An MDP-Driven Learning Function Selection Strategy for Kriging-Based Structural Reliability Analysis

Active learning Kriging is widely used in structural reliability analysis for its computational efficiency and accuracy. While numerous learning functions exist to accelerate Kriging convergence, their performance varies across problems, with no single function universally dominating. In this study, a learning function selection strategy based on the Markov Decision Process (MDP) is proposed. Specifically, the selection of learning functions is modeled as an MDP, with actions corresponding to several representative learning functions, thereby avoiding reliance on a fixed sample selection preferences. An accuracy measure for failure probability is developed and designed as the MDP reward, shifting the focus of sample selection from the state of single samples to overall model improvement. Guided by the Bellman optimality principle, the proposed method selects the learning function that maximizes the expected long-term gain in model accuracy at each iteration, thereby achieving a theoretically optimal selection strategy. Several numerical and engineering examples are adopted to validate the effectiveness of the proposed method. The results show that it effectively overcomes the limitation of blindly selecting learning functions and can even outperform the optimal learning function in the action space.