In uncertainty quantification, evaluating sensitivity measures under specific conditions (i.e., conditional Sobol' indices) is essential for systems with parameterized responses, such as spatial fields or varying operating conditions. Traditional approaches often rely on point-wise modeling, which is computationally expensive and may lack consistency across the parameter space. This paper demonstrates that for a pre-trained global Polynomial Chaos Expansion (PCE) model, the analytical conditional Sobol' indices are inherently embedded within its basis functions. By leveraging the tensor-product property of PCE bases, we reformulate the global expansion into a set of analytical coefficient fields that depend on the conditioning variables. Based on the preservation of orthogonality under conditional probability measures, we derive closed-form expressions for conditional variances and Sobol' indices. This framework bypasses the need for repetitive modeling or additional sampling, transforming conditional sensitivity analysis into a purely algebraic post-processing step. Numerical benchmarks indicate that the proposed method ensures physical coherence and offers superior numerical robustness and computational efficiency compared to conventional point-wise approaches.

翻译：在不确定性量化中，评估特定条件下的灵敏度指标（即条件Sobol'指标）对于具有参数化响应的系统（如空间场或变化运行条件）至关重要。传统方法通常依赖逐点建模，计算成本高昂，且可能在参数空间内缺乏一致性。本文证明，对于预训练的全局多项式混沌展开（PCE）模型，解析的条件Sobol'指标已内嵌于其基函数中。通过利用PCE基的张量积性质，我们将全局展开重构为一系列依赖条件变量的解析系数场。基于条件概率测度下正交性的保持，我们推导出条件方差和Sobol'指标的闭式表达式。该框架无需重复建模或额外采样，将条件灵敏度分析转化为纯粹的代数后处理步骤。数值基准测试表明，与传统逐点方法相比，所提方法确保了物理一致性，并具有卓越的数值鲁棒性和计算效率。