Abstract

The elementary effects method is a screening global sensitivity measure to identify the few important inputs in a model which contains many inputs. In this work, a new advanced trajectory design method (NAT method) is developed to calculate the global sensitivity indices based on the elementary effects method. The conception of trajectory cube is proposed to define a trajectory, and then the central point of trajectory is defined. The quantitative relationship is constructed between the sample points in a trajectory and the central point in the trajectory. By taking exploration coverage and exploration accuracy into consideration, the length of the trajectory cube, i.e. exploration step length, is derived quantitatively. Before generating sampling points, the NAT method needs to generate central points of trajectories at first. In order to facilitate a better scanning of the input space, Sobol’s sequence and centroidal Voronoi tessellation (CVT) sampling are adopted. Next, sampling points of the trajectories are generated according to the relationship between sampling points and central points of trajectories. Afterward, the global sensitivity indices of the elementary effects can be estimated by the trajectories resulted from the NAT method. Compared with the advanced trajectory sampling design method proposed by Campolongo et al. in 2007, the NAT method decreases the computational cost and improves the accuracy in screening important inputs, and it is demonstrated by the numerical examples.

摘要

基本效应方法是一种筛选全局灵敏度度量，用于识别包含许多输入的模型中的少数重要输入。在这项工作中，开发了一种新的高级轨迹设计方法（NAT 方法）来计算基于基本效应方法的全局灵敏度指数。提出轨迹立方体的概念来定义轨迹，进而定义轨迹的中心点。在轨迹中的样本点与轨迹中的中心点之间建立定量关系。综合考虑勘探覆盖范围和勘探精度，定量推导出轨迹立方体的长度，即勘探步长。在生成采样点之前，NAT 方法需要首先生成轨迹的中心点。为了便于更好地扫描输入空间，采用了Sobol序列和质心Voronoi tessellation (CVT)采样。接着，根据采样点与轨迹中心点的关系生成轨迹的采样点。之后，可以通过 NAT 方法产生的轨迹来估计基本效应的全局灵敏度指数。与Campolongo等人提出的先进轨迹采样设计方法相比。2007年，NAT方法降低了计算成本并提高了筛选重要输入的准确性，并通过数值示例进行了证明。根据采样点与轨迹中心点的关系生成轨迹的采样点。之后，可以通过 NAT 方法产生的轨迹来估计基本效应的全局灵敏度指数。与Campolongo等人提出的先进轨迹采样设计方法相比。2007年，NAT方法降低了计算成本并提高了筛选重要输入的准确性，并通过数值示例进行了证明。根据采样点与轨迹中心点的关系生成轨迹的采样点。之后，可以通过 NAT 方法产生的轨迹来估计基本效应的全局灵敏度指数。与Campolongo等人提出的先进轨迹采样设计方法相比。2007年，NAT方法降低了计算成本并提高了筛选重要输入的准确性，并通过数值示例进行了证明。