Abstract

In the study of reliability of systems with multiple failure modes, approximations can be obtained by calculating the probability of failure for each state function. The first-order reliability method and the second-order reliability method are effective, but they may introduce significant errors when dealing with certain nonlinear situations. Simulation methods such as line sampling method and response surface method can solve implicit function problems, but the large amount of calculation results in low efficiency. The curved surface integral method (CSI) has good accuracy in dealing with nonlinear problems. Therefore, a system reliability analysis method (CSIMMS) is proposed on the basis of CSI for solving multiple failure modes system reliability problems with nonoverlapping failure domains. The order of magnitude of the failure probability is evaluated based on the reliability index and the degree of nonlinearity, ignoring the influence of low order of magnitude failure modes, and reducing the calculation of the system failure probability. Finally, CSIMMS and other methods are compared with three numerical examples, and the results show the stability and accuracy of the proposed method.

References

1.
Wu
,
Z.
,
Chen
,
Z.
,
Chen
,
G.
,
Li
,
X.
,
Jiang
,
C.
,
Gan
,
X.
,
Gao
,
L.
, and
Wang
,
S.
,
2021
, “
A Probability Feasible Region Enhanced Important Boundary Sampling Method for Reliability-Based Design Optimization
,”
Struct. Multidisc. Optim.
,
63
(
1
), pp.
341
355
.10.1007/s00158-020-02702-4
2.
Zhou
,
K.
,
Wang
,
Z.
,
Gao
,
Q.
,
Yuan
,
S.
, and
Tang
,
J.
,
2023
, “
Recent Advances in Uncertainty Quantification in Structural Response Characterization and System Identification
,”
Probab. Eng. Mech.
,
74
, p.
103507
.10.1016/j.probengmech.2023.103507
3.
Wang
,
Z.
,
Fu
,
Y.
,
Yang
,
R.
,
Barbat
,
S.
, and
Chen
,
W.
,
2016
, “
Validating Dynamic Engineering Models Under Uncertainty
,”
ASME J. Mech. Des.
,
138
(
11
), p.
111402
.10.1115/1.4034089
4.
Wang
,
Z.
, and
Wang
,
P.
,
2015
, “
A Double-Loop Adaptive Sampling Approach for Sensitivity-Free Dynamic Reliability Analysis
,”
Reliab. Eng. Syst. Saf.
,
142
, pp.
346
356
.10.1016/j.ress.2015.05.007
5.
Zhang
,
C.
,
Lu
,
C.
,
Fei
,
C.
,
Jing
,
H.
, and
Li
,
C.
,
2018
, “
Dynamic Probabilistic Design Technique for Multi-Component System With Multi-Failure Modes
,”
J. Cent. South Univ.
,
25
(
11
), pp.
2688
2700
.10.1007/s11771-018-3946-x
6.
Zhang
,
D.
,
Han
,
X.
,
Jiang
,
C.
,
Liu
,
J.
, and
Li
,
Q.
,
2017
, “
Time-Dependent Reliability Analysis Through Response Surface Method
,”
ASME J. Mech. Des.
,
139
(
4
), p.
041404
.10.1115/1.4035860
7.
Wu
,
H.
,
Xu
,
Y.
,
Liu
,
Z.
,
Li
,
Y.
, and
Wang
,
P.
,
2023
, “
Adaptive Machine Learning With Physics-Based Simulations for Mean Time to Failure Prediction of Engineering Systems
,”
Reliab. Eng. Syst. Saf.
,
240
(
4
), p.
109553
.10.1016/j.ress.2023.109553
8.
Song
,
H.
,
Choi
,
K.
,
Lee
,
I.
,
Zhao
,
L.
, and
Lamb
,
D.
,
2013
, “
Adaptive Virtual Support Vector Machine for the Reliability Analysis of High-Dimensional Problems
,”
Struct. Multidisc. Optim.
,
47
(
4
), pp.
479
491
.10.1007/s00158-012-0857-6
9.
Roy
,
A.
,
Manna
,
R.
, and
Chakraborty
,
S.
,
2019
, “
Support Vector Regression-Based Metamodeling for Structural Reliability Analysis
,”
Probab. Eng. Mech.
,
55
, pp.
78
89
.10.1016/j.probengmech.2018.11.001
10.
Wu
,
H.
,
Zhu
,
Z.
, and
Du
,
X.
,
2020
, “
System Reliability Analysis With Autocorrelated Kriging Predictions
,”
ASME J. Mech. Des.
,
142
(
10
), p.
