Abstract
The degradation of metallic systems under cyclic loading is subject to significant uncertainty, which affects the reliability of residual lifetime predictions and subsequent decisions on optimum maintenance schedules. This paper focuses two main challenges in developing a reliable framework for the lifecycle management of fatigue-critical components: constructing a stochastic model that captures uncertainties in crack growth histories, and presenting a computationally efficient strategy for solving the stochastic optimization associated with maintenance scheduling. Polynomial chaos (PC) representation is proposed to propagate uncertainty in the fatigue-induced crack growth process, using a database from constant amplitude loading experiments. Additionally, an optimization strategy is implemented based on Gaussian process surrogate modeling to solve the stochastic optimization problem under maximum probability of failure constraints. The sensitivity of the optimum solution to different probability of failure thresholds is examined. The proposed framework offers a decision support tool for informed decision-making under uncertainty, aiming to mitigate fatigue failure.
Issue Section:
Research Papers
References
1.
Frangopol
,
D. M.
, 2011
, “
Life-Cycle Performance, Management, and Optimisation of Structural Systems Under Uncertainty: Accomplishments and Challenges
,” Struct. Infrastruct. Eng.
,
7
(6
), pp. 389
–413
.10.1080/157324710035944272.
Frangopol
,
D. M.
,
Kallen
,
M.-J.
, and
Noortwijk
,
J. M. V.
, 2004
, “
Probabilistic Models for Life-Cycle Performance of Deteriorating Structures: Review and Future Directions
,” Prog. Struct. Eng. Mater.
,
6
(4
), pp. 197
–212
.10.1002/pse.1803.
Ghonem
,
H.
, and
Dore
,
S.
, 1985
, “
Probabilistic Description of Fatigue Crack Growth in Polycrystalline Solids
,” Eng. Fract. Mech.
,
21
(6
), pp. 1151
–1168
.10.1016/0013-7944(85)90174-24.
Ghonem
,
H.
, 1988
, “
Constant-Probability Crack Growth Curves
,” Eng. Fract. Mech.
,
30
(5
), pp. 685
–699
.10.1016/0013-7944(88)90159-25.
Shimokawa
,
T.
, and
Hamaguchi
,
Y.
, 1985
, “
Relationship Between Fatigue Life Distribution, Notch Configuration, and SN Curve of a 2024-T4 Aluminum Alloy
,” ASME J. Eng. Mater. Technol.
,
107
(3
), pp. 214
–220
.10.1115/1.32258046.
Ortiz
,
K.
, and
Kiremidjian
,
A. S.
, 1988
, “
Stochastic Modeling of Fatigue Crack Growth
,” Eng. Fract. Mech.
,
29
(3
), pp. 317
–334
.10.1016/0013-7944(88)90020-37.
Paris
,
P.
, and
Erdogan
,
F.
, 1963
, “
A Critical Analysis of Crack Propagation Laws
,” ASME J. Basic Eng.
,
85
(4
), pp. 528
–533
.10.1115/1.36569008.
Yang
,
J.
, and
Manning
,
S.
, 1996
, “
A Simple Second Order Approximation for Stochastic Crack Growth Analysis
,” Eng. Fract. Mech.
,
53
(5
), pp. 677
–686
.10.1016/0013-7944(95)00130-19.
Kozin
,
F.
, and
Bogdanoff
,
J.
, 1981
, “
A Critical Analysis of Some Probabilistic Models of Fatigue Crack Growth
,” Eng. Fract. Mech.
,
14
(1
), pp. 59
–89
.10.1016/0013-7944(81)90019-910.
Ghonem
,
H.
, and
Provan
,
J.
, 1980
, “
Micromechanics Theory of Fatigue Crack Initiation and Propagation
,” Eng. Fract. Mech.
,
13
(4
), pp. 963
–977
.10.1016/0013-7944(80)90026-011.
Guida
,
M.
, and
Penta
,
F.
, 2015
, “
A Gamma Process Model for the Analysis of Fatigue Crack Growth Data
,” Eng. Fract. Mech.
,
142
, pp. 21
–49
.10.1016/j.engfracmech.2015.05.02712.
Qiu
,
Z.
, and
Zheng
,
Y.
, 2017
, “
Fatigue Crack Growth Modeling and Prediction With Uncertainties Via Stochastic Perturbation Series Expansion Method
,” Int. J. Mech. Sci.
,
134
, pp. 284
–290
.10.1016/j.ijmecsci.2017.10.02013.
Beck
,
A. T.
, and
de Santana Gomes
,
W. J.
, 2013
, “
Stochastic Fracture Mechanics Using Polynomial Chaos
,” Probab. Eng. Mech.
,
34
, pp. 26
–39
.10.1016/j.probengmech.2013.04.00214.
Qiu
,
Z.
, and
Zhang
,
Z.
, 2020
, “
Fatigue Crack Propagation Analysis in Structures With Random Parameters Based on Polynomial Chaos Expansion Method
,” Theor. Appl. Fract. Mech.
,
105
, p. 102404
.10.1016/j.tafmec.2019.10240415.
