论文标题
关于分布参数的概率灵敏度分析的一般框架
A general framework for probabilistic sensitivity analysis with respect to distribution parameters
论文作者
论文摘要
概率敏感性分析确定了有影响力的不确定输入以指导决策。我们提出了一个关于输入分布参数的一般灵敏度框架，该框架统一了广泛的灵敏度度量，包括信息理论指标，例如Fisher信息。该框架是通过受约束的最大化分析得出的，并将灵敏度分析重新构成特征值问题。利用蒙特卡洛类型采样，然后求解特征值方程，只有两个主要步骤可以实现敏感性框架。然后，所得的特征向量为输入参数的同时变化提供了方向，并指导焦点以最大程度地扰动不确定性。它不仅在概念上很简单，而且数值示例表明，所提出的框架还提供了新的灵敏度见解，例如多个相关不确定性指标的综合灵敏度，具有熵约束的强大灵敏度分析以及确定性敏感性的近似。从简单的悬臂梁到离岸海洋立管的三个不同的例子，用于证明所提出的灵敏度框架在应用机械问题上的潜在应用。
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.
