AK-SYS-t: New Time-Dependent Reliability Method Based on Kriging Metamodeling
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7, Issue 4
Abstract
Computing the cumulative failure probability for a given period of time is the main goal of a time-dependent reliability analysis. Estimating this probability is challenging for problems with nonmonotonic performance functions, especially when they are costly to evaluate and have high dimensionality. Discretizing the time interval is one main step in most of the time-dependent reliability methods. Hence, the problem can be converted into a serially connected system reliability problem. Therefore, efficient system reliability methods can be used for time-dependent reliability analysis. AK-SYS (Active learning and Kriging-based SYStem reliability method) is a Kriging-based method for system reliability assessment, including an active learning procedure for the enrichment process. In this paper, we exploit the efficiency of AK-SYS to propose a new time-dependent reliability method that is called AK-SYS-t. Two examples are used to compare the efficiency of the proposed method with competing methods, and a third example is used to highlight the opportunities offered by this method for fatigue reliability analysis. In the end, a crude approach is also proposed to provide the full curve of the cumulative failure probability.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
Due to the fact that this study is a shared work between different partners, the codes and algorithms generated during this study are proprietary or confidential in nature and may only be provided with restrictions.
Acknowledgments
This research has been performed under the INFRASTAR program that has received funding from the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Skłodowska-Curie Grant Agreement No. 676139. To perform numerical simulations and programming, we have used Open TURNS (Baudin et al. 2015). Also, we would like to show our gratitude to the Reliability and Uncertainty group in PHIMECA Engineering for their invaluable help.
References
Andrieu-Renaud, C., B. Sudret, and M. Lemaire. 2004. “The PHI2 method: A way to compute time-variant reliability.” Reliab. Eng. Syst. Saf. 84 (1): 75–86. https://doi.org/10.1016/j.ress.2003.10.005.
Baudin, M., A. Dutfoy, B. Iooss, and A.-L. Popelin. 2015. “Openturns: An industrial software for uncertainty quantification in simulation.” Preprint, submitted January 21, 2015. https://arxiv.org/abs/1501.05242.
Bourinet, J.-M. 2016. “Rare-event probability estimation with adaptive support vector regression surrogates.” Reliab. Eng. Syst. Saf. 150 (Jun): 210–221. https://doi.org/10.1016/j.ress.2016.01.023.
Bourinet, J.-M., and M. Lemaire. 2008. “Form sensitivities to correlation: Application to fatigue crack propagation based on Virkler data.” In Proc., 4th Int. ASRANet Colloquium. Glasgow, UK: ASRANet.
Ditlevsen, O., and R. Olesen. 1986. “Statistical analysis of the Virkler data on fatigue crack growth.” Eng. Fract. Mech. 25 (2): 177–195. https://doi.org/10.1016/0013-7944(86)90217-1.
Du, X. 2012. “Toward time-dependent robustness metrics.” J Mech Des N Y 134 (1): 011004. https://doi.org/10.1115/1.4005445.
Dubourg, V. 2011. “Adaptive surrogate models for reliability analysis and reliability-based design optimization.” Ph.D. thesis, Laboratoire de Mécanique et Ingénieries, Université Blaise Pascal Clermont II.
Echard, B., N. Gayton, and M. Lemaire. 2011. “AK-MCS: An active learning reliability method combining Kriging and Monte Carlo simulation.” Struct. Saf. 33 (2): 145–154. https://doi.org/10.1016/j.strusafe.2011.01.002.
Fauriat, W., and N. Gayton. 2014. “AK-SYS: An adaptation of the AK-MCS method for system reliability.” Reliab. Eng. Syst. Saf. 123 (Mar): 137–144. https://doi.org/10.1016/j.ress.2013.10.010.
Hawchar, L. 2017. “Development of metamodeling methods for time-dependent structural reliability analysis.” Ph.D. thesis, Institut de Recherche en Génie Civil et Mécanique, Université de Nantes.
Hawchar, L., C. Soueidy, and F. Schoefs. 2015. “Time-variant reliability analysis using polynomial chaos expansion.” In Proc., Int. Conf. on Applications of Statistics and Probability. Vancouver, Canada: The University of British Columbia.
Hawchar, L., C.-P. E. Soueidy, and F. Schoefs. 2017. “Principal component analysis and polynomial chaos expansion for time-variant reliability problems.” Reliab. Eng. Syst. Saf. 167 (Nov): 406–416. https://doi.org/10.1016/j.ress.2017.06.024.
