Probabilistic sensitivity analysis identifies the influential uncertain input to guide decision-making. We propose a general sensitivity framework with respect to the input distribution parameters that unifies a wide range of sensitivity measures, including information theoretical metrics such as the Fisher information. The framework is derived analytically via a constrained maximization and the sensitivity analysis is reformulated into an eigenvalue problem. There are only two main steps to implement the sensitivity framework utilising the likelihood ratio/score function method, a Monte Carlo type sampling followed by solving an eigenvalue equation. The resulting eigenvectors then provide the directions for simultaneous variations of the input parameters and guide the focus to perturb uncertainty the most. Not only is it conceptually simple, but numerical examples demonstrate that the proposed framework also provides new sensitivity insights, such as the combined sensitivity of multiple correlated uncertainty metrics, robust sensitivity analysis with an entropic constraint, and approximation of deterministic sensitivities. Three different examples, ranging from a simple cantilever beam to an offshore marine riser, are used to demonstrate the potential applications of the proposed sensitivity framework to applied mechanics problems.

翻译：概率敏感性分析旨在识别影响决策的关键不确定性输入。我们提出了一种关于输入分布参数的一般敏感性分析框架，该框架统一了多种敏感性度量，包括Fisher信息等信息论指标。该框架通过约束最大化分析推导得出，并将敏感性分析问题转化为特征值问题。利用似然比/得分函数方法实施该敏感性框架仅需两个主要步骤：首先进行蒙特卡罗型采样，随后求解特征值方程。所得特征向量提供了输入参数同步变化的方向，并引导我们聚焦于扰动不确定性最剧烈的部分。该框架不仅概念简单，数值实例也表明，它能提供新的敏感性见解，例如多个相关不确定性度量的联合敏感性、基于熵约束的鲁棒敏感性分析以及确定性敏感性的近似计算。我们通过从简支梁到海洋立管等三个不同实例，展示了该敏感性框架在应用力学问题中的潜在应用。