Maintaining high accuracy and efficiency is a challenging issue in time-dependent reliability analysis. In this work, an accurate and efficient method is proposed for limit-state functions with the following features: The limit-state function is implicit with respect to time. There is only one stochastic process in the input to the limit-sate function. The stochastic process could be either a general strength or a general stress variable so that the limit-state function is monotonic to the stochastic process. The new method employs a sampling approach to estimate the distributions of the extreme value of the stochastic process. The extreme value is then used to replace the corresponding stochastic process. Consequently the time-dependent reliability analysis is converted into its time-invariant counterpart. The commonly used time-invariant reliability method, the first order reliability method, is then applied to calculate the probability of failure over a given period of time. The results show that the proposed method significantly improves the accuracy and efficiency of time-dependent reliability analysis.

References

References
1.
Singh
,
A.
,
Mourelatos
,
Z. P.
, and
Li
,
J.
,
2010
, “
Design for Lifecycle Cost Using Time-Dependent Reliability
,”
J. Mech. Des., Trans. ASME
,
132
(
9
), p.
0910081
.10.1115/1.4002200
2.
Nielsen
,
U. D.
,
2010
, “
Calculation of Mean Outcrossing Rates of Non-Gaussian Processes With Stochastic Input Parameters-Reliability of Containers Stowed on Ships in Severe Sea
,”
Probab. Eng. Mech.
,
25
(
2
), pp.
206
217
.10.1016/j.probengmech.2009.11.002
3.
Sergeyev
,
V. I.
,
1974
, “
Methods for Mechanism Reliability Calculation
,”
Mech. Mach. Theory
,
9
(
1
), pp.
97
106
.10.1016/0094-114X(74)90010-X
4.
Singh, A.
,
Mourelatos, Z.
, and
Nikolaidis, E.
,
2011
, “An importance sampling approach for time-dependent reliability,”
ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
,
IDETC/CIE
,
Washington, DC
, pp.
1077
1088
.
5.
Van Noortwijk
,
J. M.
,
Van Der Weide
,
J. A. M.
,
Kallen
,
M. J.
, and
Pandey
,
M. D.
,
2007
, “
Gamma Processes and Peaks-Over-Threshold Distributions for Time-Dependent Reliability
,”
Reliab. Eng. Syst. Saf.
,
92
(
12
), pp.
1651
1658
.10.1016/j.ress.2006.11.003
6.
Tont
,
G.
,
Vlădăreanu
,
L.
,
Munteanu
,
M. S.
, and
Tont
,
D. G.
,
2010
, “
Markov Approach of Adaptive Task Assignment for Robotic System in Non-Stationary Environments
,”
WSEAS Trans. Circuits Syst.
,
9
(
3
), pp.
273
282
. Available at: http://www.worldses.org/journals/systems/systems-2010.htm
7.
Li
,
J.
,
Chen
,
J. B.
, and
Fan
,
W. L.
,
2007
, “
The Equivalent Extreme-Value Event and Evaluation of the Structural System Reliability
,”
Struct. Safety
,
29
(
2
), pp.
112
131
.10.1016/j.strusafe.2006.03.002
8.
Chen
,
J. B.
, and
Li
,
J.
,
2007
, “
The Extreme Value Distribution and Dynamic Reliability Analysis of Nonlinear Structures With Uncertain Parameters
,”
Struct. Safety
,
29
(
2
), pp.
77
93
.10.1016/j.strusafe.2006.02.002
9.
Lutes
,
L. D.
, and
Sarkani
,
S.
,
2009
, “
Reliability Analysis of Systems Subject to First-Passage Failure
,” NASA Technical Report No. NASA/CR-2009-215782.
10.
Sudret
,
B.
,
2008
, “
Analytical Derivation of the Outcrossing Rate in Time-Variant Reliability Problems
,”
Struct. Infrastructure Eng.
,
4
(
5
), pp.
353
362
.10.1080/15732470701270058
11.
Rice
,
S. O.
,
1944
, “
Mathematical Analysis of Random Noise
,”
Bell Syst. Tech. J.
,
23
, pp.
282
332
. Available at: http://www3.alcatel-lucent.com/bstj/vol23-1944/articles/bstj23-3-282.pdf
12.
Andrieu-Renaud
,
C.
,
Sudret
,
B.
, and
Lemaire
,
M.
,
2004
, “
The Phi2 Method: A Way to Compute Time-Variant Reliability
,”
Reliab. Eng. Syst. Saf.
,
84
(
1
), pp.
75
86
.10.1016/j.ress.2003.10.005
13.
Zhang
,
J. F.
, and
Du
,
X.
,
2011
, “
Time-Dependent Reliability Analysis for Function Generator Mechanisms
,”
ASME J. Mech. Des.
,
133
(
3
), p.
031005
.10.1115/1.4003539
14.
Mejri
,
M.
,
Cazuguel
,
M.
, and
Cognard
,
J. Y.
,
2011
, “
A Time-Variant Reliability Approach for Ageing Marine Structures With Non-Linear Behaviour
,”
Comput. Struct.
,
89
(
19–20
), pp.
1743
1753
.10.1016/j.compstruc.2010.10.007
15.
Madsen
,
P. H.
and
Krenk
,
S.
,
1984
, “
Integral Equation Method for the First-Passage Problem in Random Vibration
,”
Trans. ASME, J. Appl. Mech.
,
51
(
3
), pp.
674
679
.10.1115/1.3167691
16.
