Reliability-Based Design Optimization Using Quantile Surrogates by Adaptive Gaussian Process
Publication: Journal of Engineering Mechanics
Volume 147, Issue 5
Abstract
It is of great significance to incorporate various uncertainties into the design optimization of structures and other engineering systems. Many reliability-based design optimization (RBDO) methods have been developed, but their practical applications can be limited if the reliability consideration entails a large number of evaluations of performance functions, especially for those requiring time-consuming simulations. To overcome the challenge, this paper proposes a new RBDO method that employs quantile surrogates of the performance functions to identify the admissible domain, termed the probability-feasible design domain. Gaussian process models of the quantile surrogates are updated adaptively through an exploration-exploitation trade-off based on inherent randomness and the model uncertainty of the surrogate. The method guides the computational simulations toward the domain in which the quantile estimation can make the greatest contribution to the optimization process. The validity and efficiency of the proposed RBDO method using quantile surrogates by adaptive Gaussian process (QS-AGP) are demonstrated using several numerical examples. The results confirm that QS-AGP facilitates convergence to a reliable optimum design with a significantly reduced number of function evaluations compared to existing RBDO approaches.
Get full access to this article
View all available purchase options and get full access to this article.
Data Availability Statement
All data, models, or code that support the findings of this study are available from the first author on reasonable request.
Acknowledgments
The research was supported by a Grant (21SCIP-B146946-04) from the Smart Civil Infrastructure Research Program funded by the Ministry of Land, Infrastructure and Transport (MOLIT) of the Korean government. The authors are supported by the Institute of Construction and Environmental Engineering at Seoul National University. This support is gratefully acknowledged.
References
Arnold, B. C., N. Balakrishnan, and H. N. Nagaraja. 1992. A first course in order statistics. New York: Wiley.
Caflisch, R. E. 1998. “Monte Carlo and quasi-Monte Carlo methods.” Acta Numer. 7: 1–49. https://doi.org/10.1017/S0962492900002804.
Chan, K. Y., S. J. Skerlos, and P. Papalambros. 2007. “An adaptive sequential linear programming algorithm for optimal design problems with probabilistic constraints.” J. Mech. Des. 129 (2): 140–149. https://doi.org/10.1115/1.2337312.
Chen, X., T. K. Hasselman, and D. F. Neill. 1997. “Reliability based structural design optimization for practical applications.” In Proc., 38th AIAA/ASME/SCE/AHS/ASC Structures, Structural Dynamics, and Material Conf., AIAA-97-1403. Reston, VA: American Institute of Aeronautics and Astronautics. https://doi.org/10.2514/6.1997-1403.
Chen, Z., H. Qiu, L. Gao, L. Su, and P. Li. 2013. “An adaptive decoupling approach for reliability-based design optimization.” Comput. Struct. 117 (Feb): 58–66. https://doi.org/10.1016/j.compstruc.2012.12.001.
Choi, K. K., B. D. Youn, and R. J. Yang. 2001. “Moving least squares method for reliability-based design optimization.” In Proc., 4th World Congress of Structural and Multidisciplinary Optimization. Berchtesgaden, Germany: International Society for Structural and Multidisciplinary Optimization.
Der Kiureghian, A. 2005. “First-And second-order reliability methods.” Chap. 14 in Engineering design reliability handbook, edited by E. Nikolaidis, D. Ghiocel, and S. Singhal. Boca Raton, FL: CRC Press.
Der Kiureghian, A., and O. Ditlevsen. 2009. “Aleatory or epistemic? Does it matter?” Struct. Saf. 31 (2): 105–112. https://doi.org/10.1016/j.strusafe.2008.06.020.
Du, X., and W. Chen. 2004. “Sequential optimization and reliability assessment method for efficient probabilistic design.” J. Mech. Des. 126 (2): 225–233. https://doi.org/10.1115/1.1649968.
Dubourg, V., B. Sudret, and J. M. Bourinet. 2011. “Reliability-based design optimization using kriging surrogates and subset simulation.” Struct. Multidiscip. Optim. 44 (5): 673–690. https://doi.org/10.1007/s00158-011-0653-8.
Enevoldsen, I., and J. D. Sorensen. 1994. “Reliability-based optimization in structural engineering.” Struct. Saf. 15 (3): 169–196. https://doi.org/10.1016/0167-4730(94)90039-6.
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.
Girard, A., C. E. Rasmussen, J. Q. Candela, and R. M. Smith. 2003. “Gaussian process priors with uncertain inputs application to multiple-step ahead time series forecasting.” Adv. Neural Inf. Process. Syst. 15: 545–552. https://doi.org/10.5555/2968618.2968686.
Guilleminot, J., and C. Soize. 2020. “Non-Gaussian random fields in multiscale mechanics of heterogeneous materials.” In Encyclopedia of continuum mechanics, edited by H. Altenbach and A. Oshsner. Berlin: Springer.
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.
Kim, J., and J. Song. 2020. “Probability-adaptive Kriging in n-Ball (PAK-Bn) for reliability analysis.” Struct. Saf. 85 (Jul): 101924. https://doi.org/10.1016/j.strusafe.2020.101924.
Kim, T., O. S. Kwon, and J. Song. 2020. “Probabilistic evaluation of seismic responses using deep learning method.” Struct. Saf. 84 (May): 101913. https://doi.org/10.1016/j.strusafe.2019.101913.
