Metamodeling methods provide useful tools to replace expensive numerical simulations in engineering reliability analysis and design optimization. The radial basis functions (RBFs) and augmented RBFs can be used to create accurate metamodels; therefore they can be integrated with a reliability analysis method such as the Monte Carlo simulations (MCS). However the model accuracy of RBFs depends on the sample size, and the accuracy generally increases as the sample size increases. Since the optimal sample size used to create RBF metamodels is not known before the creation of the models, a sequential RBF metamodeling method was studied. In each iteration of reliability analysis, augmented RBFs were used to generate metamodels of a limit state or performance function, and the failure probability was calculated using MCS. Additional samples were generated in subsequent analysis iterations in order to improve the metamodel accuracy. Numerical examples from literature were solved, and the failure probabilities based on the RBF metamodels were found to have a good accuracy. In addition, only small numbers of iterations were required for the reliability analysis to converge. The proposed method based on sequential RBF metamodels is useful for probabilistic analysis of practical engineering systems.
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