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. Derennes, Pierre; Morio, Jérôme; Simatos, Florian: Simultaneous estimation of complementary moment independent and reliability-oriented sensitivity measures (2021)
  2. 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)
  3. 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)
  4. Benoumechiara, Nazih; Bousquet, Nicolas; Michel, Bertrand; Saint-Pierre, Philippe: Detecting and modeling critical dependence structures between random inputs of computer models (2020)
  5. Chen, Hanshu; Meng, Zeng; Zhou, Huanlin: A hybrid framework of efficient multi-objective optimization of stiffened shells with imperfection (2020)
  6. Faes, Matthias G. R.; Valdebenito, Marcos A.: Fully decoupled reliability-based design optimization of structural systems subject to uncertain loads (2020)
  7. Ghalehnovi, Mansour; Rashki, Mohsen; Ameryan, Ala: First order control variates algorithm for reliability analysis of engineering structures (2020)
  8. Giovanis, D. G.; Shields, M. D.: Data-driven surrogates for high dimensional models using Gaussian process regression on the Grassmann manifold (2020)
  9. Jiang, Chen; Qiu, Haobo; Gao, Liang; Wang, Dapeng; Yang, Zan; Chen, Liming: Real-time estimation error-guided active learning kriging method for time-dependent reliability analysis (2020)
  10. Ling, Chunyan; Lu, Zhenzhou: Adaptive Kriging coupled with importance sampling strategies for time-variant hybrid reliability analysis (2020)
  11. Ling, Chunyan; Lu, Zhenzhou; Sun, Bo; Wang, Minjie: An efficient method combining active learning kriging and Monte Carlo simulation for profust failure probability (2020)
  12. Liu, Baoshou; Jiang, Chao; Li, Guangyao; Huang, Xiaodong: Topology optimization of structures considering local material uncertainties in additive manufacturing (2020)
  13. Shi, Yan; Lu, Zhenzhou; Zhou, Jiayan; Zio, Enrico: A novel time-dependent system constraint boundary sampling technique for solving time-dependent reliability-based design optimization problems (2020)
  14. Song, Jingwen; Wei, Pengfei; Valdebenito, Marcos; Beer, Michael: Adaptive reliability analysis for rare events evaluation with global imprecise line sampling (2020)
  15. Uy, Wayne Isaac T.; Grigoriu, Mircea D.: Identification of input random field samples causing extreme responses (2020)
  16. Wei, Pengfei; Zhang, Xing; Beer, Michael: Adaptive experiment design for probabilistic integration (2020)
  17. Xiao, Ning-Cong; Yuan, Kai; Zhou, Chengning: Adaptive kriging-based efficient reliability method for structural systems with multiple failure modes and mixed variables (2020)
  18. Xiao, Ning-Cong; Zhan, Hongyou; Yuan, Kai: A new reliability method for small failure probability problems by combining the adaptive importance sampling and surrogate models (2020)
  19. Xu, Jun; Zhou, Lijuan: An adaptive trivariate dimension-reduction method for statistical moments assessment and reliability analysis (2020)
  20. Zafar, Tayyab; Zhang, Yanwei; Wang, Zhonglai: An efficient Kriging based method for time-dependent reliability based robust design optimization via evolutionary algorithm (2020)

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