Abstract

Structural reliability theory has been applied to many engineering problems in the last decades, with the primary objective of quantifying the safety of such structures. Although in some cases approximated methods may be used, many times the only alternatives are those involving more demanding approaches, such as Monte Carlo simulation (MCS). In this context, surrogate models have been widely employed as an attempt to keep the computational effort acceptable. In this paper, an adaptive approach for reliability analysis using surrogate models, proposed in the literature in the context of Kriging and polynomial chaos expansions (PCEs), is adapted for the case of multilayer perceptron (MLP) artificial neural networks (ANNs). The methodology is employed in the solution of three benchmark reliability problems and compared to MCS and other methods from the literature. In all cases, the ANNs led to results very close to those obtained by MCS and required much less limit state function evaluations. Also, the performance of the ANNs was found comparable, in terms of accuracy and efficiency, to the performance of the other methods.

References

References
1.
Madsen
,
H. O.
,
Skjong
,
R.
,
Tallin
,
A.
, and
Kirkemo
,
F.
,
1987
, “
Probabilistic Fatigue Crack Growth Analysis of Offshore Structures, With Reliability Updating Through Inspection
,”
Marine Structural Reliability Symposium
, Society of Naval Architects and Marine Engineers, Arlington, VA, Oct. 5–6, pp. 45–55.
2.
Biondini
,
F.
,
Bontempi
,
F.
,
Frangopol
,
D. M.
, and
Giorgio
,
P. G.
,
2004
, “
Reliability of Material and Geometrically Non-Linear Reinforced and Prestressed Concrete Structures
,”
Comput. Struct.
,
82
(
13–14
), pp.
1021
1031
.10.1016/j.compstruc.2004.03.010
3.
Estes
,
A. C.
,
Frangopol
,
D. M.
, and
Foltz
,
S. D.
,
2004
, “
Updating Reliability of Steel Miter Gates on Locks and Dams Using Visual Inspection Results
,”
Eng. Struct.
,
26
(
3
), pp.
319
333
.10.1016/j.engstruct.2003.10.007
4.
Hart
,
G. C.
,
Conte
,
J. P.
,
Park
,
K.
,
Ellingwood
,
B. R.
, and
Wong
,
K. K. F.
,
2014
, “
Performance-Based Evaluation and Strengthening of Tall Buildings in the Los Angeles Region by Using Bayesian Structural Reliability
,”
Struct. Des. Tall Spec.
,
23
(
10
), pp.
760
780
.10.1002/tal.1083
5.
Faravelli
,
L.
,
1989
, “
Response-Surface Approach for Reliability Analysis
,”
J. Eng. Mech.
,
115
(
12
), pp.
2763
2781
.10.1061/(ASCE)0733-9399(1989)115:12(2763)
6.
Soares
,
R. C.
,
Mohamed
,
A.
,
Venturini
,
W. S.
, and
Lemaire
,
M.
,
2002
, “
Reliability Analysis of Non-Linear Reinforced Concrete Frames Using the Response Surface Method
,”
Reliab. Eng. Syst. Safe.
,
75
(
1
), pp.
1
16
.10.1016/S0951-8320(01)00043-6
7.
Stein
,
M.
,
1999
,
Statistical Interpolation of Spatial Data: Some Theory for Kriging
,
Springer
,
New York
.
8.
Dubourg
,
V.
,
Sudret
,
B.
, and
Deheeger
,
F.
,
2013
, “
Metamodel-Based Importance Sampling for Structural Reliability Analysis
,”
Probab. Eng. Mech.
,
33
, pp.
47
57
.10.1016/j.probengmech.2013.02.002
9.
Ghanem
,
R. G.
, and
Spanos
,
P. D.
,
1991
,
Stochastic Finite Elements—A Spectral Approach
,
Springer-Verlag
,
New York
.
10.
Blatman
,
G.
, and
Sudret
,
B.
,
2010
, “
An Adaptive Algorithm to Build Up Sparse Polynomial Chaos Expansions for Stochastic Finite Element Analysis
,”
Probab. Eng. Mech.
,
25
(
2
), pp.
183
197
.10.1016/j.probengmech.2009.10.003
11.
