In the framework of stochastic analysis, the extreme response value of a structural system is completely described by its CDF. However, the CDF does not represent a direct design provision. A more meaningful parameter is the response level which has a specified probability, p, of not being exceeded during a specified time interval. This quantity, which is basically the inverse of the CDF, is referred to as a fractile of order p of the structural response. This study presents an analytical procedure for evaluating the lower bound and upper bound of the fractile of order p of the response of linear structures, with uncertain stiffness properties modeled as interval variables subjected to stationary stochastic excitations. The accuracy of the proposed approach is demonstrated by numerical results concerning a wind-excited truss structure with uncertain Young’s moduli.

References

References
1.
Lutes
,
L. D.
, and
Sarkani
,
S.
,
1997
,
Stochastic Analysis of Structural and Mechanical Vibrations
,
Prentice-Hall
,
Upper Saddle River, NJ
.
2.
Der Kiureghian
,
A.
,
2008
, “
Analysis of Structural Reliability Under Parameter Uncertainties
,”
Probab. Eng. Mech.
,
23
(
4
), pp.
351
358
.10.1016/j.probengmech.2007.10.011 0266-8920
3.
Elishakoff
,
I.
, and
Ohsaki
,
M.
,
2010
,
Optimization and Anti-Optimization of Structures Under Uncertainty
,
Imperial College Press
,
London
.
4.
Ben-Haim
,
Y.
,
1994
, “
A Non-Probabilistic Concept of Reliability
,”
Struct. Saf.
,
14
(
4
), pp.
227
245
.10.1016/0167-4730(94)90013-2
5.
Penmetsa
,
R. C.
, and
Grandhi
,
R. V.
,
2002
, “
Efficient Estimation of Structural Reliability for Problems With Uncertain Intervals
,”
Comput. Struct.
,
80
(
12
), pp.
1103
1112
.10.1016/S0045-7949(02)00069-X 0045-7949
6.
Beer
,
M.
,
Zhang
,
Y.
,
Quek
,
S. T.
, and
Phoon
,
K. K.
,
2013
, “
Reliability Analysis With Scarce Information: Comparing Alternative Approaches in a Geotechnical Engineering Context
,”
Struct. Saf.
,
41
, pp.
1
10
.10.1016/j.strusafe.2012.10.003
7.
Jiang
,
C.
, , and
Bi
,
R. G.
,
Lu
,
G. Y.
, and
Han
,
X.
,
2013
, “
Structural Reliability Analysis Using Non-Probabilistic Convex Model
,”
Comput. Methods Appl. Mech. Eng.
,
254
, pp.
83
98
.10.1016/j.cma.2012.10.020 0045-7825
8.
Alvarez
,
D. A.
, and
Hurtado
,
J. E.
,
2014
, “
An Efficient Method for the Estimation of Structural Reliability Intervals With Random Sets, Dependence Modeling and Uncertain Inputs
,”
Comput. Struct.
,
142
, pp.
54
63
.10.1016/j.compstruc.2014.07.006 0045-7949
9.
Jahani
,
E.
,
Muhanna
,
R. L.
,
Shayanfar
,
M. A.
, and
Barkhordari
,
M. A.
,
2014
, “
Reliability Assessment With Fuzzy Random Variables Using Interval Monte Carlo Simulation
,”
Comp.-Aided Civil Infrastr. Eng.
,
29
(
3
), pp.
208
220
.10.1111/mice.2014.29.issue-3
10.
Muscolino
,
G.
,
Santoro
,
R.
, and
Sofi
,
A.
,
2015
, “
Explicit Reliability Sensitivities of Linear Structures With Interval Uncertainties under Stationary Stochastic Excitations
,”
Struct. Saf.
,
52
(
Part B
), pp.
219
232
.10.1016/j.strusafe.2014.03.001
11.
Michaelov
,
G.
,
Sarkani
,
S.
, and
Lutes
,
L. D.
,
1996
, “
Fractile Levels for Non-Stationary Extreme Response of Linear Structures
,”
Struct. Saf.
,
18
(
1
), pp.
11
31
.10.1016/0167-4730(96)00002-1
12.
Muscolino
,
G.
, and
Sofi
,
A.
,
2012
, “
Stochastic Analysis of Structures With Uncertain-but-Bounded Parameters via Improved Interval Analysis
,”
Probab. Eng. Mech.
