[1] BRENNER S C, SCOTT L R. The mathematical theory of finite element methods[J]. Texts in Applied Mathematics, 2002, 3(298):263-291. [2] 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. [3] DUBOURG V, SUDRET B, DEHEEGER F. Metamodelbased importance sampling for structural reliability analysis[J]. Probabilistic Engineering Mechanics, 2013, 33(1):47-57. [4] CADINI F, SANTOS F, ZIO E. Passive systems failure probability estimation by the meta-AK-IS 2 algorithm[J]. Nuclear Engineering & Design, 2014, 277(1):203-211. [5] CADINI F, SANTOS F, ZIO E. An improved adaptive kriging-based importance technique for sampling multiple failure regions of low probability[J]. Reliability Engineering & System Safety, 2014, 131(3):109-117. [6] XIU D, KARNIADAKIS G E. The Wiener-Askey polynomial chaos for stochastic differential equations[J]. SIAM journal on scientific computing, 2002, 24(2):619-644. [7] WAN X, KARNIADAKIS GE. An adaptive multi-element generalized polynomial chaos method for stochastic differential equations[J]. Journal of Computational Physics, 2005, 209(2):617-642. [8] HU C, YOUN B D. Adaptive-sparse polynomial chaos expansion for reliability analysis and design of complex engineering systems[J]. Structural & Multidisciplinary Optimization, 2011, 43(3):419-442. [9] SUDRET B. Global sensitivity analysis using polynomial chaos expansions[J]. Reliability Engineering and System Safety, 2008, 93(7):964-979. [10] STEFANO M, BRUNO S. An active-learning algorithm that combines sparse polynomial chaos expansions and bootstrap for structural reliability analysis[J]. Structural Safety, 2018, 75:67-74. [11] BLATMAN G, SUDRET B. Sparse polynomial chaos expansions and adaptive stochastic finite elements using a regression approach[J]. Comptes Rendus Mécanique, 2008, 336(6):518-523. [12] KIM S H, NA S W. Response surface method using vector projected sampling points[J]. Structural Safety, 1997, 19(1):3-19. [13] KAYMAZ I, MCMAHON C A. A response surface method based on weighted regression for structural reliability analysis[J]. Probabilistic Engineering Mechanics, 2005, 20(1):11-17. [14] PAPADOPOULOS V,GIOVANIS D G,LAGAROS N D, et al. Accelerated subset simulation with neural networks for reliability analysis[J]. Computer Methods in Applied Mechanics and Engineering, 2012, 223-224(none):70-80. [15] CHENG J, LI Q S, XIAO R C. A new artificial neural network-based response surface method for structural reliability analysis[J]. Probabilistic Engineering Mechanics, 2008, 23(1):51-63. [16] DENG J. Structural reliability analysis for implicit performance function using radial basis function network[J]. International Journal of Solids and Structures, 2006, 43(11-12):3255-3291. [17] BICHON B J, ELDRED M S, SWILER L P, et al. Efficient global reliability analysis for non-linear implicit performance functions[J]. AIAA, 2008, 46:2459-2468. [18] LV Z Y, LU Z Z, WANG P. A new learning function for Kriging and its application to solve reliability problems in engineering[J]. Computers & Mathematics with Applications, 2015, 70:1182-1197. [19] SUN Z L, WANG J, LI R, et al. LIF:a new kriging based learning function and its application to structural reliability analysis[J]. Reliability Engineering & System Safety, 2017, 157:152-65. [20] CORTES C, VAPNIK V. Support-vector networks[J]. Machine Learning, 1995, 20(3):273-297. [21] BURGES C. A Tutorial on support vector machines for pattern recognition[J]. Data Mining and Knowledge Discovery, 1998, 2(2):121-167. [22] ROCCO C M, JOSÉ A M. Fast monte carlo reliability evaluation using support vector machine[J]. Reliability Engineering & System Safety, 2002, 76(3):237-243. [23] HURTADO J E. An examination of methods for approximating implicit limit state functions from the viewpoint of statistical learning theory[J]. Structural Safety, 2004, 26(3):271-293. [24] LI X, LI X, SU Y. A hybrid approach combining uniform design and support vector machine to probabilistic tunnel stability assessment[J]. Structural Safety, 2016, 61:22-42. [25] ZHAO H B. Slope reliability analysis using a support vector machine[J]. Computers & Geotechnics, 2008, 35(3):459-467. [26] ZHAO H B, RU Z, CHANG X, et al. Reliability analysis of tunnel using least square support vector machine[J]. Tunnelling & Underground Space Technology Incorporating Trenchless Technology Research, 2014, 41:14-23. [27] TAN X H, BI W H, HOU X L, et al. Reliability analysis using radial basis function networks and support vector machines[J]. Computers and Geotechnics, 2011, 38(2):178-186. [28] 李洪双,吕震宙,岳珠峰. 结构可靠性分析的支持向量机方法[J]. 应用数学和力学, 2006, 10:1135-1143. LI Hongshuang, LU Zhengzhou, YUE Zhufeng. Support Vector Machine for Structural Reliability Analysis. Applied Mathematics and Mechanics[J]. 2006, 10:1135-1143 [29] BOURINET J M, DEHEEGER F, LEMAIRE M. Assessing small failure probabilities by combined subset simulation and support vector machines[J]. Structural Safety, 2011, 33(6):343-353. [30] BOURINET J M. Rare-event probability estimation with adaptive support vector regression surrogates[J]. Reliability Engineering & System Safety, 2016, 150:210-221. [31] JI J, ZHANG C, GUI Y, LV Q, et al. New observations on the application of LS-SVM in slope system reliability analysis[J]. Journal of Computing in Civil Engineering, 2016, 6(1):02-06. [32] JIN R, CHEN W, SIMPSON T W. Comparative studies of metamodelling techniques under multiple modelling criteria[J]. Structural & Multidisciplinary Optimization, 2001, 23(1):1-13. [33] ANDREW A M. An introduction to support vector machines and other kernel-based learning methods[M]. London:United Kingdom at the Cambridge University Press, 2000. [34] XIANG H,LI Y,LIAO H,et al. An adaptive surrogate model based on support vector regression and its application to the optimization of railway wind barriers[J]. Structural & Multidisciplinary Optimization, 2017, 55(2):1-13. [35] WORTON B J. Kernel methods for estimating the utilization distribution in home-range studies[J]. Ecology, 1989, 70(1):164-168. [36] FRIEDRICHS F, IGEL C. Evolutionary tuning of multiple SVM parameters[J]. Neurocomputing, 2005, 64(1):107-117. [37] DEB K, PRATAP A, AGARWAL S, et al. A fast and elitist multi-objective genetic algorithm:NSGA-II[J]. IEEE Transactions on Evolutionary Computation, 2002, 6(2):182-197. [38] HWANG C R. Simulated annealing:Theory and applications[J]. Acta Applicandae Mathematica, 1988, 12(1):108-111. [39] FRIEDMAN J H. Greedy function approximation:A gradient boosting machine.[J]. Annals of Statistics, 2001, 29(5):1189-1232. [40] CARLSON D, HAYNSWORTH E, MARKHAM T. A generalization of the schur complement by means of the moore-penrose inverse[J]. Siam Journal on Applied Mathematics, 1974, 26(1):169-175. [41] PAN Q, DIAS D. An efficient reliability method combining adaptive support vector machine and monte carlo simulation[J]. Structural Safety, 2017, 67:85-95. |