AK-MCS swMATH ID: 18303 Software Authors: B. Echard, N. Gayton, M. Lemaire Description: AK-MCS: An active learning reliability method combining Kriging and Monte Carlo Simulation. An important challenge in structural reliability is to keep to a minimum the number of calls to the numerical models. Engineering problems involve more and more complex computer codes and the evaluation of the probability of failure may require very time-consuming computations. Metamodels are used to reduce these computation times. To assess reliability, the most popular approach remains the numerous variants of response surfaces. Polynomial Chaos [1] and Support Vector Machine [2] are also possibilities and have gained considerations among researchers in the last decades. However, recently, Kriging, originated from geostatistics, have emerged in reliability analysis. Widespread in optimisation, Kriging has just started to appear in uncertainty propagation [3] and reliability and studies. It presents interesting characteristics such as exact interpolation and a local index of uncertainty on the prediction which can be used in active learning methods. The aim of this paper is to propose an iterative approach based on Monte Carlo Simulation and Kriging metamodel to assess the reliability of structures in a more efficient way. The method is called AK-MCS for Active learning reliability method combining Kriging and Monte Carlo Simulation. It is shown to be very efficient as the probability of failure obtained with AK-MCS is very accurate and this, for only a small number of calls to the performance function. Several examples from literature are performed to illustrate the methodology and to prove its efficiency particularly for problems dealing with high non-linearity, non-differentiability, non-convex and non-connex domains of failure and high dimensionality Homepage: http://www.sciencedirect.com/science/article/pii/S0167473011000038 Related Software: DACE; EGO; UQLab; Matlab; top.m; PRMLT; GitHub; Scikit; top88.m; Qhull; L-BFGS; Chaospy; TOMS659; Adam; quadva; quadgk; QRM; CST Studio Suite; tmvtnorm; MrDIRECT Cited in: 75 Publications all top 5 Cited by 183 Authors 7 Lü, Zhenzhou 5 Gao, Liang 5 Liu, Yongshou 4 Shields, Michael D. 4 Xiao, Mi 4 Zhang, Jinhao 4 Zhang, Yishang 3 Hong, Linxiong 3 Li, Huacong 3 Meng, Zeng 3 Sudret, Bruno 3 Xiao, Ningcong 3 Yang, Xufeng 3 Yue, Zhufeng 3 Zhou, Huanlin 2 Beer, Michael A. 2 Derennes, Pierre 2 Fu, Jiangfeng 2 Hu, Hao 2 Jiang, Chao 2 Keshtegar, Behrooz 2 Ling, Chunyan 2 Morio, Jérôme 2 Peng, Kai 2 Rashki, Mohsen 2 Valdebenito, Marcos A. 2 Wang, Pan 2 Wei, Pengfei 2 Yao, Qin 2 Yuan, Kai 2 Zio, Enrico 1 Alvarez, Diego A. 1 Ameryan, Ala 1 Azizyan, Gholamreza 1 Baroth, Julien 1 Bect, Julien 1 Benoumechiara, Nazih 1 Bolisetti, Chandrakanth 1 Bousquet, Nicolas 1 Briffaut, M. 1 Cao, Lixiong 1 Chakroborty, Promit 1 Chen, Bingqian 1 Chen, Guohai 1 Chen, Hanshu 1 Chu, Sheng 1 Congedo, Pietro Marco 1 Cui, Haichao 1 Defaux, Gilles 1 Dhulipala, Somayajulu L. N. 1 Diazdelao, F. A. 1 Du, Xiuli 1 Dufour, Frédéric 1 Ehre, Max 1 Faes, Matthias G. R. 1 Feng, Kaixuan 1 Fetz, Thomas 1 Fu, Junjian 1 Fuhrländer, Mona 1 Gao, Ning 1 Gao, Zongzhan 1 Garnier, Josselin 1 Ghalehnovi, Mansour 1 Ghasemi, Mohammad Reza 1 Gong, Xianliang 1 Grigoriu, Mircea D. 1 Guo, Qing 1 Guo, Wei 1 Han, Qiang 1 Han, Xu 1 Hao, Hong 1 Hou, Xu 1 Hristov, P. O. 1 Hu, Yingshi 1 Huang, Hongzhong 1 Huang, Xiaodong 1 Hurtado, Jorge E. 1 Jia, Gaofeng 1 Jiang, Chen 1 Jiang, Chen 1 Jiang, Xia 1 Kareem, Ahsan 1 Kersaudy, Pierric 1 Kisi, Ozgur 1 Kubiak, K. J. 1 Laboure, Vincent M. 1 Li, Chenfeng 1 Li, Guangyao 1 Li, Heng 1 Li, Jinglai 1 Li, Jun 1 Li, Lei 1 Li, Ling 1 Li, Peigen 1 Li, Qing 1 Li, Xiaolan 1 Li, Yanfeng 1 Li, Yongle 1 Lin, Guang 1 Liu, Baoshou ...and 83 more Authors all top 5 Cited in 19 Serials 24 Computer Methods in Applied Mechanics and Engineering 24 Applied Mathematical Modelling 9 Journal of Computational Physics 2 Acta Mechanica 2 Mathematical Problems in Engineering 1 Computers & Mathematics with Applications 1 Automatica 1 Fuzzy Sets and Systems 1 Mathematics and Computers in Simulation 1 International Journal of Approximate Reasoning 1 Journal of Scientific Computing 1 SIAM Journal on Scientific Computing 1 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 1 Discrete Dynamics in Nature and Society 1 International Journal of Computational Methods 1 Inverse Problems in Science and Engineering 1 Journal of Mathematics in Industry 1 Dependence Modeling 1 SIAM/ASA Journal on Uncertainty Quantification all top 5 Cited in 14 Fields 49 Statistics (62-XX) 31 Operations research, mathematical programming (90-XX) 23 Numerical analysis (65-XX) 21 Mechanics of deformable solids (74-XX) 17 Probability theory and stochastic processes (60-XX) 7 Computer science (68-XX) 3 Systems theory; control (93-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Biology and other natural sciences (92-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Fluid mechanics (76-XX) 1 Geophysics (86-XX) 1 Information and communication theory, circuits (94-XX) Citations by Year