This paper presents a new adaptive sampling approach based on a novel integrated performance measure approach, referred to as “iPMA,” for system reliability assessment with multiple dependent failure events. The developed approach employs Gaussian process (GP) regression to construct surrogate models for each component failure event, thereby enables system reliability estimations directly using Monte Carlo simulation (MCS) based on surrogate models. To adaptively improve the accuracy of the surrogate models for approximating system reliability, an iPM, which envelopes all component level failure events, is developed to identify the most useful sample points iteratively. The developed iPM possesses three important properties. First, it represents exact system level joint failure events. Second, the iPM is mathematically a smooth function “almost everywhere.” Third, weights used to reflect the importance of multiple component failure modes can be adaptively learned in the iPM. With the weights updating process, priorities can be adaptively placed on critical failure events during the updating process of surrogate models. Based on the developed iPM with these three properties, the maximum confidence enhancement (MCE) based sequential sampling rule can be adopted to identify the most useful sample points and improve the accuracy of surrogate models iteratively for system reliability approximation. Two case studies are used to demonstrate the effectiveness of system reliability assessment using the developed iPMA methodology.

References

1.
Youn
,
B. D.
,
Choi
,
K. K.
, and
Du
,
L.
,
2005
, “
Enriched Performance Measure Approach (PMA+) for Reliability-Based Design Optimization
,”
AIAA J.
,
43
(
4
), pp.
874
884
.10.2514/1.6648
2.
Youn
,
B. D.
,
Choi
,
K. K.
, and
Du
,
L.
,
2005
, “
Adaptive Probability Analysis Using an Enhanced Hybrid Mean Value (HMV+) Method
,”
J. Struct. Multidiscip. Optim.
,
29
(
2
), pp.
134
148
.10.1007/s00158-004-0452-6
3.
Wang
,
L. P.
, and
Grandhi
,
R. V.
,
1996
, “
Safety Index Calculation Using Intervening Variables for Structural Reliability
,”
Comput. Struct.
,
59
(
6
), pp.
1139
1148
.10.1016/0045-7949(96)00291-X
4.
Rahman
,
S.
, and
Xu
,
H.
,
2004
, “
A Univariate Dimension-Reduction Method for Multi-Dimensional Integration in Stochastic Mechanics
,”
Probab. Eng. Mech.
,
19
(
4
), pp.
393
408
.10.1016/j.probengmech.2004.04.003
5.
Xu
,
H.
, and
Rahman
,
S.
,
2005
, “
Decomposition Methods for Structural Reliability Analysis
,”
Probab. Eng. Mech.
,
20
(
3
), pp.
239
250
.10.1016/j.probengmech.2005.05.005
6.
Youn
,
B. D.
,
Xi
,
Z.
, and
Wang
,
P.
,
2008
, “
Eigenvector Dimension-Reduction (EDR) Method for Sensitivity-Free Uncertainty Quantification
,”
Struct. Multidiscip. Optim.
,
37
(
1
), pp.
13
28
.10.1007/s00158-007-0210-7
7.
Paffrath
,
M.
, and
Wever
,
U.
,
2007
, “
Adapted Polynomial Chaos Expansion for Failure Detection
,”
J. Comput. Phys.
,
226
(
1
), pp.
263
281
.10.1016/j.jcp.2007.04.011
8.
Xiu
,
D.
, and
Karniadakis
,
G. E.
,
2003
, “
The Wiener−Askey Polynomial Chaos for Stochastic Differential Equations
,”
SIAM J. Sci. Comput.
,
24
(2), pp.
670
674
.10.1137/S1064827501387826
9.
Sudret
,
B.
,
2008
, “
Global Sensitivity Analysis Using Polynomial Chaos Expansions
,”
Reliab. Eng. Syst. Saf.
,
93
(
7
), pp.
964
979
.10.1016/j.ress.2007.04.002
10.
Hu
,
C.
, and
Youn
,
B. D.
,
2011
, “
Adaptive-Sparse Polynomial Chaos Expansion for Reliability Analysis and Design of Complex Engineering Systems
,”
Struct. Multidiscip. Optim.
,
43
(
3
), pp.
419
442
.10.1007/s00158-010-0568-9
11.
Wang
,
Z.
, and
Wang
,
P.
,
2013
, “
A Maximum Confidence Enhancement Based Sequential Sampling Scheme for Simulation-Based Design
,”
ASME J. Mech. Des.
,
136
(
2
), p.
021006
.10.1115/1.4026033
12.
Queipo
,
N. V.
,
Haftka
,
R. T.
,
Shyy
,
W.
,
Goel
,
T.
,
Vaidyanathan
,
R.
, and
Tucker
,
P. K.
,
2005
, “
Surrogate-Based Analysis and Optimization
,”
Prog. Aerosp. Sci.
,
41
(
1
), pp.
1
28
.10.1016/j.paerosci.2005.02.001
13.
Wang
,
P.
,
Youn
,
B. D.
,
Xi
,
Z.
, and
Kloess
,
A.
,
2009
, “
Bayesian Reliability Analysis With Evolving, Insufficient, and Subjective Data Sets
,”
ASME J. Mech. Des.
,
131
(
11
), p.
111008
.10.1115/1.4000251
14.
Hong-Zhong
,
H.
,
Zuo
,
M. J.
, and
Sun
,
Z.-Q.
,
2006
, “
Bayesian Reliability Analysis for Fuzzy Lifetime Data
,”
Fuzzy Sets Syst.
,
157
(
12
), pp.
