Adaptive Kriging Adopting PSO with Hollow-Hypersphere space in structural reliability assessment

Reliability assessments using the adaptive Kriging method have gained significant attention in the past decade. The Kriging model is often paired with simulation-based reliability assessments (e.g., Monte Carlo simulation (MCS)), wherein the training sample size is a key efficiency indicator. This study proposes a novel Hollow-Hypersphere space (HHs) that is adaptively bounded by the outer and inner sphere radii at each iteration to drastically reduce the sampling pool region. Furthermore, Particle Swarm Optimization (PSO) is utilized with HHs to determine the best training sample for Kriging. In addition to the number of function evaluations, the HHs significantly reduce the number of Kriging evaluations in the PSO assessment and final reliability analysis. To demonstrate the efficiency of the proposed method, four different groups of reliability problems with various nonlinearities, dimensions, and limit state shapes were investigated and compared with other notable adaptive Kriging methods that also utilize the space manipulation approach. The results showed that the proposed method provided better efficiency in terms of function evaluation in most cases. Moreover, in terms of the Kriging evaluation, the proposed method exhibited superior efficiency in each case. The supporting source codes are available at https://github.com/johnthedy/KrigingPSO.