Gomes
,
W. J. S.
, and
Beck
,
A. T.
,
2013
, “
Global Structural Optimization Considering Expected Consequences of Failure and Using ANN Surrogates
,”
Comput. Struct.
,
126
, pp.
56
68
.10.1016/j.compstruc.2012.10.013
12.
Bucher
,
C.
, and
Most
,
T.
,
2008
, “
A Comparison of Approximate Response Functions in Structural Reliability Analysis
,”
Probabilist. Eng. Mech.
,
23
(
2–3
), pp.
154
163
.10.1016/j.probengmech.2007.12.022
13.
Kroetz
,
H. M.
,
Tessari
,
R. K.
, and
Beck
,
A. T.
,
2017
, “
Performance of Global Metamodeling Techniques in Solution of Structural Reliability Problems
,”
Adv. Eng. Software
,
114
, pp.
394
404
.10.1016/j.advengsoft.2017.08.001
14.
Chojaczyk
,
A. A.
,
Teixeira
,
A. P.
,
Neves
,
L. C.
,
Cardoso
,
J. B.
, and
Soares
,
C. G.
,
2015
, “
Review and Application of Artificial Neural Networks Models in Reliability Analysis of Steel Structures
,”
Struct. Saf.
,
52
, pp.
78
89
.10.1016/j.strusafe.2014.09.002
15.
Papadrakakis
,
M.
, and
Lagaros
,
N. D.
,
2002
, “
Reliability-Based Structural Optimization Using Neural Networks and Monte Carlo Simulation
,”
Comput. Methods Appl. Mech. Eng.
,
191
(
32
), pp.
3491
3507
.10.1016/S0045-7825(02)00287-6
16.
Papadopoulos
,
V.
,
Giovanis
,
D. G.
,
Lagaros
,
N. D.
, and
Papadrakakis
,
M.
,
2012
, “
Accelerated Subset Simulation With Neural Networks for Reliability Analysis
,”
Comput. Methods Appl. Mech. Eng.
,
223–224
, pp.
70
80
.10.1016/j.cma.2012.02.013
17.
Deng
,
J.
,
Gu
,
D.
,
Li
,
X.
, and
Yue
,
Z. Q.
,
2005
, “
Structural Reliability Analysis for Implicit Performance Functions Using Artificial Neural Network
,”
Struct. Saf.
,
27
(
1
), pp.
25
48
.10.1016/j.strusafe.2004.03.004
18.
Gomes
,
H. M.
, and
Awruch
,
A. M.
,
2004
, “
Comparison of Response Surface and Neural Network With Other Methods for Structural Reliability Analysis
,”
Struct. Saf.
,
26
(
1
), pp.
49
67
.10.1016/S0167-4730(03)00022-5
19.
Tan
,
X.-H.
,
Bi
,
W.-H.
,
Hou
,
X.-L.
, and
Wang
,
W.
,
2011
, “
Reliability Analysis Using Radial Basis Function Networks and Support Vector Machines
,”
Comput. Geotech.
,
38
(
2
), pp.
178
186
.10.1016/j.compgeo.2010.11.002
20.
Gomes
,
H. M.
,
Awruch
,
A. M.
, and
Lopes
,
P. A. M.
,
2011
, “
Reliability Based Optimization of Laminated Composite Structures Using Genetic Algorithms and Artificial Neural Networks
,”
Struct. Saf.
,
33
(
3
), pp.
186
195
.10.1016/j.strusafe.2011.03.001
21.
Shao
,
S.
, and
Murotsu
,
Y.
,
1997
, “
Structural Reliability Analysis Using a Neural Network
,”
JSME Int. J. A. Solid M.
,
40
(
3
), pp.
242
246
.10.1299/jsmea.40.242
22.
Schueremans
,
L.
, and
Van Gemert
,
D.
,
2005
, “
Benefit of Splines and Neural Networks in Simulation Based Structural Reliability Analysis
,”
Struct. Saf.
,
27
(
3
), pp.
246
261
.10.1016/j.strusafe.2004.11.001
23.
Marelli
,
S.
, and
Sudret
,
B.
,
2016
, “
Bootstrap-Polynomial Chaos Expansions and Adaptive Designs for Reliability Analysis
,”
Sixth Asian-Pacific Symposium on Structural Reliability and Its Applications
(
APSSRA6
), Shangai, China, May 28–30, pp. 217–224.
