Optimization of the Shape of a Hydrokinetic Turbine's Draft Tube and Hub Assembly Using Design-by-Morphing with Bayesian Optimization

Abstract

Finding the optimal design of a hydrodynamic or aerodynamic surface is often impossible due to the expense of evaluating the cost functions (say, with computational fluid dynamics) needed to determine the performances of the flows that the surface controls. In addition, inherent limitations of the design space itself due to imposed geometric constraints, conventional parameterization methods, and user bias can restrict all of the designs within a chosen design space regardless of whether traditional optimization methods or newer, data-driven design algorithms with machine learning are used to search the design space. We present a 2-pronged attack to address these difficulties: we propose (1) a methodology to create the design space using morphing that we call Design-by-Morphing (DbM); and (2) an optimization algorithm to search that space that uses a novel Bayesian Optimization (BO) strategy that we call Mixed variable, Multi-Objective Bayesian Optimization (MixMOBO). We apply this shape optimization strategy to maximize the power output of a hydrokinetic turbine. Applying these two strategies in tandem, we demonstrate that we can create a novel, geometrically-unconstrained, design space of a draft tube and hub shape and then optimize them simultaneously with a minimum number of cost function calls. Our framework is versatile and can be applied to the shape optimization of a variety of fluid problems.

Airfoil Optimization using Design-by-Morphing

“…generally requires two or more 'baseline shapes', usually chosen from pre-existing designs in the literature, for the design search space creation. In order to be 'morphed' together, these baseline shapes must be homeomorphic, which can be achieved by establishing a one-to-one correspondence between the shapes via some systematic shape collocation methods in either the functional [36] or geometric space [37,38]. The new shapes can then be generated by applying weights to the baseline shape collocation vectors and summing them together.…”

“…In this paper, we apply the Design-by-Morphing (DbM) parameterization technique, a novel design strategy that was introduced by Oh et al [36] and has been used in recent years for geometry optimization of different problems [36][37][38], to the airfoil optimization problem. Specifically, our DbM method 'morphs' the baseline shapes together to create new shapes and can interpolate as well as extrapolate the design space, which allows for both the highfidelity representation of shapes without the curse of dimensionality and radical improvements in the shapes without any geometric constraints [36,38]. Our paper makes the following scientific contributions:…”