Yang
,
D. Y.
, and
Frangopol
,
D. M.
, 2018
, “
Probabilistic Optimization Framework for Inspection/Repair Planning of Fatigue-Critical Details Using Dynamic Bayesian Networks
,” Comput. Struct.
,
198
, pp. 40
–50
.10.1016/j.compstruc.2018.01.00616.
Long
,
X.
,
Jiang
,
C.
,
Liu
,
K.
,
Han
,
X.
,
Gao
,
W.
, and
Li
,
B.
, 2018
, “
An Interval Analysis Method for Fatigue Crack Growth Life Prediction With Uncertainty
,” Comput. Struct.
,
210
, pp. 1
–11
.10.1016/j.compstruc.2018.09.00517.
Valdebenito
,
M.
, and
Schuëller
,
G.
, 2010
, “
Design of Maintenance Schedules for Fatigue-Prone Metallic Components Using Reliability-Based Optimization
,” Comput. Methods Appl. Mech. Eng.
,
199
(33–36
), pp. 2305
–2318
.10.1016/j.cma.2010.03.02818.
Beaurepaire
,
P.
,
Valdebenito
,
M.
,
Schuëller
,
G.
, and
Jensen
,
H.
, 2012
, “
Reliability-Based Optimization of Maintenance Scheduling of Mechanical Components Under Fatigue
,” Comput. Methods Appl. Mech. Eng.
,
221–222
, pp. 24
–40
.10.1016/j.cma.2012.01.01519.
Gomes
,
W. J.
, and
Beck
,
A. T.
, 2014
, “
Optimal Inspection Planning and Repair Under Random Crack Propagation
,” Eng. Struct.
,
69
, pp. 285
–296
.10.1016/j.engstruct.2014.03.02120.
Arzaghi
,
E.
,
Abaei
,
M. M.
,
Abbassi
,
R.
,
Garaniya
,
V.
,
Chin
,
C.
, and
Khan
,
F.
, 2017
, “
Risk-Based Maintenance Planning of Subsea Pipelines Through Fatigue Crack Growth Monitoring
,” Eng. Failure Anal.
,
79
, pp. 928
–939
.10.1016/j.engfailanal.2017.06.00321.
Ghonem
,
H.
, 1987
, “
Study of Probabilistic Fatigue Crack Growth and Associated Scatter Under Constant-and-Variable Amplitude Loading Spectrum
,” Annual Rept, 15.22.
Virkler
,
D. A.
,
Hillberry
,
B.
, and
Goel
,
P.
, 1979
, “
The Statistical Nature of Fatigue Crack Propagation
,” ASME J. Eng. Mater. Technol.
,
101
(2
), pp. 148
–153
.10.1115/1.344366623.
Schijve
,
J.
, 1994
, “
Fatigue Predictions and Scatter
,” Fatigue Fract. Eng. Mater. Struct.
,
17
(4
), pp. 381
–396
.10.1111/j.1460-2695.1994.tb00239.x24.
Ghosh
,
S.
, and
Henderson
,
S. G.
, 2003
, “
Behavior of the Norta Method for Correlated Random Vector Generation as the Dimension Increases
,” ACM Trans. Model. Comput. Simul. (TOMACS)
,
13
(3
), pp. 276
–294
.10.1145/937332.93733625.
Sakamoto
,
S.
, and
Ghanem
,
R.
, 2002
, “
Polynomial Chaos Decomposition for the Simulation of Non-Gaussian Nonstationary Stochastic Processes
,” J. Eng. Mech.
,
128
(2
), pp. 190
–201
.10.1061/(ASCE)0733-9399(2002)128:2(190)26.
Cameron
,
R. H.
, and
Martin
,
W. T.
, 1947
, “
The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals
,” Ann. Math.
,
48
(2
), pp. 385
–392
.10.2307/196917827.
Le Maître
,
O.
, and
Knio
,
O. M.
, 2010
, Spectral Methods for Uncertainty Quantification: With Applications to Computational Fluid Dynamics
,
Springer Science & Business Media
, Berlin, Germany
.28.
Xiu
,
D.
, and
Karniadakis
,
G. E.
, 2002
, “
The Wiener–Askey Polynomial Chaos for Stochastic Differential Equations
,” SIAM J. Sci. Comput.
,
24
(2
), pp. 619
–644
.10.1137/S106482750138782629.
Das
,
S.
,
Ghanem
,
R.
, and
Finette
,
S.
, 2009
, “
Polynomial Chaos Representation of Spatio-Temporal Random Fields From Experimental Measurements
,” J. Comput. Phys.
,
228
(23
), pp. 8726
–8751
.10.1016/j.jcp.2009.08.02530.
Rosenblatt
,
M.
, 1952
, “
Remarks on a Multivariate Transformation
,” Ann. Math. Stat.
,
23
(3
), pp. 470
–472
.10.1214/aoms/117772939431.
Anderson
,
T. L.
, 2017
, Fracture Mechanics: Fundamentals and Applications
,
CRC Press
, Boca Raton, FL
.32.
