Reliability assessment of complex structures using simulation methods is time-consuming. Thus, surrogate models are usually employed to reduce computational cost. AK-MCS is a surrogate-based Active learning method combining Kriging and Monte-Carlo Simulation for structural reliability analysis. This paper proposes three modifications of the AK-MCS method to reduce the number of calls to the performance function. The first modification is related to the definition of an initial Design of Experiments (DoE). In the original AK-MCS method, an initial DoE is created by a random selection of samples among the Monte Carlo population. Therefore, samples in the failure region have fewer chances to be selected, because a small number of samples are usually located in the failure region compared to the safe region. The proposed method in this paper is based on a uniform selection of samples in the predefined domain, so more samples may be selected from the failure region. Another important parameter in the AK-MCS method is the size of the initial DoE. The algorithm may not predict the exact limit state surface with an insufficient number of initial samples. Thus, the second modification of the AK-MCS method is proposed to overcome this problem. The third modification is relevant to the type of regression trend in the AK-MCS method. The original AK-MCS method uses an ordinary Kriging model, so the regression part of Kriging model is an unknown constant value. In this paper, the effect of regression trend in the AK-MCS method is investigated for a benchmark problem, and it is shown that the appropriate choice of regression type could reduce the number of calls to the performance function. A stepwise approach is also presented to select a suitable trend of the Kriging model. The numerical results show the effectiveness of the proposed modifications.
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