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In this paper, we devoted the reliability analysis by integrating artificial neural network (ANN) and the first-order reliability method (FORM) in a single framework. The proposed framework is based on two main steps. In the first step, we approximate the state limit function by ANN trained by a two stage eagle strategy based on moth flame optimizer. Then the proposed method named ES-MFO is combined with FORM in the second step to calculate the reliability index as well as the probability of failure. In order to investigate the efficiencies of the proposed framework in reliability analysis, four classic examples, as well as a roof truss model are employed. The results are compared to four well-known heuristic algorithms. The results show that reliability analysis based on ANN-FORM-ES-MFO is significantly better than the current heuristic algorithms. Also, we have tested the new trainer ES-MFO using a selected function approximation datasets from the UCI machine-learning repository.
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