A collaborative adaptive Kriging-based algorithm for the reliability analysis of nested systems

Complex engineering systems that involve multiple disciplines or scales are often decomposed into multiple subsystems in a nested or hierarchical manner to enhance the analysis efficiency. However, uncertainties inherent in input parameters will propagate with hierarchy, and severely threaten the reliability of engineering systems. Adaptive surrogate modeling technique is a potent tool to alleviate the computational burden of reliability analysis, especially involving time-consuming computer experiments. Conventional black-box adaptive surrogate modeling framework did not incorporate nested characteristic, which is inefficient for the reliability analysis of complex systems with nested or hierarchical characteristics. This paper develops a collaborative adaptive Kriging-based algorithm for the reliability analysis of nested systems. First, we propose a nested U-function to propel the adaptive updating of underlying Kriging models and derive its approximate closed form based on a defined most probable misclassification point. Then, an accuracy enhancement stage is devised to compensate for the inaccuracies of first-order approximation in early iterations. A parallel radius-based importance sampling technique is presented to mitigate the computational effort at multiple candidates. Finally, an index considering the reduction of model uncertainty is exploited to quantify the contribution of individual Kriging model and select the to-be-refined Kriging model in one iteration. Through numerical examples and case studies, the superiority of the proposed methodology is comprehensively illustrated compared with other benchmark methods.