Dimension reduction in magnetohydrodynamics power generation models: Dimensional analysis and active subspaces

Statistical Analysis and Data Mining

Wildey, Timothy M.¹  Shadid, John N.²  Constantine, Paul G.³  Glaws, Andrew³ 

[1]Sandia National Laboratories Center for Computing Research Albuquerque New Mexico

[2]Sandia National Laboratories Center for Computing Research Albuquerque New Mexico . University of New Mexico Department of Mathematics and Statistics Albuquerque New Mexico

[3]University of Colorado Department of Computer Science Boulder Colorado

关键词: active subspaces;    dimension reduction;    dimensional analysis;    magnetohydrodynamics;    MHD generator;   

DOI  :  10.1002/sam.11355

学科分类：社会科学、人文和艺术（综合）

来源: John Wiley & Sons, Inc.

【 摘 要 】

Magnetohydrodynamics (MHD)—the study of electrically conducting fluids—can be harnessed to produce efficient, low-emissions power generation. Today, computational modeling assists engineers in studying candidate designs for such generators. However, these models are computationally expensive, so thoroughly studying the effects of the model's many input parameters on output predictions is typically infeasible. We study two approaches for reducing the input dimension of the models: (i) classical dimensional analysis based on the inputs' units and (ii) active subspaces, which reveal low-dimensional subspaces in the space of inputs that affect the outputs the most. We also review the mathematical connection between the two approaches that leads to consistent application. We study both the simplified Hartmann problem, which admits closed form expressions for the quantities of interest, and a large-scale computational model with adjoint capabilities that enable the derivative computations needed to estimate the active subspaces. The dimension reduction yields insights into the driving factors in the MHD power generation models, which may aid generator designers who employ high-fidelity computational models.

【 授权许可】

Unknown