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Dimension reduction in magnetohydrodynamics power generation models: Dimensional analysis and active subspaces
Author(s) -
Glaws Andrew,
Constantine Paul G.,
Shadid John N.,
Wildey Timothy M.
Publication year - 2017
Publication title -
statistical analysis and data mining: the asa data science journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.381
H-Index - 33
eISSN - 1932-1872
pISSN - 1932-1864
DOI - 10.1002/sam.11355
Subject(s) - linear subspace , dimension (graph theory) , reduction (mathematics) , computer science , magnetohydrodynamics , dimensionality reduction , computation , mathematical optimization , algorithm , mathematics , artificial intelligence , physics , geometry , plasma , quantum mechanics , pure mathematics
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.