关于分布参数的概率敏感性分析的一般框架
A general framework for probabilistic sensitivity analysis with respect to distribution parameters
摘要：
概率敏感性分析识别出有影响的不确定性输入，指导决策。我们提出了一个通用的敏感性框架，相对于输入分布参数，统一了广泛的敏感性措施，包括信息理论指标，如费舍尔信息。通过约束最大化和敏感性分析的框架推导解析转化为特征值问题。利用似然比/得分函数方法、蒙特卡罗型采样以及随后求解特征值方程来实现灵敏度框架只有两个主要步骤。由此产生的特征向量，然后提供的方向，同时变化的输入参数和指导的重点扰动不确定性最大。它不仅是概念上简单，但数值例子表明，所提出的框架还提供了新的灵敏度的见解，如多个相关的不确定性度量的组合灵敏度，鲁棒的敏感性分析与熵约束，确定性灵敏度的近似。三个不同的例子，从一个简单的悬臂梁的海上海洋立管，被用来证明所提出的敏感性框架的应用力学问题的潜在应用。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