Hu, Z., and X. Du. 2014. “Lifetime cost optimization with time-dependent reliability.” Eng. Optim. 46 (10): 1389–1410. https://doi.org/10.1080/0305215X.2013.841905.
Hu, Z., and X. Du. 2015. “Mixed efficient global optimization for time-dependent reliability analysis.” J. Mech. Des. N. Y. 137 (5): 051401. https://doi.org/10.1115/1.4029520.
Hu, Z., and S. Mahadevan. 2016. “A single-loop kriging surrogate modeling for time-dependent reliability analysis.” J. Mech. Des. N. Y. 138 (6): 061406. https://doi.org/10.1115/1.4033428.
Jones, D. R., M. Schonlau, and W. J. Welch. 1998. “Efficient global optimization of expensive black-box functions.” J. Global Optim. 13 (4): 455–492. https://doi.org/10.1023/A:1008306431147.
Li, C., and A. D. Kiureghian. 1993. “Optimal discretization of random fields.” J. Eng. Mech. 119 (6): 1136–1154. https://doi.org/10.1061/(ASCE)0733-9399(1993)119:6(1136).
Loeve, M. 1977. Probability theory I. Berlin: Springer.
Melchers, R. E. 1999. Structural reliability analysis and prediction. New York: Wiley.
Rice, S. 1944. “Mathematical analysis of random noise.” Bell Syst. Tech. 23 (3): 282–332. https://doi.org/10.1002/j.1538-7305.1944.tb00874.x.
Singh, A., Z. Mourelatos, and J. Li. 2010. “Design for lifecycle cost using time-dependent reliability.” J. Mech. Des. N. Y. 132 (9): 091008. https://doi.org/10.1115/1.4002200.
Sudret, B. 2008. “Analytical derivation of the outcrossing rate in time-variant reliability problems.” Struct. Infrastruct. Eng. 4 (5): 353–362. https://doi.org/10.1080/15732470701270058.
Virkler, D. A., B. M. Hillberry, and P. K. Goel. 1979. “The statistical nature of fatigue crack propagation.” J. Eng. Mater. Technol. 101 (2): 148–153. https://doi.org/10.1115/1.3443666.
Wang, Z., and W. Chen. 2013. “Confidence-based adaptive extreme response surface for time-variant reliability analysis under random excitation.” Struct. Saf. 64 (0167–4730: 76–86. https://doi.org/10.1016/j.strusafe.2016.10.001.
Wang, Z., and W. Chen. 2017. “Confidence-based adaptive extreme response surface for time-variant reliability analysis under random excitation.” Struct. Saf. 64 (Jan): 76–86. https://doi.org/10.1016/j.strusafe.2016.10.001.
Wang, Z., and P. Wang. 2012. “A nested extreme response surface approach for time-dependent reliability-based design optimization.” J. Mech. Des. N. Y. 134 (12): 121007. https://doi.org/10.1115/1.4007931.
Youn, B. D., C. Hu, and P. Wang. 2011. “Resilience-driven system design of complex engineered systems.” J. Mech. Des. N. Y. 133 (10): 101011. https://doi.org/10.1115/1.4004981.
Zhang, J., and X. Du. 2011. “Time-dependent reliability analysis for function generator mechanisms.” J. Mech. Des. N. Y. 133 (3): 031005. https://doi.org/10.1115/1.4003539.
Information & Authors
Information
Published In
ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 7 • Issue 4 • December 2021
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Dec 18, 2020
Accepted: Apr 23, 2021
Published online: Jul 16, 2021
Published in print: Dec 1, 2021
Discussion open until: Dec 16, 2021
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.
Cited by
- Franck Schoefs, Mestapha Oumouni, Morteza Ahmadivala, Neil Luxcey, Florian Dupriez-Robin, Patrick Guerin, Unified System Analysis for Time-Variant Reliability of a Floating Offshore Substation, Journal of Marine Science and Engineering, 10.3390/jmse11101924, 11, 10, (1924), (2023).
- Cao Wang, Hao Zhang, Michael Beer, Structural Time-Dependent Reliability Assessment: Advanced Approaches for Engineered Structures, ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 10.1061/AJRUA6.RUENG-1010, 9, 1, (2023).