一种基于Kriging和Monte Carlo的主动学习可靠度算法

doi:10.7527/S1000-6893.2014.0361

Abstract

Abstract:

In structural reliability analysis, surrogate models are usually used to approximate implicit performance function in order to solve the problem of large computation. However, selection of the design of numerical experiments should consider the accuracy of fitting surrogate model and the precision of calculating reliability simultaneously. Therefore, in order to make full use of the few sample information as little as possible and to maximize the accuracy of reliability calculation, an active learning reliability calculation method is proposed. Firstly, a learning function based on Kriging prediction is proposed similar to the improved function determining the selection of point in the optimization problem. And the best sampling point corresponding to the minimum of learning function is selected from the Monte Carlo population. Secondly, an iterative stopping criterion is proposed to ensure the correctness of Monte Carlo sample points' sign, and the iterations decrease dramatically. Finally, the correctness and efficiency of the proposed method are proved by two academic examples from literature; it is shown that the proposed method requires fewer calls to the performance function than other methods and the failure probability obtained from the proposed method is more accurate.

Key words: reliability, Monte Carlo, Kriging model, active learning, failure probability

CLC Number:

TONG Cao, SUN Zhili, YANG Li, SUN Anbang. An active learning reliability method based on Kriging and Monte Carlo[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2015, 36(9): 2992-3001.

References

[1] Ditlevsen O, Madsen H O. Structural reliability methods[M]. New York: Wiley, 1996: 87-109.
[2] Melchers R E. Structural reliability analysis and predictions[M]. New York: Wiley, 1999: 124-156.
[3] Nowak A S, Collins K R. Reliability of structures[M]. Boston: McGraw-Hill, 2000: 32-35.
[4] Zhang M. Structural reliability analysis: methods and procedures[M]. Beijing: Science Press, 2009: 143-174 (in Chinese). 张明. 结构可靠度分析: 方法与程序[M]. 北京: 科学出版社, 2009: 143-174.
[5] Jones D R, Schonlau M, Welch W J. Efficient global optimization of expensive black-box functions[J]. Journal of Global Optimization, 1998, 13(4): 455-492.
[6] Huang D, Allen T T, Notz W I, et al. Global optimization of stochastic black-box systems via sequential kriging meta-models[J]. Journal of Global Optimization, 2006, 34(3): 441-466.
[7] Ranjan P, Bingham D, Michailidis G. Sequential experiment design for contour estimation from complex computer codes[J]. Technometrics, 2008, 50(4): 527-541.
[8] Bichon B J, Eldred M S, Swiler L P, et al. Efficient global reliability analysis for nonlinear implicit performance functions[J]. AIAA Journal, 2008, 46(10): 2459-2468.
[9] Xu J K, Bai J Q, Huang J T, et al. Aerodynamic optimization design of wing under the interaction of propeller slipstream[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(11): 2910-2920 (in Chinese). 徐家宽, 白俊强, 黄江涛, 等. 考虑螺旋桨滑流影响的机翼气动优化设计[J]. 航空学报, 2014, 35(11): 2910-2920.
[10] Chang M, Zhou Z, Wang R, et al. Primary parameters determination for year- round solar-powered aircraft of wing-sail type at higher latitudes[J]. Acta Aeronautica et Astronautica Sinica, 2014, 35(6): 1592-1603 (in Chinese). 昌敏, 周洲, 王睿, 等. 基于机翼-帆尾的高纬度跨年驻留太阳能飞机总体参数设计方法[J]. 航空学报, 2014, 35(6): 1592-1603.
[11] Echard B, Gayton N, Lemaire M. AK-MCS: An active learning reliability method combining Kriging and Monte Carlo simulation[J]. Structural Safety, 2011, 33(2): 145-154.
[12] Xie Y M, Yu H P, Chen J, et al. The reliability estimation nased on Kriging model[J]. Journal of Shanghai Jiaotong University, 2007, 41(2): 177-180 (in Chinese). 谢延敏, 于沪平, 陈军, 等. 基于Kriging模型的可靠度计算[J]. 上海交通大学学报, 2007, 41(2): 177-180.
[13] Chen Z Y, Ren Y, Bai G C, et al. Particle swarm optimized Kriging approximate model and its application to reliability analysis[J]. Journal of Aerospace Power, 2011, 26(7): 1522-1530 (in Chinese). 陈志英, 任远, 白广忱, 等. 粒子群优化的Kriging近似模型及其在可靠性分析中的应用[J]. 航空动力学报, 2011, 26(7): 1522-1530.
[14] Liu Z, Zhang J G, Wang C C, et al. Hybrid structure reliability method combining optimized Kriging model and importance sampling[J]. Acta Aeronautica et Astronautica Sinica, 2013, 34(6): 1347-1355 (in Chinese). 刘瞻, 张建国, 王灿灿, 等. 基于优化Kriging模型和重要抽样法的结构可靠度混合算法[J]. 航空学报, 2013, 34(6): 1347-1355.
[15] Matheron G. The intrinsic random functions and their applications[J]. Advances in Applied Probability, 1973, 5(3): 439-468.
[16] Sacks J, Welch W J, Mitchell T J, et al. Design and analysis of computer experiments[J]. Statistical Science, 1989, 4(4): 409-435.
[17] Lophaven S N, Nielsen H B, Sndergaard J. Surrogate modeling by Kriging[R]. Denmark: Technical University of Denmark, 2003.
[18] Schueremans L, Gemert D V. Benefit of splines and neural networks in simulation based structural reliability analysis[J]. Structural Safety, 2005, 27(3): 246-261.
[19] Rajashekhar M R, Ellingwood B R. A new look at the response surface approach for reliability analysis[J]. Structural Safety, 1993, 12(3): 205-220.
[20] Gayton N, Bourinet J M, Lemaire M. CQ2RS: A new statistical approach to the response surface method for reliability analysis[J]. Structural Safety, 2003, 25(1): 99-121.

An active learning reliability method based on Kriging and Monte Carlo

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