101702
.10.1115/1.4046648
11.
Gaspar
,
B.
,
Naess
,
A.
,
Leira
,
B. J.
, and
Soares
,
C. G.
,
2014
, “
System Reliability Analysis by Monte Carlo Based Method and Finite Element Structural Models
,”
ASME J. Offshore Mech. Arct. Eng.
,
136
(
3
), p.
031603
.10.1115/1.4025871
12.
Chen
,
Z.
,
Wu
,
Z.
,
Li
,
X.
,
Chen
,
G.
,
Gao
,
L.
,
Gan
,
X.
,
Chen
,
G.
, and
Wang
,
S.
,
2019
, “
A Multiple-Design-Point Approach for Reliability-Based Design Optimization
,”
Eng. Optimiz.
,
51
(
5
), pp.
875
895
.10.1080/0305215X.2018.1500561
13.
Hu
,
X.
,
Duan
,
Y.
,
Wang
,
R.
,
Liang
,
X.
, and
Chen
,
J.
,
2019
, “
An Adaptive Response Surface Methodology Based on Active Subspaces for Mixed Random and Interval Uncertainties
,”
ASME J. Verif. Valid. Uncert.
,
4
(
2
), p.
021006
.10.1115/1.4045200
14.
Melchers
,
R. E.
,
1990
, “
Radial Importance Sampling for Structural Reliability,” ASCE
,”
J. Eng. Mech.
,
116
(
1
), pp.
189
203
.10.1061/(ASCE)0733-9399(1990)116:1(189)
15.
Schuëller
,
G. I.
,
Pradlwarter
,
H. J.
, and
Koutsourelakis
,
P. S.
,
2004
, “
A Critical Appraisal of Reliability Estimation Procedures for High Dimensions
,”
Probab. Eng. Mech.
,
19
(
4
), pp.
463
474
.10.1016/j.probengmech.2004.05.004
16.
Hasofer
,
A. M.
, and
Lind
,
N. C.
,
1974
, “
Exact and Invariant Second-Moment Code Format
,”
ASCE J. Eng. Mech. Div.
,
100
(
1
), pp.
111
121
.10.1061/JMCEA3.0001848
17.
Santos
,
S. R.
,
Matioli
,
L. C.
, and
Beck
,
A. T.
,
2012
, “
New Optimization Algorithms for Structural Reliability Analysis
,”
Comp. Model. Eng. Sci.
,
83
(
1
), pp.
23
55
.10.3970/cmes.2012.083.023
18.
Chen
,
Z.
,
Wu
,
Z.
,
Li
,
X.
,
Chen
,
G.
,
Chen
,
G.
,
Gao
,
L.
, and
Qiu
,
H.
,
2019
, “
An Accuracy Analysis Method for First-Order Reliability Method
,”
Proc. Inst. Mech. Eng. C. J. Mech. Eng. Sci.
,
233
(
12
), pp.
4319
4327
.10.1177/0954406218813389
19.
Wang
,
Z.
,
Zhang
,
Y.
, and
Song
,
Y.
,
2020
, “
An Adaptive First-Order Reliability Analysis Method for Nonlinear Problems
,”
Math. Probl. Eng.
,
2020
(
1
), pp.
1
11
.10.1155/2020/3925689
20.
Gong
,
C.
, and
Frangopol
,
D. M.
,
2019
, “
An Efficient Time-Dependent Reliability Method
,”
Struct. Saf.
,
81
, p.
101864
.10.1016/j.strusafe.2019.05.001
21.
Breitung
,
K.
,
1984
, “
Asymptotic Approximations for Multinormal Integrals
,”
ASCE J. Eng. Mech. Div.
,
110
(
3
), pp.
357
366
.10.1061/(ASCE)0733-9399(1984)110:3(357)
22.
Tvedt
,
L.
,
1984
,
Two Second-Order Approximations to the Failure Probability: Section on Structural Reliability
,
A/S Vertas Research
,
Hovik, Norway
.
23.
Tvedt
,
L.
,
1990
, “
Distribution of Quadratic Forms in Normal Space Applications to Structural Reliability
,”
ASCE J. Eng. Mech. Div.
,
116
(
6
), pp.
1183
1197
.10.1061/(ASCE)0733-9399(1990)116:6(1183)
24.
Zhao
,
Y. G.
, and
Ono
,
T.
,
1999
, “
New Approximations for SORM: Part 1
,”
ASCE J. Eng. Mech.
,
125
(
1
), pp.
79
85
.10.1061/(ASCE)0733-9399(1999)125:1(79)
25.
