An efficient trajectory sampling design method for elementary effect based global sensitivity analysis

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.

Keywords:

• Centroidal Voronoi tessellation sampling
• Elementary effects method
• Global sensitivity analysis
• Sobol’s sequence
• Trajectory cube
• Trajectory sampling design

Additional information

Funding

This work was supported by the National Natural Science Foundation of China (Grant No. NSFC 51775439), the National Science and Technology Major Project (2017-IV-0009-0046), and the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (Grant No. CX201934).