An active learning reliability method with multiple kernel functions based on radial basis function

  • Lingjian Shi
  • Beibei SunEmail author
  • Dauda Sh. Ibrahim
Research Paper


Surrogate models combined with Monte Carlo simulation (MCS) are effective ways to address failure probability problems, which involve time-consuming computer codes, in structural reliability analysis. Recently, many active learning functions based on the Kriging model have been developed to conduct adaptive sequential sampling due to its predicted value and variance. However, effective methods for learning functions based on other surrogate models to address failure probability problems remain sparse. Hence, this paper presents a new adaptive sampling function that combines the radial basis function (RBF) approximate model with MCS to calculate the failure probability of structures. The new learning function is named the active RBF method with multiple kernel functions and Monte Carlo simulation (ARBFM-MCS). It uses several RBF kernel functions to estimate the local uncertainty of the predicted values based on interquartile range (IQR) to formulate the active learning function. This method can establish several surrogate models simultaneously for application to different problems. The stopping criterion of this method is that if one of the errors calculated by the various RBF models meets the demand, the learning process stops automatically. Furthermore, the method is also compared with the k-fold cross-validation approach based on a single RBF kernel function and some other approaches presented in the literature. Six numerical examples are considered to verify the accuracy and the efficiency of the proposed method. The results reveal that the multiple kernel function method is effective and has the same accuracy level as other methods. Moreover, for these examples, the method often calls the limit state function in fewer times to obtain accurate failure probabilities.


Radial basis function Active learning function Surrogate model Reliability analysis Monte Carlo simulation 



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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringSoutheast UniversityNanjingPeople’s Republic of China
  2. 2.Department of Mechatronics Engineering, Faculty of EngineeringBayero UniversityKanoNigeria

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