Vanmarcke
,
E. H.
,
1975
, “
On the Distribution of the First-Passage Time for Normal Stationary Random Processes
,”
Trans. ASME, J. Appl. Mech.
,
42
(
1
), pp.
215
220
.10.1115/1.3423521
17.
Preumont
,
A.
,
1985
, “
On the Peak Factor of Stationary Gaussian Processes
,”
J. Sound Vib.
,
100
(
1
), pp.
15
34
.10.1016/0022-460X(85)90339-6
18.
Huang
,
B.
, and
Du
,
X.
,
2008
, “
Probabilistic Uncertainty Analysis by Mean-Value First Order Saddlepoint Approximation
,”
Reliab. Eng. Syst. Saf.
,
93
(
2
), pp.
325
336
.10.1016/j.ress.2006.10.021
19.
Vennell
,
R.
,
2011
, “
Estimating the Power Potential of Tidal Currents and the Impact of Power Extraction on Flow Speeds
,”
Renewable Energy
,
36
(
12
), pp.
3558
3565
.10.1016/j.renene.2011.05.011
20.
Lutes
,
L. D.
, and
Sarkani
,
S.
,
Random Vibrations: Analysis of Structural and Mechanical Systems
(
Elsevier
,
New York
,
2004
).
21.
Yang
,
H. Z.
, and
Zheng
,
W.
,
2011
, “
Metamodel Approach for Reliability-Based Design Optimization of a Steel Catenary Riser
,”
J. Mar. Sci. Technol.
,
16
(
2
), pp.
202
213
.10.1007/s00773-011-0121-6
22.
Sheu
,
S. H.
,
Yeh
,
R. H.
,
Lin
,
Y. B.
, and
Juang
,
M. G.
,
2001
, “
Bayesian Approach to an Adaptive Preventive Maintenance Model
,”
Reliab. Eng. Syst. Saf.
,
71
(
1
), pp.
33
44
.10.1016/S0951-8320(00)00072-7
23.
Hu
,
Z.
, and
Du
,
X.
,
2012
, “
Reliability Analysis for Hydrokinetic Turbine Blades
,”
Renewable Energy
,
48
, pp.
251
262
.10.1016/j.renene.2012.05.002
24.
Li
,
C. C.
, and
Kiureghian
,
A. D.
,
1993
, “
Optimal Discretization of Random Fields
,”
J. Eng. Mech.
,
119
(
6
), pp.
1136
1154
.10.1061/(ASCE)0733-9399(1993)119:6(1136)
25.
Daniels
,
H.
,
1954
, “
Saddlepoint Approximations in Statistics
,”
Ann. Math. Stat.
,
25
(
4
), pp.
631
650
.10.1214/aoms/1177728652
26.
Du
,
X.
, and
Sudjianto
,
A.
,
2004
, “
First-Order Saddlepoint Approximation for Reliability Analysis
,”
AIAA J.
,
42
(
6
), pp.
1199
1207
.10.2514/1.3877
27.
Marsh
,
P.
,
1998
, “
Saddlepoint Approximations for Noncentral Quadratic Forms
,”
Econometric Theory
,
14
(
05
), pp.
539
559
.10.1017/S0266466698145012
28.
Du
,
X.
,
2010
, “
System Reliability Analysis with Saddlepoint Approximation
,”
Struct. Multidiscip. Optim.
,
42
(
2
), pp.
193
208
.10.1007/s00158-009-0478-x
29.
Huang
,
B.
, and
Du
,
X.
,
2006
, “
A Saddlepoint Approximation Based Simulation Method for Uncertainty Analysis
,”
Int. J. Reliab. Saf.
,
1
(
1/2
), pp.
206
224
.10.1504/IJRS.2006.010698
30.
Fisher
,
R. A.
,
1928
, “
Moments and Product Moments of Sampling Distribution
,”
Proc. London Math. Soc.
,
30
(
2
), pp.
199
238
.10.1112/plms/s2-30.1.199
31.
Lugannani
,
R.
, and
Rice
,
S. O.
,
1980
, “
Saddlepoint Approximation for the Distribution of the Sum of Independent Random Variables
,”
Adv. Appl. Probab.
,
12
(
2
), pp.
475
490
.10.2307/1426607
32.
Du
,
X.
,
2008
, “
Saddlepoint Approximation for Sequential Optimization and Reliability Analysis
,”
Trans. ASME, J. Mech. Des.
,
130
(
1
), p.
011011
.10.1115/1.2717225
33.
Chiralaksanakul
,
A.
, and
Mahadevan
,
S.
,
2005
, “
First-Order Approximation Methods in Reliability-Based Design Optimization
,”
Trans. ASME, J. Mech. Des.
,
127
(
5
), pp.
851
857
.10.1115/1.1899691
34.
Koduru
,
S. D.
, and
Haukaas
,
T.
,
2010
, “
Feasibility of Form in Finite Element Reliability Analysis
,”
Struct. Safety
,
32
(
2
), pp.
145
153
.10.1016/j.strusafe.2009.10.001
35.
Lee
,
S. H.
, and
Kwak
,
B. M.
,
2006
, “
Response Surface Augmented Moment Method for Efficient Reliability Analysis
,”
Struct. Safety
,
28
(
3
), pp.
261
272
.10.1016/j.strusafe.2005.08.003
36.
Martin
,
O. L. H.
,
2008
,
Aerodynamics of Wind Turbines
,
2nd ed.
,
Earthscan
,
Sterling
.
You do not currently have access to this content.