P-AK-MCS: Parallel AK-MCS method for structural reliability analysis

In recent years, the active learning reliability method that combines the Kriging model and Monte Carlo simulation (AK-MCS) has emerged as a promising approach due to its computational efficiency and accuracy. However, the commonly used learning functions, such as the expected feasibility function (EFF), U function, H function, and expected risk function (ERF), can only select one training point at each iteration which is time-wasteful when parallel computing is available. Therefore, this paper proposes a parallel active learning Kriging strategy, namely P-AK-MCS, for structural reliability analysis. By introducing an influence function that reflects the impact of the added point on the original learning function, four parallel learning functions are constructed: pseudo-U (PU) function, pseudo-EFF (PEFF), pseudo-H (PH) function, and pseudo-ERF (PERF). These functions aim to identify multiple training points at each iteration without requiring additional functional evaluations. The effectiveness of the proposed method is validated using four examples. The results demonstrate that compared to the standard AK-MCS, the proposed P-AK-MCS significantly reduces the number of computation loops and greatly decreases computational costs. Moreover, the total number of functional evaluations required is similar to that of the standard AK-MCS and remains insensitive to the number of multiple training points.