Abstract: To address the low efficiency of interval-extremum search and active-learning sample updating in random–interval hybrid reliability analysis, an active-learning Kriging-based hybrid reliability analysis method incorporating a conjugate projected gradient strategy, termed ALK-HRA-CPG, is proposed. An active set is identified according to the positions of the interval variables relative to their bounds, and a hybrid conjugate direction is constructed in the free-variable subspace. The interval response extrema are then obtained using a projected Armijo backtracking line search. The resulting interval-extremum points are used to construct the active-learning candidate set, from which new samples are selected using the U-learning function to iteratively update the Kriging model and estimate the failure-probability interval. Four examples involving a nonlinear function, a six-dimensional hybrid-uncertainty function, a roof-truss structure, and a rectangular-section cantilever beam were investigated. For all four examples, the relative errors in both failure-probability bounds were below 1%, and the proposed method required fewer performance-function evaluations than the four benchmark methods. A parametric computational fluid dynamics (CFD)-based hybrid cavitation reliability analysis platform is further developed for an aviation fuel centrifugal pump. The estimated upper and lower bounds of failure probability are 0.0467 and 0.00243, respectively, with relative errors of 1.268% and 4.741% compared with the Monte Carlo simulation (MCS) reference results. The numbers of parametric CFD model evaluations are reduced by 41.24% and 23.19% relative to the two benchmark methods. The results indicate that the proposed method achieves a favorable balance between the accuracy of failure-probability interval estimation and the computational efficiency of high-cost numerical models, making it suitable for random–interval hybrid reliability analysis of complex engineering systems.

Key words: random–interval hybrid reliability, Kriging model, conjugate projected gradient, active learning, aviation fuel centrifugal pump