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.

翻译：在全局灵敏度分析（GSA）中，量化混合偶然不确定性和认知不确定性对高维系统响应的影响仍是一项重大挑战。现有的基于希尔伯特-施密特独立性准则（HSIC）的方法主要局限于单输出场景，且缺乏对异质不确定性源及其相互作用进行严格分解的能力。为克服这一局限，本文提出了一种新颖的双空间张量积再生核希尔伯特空间（RKHS）框架，用于混合不确定性下的灵敏度分析。通过在隐式输入空间和多维输出空间上构造因子化核，推导出了同步双Möbius变换，从而将全局依赖度量正交分解为纯偶然效应、纯认知效应及其交互贡献。由此得到的维度级灵敏度指标保留了所有输出维度上的不确定性归因结构。为满足分解所需的独立性假设，引入了基于逆概率积分变换的辅助变量表示方法，从而能够在统一的隐式空间中处理层次化不确定性和Copula诱导的相关性。进一步开发了全向量化的单循环实现方案，以避免嵌套蒙特卡洛模拟带来的计算负担。通过置换检验和Bootstrap置信区间量化了统计显著性和估计不确定性。基于修正的多输出Ishigami函数和空气动力学压力场问题的数值研究，验证了所提框架的准确性、可扩展性和实际应用性。