Nested adaptive Kriging-based reliability analysis and computational resource allocation for complex systems

Efficient reliability analysis of complex engineering systems faces significant challenges due to the integration of multiple subproblems, multidisciplinary coupling, high-dimensional characteristics, and resource incompatibility. These systems are often decomposed into multiple cascading subsystems, which enables concurrent analysis to manage this complexity. Surrogate-based techniques are widely utilized to alleviate the computational burden associated with time-consuming simulations. This study proposes a nested adaptive Kriging-based method for the reliability analysis of complex systems by integrating system decomposition with adaptive surrogate-based methods. The proposed method operates within a multilayer framework and proceeds in two stages, namely, a sequential updating stage and a resource allocation stage. In the first stage, an efficient nested reliability-oriented acquisition function is developed to guide model updating, and its closed-form expression is derived. In the second stage, a cost-effectiveness strategy that accounts for both simulation costs and modeling costs is introduced to determine which model combinations should be updated at each iteration. Finally, the proposed method is validated to be superior to the benchmark method and strategy through two mathematical examples and two practical applications.