Hybrid Uncertainty Sensitivity Analysis Based on the HSIC for High-Dimensional Responses with Aleatory--Epistemic Separation
For engineers and scientists dealing with high-dimensional system responses under mixed uncertainty types, this work provides a rigorous decomposition method that existing HSIC-based approaches lack.
The paper proposes a double-space tensor-product RKHS framework for global sensitivity analysis under hybrid aleatory and epistemic uncertainties, enabling orthogonal decomposition of dependence measures into pure aleatory, pure epistemic, and interaction effects for high-dimensional outputs. Numerical studies on multi-output functions and an aerodynamic problem demonstrate accuracy and scalability.
Quantifying the influence of hybrid aleatory and epistemic uncertainties on high-dimensional system responses remains a major challenge in global sensitivity analysis (GSA). Existing Hilbert--Schmidt Independence Criterion (HSIC)-based approaches are primarily restricted to single-output settings and lack a rigorous decomposition of heterogeneous uncertainty sources and their interactions. To address this limitation, a novel double-space tensor-product RKHS framework is proposed for sensitivity analysis under hybrid uncertainty. By constructing factorized kernels over both the latent input space and the multidimensional output space, a concurrent double Möbius inversion is derived to orthogonally decompose the global dependence measure into pure aleatory effects, pure epistemic effects, and their interaction contributions. The resulting dimension-wise sensitivity indices preserve the uncertainty attribution structure across all output dimensions. To satisfy the independence assumptions required by the decomposition, an auxiliary-variable representation based on the inverse probability integral transform is introduced, enabling the treatment of hierarchical uncertainties and Copula-induced correlations within a unified latent space. A fully vectorized single-loop implementation is further developed to avoid the computational burden of nested Monte Carlo simulation. Statistical significance and estimation uncertainty are quantified through permutation testing and Bootstrap confidence intervals. Numerical studies on a modified multi-output Ishigami function and an aerodynamic pressure-field problem demonstrate the accuracy, scalability, and practical applicability of the proposed framework.