1674
1686
.10.1016/j.fss.2005.11.009
15.
Coolen
,
F. P. A.
, and
Newby
,
M. J.
,
1994
, “
Bayesian Reliability Analysis With Imprecise Prior Probabilities
,”
Reliab. Eng. Syst. Saf.
,
43
(
1
), pp.
75
85
.10.1016/0951-8320(94)90096-5
16.
Wang
,
Z.
, and
Wang
,
P.
,
2012
, “
A Nested Extreme Response Surface Approach for Time-Dependent Reliability-Based Design Optimization
,”
ASME J. Mech. Des.
,
134
(
2
), p.
121007
.10.1115/1.4007931
17.
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
18.
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
19.
Hu
,
Z.
, and
Du
,
X.
,
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
20.
Hu
,
Z.
, and
Du
,
X.
,
2013
, “
Time-Dependent Reliability Analysis With Joint Upcrossing Rates
,”
Struct. Multidiscip. Optim.
,
48
(
5
), pp.
893
907
.
21.
Ang
,
A. H.-S.
, and
Amin
,
M.
,
1967
,
Studies of Probabilistic Safety Analysis of Structures and Structural Systems
,
University of Illinois
,
Urbana
.
22.
Bennett
,
R. M.
, and
Ang
,
A. H.-S.
, 1983, “
Investigation of Methods for Structural System Reliability
,” Ph.D. thesis, University of Illinois, Urbana, IL.
23.
Ditlevsen
,
O.
,
1979
, “
Narrow Reliability Bounds for Structural Systems
,”
J. Struct. Mech.
,
7
(
4
), pp.
453
472
.10.1080/03601217908905329
24.
Thoft-Christensen
,
P.
, and
Murotsu
,
Y.
,
1986
,
Application of Structural Reliability Theory
,
Springer
,
Berlin
, Germany.
25.
Song
,
J.
, and
Der Kiureghian
,
A.
,
2003
, “
Bounds on System Reliability by Linear Programming
,”
J. Eng. Mech.
,
129
(
6
), pp.
627
636
.10.1061/(ASCE)0733-9399(2003)129:6(627)
26.
Kang
,
W.-H.
,
Song
,
J.
, and
Gardoni
,
P.
,
2008
, “
Matrix-Based System Reliability Method and Applications to Bridge Networks
,”
Reliab. Eng. Syst. Saf.
,
93
(
11
), pp.
1584
1593
.10.1016/j.ress.2008.02.011
27.
Karamchandani
,
A.
,
1987
, “
Structural System Reliability Analysis Methods
,” John A. Blume Earthquake Engineering Center, Stanford University, Report No. 83.
28.
Xiao
,
Q.
, and
Mahadevan
,
S.
,
1998
, “
Second-Order Upper Bounds on Probability of Intersection of Failure Events
,”
J. Eng. Mech.
,
120
(
3
), pp.
49
57
.
29.
Ramachandran
,
K.
,
2004
, “
System Reliability Bounds: A New Look With Improvements
,”
Civ. Eng. Environ. Syst.
,
21
(
4
), pp.
265
278
.10.1080/10286600412331330368
30.
Youn
,
B. D.
, and
Wang
,
P.
,
2009
, “
Complementary Interaction Method (CIM) for System Reliability Assessment
,”
ASME J. Mech. Des.
,
131
(
4
), p.
041004
.10.1115/1.3086794
31.
Wang
,
P.
,
Hu
,
C.
, and
Youn
,
B. D.
,
2011
, “
A Generalized Complementary Intersection Method for System Reliability Analysis and Design
,”
ASME J. Mech. Des.
,
133
(
7
), p.
071003
10.1115/1.4004198
32.
Bichon
,
B. J.
,
McFarland
,
J. M.
, and
Mahadevan
,
S.
,
2011
, “
Efficient Surrogate Models for Reliability Analysis of Systems With Multiple Failure Modes
,”
Reliab. Eng. Syst. Saf.
,
96
(
10
), pp.
1386
1395
.10.1016/j.ress.2011.05.008
33.
Fauriat
,
W.
, and
Gayton
,
N.
,
2014
, “
AK-SYS: An Adaptation of the AK-MCS Method for System Reliability
,”
Reliab. Eng. Syst. Saf.
,
123
, pp.
137
144
.10.1016/j.ress.2013.10.010
34.
Pearson
,
K.
,
1895
, “
Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material
,”
Philos. Trans. R. Soc. London, Ser. A
,
186
, pp.
343
414
.10.1098/rsta.1895.0010
35.
Wang
,
L.
,
Beeson
,
D.
,
Akkaram
,
S.
, and
Wiggs
,
G.
,
2005
, “
Gaussian Process Meta-Models for Efficient Probabilistic Design in Complex Engineering Design Spaces
,”
ASME
Paper No. DETC2005-85406.10.1115/DETC2005-85406
36.
Quinonero-Candela
,
J.
,
Rasmussen
,
C. E.
, and
Williams
,
C. K. I.
,
2007
, “
Approximation Methods for Gaussian Process Regression
,”
Large-Scale Kernel Machines
, MIT Press, Cambridge, MA, pp.
203
224
.
37.
Youn
,
B. D.
,
Choi
,
K.
,
Yang
,
R.-J.
, and
Gu
,
L.
,
2004
,“
Reliability-Based Design Optimization for Crashworthiness of Vehicle Side Impact
,”
Struct. Multidiscip. Optim.
,
26
(
3–4
), pp.
272
283
.10.1007/s00158-003-0345-0
You do not currently have access to this content.