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This work proposes a new method for using reduced order models in lieu of high fidelity analysis during the sensitivity analysis step of gradient based design optimization. The method offers a reduction in the computational cost of finite difference based sensitivity analysis in that context. The method relies on interpolating reduced order models which are based on proper orthogonal decomposition. The interpolation process is performed using radial basis functions and Grassmann manifold projection. It does not require additional high fidelity analyses to interpolate a reduced order model for new points in the design space. The interpolated models are used specifically for points in the finite difference stencil during sensitivity analysis. The proposed method is applied to an airfoil shape optimization (ASO) problem and a transport wing optimization (TWO) problem. The errors associated with the reduced order models themselves as well as the gradients calculated from them are evaluated. The effects of the method on the overall optimization path, computation times, and function counts are also examined. The ASO results indicate that the proposed scheme is a viable method for reducing the computational cost of these optimizations. They also indicate that the adaptive step is an effective method of improving interpolated gradient accuracy. The TWO results indicate that the interpolation accuracy can have a strong impact on optimization search direction.

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An effective approach to determine optimum welding process parameters is implementation of advanced computer aided engineering (CAE) tool that integrates efficient optimization techniques and numerical welding simulation. In this thesis, an automated computational methodology to determine optimum arc welding process parameters is proposed. It is a coupled Genetic Algorithms (GA) and Finite Element (FE) based optimization method where GA directly utilizes output responses of FE based welding simulations for iterative optimization. Effectiveness of the method has been demonstrated by predicting optimum parameters of a lap joint specimen of two thin steel plates and automotive structure of nonlinear welding path for minimum distortion. Three dimensional FE models have been developed to simulate the arc welding process and subsequently, the models have been used by GA as the evaluation model for optimization. The optimization results show that such a CAE based methodology can contribute to facilitate the product design and development.

Design of thermoelastic structures can be highly counterintuitive due to design-dependent loading and impact of geometric nonlinearity on the structural response. Thermal loading generates in-plane stresses in a restrained panel, but the presence of geometric nonlinearity creates an extension-bending coupling that results in considerable transverse displacement and variation in stiffness characteristics, and these affects are enhanced in post-bucking regimes. Herein a methodology for structural sizing of thermally stressed post-buckled stiffened panels is proposed and applied for optimization of the blade and hat stiffeners using a gradient-based optimizer. The stiffened panels are subjected to uniform thermal loading and optimized for minimum mass while satisfying stress and stability constraints. The stress constraints are used to avoid yielding of the structure, whereas the stability constraints are used to ensure static stability. Corrugation of the hat stiffeners is also studied through variation of its magnitude and position. A continuation solver has been validated to tackle the highly nonlinear nature of the thermoelastic problem, and formulations for the stability constraints have been derived and imposed to satisfy the static stability of the structure. The study confirms that geometric nonlinearity is an important aspect of sizing optimization and is needed for an accurate modeling of the structural behavior. The results also show that modeling of geometric nonlinearity adds extra complexity to the thermoelastic problem and requires a path-tracking solver. Finally, this work supports that corrugation enhances the stability features of the panel but requires a blending function to reduce stresses at the panel boundaries.

Recent interest surrounding large scale satellite constellations has increased analysis efforts to create the most efficient designs. Multiple studies have successfully optimized constellation patterns using equations of motion propagation methods and genetic algorithms to arrive at optimal solutions. However, these approaches are computationally expensive for large scale constellations, making them impractical for quick iterative design analysis. Therefore, a minimalist algorithm and efficient computational method could be used to improve solution times. This thesis will provide a tool for single target constellation optimization using spherical trigonometry propagation, and an evolutionary genetic algorithm based on a multi-objective optimization function. Each constellation will be evaluated on a normalized fitness scale to determine optimization. The performance objective functions are based on average coverage time, average revisits, and a minimized number of satellites. To adhere to a wider audience, this design tool was written using traditional Matlab, and does not require any additional toolboxes. To create an efficient design tool, spherical trigonometry propagation will be utilized to evaluate constellations for both coverage time and revisits over a single target. This approach was chosen to avoid solving complex ordinary differential equations for each satellite over a long period of time. By converting the satellite and planetary target into vectors of latitude and longitude in a common celestial sphere (i.e. ECI), the angle can be calculated between each set of vectors in three-dimensional space. A comparison of angle against a maximum view angle, , controlled by the elevation angle of the target and the satellite’s altitude, will determine coverage time and number of revisits during a single orbital period. Traditional constellations are defined by an altitude (a), inclination (I), and Walker Delta Pattern notation: T/P/F. Where T represents the number of satellites, P is the number of orbital planes, and F indirectly defines the number of adjacent planes with satellite offsets. Assuming circular orbits, these five parameters outline any possible constellation design. The optimization algorithm will use these parameters as evolutionary traits to iterate through the solutions space. This process will pass down the best traits from one generation to the next, slowly evolving and converging the population towards an optimal solution. Utilizing tournament style selection, multi-parent recombination, and mutation techniques, each generation of children will improve on the last by evaluating the three performance objectives listed. The evolutionary algorithm will iterate through 100 generations (G) with a population (n) of 100. The results of this study explore optimal constellation designs for seven targets evenly spaced from 0° to 90° latitude on Earth, Mars and Jupiter. Each test case reports the top ten constellations found based on optimal fitness. Scatterplots of the constellation design solution space and the multi-objective fitness function breakdown are provided to showcase convergence of the evolutionary genetic algorithm. The results highlight the ratio between constellation altitude and planetary radius as the most influential aspects for achieving optimal constellations due to the increased field of view ratio achievable on smaller planetary bodies. The multi-objective fitness function however, influences constellation design the most because it is the main optimization driver. All future constellation optimization problems should critically determine the best multi-objective fitness function needed for a specific study or mission.

