VC-HSMM: Vine Copula-based hybrid surrogate modeling method for multi-failure correlation reliability analyses

In multi-objective reliability analysis, hybrid surrogate modeling method exhibits superior predictive performance and generalization ability compared to traditional surrogate models. However, conventional hybrid models primarily focus on global errors, which may lead to inaccuracies in regions with strong local variations. To address this issue, this study proposes a novel hybrid surrogate modeling approach based on local and global measures. Specifically, the global weight allocation is achieved by calculating the prediction sum of squares for individual surrogate models. For the local weight allocation, it is determined by considering the cross-validation errors of both interpolation and regression models at the prediction points. This enables the dynamic adjustment of weight allocation among individual models. Moreover, traditional multi-failure reliability analysis often assumes independent failure modes, whereas practical scenarios involve varying degrees of correlation, leading to deviations in reliability estimation. To account for these dependencies, the Vine Copula theory is introduced. By decomposing high-dimensional joint distributions into a series of Pair Copulas, the proposed method more flexibly captures the intricate dependencies among failure modes. The effectiveness of this approach is validated through the approximation and probabilistic analysis of multi-response nonlinear function, and the multi-objective reliability evaluation of turbine blisk in an aero-engine.