UC Berkeley

Fluid flows are non-intuitive. Even with years of experience, non-intuitive behavior of fluids can mean the optimal geometry of fluid machinery is surprising or even extreme (consider, for instance, the bulbous bow of a ship). Finding the optimal design of a hydrodynamic or aerodynamic surfaces 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.

This dissertation presents two methodologies to address these difficulties: (1) Design-by-Morphing (DbM), a novel strategy for creating a design search space by morphing homeomorphic shapes to create a continuous and constraint-free design search space that can produce radical extrapolated shapes, something which is unique from existing design strategies; and (2) an optimization algorithm to search that space that uses a novel Mixed-variable, Multi-Objective Bayesian Optimization that we call MixMOBO, that can optimize such expensive, black-box problems with minimum number of functions calls. We apply these methodologues for optimization of several problems and present shape optimization of airfoils, draft-tubes for hydrokinetic turbines, and architected meta-materials. In all cases, we show significantly improved and radical designs.

Chapter One of this thesis focuses on the details of the MixMOBO algorithm, the first mixed-variable, multi-objective Bayesian optimization algorithm. MixMOBO outperforms existing algorithms for mixed-variable problems. It details HedgeMO strategy for hedging acquisition function portfolios for multi-objective problems. MixMOBO is then applied for optimization of strain energy density of an architected meta-material structure with categorical variables. From a design space of 8.5 billion possible candidates, our algorithm is able to optimize the design space with only 250 function evaluation and achieve 10^4 times improvement in strain energy density over existing structures [1,2]. Chapter Two focuses on applying MixMOBO for design of Cauchy-Symmetric architected meta-material structures. With only 69 function calls, MixMOBO is able to find such a structure from a design space of 10^7 possible structures. Chapter Three demonstrates the use of Design-by-Morphing for optimization of airfoils. We show that with just 25 baseline shapes, we are able to reproduce the UIUC airfoil database with high fidelity and optimize this space to create aerodynamically superior and safer airfoils [3]. Chapter Four focuses on application of design of a draft tube for a hydrokinetic turbine to maximize pressure recovery at the exit of the turbine [4].