Kim, T., and J. Song. 2018. “Generalized reliability importance measure (GRIM) using Gaussian mixture.” Reliab. Eng. Syst. Saf. 173 (May): 105–115. https://doi.org/10.1016/j.ress.2018.01.005.
Kurtz, N., and J. Song. 2013. “Cross-entropy-based adaptive importance sampling using Gaussian mixture.” Struct. Saf. 42 (May): 35–44. https://doi.org/10.1016/j.strusafe.2013.01.006.
Lee, T. H., and J. J. Jung. 2008. “A sampling technique enhancing accuracy and efficiency of metamodel-based RBDO: Constraint boundary sampling.” Comput. Struct. 86 (13–14): 1463–1476. https://doi.org/10.1016/j.compstruc.2007.05.023.
Li, M., and Z. Wang. 2019. “Surrogate model uncertainty quantification for reliability-based design optimization.” Reliab. Eng. Syst. Saf. 192 (Dec): 106432. https://doi.org/10.1016/j.ress.2019.03.039.
Liang, J., Z. P. Mourelatos, and E. Nikolaidis. 2007. “A single-loop approach for system reliability-based design optimization.” J. Mech. Des. 129 (12): 1215–1224. https://doi.org/10.1115/1.2779884.
Marelli, S., and B. Sudret. 2018. “An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis.” Struct. Saf. 75 (Nov): 67–74. https://doi.org/10.1016/j.strusafe.2018.06.003.
Moustapha, M., and B. Sudret. 2019. “Surrogate-assisted reliability-based design optimization: A survey and a unified modular framework.” Struct. Multidiscip. Optim. 60: 2157–2176. https://doi.org/10.1007/s00158-019-02290-y.
Moustapha, M., B. Sudret, J. M. Bourinet, and B. Guillaume. 2016. “Quantile-based optimization under uncertainties using adaptive Kriging surrogate models.” Struct. Multidiscip. Optim. 54 (6): 1403–1421. https://doi.org/10.1007/s00158-016-1504-4.
Nguyen, T. H., J. Song, and G. H. Paulino. 2010. “Single-loop system reliability based design optimization using matrix-based system reliability method: Theory and applications.” J. Mech. Des. 132 (1): 011005. https://doi.org/10.1115/1.4000483.
Rashki, M., M. Miri, and M. A. Moghaddam. 2014. “A simulation-based method for reliability-based design optimization problems with highly nonlinear constraints.” Autom. Constr. 47 (Nov): 24–36. https://doi.org/10.1016/j.autcon.2014.07.004.
Rasmussen, C. E., and H. Nickisch. 2015. “Gaussian processes for machine learning (GPML) toolbox.” J. Mach. Learn. Res. 11 (Nov): 3011–3015. https://doi.org/10.5555/1756006.1953029.
Shan, S., and G. G. Wang. 2008. “Reliable design space and complete single-loop reliability-based design optimization.” Reliab. Eng. Syst. Saf. 93 (8): 1218–1230. https://doi.org/10.1016/j.ress.2007.07.006.
Spence, S. M. J., and M. Gioffrè. 2012. “Large scale reliability-based design optimization of wind excited tall buildings.” Probab. Eng. Mech. 28 (Apr): 206–215. https://doi.org/10.1016/j.probengmech.2011.08.001.
Tu, J., K. K. Choi, and Y. H. Park. 1998. “A new study on reliability based design optimization.” J. Mech. Des. 121 (4): 557–564. https://doi.org/10.1115/1.2829499.
Wang, X., and K. T. Fang. 2003. “The effective dimension and quasi-Monte Carlo integration.” J. Complexity 19 (2): 101–124. https://doi.org/10.1016/S0885-064X(03)00003-7.
Wang, Z., and M. Broccardo. 2020. “A novel active learning-based Gaussian process metamodeling strategy for estimating the full probability distribution in forward UQ analysis.” Struct. Saf. 84 (May): 101937. https://doi.org/10.1016/j.strusafe.2020.101937.
Wang, Z., and J. Song. 2018. “Hyper-spherical extrapolation method (HEM) for general high dimensional reliability problems.” Struct. Saf. 72 (May): 65–73. https://doi.org/10.1016/j.strusafe.2017.12.005.
Youn, B. D., and K. K. Choi. 2004. “A new response surface methodology for reliability-based design optimization.” Comput. Struct. 82 (2–3): 241–256. https://doi.org/10.1016/j.compstruc.2003.09.002.
Youn, B. D., K. K. Choi, and Y. H. Park. 2003. “Hybrid analysis method for reliability-based design optimization.” J. Mech. Des. 125 (2): 221–232. https://doi.org/10.1115/1.1561042.
Zhang, J., A. A. Taflanidis, and J. C. Medina. 2017. “Sequential approximate optimization for design under uncertainty problems utilizing Kriging metamodeling in augmented input space.” Comput. Methods Appl. Mech. Eng. 315 (Mar): 369–395. https://doi.org/10.1016/j.cma.2016.10.042.
Information & Authors
Information
Published In
Copyright
© 2021 American Society of Civil Engineers.
History
Received: Jul 30, 2020
Accepted: Nov 30, 2020
Published online: Feb 24, 2021
Published in print: May 1, 2021
Discussion open until: Jul 24, 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.