Hybrid Uncertainty Sensitivity Analysis Based on the HSIC for High-Dimensional Responses with Aleatory--Epistemic Separation

2026-06-11

AI Summary

Existing approaches struggle to effectively decompose the individual and interactive effects of aleatory and epistemic uncertainties in high-dimensional multi-output systems. This work proposes a dual-space tensor-product reproducing kernel Hilbert space (RKHS) framework that achieves an orthogonal decomposition of global dependencies through input–output factorized kernel functions. A concurrent dual Möbius inversion mechanism is introduced to preserve the structure of high-dimensional outputs, while inverse probability integral transforms combined with auxiliary variables enforce independence assumptions. Furthermore, a fully vectorized single-loop algorithm is developed to circumvent computationally expensive nested simulations. Numerical experiments on a modified multi-output Ishigami function and an aerodynamic pressure field problem demonstrate that the proposed method significantly enhances the accuracy, scalability, and computational efficiency of mixed uncertainty sensitivity analysis.

Abstract

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.

Problem

• hybrid uncertainty
• global sensitivity analysis
• high-dimensional responses
• aleatory-epistemic separation
• HSIC

Innovation

• HSIC
• hybrid uncertainty
• high-dimensional responses
• tensor-product RKHS
• Möbius inversion