Mansour
,
R.
, and
Olsson
,
M.
,
2014
, “
A Closed-Form Second-Order Reliability Method Using Noncentral Chi-Squared Distributions
,”
ASME J. Mech. Des.
,
136
(
10
), p.
101402
.10.1115/1.4027982
26.
Hu
,
Z. L.
, and
Du
,
X. P.
,
2018
, “
Multiple Non-Overlapping Failure Domains Approximation Reliability Method for Quadratic Functions in Normal Variables
,”
Struct. Saf.
,
71
, pp.
24
32
.10.1016/j.strusafe.2017.11.001
27.
Wu
,
H.
, and
Du
,
X.
,
2020
, “
System Reliability Analysis With Second-Order Saddlepoint Approximation
,”
ASCE-ASME J. Risk Uncert. Engrg. Sys. Part B Mech. Eng.
,
6
(
4
), p.
041001
.10.1115/1.4047217
28.
Wu
,
H.
,
Hu
,
Z.
, and
Du
,
X.
,
2021
, “
Time-Dependent System Reliability Analysis With Second-Order Reliability Method
,”
ASME J. Mech. Des.
,
143
(
3
), p.
031101
.10.1115/1.4048732
29.
Rackwitz
,
R.
, and
Flessler
,
B.
,
1978
, “
Structural Reliability Under Combined Random Load Sequences
,”
Comput. Struct.
,
9
(
5
), pp.
489
494
.10.1016/0045-7949(78)90046-9
30.
Rosenblatt
,
M.
,
1952
, “
Remarks on a Multivariate Transformation
,”
Ann. Math. Statist.
,
23
(
3
), pp.
470
472
.10.1214/aoms/1177729394
31.
Lebrun
,
R.
, and
Dutfoy
,
A.
,
2009
, “
A Generalization of the Nataf Transformation to Distributions With Elliptical Copula
,”
Probab. Eng. Mech.
,
24
(
2
), pp.
172
178
.10.1016/j.probengmech.2008.05.001
32.
Li
,
X.
,
Qiu
,
H.
,
Chen
,
Z.
,
Gao
,
L.
, and
Shao
,
X.
,
2016
, “
A Local Kriging Approximation Method Using MPP for Reliability-Based Design Optimization
,”
Comput. Struct.
,
162
, pp.
102
115
.10.1016/j.compstruc.2015.09.004
33.
Wang
,
Z.
,
2017
, “
Piecewise Point Classification for Uncertainty Propagation With Nonlinear Limit States
,”
Struct. Multidisc. Optim.
,
56
(
2
), pp.
285
296
.10.1007/s00158-017-1664-x
34.
Chen
,
Z.
,
Huang
,
D.
,
Li
,
X.
, et al
2023
, “
A New Curved Surface Integral Method for Reliability Analysis
,”
Proceedings of 13th International Conference on Quality, Reliability, Risk, Maintenance, and Safety Engineering, Kunming
, China, June 26–29, pp.
652
656
.
35.
Zhao
,
H.
,
Yue
,
Z.
,
Liu
,
Y.
,
Gao
,
Z.
, and
Zhang
,
Y.
,
2015
, “
An Efficient Reliability Method Combining Adaptive Importance Sampling and Kriging Metamodel
,”
Appl. Math. Model.
,
39
(
7
), pp.
1853
1866
.10.1016/j.apm.2014.10.015
36.
Katsuki
,
S.
, and
Frangopol
,
D. M.
,
1994
, “
Hyperspace Division Method for Structural Reliability
,”
ASCE J. Eng. Mech.
,
120
(
11
), pp.
2405
2427
.10.1061/(ASCE)0733-9399(1994)120:11(2405)
37.
Xia
,
Y.
,
Hu
,
Y.
,
Tang
,
F.
, and
Yu
,
Y.
,
2023
, “
An Armijo-Based Hybrid Step Length Release First Order Reliability Method Based on Chaos Control for Structural Reliability Analysis
,”
Struct. Multidisc. Optim.
,
66
(
4
), p.
77
.10.1007/s00158-023-03542-8
38.
Huang
,
X.
,
Lv
,
C.
,
Li
,
C.
, and
Zhang
,
Y.
,
2021
, “
Structural System Reliability Analysis Based on Multi-Modal Optimization and Saddlepoint Approximation
,”
Mech. Adv. Mater. Struct.
,
29
(
27
), pp.
5876
5884
.10.1080/15376494.2021.1968083
You do not currently have access to this content.