Over the past decades, surrogate model-aided reliability analysis approaches grounded in active learning have undergone extensive development. However, Gaussian process models like Kriging suffer from severe computational burdens when handling high-dimensional problems or large samples. Conversely, machine learning algorithms such as extreme learning machines exhibit high computational efficiency but lack variance output and stability, making them difficult to employ for adaptive active learning strategies. To address these limitations, this study proposes a population Monte Carlo method based on an adaptive closed neuron extreme learning machine. First, a closed neuron strategy uses a consistency metric to screen and retain neurons containing the most informative features. This preserves the fast analytical solution advantage of extreme learning machines while significantly improving the reconstruction accuracy and stability of the true limit state surface. Second, to overcome the lack of variance in the output, an ensemble model is constructed. By calculating predictive mean and standard deviation, a learning function is formulated for efficient adaptive sample enrichment. Finally, utilizing the adaptive importance sampling mechanism of the population Monte Carlo framework, the auxiliary density function is optimized to progressively shift the sampling center toward high contribution failure regions. Four engineering examples confirm that the proposed method achieves exceptional computational efficiency and high accuracy for complex reliability analysis involving extremely small failure probabilities.
Teng et al. (Thu,) studied this question.