Abstract
In the reliability analysis, rare-event probability estimation imposes serious difficulties on conventional simulation methods like crude Monte Carlo. Several advanced variance reduction techniques such as importance sampling and importance splitting are presented to address this issue. Even though these methods require a low number of samples compared with crude Monte Carlo of the same accuracy, their implementation on time-consuming simulation codes is still very demanding. A joint employment of sampling methods and surrogate models is a proper solution. In this study, we integrate the Kriging surrogate model with a cross-entropy-based adaptive importance sampling, which uses the Gaussian mixture as the auxiliary sampling function. The novelty resides in efficient integration of the importance sampling and Kriging model. Results of various presented tests show a remarkable improvement with respect to importance sampling without surrogate. The statistical analysis results reveal that this advantage is achievable without any significant loss of accuracy.
Similar content being viewed by others
References
Balesdent M, Morio J, Marzat J (2013) Kriging-based adaptive importance sampling algorithms for rare event estimation. Struct Saf 44:1–10
Baudoui V, Klotz P, Hiriart-Urruty J-B, Jan S, Morel F (2012) Local Uncertainty Processing (LOUP) method for multidisciplinary robust design optimization. Struct Multidiscip Optim 46(5):711–726
Bect J, Ginsbourger D, Li L, Picheny V, Vazquez E (2012) Sequential design of computer experiments for the estimation of a probability of failure. Stat Comput 22(3):773–793
Bourinet JM, Deheeger F, Lemaire M (2011) Assessing small failure probabilities by combined subset simulation and support vector machines. Struct Saf 33(6):343–353
Bucher CG, Bourgund U (1990) A fast and efficient response surface approach for structural reliability problems. Struct Saf 7(1):57–66
Der Kiureghian A, Dakessian T (1998) Multiple design points in first and second-order reliability. Struct Saf 20(1):37–49
Dubourg V, Sudret B, Deheeger F (2013) Metamodel-based importance sampling for structural reliability analysis. Probab Eng Mech 33:47–57
Echard B, Gayton N, Lemaire M (2011) AK-MCS: an active learning reliability method combining Kriging and Monte Carlo Simulation. Struct Saf 33(2):145–154
Jahani E, Shayanfar M, Barkhordari M (2013) A new adaptive importance sampling Monte Carlo method for structural reliability. KSCE J Civ Eng 17(1):210–215
Janusevskis J, Le Riche R (2013) Simultaneous Kriging-based estimation and optimization of mean response. J Glob Optim 55(2):313–336
Kaveh A, Massoudi MS, Ghanoonibagha M (2014) Structural reliability analysis using charged system search algorithm. Iran J Sci Technol Trans Civil Eng 38(C2):439–448
Kurtz N, Song J (2013) Cross-entropy-based adaptive importance sampling using Gaussian mixture. Struct Saf 42:35–44
Li L, Chu X (2015) Risk assessment of slope failure by representative slip surfaces and response surface function. KSCE J Civ Eng 20(5):1783–1792
Li J, Xiu D (2010) Evaluation of failure probability via surrogate models. J Comput Phys 229(23):8966–8980
Lophaven S, Nielsen H, Søndergaard J (2002) DACE a Matlab Kriging toolbox. Technical University of Denmark, Copenhagen
Melchers RE, Ahammed M (2001) Estimation of failure probabilities for intersections of non-linear limit states. Struct Saf 23(2):123–135
Shim H (2005) Design & analysis of corrosion free service life of concrete structures using Monte Carlo method. KSCE J Civ Eng 9(5):377–384
Sudret B (2012) Meta-models for structural reliability and uncertainty quantification. In: Asian-Pacific symposium on structural reliability and its applications. Singapore
Welch WJ, Robert JB, Sacks J, Wynn HP, Mitchell TJ, Morris MD (1992) Screening, predicting, and computer experiments. Technometrics 34(1):15–25
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Barkhori, M., Shayanfar, M.A., Barkhordari, M.A. et al. Kriging-Aided Cross-Entropy-Based Adaptive Importance Sampling Using Gaussian Mixture. Iran J Sci Technol Trans Civ Eng 43 (Suppl 1), 81–88 (2019). https://doi.org/10.1007/s40996-018-0143-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40996-018-0143-y