24.
Echard
,
B.
,
Gayton
,
N.
, and
Lemaire
,
M.
,
2011
, “
AK-MCS: An Active Learning Reliability Method Combining Kriging and Monte Carlo Simulation
,”
Struct. Saf.
,
33
(
2
), pp.
145
154
.10.1016/j.strusafe.2011.01.002
25.
Madsen
,
H. O.
,
Krenk
,
S.
, and
Lind
,
N. C.
,
1986
,
Methods of Structural Safety
,
Prentice Hall
,
Englewood Cliffs, NJ
.
26.
Melchers
,
R. E.
, and
Beck
,
A. T.
,
2018
,
Structural Reliability Analysis and Prediction
,
3rd ed.
,
Wiley
,
New York
.
27.
McCulloch
,
W.
, and
Pitts
,
W.
,
1943
, “
A Logical Calculus of the Ideas Immanent in Nervous Activity
,”
Bull. Math. Biol.
,
5
(4), pp.
115
133
.10.1007/BF02478259
28.
Hornik
,
K.
,
Stinchcombe
,
M.
, and
White
,
H.
,
1990
, “
Universal Approximation of an Unknown Mapping and Its Derivatives Using Multilayer Feedforward Networks
,”
Neural Networks
,
3
(
5
), pp.
551
560
.10.1016/0893-6080(90)90005-6
29.
Hecht-Nielsen
,
R.
,
1990
,
Neurocomputing
,
Addison-Wesley
,
Boston, MA
.
30.
Beale
,
M. H.
,
Hagan
,
M. T.
, and
Demuth
,
H. B.
,
2011
,
Neural Network Toolbox: User's Guide
,
The Mathworks Inc
.,
Natick, MA
.
31.
Hagan
,
M. T.
, and
Menhaj
,
M. B.
,
1994
, “
Training Feedforward Networks With the Marquardt Algorithm
,”
IEEE Trans. Neural Networks
,
5
(
6
), pp.
989
993
.10.1109/72.329697
32.
Haykin
,
S.
,
1999
,
Neural Networks
,
2nd ed.
,
Prentice Hall
,
Upper Saddle River, NJ
.
33.
Efron
,
B.
,
1992
,
Bootstrap Methods: Another Look at the Jackknife
,
Springer
,
New York
.
34.
Efron
,
B.
, and
Tibshirani
,
R. J.
,
1993
,
An Introduction to the Bootstrap
,
Chapman and Hall
,
London
.
35.
Gomes
,
W. J. S.
,
2018
, “
Structural Reliability Analysis Using Artificial Neural Networks and Bootstrap Techniques
,”
ICVRAM ISUMA UNCERTAINTIES 2018
, American Society of Civil Engineers and Brazilian Society of Mechanical Sciences and Engineering, Florianópolis, SC, Brazil, Apr. 8–11, Paper No.
0038
.
36.
Nguyen
,
D.
, and
Widrow
,
B.
,
1990
, “
Improving the Learning Speed of 2-Layer Neural Networks by Choosing Initial Values of the Adaptive Weights
,”
International Joint Conference on Neural Networks
(
IJCNN
), San Diego, CA, June 17–21, pp.
21
26
.10.1109/IJCNN.1990.137819
37.
Schöbi
,
R.
,
Sudret
,
B.
, and
Marelli
,
S.
,
2017
, “
Rare Event Estimation Using Polynomial-Chaos Kriging
,”
ASCE ASME J. Risk Uncertain. Eng. Syst. A. Civ. Eng.
,
3
(
2
), p. D4016002.10.1061/AJRUA6.0000870
38.
Haykin
,
S.
,
1996
,
Adaptive Filter Theory
,
3rd ed.
,
Prentice Hall
,
Upper Saddle River, NJ
.
39.
Waarts
,
P.-H.
,
2000
, “
Structural Reliability Using Finite Element Methods. An Appraisal of DARS: Directional Adaptive Response Surface Sampling
,”
Ph.D. thesis
, Technical University of Delft, Delft, The Netherlands.
40.
Rackwitz
,
R.
,
2001
, “
Reliability Analysis—A Review and Some Perspective
,”
Struct. Saf.
,
23
(
4
), pp.
365
395
.10.1016/S0167-4730(02)00009-7
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