Dimension reduction in magnetohydrodynamics power generation models: Dimensional analysis and active subspaces. (23rd August 2017)

• Record Type: Journal Article
• Authors: Glaws, Andrew; Constantine, Paul G.; Shadid, John N.; Wildey, Timothy M.
• Is Part Of: Statistical analysis and data mining. Volume 10:Number 5(2017)
• Page Start: 312
• Page End: 325
• Publication Date: 2017-08-23
• Subjects: active subspaces -- dimension reduction -- dimensional analysis -- magnetohydrodynamics -- MHD generator; Data mining -- Statistical methods -- Periodicals; 006.312
• DOI: 10.1002/sam.11355
• Languages: English
• ISSNs: 1932-1864

Abstract

Abstract : 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.