A significant challenge in the design of multidisciplinary systems (e.g., airplanes, robots, cell phones) is to predict the effects of design decisions at the time these decisions are being made early in the design process. These predictions are used to choose among design options and to validate design decisions. System behavioral models, which predict a system's response to stimulus, provide an analytical method for evaluating a system's behavior. Because multidisciplinary systems contain many different types of components that have diverse interactions, system behavioral models are difficult to develop early in system design and are challenging to maintain as designs are refined. This research develops methods to create, verify, and maintain multidisciplinary system models developed from models that are already part of system design. First, this research introduces a system model formulation that enables virtually any existing engineering model to become part of a large, trusted population of component models from which system behavioral models can be developed. Second, it creates a new algorithm to efficiently quantify the feasible domain over which the system model can be used. Finally, it quantifies system model accuracy early in system design before system measurements are available so that system models can be used to validate system design decisions. The results of this research are enabling system designers to evaluate the effects of design decisions early in system design, improving the predictability of the system design process, and enabling exploration of system designs that differ greatly from existing solutions.

The development in power conversion technology is in constant demand of high power efficiency and high power density. The DC-DC power conversion is an indispensable stage for numerous power supplies and energy related applications. Particularly, in PV micro-inverters and front-end converter of power supplies, great challenges are imposed on the power performances of the DC-DC converter stage, which not only require high efficiency and density but also the capability to regulate a wide variation range of input voltage and load conditions. The resonant DC-DC converters are good candidates to meet these challenges with the advantages of achieving soft switching and low EMI. Among various resonant converter topologies, the LLC converter is very attractive for its wide gain range and providing ZVS for switches from full load to zero load condition. The operation of the LLC converter is complicated due to its multiple resonant stage mechanism. A literature review of different analysis methods are presented, and it shows that the study on the LLC is still incomplete. Therefore, an operation mode analysis method is proposed, which divides the operation into six major modes based on the occurrence of resonant stages. The resonant currents, voltages and the DC gain characteristics for each mode is investigated. To obtain a thorough view of the converter behavior, the boundaries of every mode are studied, and mode distribution regarding the gain, load and frequency is presented and discussed. As this operation mode model is a precise model, an experimental prototype is designed and built to demonstrate its accuracy in operation waveforms and gain prediction. iv Since most of the LLC modes have no closed-form solutions, simplification is necessary in order to utilize this mode model in practical design. Some prior approximation methods for converter’s gain characteristics are discussed. Instead of getting an entire gain-vs.-frequency curve, we focus on peak gains, which is an important design parameters indicating the LLC’s operating limit of input voltage and switching frequency. A numerical peak gain approximation method is developed, which provide a direct way to calculate the peak gain and its corresponding load and frequency condition. The approximated results are compared with experiments and simulations, and are proved to be accurate. In addition, as PO mode is the most favorable operation mode of the LLC, its operation region is investigated and an approximation approach is developed to determine its boundary. The design optimization of the LLC has always been a difficult problem as there are many parameters affecting the design and it lacks clear design guidance in selecting the optimal resonant tank parameters. Based on the operation mode model, three optimization methods are proposed according to the design scenarios. These methods focus on minimize the conduction loss of resonant tank while maintaining the required voltage gain level, and the approximations of peak gains and PO mode boundary can be applied here to facilitate the design. A design example is presented using one of the proposed optimization methods. As a comparison, the L-C component values are reselected and tested for the same design specifications. The experiments show that the optimal design has better efficiency performance. Finally, a generalized approach for resonant converter analysis is developed. It can be implemented by computer programs or numerical analysis tools to derive the operation waveforms and DC characteristics of resonant converters

To achieve a high level of performance and efficiency, contemporary aerospace systems must become increasingly complex. While complexity management traditionally focuses on a product’s components and their interconnectedness, organizational representation in complexity analysis is just as essential. This thesis addresses this organizational aspect of complexity through an Organizational Complexity Metric (OCM) to aid complexity management. The OCM augments Sinha’s structural complexity metric for product architectures into a metric that can be applied to organizations. Utilizing nested numerical design structure matrices (DSMs), a compact visual representation of organizational complexity was developed. Within the nested numerical DSM are existing organizational datasets used to quantify the complexity of both organizational system components and their interfaces. The OCM was applied to a hypothetical system example, as well as an existing aerospace organizational architecture. Through the development of the OCM, this thesis assumed that each dataset was collected in a statistically sufficient manner and has a reasonable correlation to system complexity. This thesis recognizes the lack of complete human representation and aims to provide a platform for expansion. Before a true organizational complexity metric can be applied to real systems, additional human considerations should be considered. These limitations differ from organization to organization and should be taken into consideration before implementation into a working system. The visualization of organizational complexity uses a color gradient to show the relative complexity density of different parts of the organization.