Time-variant reliability problems caused by deterioration in material properties, dynamic load uncertainty, and other causes are widespread among practical engineering applications. This study proposes a novel time-variant reliability analysis method based on stochastic process discretization (TRPD), which provides an effective analytical tool for assessing design reliability over the whole lifecycle of a complex structure. Using time discretization, a stochastic process can be converted into random variables, thereby transforming a time-variant reliability problem into a conventional time-invariant system reliability problem. By linearizing the limit-state function with the first-order reliability method (FORM) and furthermore, introducing a new random variable, the converted system reliability problem can be efficiently solved. The TRPD avoids the calculation of outcrossing rates, which simplifies the process of solving time-variant reliability problems and produces high computational efficiency. Finally, three numerical examples are used to verify the effectiveness of this approach.

References

1.
Rice
,
S. O.
,
1944
, “
Mathematical Analysis of Random Noise
,”
Bell Syst. Tech. J.
,
23
(
3
), pp.
282
332
.10.1002/j.1538-7305.1944.tb00874.x
2.
Siegert
,
A. J. F.
,
1951
, “
On the First Passage Time Probability Problem
,”
Phys. Rev.
,
81
(
4
), pp.
617
623
.10.1103/PhysRev.81.617
3.
Helstrom
,
C. W.
, and
Isley
,
C. T.
,
1959
, “
Two Notes on a Markov Envelope Process
,”
IRE Trans. Inf. Theory
,
5
, pp.
139
140
.10.1109/TIT.1959.1057511
4.
Coleman
,
J. J.
,
1959
, “
Reliability of Aircraft Structures in Resisting Chance Failure
,”
Operat. Res.
,
7
(
5
), pp.
639
645
.10.1287/opre.7.5.639
5.
Crandall
,
S. H.
,
Chandiramani
,
K. L.
, and
Cook
,
R. G.
,
1966
, “
Some First-Passage Problems in Random Vibration
,”
ASMEJ. Appl. Mech.
,
33
(
3
), pp.
532
538
.10.1115/1.3625118
6.
Zhang
,
Y. M.
,
Wen
,
B. C.
, and
Liu
,
Q. L.
,
1998
, “
First Passage of Uncertain Single Degree-of-Freedom Nonlinear Oscillators
,”
Comput. Methods Appl. Mech. Eng.
,
165
(
1
), pp.
223
231
.10.1016/S0045-7825(98)00042-5
7.
Breitung
,
K.
,
1988
, “
Asymptotic Approximations for the Out-Crossing Rates of Stationary Vector Processes
,”
Stoch. Proc. Appl.
,
13
, pp.
195
207
.10.1016/0304-4149(88)90037-3
8.
Schall
,
G.
,
Faber
,
M. H.
, and
Rackwitz
,
R.
,
1991
, “
The Ergodicity Assumption for Sea States in the Reliability Estimation of Offshore Structures
,”
ASME J. Offshore Mech. Eng. Arct.
,
113
(
3
), pp.
241
246
.10.1115/1.2919926
9.
Engelung
,
S.
,
Rackwitz
,
R.
, and
Lange
,
C.
,
1995
, “
Approximations of First Passage Times for Differentiable Processes Based on Higher Order Threshold Crossings
,”
Prob. Eng. Mech.
,
10
(
1
), pp.
53
60
.10.1016/0266-8920(94)00008-9
10.
Rackwitz
,
R.
,
1998
, “
Computational Techniques in Stationary and Nonstationary Load Combination—A Review and Some Extensions
,”
J. Struct. Eng.
,
25
(
1
), pp.
1
20
.
11.
Melchers
,
R. E.
,
1999
,
Structural Reliability Analysis and Prediction
,
Wiley
,
Chichester, UK
.
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.
Li
,
C. C.
, and
Der Kiureghian
,
A.
,
1995
, “
Mean Out-Crossing Rate of Nonlinear Response to Stochastic Input
,”
Proceedings of the ICASP-7
, Balkema, Rotterdam, pp.
295
302
.
14.
Der Kiureghian
,
A.
,
2000
, “
The Geometry of Random Vibrations and Solutions by FORM and SORM
,”
Prob. Eng. Mech.
,
15
(
1
), pp.
81
90
.10.1016/S0266-8920(99)00011-9
15.
Der Kiureghian
,
A.
, and
Li
,
C. C.
,
1996
, “
Nonlinear Random Vibration Analysis Through Optimization
,”
Proceedings of the Seventh IFIP WG 7.5 Conference on Optimization of Structural Systems
, D. Frangopol and R. Rackwitz, eds., Boulder, CO, pp.
197
206
.
16.
Gong
,
J. X.
, and
Zhao
,
G. F.
,
1998
, “
Reliability Analysis for Deteriorating Structures
,”
J. Build. Struct.
,
19
(
5
), pp.
43
51
(in Chinese).
17.
Li
,
J.
, and
Mourelatos
,
Z. P.
,
2009
, “
Time-Dependent Reliability Estimation for Dynamic Problems Using a Niching Genetic Algorithm
,”
ASME J. Mech. Des.
,
131
(
7
), p.
071009
.10.1115/1.3149842
18.
Singh
,
A.
,
Mourelatos
,
Z. P.
, and
Nikolaidis
,
E.
,
2011
, “
An Importance Sampling Approach for Time-Dependent Reliability
,” Proceedings of the
ASME
2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, IDETC/CIE 2011, Washington DC, Aug. 28–31, Paper No. DETC No. 2011-47200. 10.1115/DETC2011-47200
19.
Zhang
,
X. L.
,
Huang
,
H. Z.
, and
Wang
,
Z. L.
,
2011
, “
System Optimization Design Under Time Variant Reliability Constraints
,” Proceedings of the
ASME
2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
, IDETC/CIE 2011, Washington DC, Aug. 28–31, Paper No. DETC No. 2011-48002. 10.1115/DETC2011-48002
20.