,
28
, pp.
152
163
.10.1016/j.probengmech.2011.08.011 0266-8920
13.
Muscolino
,
G.
, and
Sofi
,
A.
,
2013
, “
Bounds for the Stationary Stochastic Response of Truss Structures With Uncertain-but-Bounded Parameters
,”
Mech. Syst. Signal Process.
,
37
(
1–2
), pp.
163
181
. 10.1016/j.ymssp.2012.06.016
14.
Muscolino
,
G.
,
Santoro
,
R.
, and
Sofi
,
A.
,
2014
, “
Explicit Frequency Response Functions of Discretized Structures With Uncertain Parameters
,”
Comput. Struct.
,
133
, pp.
64
78
.10.1016/j.compstruc.2013.11.007 0045-7949
15.
Moore
,
R. E.
,
Kearfott
,
R. B.
, and
Cloud
,
M. J.
,
2009
,
Introduction to Interval Analysis
,
SIAM
,
Philadelphia
.
16.
Moore
,
R. E.
,
1966
,
Interval Analysis
,
Prentice-Hall
,
Englewood Cliffs
.
17.
Rohn
,
J.
,
1993
, “
Inverse Interval Matrix
,”
SIAM J. Num. Anal.
,
30
(
3
), pp.
864
870
.10.1137/0730044
18.
Vanmarcke
,
E. H.
,
1975
, “
On the Distribution of the First-Passage Time for Normal Stationary Random Processes
,”
ASME J. Appl. Mech.
,
42
(
Ser E, 1
), pp.
215
220
.10.1115/1.3423521
19.
Rice
,
S. O.
,
1944
, “
Mathematical Analysis of Random Noise
,”
Bell. Syst. Tech. J.
,
23
, pp.
282
332
.10.1002/bltj.1944.23.issue-3 0005-8580
20.
Vanmarcke
,
E. H.
,
1972
, “
Properties of Spectral Moments with Applications to Random Vibration
,”
J. Eng. Mech.
,
98
(
2
), pp.
425
446
.
21.
Crandall
,
S. H.
,
Chandiramani
,
K. L.
, and
Cook
,
R. G.
,
1966
, “
Some First-Passage Problems in Random Vibration
,”
ASME J. Appl. Mech.
,
33
(
3
), pp.
532
538
.10.1115/1.3625118
22.
Impollonia
,
N.
, and
Muscolino
,
G.
,
2011
, “
Interval Analysis of Structures With Uncertain-but-Bounded Axial Stiffness
,”
Comput. Methods Appl. Mech. Eng.
,
200
(
21–22
), pp.
1945
1962
.10.1016/j.cma.2010.07.019 0045-7825
23.
Muscolino
,
G.
,
Santoro
,
R.
, and
Sofi
,
A.
,
2014
, “
Explicit Sensitivities of the Response of Discretized Structures Under Stationary Random Processes
,”
Probab. Eng. Mech.
,
35
, pp.
82
95
.10.1016/j.probengmech.2013.09.006 0266-8920
24.
Simiu
,
E.
, and
Scanlan
,
R.
,
1996
,
Wind Effects on Structures: Fundamentals and Applications to Design
,
John Wiley & Sons
,
New York
.
25.
Davenport
,
A. G.
,
1961
, “
The Spectrum of Horizontal Gustiness near the Ground in High Winds
,”
Q. J. R. Meteorol. Soc.
,
87
(
372
), pp.
194
211
. 0035-900910.1002/(ISSN)1477-870X
26.
Nedialkov
,
N. S.
,
Kreinovich
,
V.
, and
Starks
,
S. A.
,
2004
, “
Interval Arithmetic, Affine Arithmetic, Taylor Series Methods: Why, What Next?
Numer. Algorithms
,
37
(
1–4
), pp.
325
336
. 1017-139810.1023/B:NUMA.0000049478.42605.cf
27.
Yamazaki
,
F.
,
Shinozuka
,
M.
, and
Dasgupta
,
G.
,
1988
, “
Neumann Expansion for Stochastic Finite Element Analysis
,”
J. Eng. Mech.
,
114
(
8
), pp.
1335
1354
. 0733-939910.1061/(ASCE)0733-9399(1988)114:8(1335)
This content is only available via PDF.
You do not currently have access to this content.