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

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  1. Hong, Linxiong; Li, Huacong; Fu, Jiangfeng: A novel surrogate-model based active learning method for structural reliability analysis (2022)
  2. Rossat, D.; Baroth, J.; Briffaut, M.; Dufour, F.: Bayesian inversion using adaptive polynomial chaos kriging within subset simulation (2022)
  3. Song, Chaolin; Wang, Zeyu; Shafieezadeh, Abdollah; Xiao, Rucheng: BUAK-AIS: efficient Bayesian updating with active learning kriging-based adaptive importance sampling (2022)
  4. Zhang, Jinhao; Xiao, Mi; Li, Peigen; Gao, Liang: Quantile-based topology optimization under uncertainty using kriging metamodel (2022)
  5. Derennes, Pierre; Morio, Jérôme; Simatos, Florian: Simultaneous estimation of complementary moment independent and reliability-oriented sensitivity measures (2021)
  6. Hong, Linxiong; Li, Huacong; Gao, Ning; Fu, Jiangfeng; Peng, Kai: Random and multi-super-ellipsoidal variables hybrid reliability analysis based on a novel active learning Kriging model (2021)
  7. Hong, Linxiong; Li, Huacong; Peng, Kai: A combined radial basis function and adaptive sequential sampling method for structural reliability analysis (2021)
  8. Hu, Yingshi; Lu, Zhenzhou; Wei, Ning; Jiang, Xia; Zhou, Changcong: Advanced single-loop kriging surrogate model method by combining the adaptive reduction of candidate sample pool for safety lifetime analysis (2021)
  9. Li, T. Z.; Pan, Q.; Dias, D.: Active learning relevant vector machine for reliability analysis (2021)
  10. Li, Xiaolan; Chen, Guohai; Cui, Haichao; Yang, Dixiong: Direct probability integral method for static and dynamic reliability analysis of structures with complicated performance functions (2021)
  11. Ni, Pinghe; Li, Jun; Hao, Hong; Han, Qiang; Du, Xiuli: Probabilistic model updating via variational Bayesian inference and adaptive Gaussian process modeling (2021)
  12. Novák, Lukáš; Vořechovský, Miroslav; Sadílek, Václav; Shields, Michael D.: Variance-based adaptive sequential sampling for polynomial chaos expansion (2021)
  13. Wang, Jinsheng; Li, Chenfeng; Xu, Guoji; Li, Yongle; Kareem, Ahsan: Efficient structural reliability analysis based on adaptive Bayesian support vector regression (2021)
  14. Zhang, Dequan; Zhou, Pengfei; Jiang, Chen; Yang, Meide; Han, Xu; Li, Qing: A stochastic process discretization method combing active learning Kriging model for efficient time-variant reliability analysis (2021)
  15. Zhou, Yanxun; Zhang, Yimin; Yao, Guo: Probabilistic analysis of dynamic stability for a rotating BDFG tapered beam with time-varying velocity and stochastic parameters (2021)
  16. Benoumechiara, Nazih; Bousquet, Nicolas; Michel, Bertrand; Saint-Pierre, Philippe: Detecting and modeling critical dependence structures between random inputs of computer models (2020)
  17. Chen, Hanshu; Meng, Zeng; Zhou, Huanlin: A hybrid framework of efficient multi-objective optimization of stiffened shells with imperfection (2020)
  18. Faes, Matthias G. R.; Valdebenito, Marcos A.: Fully decoupled reliability-based design optimization of structural systems subject to uncertain loads (2020)
  19. Feng, Kaixuan; Lu, Zhenzhou; Wang, Lu: A novel dual-stage adaptive kriging method for profust reliability analysis (2020)
  20. Fuhrländer, Mona; Schöps, Sebastian: A blackbox yield estimation workflow with Gaussian process regression applied to the design of electromagnetic devices (2020)

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