Zhang
,
J.
, and
Du
,
X.
,
2011
, “
Time-Dependent Reliability Analysis for Function Generator Mechanisms
,”
ASME J. Mech. Des.
,
133
(
3
), p.
031005
.10.1115/1.4003539
21.
Jiang
,
C.
,
Huang
,
X. P.
,
Han
,
X.
, and
Bai
,
Y. C.
,
2013
, “
A Time-Dependent Structural Reliability Analysis Method With Interval Uncertainty
,”
Chin. J. Mech. Eng.
,
49
(
10
), pp.
186
193
.10.3901/JME.2013.10.186
22.
Hu
,
Z.
, and
Du
,
X. P.
,
2013
, “
A Sampling Approach to Extreme Value Distribution for Time-Dependent Reliability Analysis
,”
ASME J. Mech. Des.
,
135
(
7
), p.
071003
.10.1115/1.4023925
23.
Wang
,
Z. Q.
, and
Wang
,
P. F.
,
2012
, “
A Nested Extreme Response Surface Approach for Time-Dependent Reliability-Based Design Optimization
,”
ASME J. Mech. Des.
,
134
(
12
), p.
121007
.10.1115/1.4007931
24.
Zayed
,
A.
,
Garbatov
,
Y.
, and
Guedes Soares
,
C.
,
2013
Time Variant Reliability Assessment of Ship Structures With Fast Integration Techniques
,”
Prob. Eng. Mech.
,
32
, pp.
93
102
.10.1016/j.probengmech.2013.01.002
25.
Ditlevsen
,
O.
,
1986
, “
Duration of Visit to Critical Set by Gaussian Process
,”
Prob. Eng. Mech.
,
1
(
2
), pp.
82
93
.10.1016/0266-8920(86)90030-5
26.
Krenk
,
S.
,
Madsen
,
H. O.
, and
Madsen
,
P. H.
,
1983
, “
Stationary and Transient Response Envelopes
,”
J. Eng. Mech.
,
109
(
1
), pp.
263
277
.10.1061/(ASCE)0733-9399(1983)109:1(263)
27.
Madsen
,
P. H.
, and
Krenk
,
S.
,
1984
, “
An Integral Equation Method for the First-Passage Problem in Random Vibration
,”
ASME J. Appl. Mech.
,
51
(
3
), pp.
674
679
.10.1115/1.3167691
28.
Yang
,
J. N.
, and
Shinozuka
,
M.
,
1971
, “
On the First Excursion Probability in Stationary Narrow-Band Random Vibration
,”
ASME J. Mech. Des.
,
38
(
4
), pp.
1017
1022
.10.1115/1.3408904
29.
Hagen
,
O.
, and
Tvedt
,
L.
,
1991
, “
Vector Process Out-Crossing as Parallel System Sensitivity Measure
,”
J. Eng. Mech.
,
117
(
10
), pp.
2201
2220
.10.1061/(ASCE)0733-9399(1991)117:10(2201)
30.
Crandall
,
S. H.
,
1970
, “
First-Crossing Probabilities of the Linear Oscillator
,”
J. Sound Vib.
,
12
(
3
), pp.
285
299
.10.1016/0022-460X(70)90073-8
31.
Liu
,
P. L.
, and
Der Kiureghian
,
A.
,
1986
, “
Multivariate Distribution Models With Prescribed Marginals and Covariances
,”
Prob. Eng. Mech.
,
1
(
2
), pp.
105
112
.10.1016/0266-8920(86)90033-0
32.
Zhang
,
M.
,
2009
, “
Structural Reliability Analysis: Methods and Programs, Science
,” Beijing, China.
33.
Gao
,
H. X.
,
2005
,
Applied Multivariate Methods for Data Analysts
,
Peking University
,
Beijing, China
.
34.
Madsen
,
H. O.
,
Krenk
,
S.
, and
Lind
,
N. C.
,
1986
,
Methods of Structural Safety
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
35.
Pandey
,
M. D.
,
1998
, “
An Effective Approximation to Evaluate Multinormal Integrals
,”
Struct. Saf.
,
20
, pp.
51
67
.10.1016/S0167-4730(97)00023-4
36.
Li
,
C. C.
, and
Der Kiureghian
,
A.
,
1993
, “
Optimal Discretization of Random Fields
,”
J. Eng. Mech.
,
119
(
6
), pp.
1136
1154
.10.1061/(ASCE)0733-9399(1993)119:6(1136)
37.
Arendt
,
P. D.
,
Apley
,
D. W.
, and
Chen
,
W.
,
2012
, “
Quantification of Model Uncertainty: Calibration, Model Discrepancy, and Identifiability
,”
ASME J. Mech. Des.
,
134
(
10
), p.
100908
.10.1115/1.4007390
38.
Du
,
X. P.
, and
Chen
,
W.
,
2000
, “
Towards a Better Understanding of Modeling Feasibility Robustness in Engineering Design
,”
ASME J. Mech. Des.
,
122
(
4
), pp.
385
394
.10.1115/1.1290247
39.
Guan
,
F. J.
,
Han
,
X.
, and
Jiang
,
C.
,
2008
, “
Uncertain Optimization of the Engine Crankshaft Using Interval Methods
,”
Eng. Mech.
,
25
(
9
), pp.
198
202
(in Chinese).
40.
Wang
,
L. G.
, and
Hu
,
D. B.
,
2000
, “
FEM Analysis on 368Q Crankshaft Fatigue Strength and Some Discuss on Relative Problems
,”
CSICE
,
18
(
3
), pp.
270
274
.
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