Efficient uncertainty quantification in aerospace analysis and design

The main purpose of this study is to apply a computationally efficient uncertainty quantification approach, Non-Intrusive Polynomial Chaos (NIPC) based stochastic expansions, to robust aerospace analysis and design under mixed (aleatory and epistemic) uncertainties and demonstrate this technique on model problems and robust aerodynamic optimization. The proposed optimization approach utilizes stochastic response surfaces obtained with NIPC methods to approximate the objective function and the constraints in the optimization formulation. The objective function includes the stochastic measures which are minimized simultaneously to ensure the robustness of the final design to both aleatory and epistemic uncertainties. For model problems with mixed uncertainties, Quadrature-Based and Point-Collocation NIPC methods were used to create the response surfaces used in the optimization process. For the robust airfoil optimization under aleatory (Mach number) and epistemic (turbulence model) uncertainties, a combined Point-Collocation NIPC approach was utilized to create the response surfaces used as the surrogates in the optimization process. Two stochastic optimization formulations were studied: optimization under pure aleatory uncertainty and optimization under mixed uncertainty. As shown in this work for various problems, the NIPC method is computationally more efficient than Monte Carlo methods for moderate number of uncertain variables and can give highly accurate estimation of various metrics used in robust design optimization under mixed uncertainties. This study also introduces a new adaptive sampling approach to refine the Point-Collocation NIPC method for further improvement of the computational efficiency. Two numerical problems demonstrated that the adaptive approach can produce the same accuracy level of the response surface obtained with oversampling ratio of 2 using less function evaluations. --Abstract, page iii

Modeling and simulation of hydrokinetic composite turbine system

The utilization of kinetic energy from the river is promising as an attractive alternative to other available renewable energy resources. Hydrokinetic turbine systems are advantageous over traditional dam based hydropower systems due to zero-head and mobility. The objective of this study is to design and analyze hydrokinetic composite turbine system in operation. Fatigue study and structural optimization of composite turbine blades were conducted. System level performance of the composite hydrokinetic turbine was evaluated. A fully-coupled blade element momentum-finite element method algorithm has been developed to compute the stress response of the turbine blade subjected to hydrodynamic and buoyancy loadings during operation. Loadings on the blade were validated with commercial software simulation results. Reliability-based fatigue life of the designed composite blade was investigated. A particle swarm based structural optimization model was developed to optimize the weight and structural performance of laminated composite hydrokinetic turbine blades. The online iterative optimization process couples the three-dimensional comprehensive finite element model of the blade with real-time particle swarm optimization (PSO). The composite blade after optimization possesses much less weight and better load-carrying capability. Finally, the model developed has been extended to design and evaluate the performance of a three-blade horizontal axis hydrokinetic composite turbine system. Flow behavior around the blade and power/power efficiency of the system was characterized by simulation. Laboratory water tunnel testing was performed and simulation results were validated by experimental findings. The work performed provides a valuable procedure for the design and analysis of hydrokinetic composite turbine systems --Abstract, page iv

A multi-level upscaling and validation framework for uncertainty quantification in additively manufactured lattice structures

Multiscale modeling techniques are playing an ever increasing role in the effective design of complex engineering systems including aircraft, automobiles, etc. Lightweight cellular lattice structures (CLSs) gained interest recently since their complex structure, composed of a network of interconnected strut members, can be fabricated by additive manufacturing (AM). However, uncertainties in the fabricated strut members of CLSs are introduced by the layer-by-layer manufacturing process. These fine scale uncertainties influence the overall product performance resulting in inaccurate predictions of reality and increased complexity in simulations. In this research, a multi-level upscaling and validation framework is established that will enable accurate estimation of the performance of AM-fabricated CLSs under uncertainties. An improved stochastic upscaling method based on Polynomial Chaos Expansion (PCE) is employed to quantify and propagate the uncertainties across multiple levels efficiently. The upscaling method is integrated with a hierarchical validation approach to ensure that accurate predictions are made with the homogenized models. The u-pooling method is incorporated with the Kolmogorov-Smirnov test as the validation metric to efficiently use the limited experimental data during validation. The framework is applied to representative examples to demonstrate its efficacy in accurately characterizing the elastic properties of CLSs under uncertainties. The framework is also used to show its applicability in designing CLSs under uncertainties without the use of expensive simulations and optimization processes. The proposed framework is generalized to apply to any complex engineering structure that incorporates computationally intensive simulations and/or expensive experiments associated with fine scale uncertainties.Ph.D