An active-learning neural network for structural reliability analysis

Structural reliability analysis faces persistent challenges due to the computational complexity and time-consuming nature of numerical simulations, particularly when applied to real-world engineering systems with high-dimensional input variables. Reducing the number of function evaluations while maintaining sufficient accuracy remains a critical objective in this field. Although many methods, such as Monte Carlo Simulation (MCS), provide a simple solution, their computational burden makes them unsuitable. To address this issue, methods based on active learning surrogate models have received widespread attention. These surrogate model methods iteratively approximate complex models using machine learning, selecting informative samples to improve the accuracy of the surrogate model. Among existing approaches, Kriging models are widely used because they can provide prediction variance for unsampled points. However, they struggle with high-dimensional input spaces. This paper proposes an Active-Learning Neural Network (ALNN) framework that combines the flexibility of back-propagation neural networks with the adaptive capabilities of active-learning strategies. The proposed method enables the estimation of prediction variance directly within the neural network structure, allowing for dynamic sample selection and efficient model refinement. The ALNN enables adaptive sampling and efficient model updates while handling high-dimensional and multi-output structural systems. The effectiveness and efficiency of the proposed method are validated through numerical examples, demonstrating improved adaptability, reduced computational costs, and enhanced accuracy in structural reliability analysis.

Keywords: Surrogate model, active-learning, learning function, backpropagation, activation function, probability of failure.