A Structural Reliability Analysis Method Based on Adaptive PC-Kriging Model

doi:10.12068/j.issn.1005-3026.2020.05.010

Abstract

Abstract: To improve the accuracy and efficiency of reliability assessment for complex structures with small failure probability and time-consuming model， a structural reliability analytical method based on PC-Kriging (polynomial-chaos-based Kriging) model and adaptive k-means clustering analysis was proposed. PC-Kriging’s regression basis function approximated the global behavior of the numerical model by using the sparse polynomial optimal truncation set， and Kriging was used to deal with the local variation of the output of the model. PC-Kriging used least angle regression (LAR) to calculate the number of possible polynomial basis function sets of performance function， and adopted Akaike information criterion (AIC) to determine the optimal polynomial form. The adaptive k-means clustering analysis ensured that some of the significant contribution sample points toward the failure probability can be added as the new training samples in each iteration. The results of two numerical examples indicated that the proposed method can not only guarantee the validity and accuracy of the estimation of failure probability but also reduce structural performance function evaluation times.

Key words: PC-Kriging(polynomial-chaos-based Kriging), reliability analysis, k-means clustering analysis, adaptive design of experiment, Monte Carlo method

CLC Number:

TB114.3

YU Zhen-liang， SUN Zhi-li， ZHANG Yi-bo， WANG Jian. A Structural Reliability Analysis Method Based on Adaptive PC-Kriging Model[J]. Journal of Northeastern University Natural Science, 2020, 41(5): 667-672.

References

[1]Zhao Y G，Ono T.A general procedure for first/second-order reliability method (FORM/SORM)［J］.Structural Safety，1999，21(2):95-112.
[2]Xiong F，Liu Y，Ying X.A double weighted stochastic response surface method for reliability analysis［J］.Journal of Mechanical Science and Technology，2012，26(8):2573-2580.
[3]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.
[4]Alibrandi U，Alani A M，Ricciardi G.A new sampling strategy for SVM-based response surface for structural reliability analysis［J］.Probabilistic Engineering Mechanics，2015，41:1-12.
[5]Kaymaz I.Application of Kriging method to structural reliability problems［J］.Structural Safety，2005，27(2):133-151.
[6]Qiu Y S，Bai J Q.Stationary flow fields prediction of variable physical domain based on proper orthogonal decomposition and Kriging surrogate model［J］.Chinese Journal of Aeronautics，2015，28(1):44-56.
[7]Han Z H，Zimmerman R，Grtz S.Alternative co-Kriging method for variable-fidelity surrogate modeling［J］.AIAA Journal，2012，50(5):1205-1210.
[8]Han Z H，Grtz S，Zimmermann R.Improving variable-fidelity surrogate modeling via gradient-enhanced Kriging and a generalized hybrid bridge function［J］.Aerospace Science & Technology，2013，25(1):177-189.
[9]Han Z H，Zhang Y，Song C X，et al.Weighted gradient-enhanced Kriging for high-dimensional surrogate modeling and design optimization［J］.AIAA Journal，2017，55(12):4330-4346.
[10]Schoebi R，Sudret B，Wiart J.Polynomial-chaos-based-Kriging［J］.International Journal for Uncertainty Quantifications，2015，5(2):171-193.
[11]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.
[12]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.
[13]Gaspar B，Teixeira A P，Soares C G.Assessment of the efficiency of Kriging surrogate models for structural reliability analysis［J］.Probabilistic Engineering Mechanics，2014，37(4):24-34.
[14]Efron B，Hastie T，Johnstone I，et al.Least angle regression［J］.Annals of Statistics，2004，32(2):407-451.
[15]Arnold T W.Uninformative parameters and model selection using Akaike’s information criterion［J］.Journal of Wildlife Management，2011，74(6):1175-1178.
[16]孙志礼，李瑞，王健，等.一种用于结构可靠性分析的Kriging学习函数［J］.哈尔滨工业大学学报，2017，49(7):146-151.(Sun Zhi-li，Li Rui，Wang Jian，et al.A Kriging based learning function for structural reliability analysis［J］.Journal of Harbin Institute of Technology，2017，49(7):146-151.)
[17]Wen Z，Pei H，Liu H，et al.A sequential Kriging reliability analysis method with characteristics of adaptive sampling regions and parallelizability［J］.Reliability Engineering & System Safety，2016，153:170-179.
[15]关守平，房少纯.一种新型的区间-粒子群优化算法［J］.东北大学学报(自然科学版)，2012，33(10):1381-1384.(Guan Shou-ping，Fang Shao-chun.A new interval particle swarm optimization algorithm［J］.Journal of Northeastern University(Natural Science)，2012，33(10):1381-1384.)