Active learning of score function based on Gaussian processes

The score function quantifies system performance by normalizing it against predefined thresholds and objectives, serving as a critical tool for performance evaluation. However, accurately learning this function typically demands extensive training data, which may be scarce due to the high experimental costs associated with complex systems. To mitigate this challenge, a Gaussian process-based active learning framework is proposed, which jointly optimizes the acquisition function and learning strategy. This approach facilitates the precise construction of the score function while minimizing the required sample size. Simulation results validate the method's efficacy in learning the score function and highlight its applicability in structural reliability analysis.