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

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.

Optimization by moving ridge functions: derivative-free optimization for computationally intensive functions

“…The majority of research into ridge function approximations has assumed that the function of interest varies along a global subspace U (Glaws et al 2017;Wong et al 2019;Gross, Seshadri, and Parks 2020). Unless the function is an exact ridge function, i.e.…”

1 Basic ideas and tools for projection-based model reduction of parametric partial differential equations

“…The active subspaces have been successfully employed in many engineering fields. We cite, among others, applications in magnetohydrodynamics power generation modeling in [50], in naval engineering for the computation of the total drag resistance with both geometrical and physical parameters in [101,38], and in constrained shape optimization [66] using the concept of shared active subspaces in [100]. There are also applications to turbomachinery in [7], to uncertainty quantification in the numerical simulation of a scramjet in [34], and to the acceleration of Markov chain Monte Carlo in [35].…”

Optimisation with Intrinsic Dimension Reduction: A Ridge Informed Trust-Region Method

“…Fortunately, many physical problems naturally exhibit such low-dimensional behaviour: 2 for instance, turbomachinery design, 3 wing design, 4 and magnetohydrodynamic power generation. 5 For problems with such low-dimensional structure, ridge function approximations have increasingly been used in reduced order modelling, 6,7 integration, 5 sensitivity studies, 3,8 and even data visualisation in a virtual reality environment. 9 However, their use in optimisation has been rather limited.…”