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. Chen, Hanshu; Meng, Zeng; Zhou, Huanlin: A hybrid framework of efficient multi-objective optimization of stiffened shells with imperfection (2020)
  2. Ghalehnovi, Mansour; Rashki, Mohsen; Ameryan, Ala: First order control variates algorithm for reliability analysis of engineering structures (2020)
  3. 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)
  4. Ling, Chunyan; Lu, Zhenzhou: Adaptive Kriging coupled with importance sampling strategies for time-variant hybrid reliability analysis (2020)
  5. Liu, Baoshou; Jiang, Chao; Li, Guangyao; Huang, Xiaodong: Topology optimization of structures considering local material uncertainties in additive manufacturing (2020)
  6. Uy, Wayne Isaac T.; Grigoriu, Mircea D.: Identification of input random field samples causing extreme responses (2020)
  7. Wei, Pengfei; Zhang, Xing; Beer, Michael: Adaptive experiment design for probabilistic integration (2020)
  8. Xiao, Ning-Cong; Yuan, Kai; Zhou, Chengning: Adaptive kriging-based efficient reliability method for structural systems with multiple failure modes and mixed variables (2020)
  9. Xu, Jun; Zhou, Lijuan: An adaptive trivariate dimension-reduction method for statistical moments assessment and reliability analysis (2020)
  10. Zhang, Mengchuang; Yao, Qin; Sun, Shouyi; Li, Lei; Hou, Xu: An efficient strategy for reliability-based multidisciplinary design optimization of twin-web disk with non-probabilistic model (2020)
  11. Hristov, P. O.; DiazDelaO, F. A.; Farooq, U.; Kubiak, K. J.: Adaptive Gaussian process emulators for efficient reliability analysis (2019)
  12. Marque-Pucheu, Sophie; Perrin, Guillaume; Garnier, Josselin: Efficient sequential experimental design for surrogate modeling of nested codes (2019)
  13. MiarNaeimi, Farid; Azizyan, Gholamreza; Rashki, Mohsen: Reliability sensitivity analysis method based on subset simulation hybrid techniques (2019)
  14. Perrin, G.; Defaux, G.: Efficient evaluation of reliability-oriented sensitivity indices (2019)
  15. Qian, Hua-Ming; Huang, Hong-Zhong; Li, Yan-Feng: A novel single-loop procedure for time-variant reliability analysis based on Kriging model (2019)
  16. Sauder, Thomas; Marelli, Stefano; Sørensen, Asgeir J.: Probabilistic robust design of control systems for high-fidelity cyber-physical testing (2019)
  17. Tong, Cao; Wang, Jian; Liu, Jinguo: A Kriging-based active learning algorithm for mechanical reliability analysis with time-consuming and nonlinear response (2019)
  18. Wang, Fan; Li, Heng: A practical non-parametric copula algorithm for system reliability with correlations (2019)
  19. Zhang, Jinhao; Xiao, Mi; Gao, Liang: A new method for reliability analysis of structures with mixed random and convex variables (2019)
  20. Zhang, Jinhao; Xiao, Mi; Gao, Liang; Chu, Sheng: A combined projection-outline-based active learning Kriging and adaptive importance sampling method for hybrid reliability analysis with small failure probabilities (2019)

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