Rolfe
,
S. T.
, and
Barsom
,
J. M.
, 1977
, Fracture and Fatigue Control in Structures: Applications of Fracture Mechanics
,
ASTM International
, West Conshohocken, PL
.33.
Mishra
,
M.
,
Keshavarzzadeh
,
V.
, and
Noshadravan
,
A.
, 2019
, “
Reliability-Based Lifecycle Management for Corroding Pipelines
,” Struct. Saf.
,
76
, pp. 1
–14
.10.1016/j.strusafe.2018.06.00734.
Frangopol
,
D. M.
,
Lin
,
K.-Y.
, and
Estes
,
A. C.
, 1997
, “
Life-Cycle Cost Design of Deteriorating Structures
,” J. Struct. Eng.
,
123
(10
), pp. 1390
–1401
.10.1061/(ASCE)0733-9445(1997)123:10(1390)35.
The MathWorks
, 2018
, “
MATLAB R2018b
,” The MathWorks, Natick, MA.36.
Kotulski
,
Z. A.
, 1998
, “
On Efficiency of Identification of a Stochastic Crack Propagation Model Based on Virkler Experimental Data
,” Arch. Mech.
,
50
(5
), pp. 829
–847
.https://www.researchgate.net/publication/228790283_On_efficiency_of_identification_of_a_stochastic_crack_propagation_model_based_on_Virkler_experimental_data37.
Ray
,
A.
,
Tangirala
,
S.
, and
Phoha
,
S.
, 1998
, “
Stochastic Modeling of Fatigue Crack Propagation
,” Appl. Math. Modell.
,
22
(3
), pp. 197
–204
.10.1016/S0307-904X(98)00013-438.
Grasso
,
M.
,
Penta
,
F.
,
Pinto
,
P.
, and
Pucillo
,
G.
, 2013
, “
A Four-Parameters Model for Fatigue Crack Growth Data Analysis
,” Fratt. Integr. Strutt.
,
7
(26
), pp. 69
–79
.10.3221/IGF-ESIS.26.0839.
Schütz
,
W.
, 1980
, “
Treatment of Scatter of Fracture Toughness Data for Design Purposes
,” Practical Applications of Fracture Mechanics, H. Liebowitz, eds., Advisory Group for Aerospace Research and Development, NATO, Brussels, Belgium.40.
Proppe
,
C.
, 2003
, “
Probabilistic Analysis of Multi-Site Damage in Aircraft Fuselages
,” Comput. Mech.
,
30
(4
), pp. 323
–329
.10.1007/s00466-002-0408-x41.
Virkler
,
D.
,
Hillberry
,
B.
, and
Goel
,
P.
, 1978
, “
The Statistical Nature of Fatigue Crack Propagation
,” Air Force Flight Dynamics Laboratory, Air Force Research Laboratory, WPAFB, Report No. AFFDLTR 78–43
.https://apps.dtic.mil/sti/pdfs/ADA056912.pdf42.
Loghin
,
A.
, and
Ismonov
,
S.
, 2022
, “
3D FEA Based Surrogate Modeling in Fatigue Crack Growth Life Assessment
,” Procedia Struct. Integr.
,
38
, pp. 331
–341
.10.1016/j.prostr.2022.03.03443.
Abbasi
,
A.
,
Nazari
,
F.
, and
Nataraj
,
C.
, 2020
, “
Application of Long Short-Term Memory Neural Network to Crack Propagation Prognostics
,” 2020 IEEE International Conference on Prognostics and Health Management (ICPHM
), Detroit, MI, June 8–10, pp. 1
–6
.10.1109/ICPHM49022.2020.918703344.
Dean
,
S. W.
,
Cross
,
R. J.
,
Makeev
,
A.
, and
Armanios
,
E.
, 2006
, “
A Comparison of Predictions From Probabilistic Crack Growth Models Inferred From Virkler's Data
,” J. ASTM Int.
,
3
(10
), p. 100574
.10.1520/JAI10057445.
Lin
,
Y.-H.
,
Ding
,
Z.-Q.
, and
Zio
,
E.
, 2019
, “
Fatigue Crack Growth Assessment Method Subject to Model Uncertainty
,” Eng. Fract. Mech.
,
219
, p. 106624
.10.1016/j.engfracmech.2019.10662446.
Ríos Goytre
,
J. I.
, 2019
, “
Exploration of Surrogate Models for Remaining Useful Life Estimation
,” Master's thesis
, Comillas Universidad Pontificia, Madrid, Spain.http://hdl.handle.net/11531/3638947.
Pais
,
M. J.
,
Viana
,
F. A.
, and
Kim
,
N. H.
, 2012
, “
Enabling High-Order Integration of Fatigue Crack Growth With Surrogate Modeling
,” Int. J. Fatigue
,
43
, pp. 150
–159
.10.1016/j.ijfatigue.2012.03.01048.
Williams
,
C. K.
, and
Rasmussen
,
C. E.
, 2006
, Gaussian Processes for Machine Learning
,
MIT Press
,
Cambridge, MA
.Copyright © 2025 by ASME
You do not currently have access to this content.
