
Scampoli
,
S. F.
, 1991, “
Structural Element Stiffness Identification from Static Test Data
,”
J. Eng. Mech.
,
117
, pp.
1021
1036
.
12.
Mohamed
,
A.
, and
Abdo
,
B.
, 2012, “
Parametric Study of Using Only Static Response in Structural Damage Detection
,”
Eng. Struct.
,
34
,
124
131
.
13.
Banan
,
M. R.
,
Banan
,
M. R.
, and
Hjelmstad
,
K. D.
, 1994, “
Parameter Estimation of Structures From Static Response. I: Computational Aspects
,”
J. Eng. Struct.
,
120
, pp.
3243
3258
.
14.
Banan
,
M. R.
,
Banan
,
M. R.
, and
Hjelmstad
,
K. D.
, 1994, “
Parameter Estimation of Structures From Static Response. II: Numerical Simulation
,”
J. Struct. Eng.
,
120
, pp.
3259
3283
.
15.
Hjelmstad
,
K. D.
, and
Shin
,
S.
, 1997, “
Damage Detection and Assessment of Structural From Static Response
,”
J. Eng. Mech.
,
123
(
6
), pp.
568
576
.
16.
Bruno
,
R. J.
, 1994, “
Identification of Nonlinear Joints in a Truss Structure
,”
AIAA/ASME/AHS Adaptive Structures Forum, American Institute of Aeronautics and Astronautics Paper
, Washington, pp.
402
410
.
17.
Cobb
,
R. G.
, and
Liebst
,
B. S.
, 1997, “
Structural Damage Identification Using Assigned Partial Eigenstructure
,”
AIAA J.
,
35
, pp.
152
158
.
18.
Jaishi
,
B.
, and
Ren
,
W. X.
, 2006, “
Damage Detection by Finite Element Model Updating Using Modal Flexibility Residual
,”
J. Sound Vib.
,
290
, pp.
369
387
.
19.
Lim
,
T. M.
, and
Kashangaki
,
T. A. -L. A.-L.
, 1994, “
Structural Damage Detection of Space Truss Structures Using Best Achievable Eigenvectors
,”
AIAA J.
,
32
, pp.
1049
1057
.
20.
Teughels
,
A.
,
Maeck
,
J.
, and
Roeck
,
G. D.
, 2002, “
Damage Assessment by FE Model Updating Using Damage Functions
,”
Comput. Struct.
,
80
, pp.
1869
1879
.
21.
Elishakoff
,
I.
, 1998, “
Three Versions of the FE Method Based on Concepts of Either Stochasticity, Fuzziness or Anti-Optimization
,”
Appl. Mech. Rev.
,
51
, pp.
209
218
.
22.
Collins
,
J. D.
,
Hart
,
G. C.
,
Hasselman
,
T. K.
, and
Kennedy
,
B.
, 1974, “
Statistical Identification of Structures
,”
AIAA J.
,
12
, pp.
185
190
.
23.
Xia
,
Y.
, and
Hao
,
H.
, 2003, “
Statistical Damage Identification of Structures with Frequency Changes
,”
J. Sound Vib.
,
263
, pp.
853
870
.
24.
Xia
,
Y.
,
Hao
,
H.
,
Brownjohn
,
J. M. W.
, and
Xia
,
P. Q.
, 2002, “
Damage Identification of Structures with Uncertain Frequency and Mode Shape Data
,”
Earthquake Eng. Struct. Dyn.
,
31
, pp.
1053
1066
.
25.
Li
,
X. Y.
, and
Law
,
S. S.
, 2008, “
Damage Identification of Structures Including System Uncertainties and Measurement Noise
,”
AIAA J.
,
46
, pp.
263
276
.
26.
Yeo
,
B. I.
,
Shin
,
S.
,
Lee
,
H. S.
, and
Chang
,
S. P.
, 2000, “
Statistical Damage Assessment of Framed Structures from Static Response
,”
J. Eng. Mech.
,
126
, pp.
414
421
.
27.
Sawyer
,
J. P.
, and
Rao
,
S. S.
, 1996, “
Structural Fault Detection Using Fuzzy Logic
,”
AIAA Dynamics Specialists Conference, American Institute of Aeronautics and Astronautics Paper
, Salt Lake City, pp.
214
222
.
28.
Moens
,
D.
, and
Vandepitte
,
D.
, 2002, “
Fuzzy Finite Element Method for Frequency Response Function Analysis of Uncertain Structures
,”
AIAA J.
,
40
,
126
136
(2002).
29.
Gabriele
,
S.
,
Valente
,
C.
, and
Brancaleoni
,
F.
, 2007, “
An Interval Uncertainty Based Method for Damage Identification
,”
Key Eng. Mater.
,
347
, pp.
551
556
(2007).
30.
García
,
O.
,
Vehí
,
J.
,
Matos
,
J. C.
, and
Casas
,
J. R.
, 2008, “
Structural Assessment Under Uncertain Parameters via Interval Analysis
,”
J. Comput. Appl. Math.
,
218
, pp.
43
52
.
You do not currently have access to this content.