Use of Slotted Waveguide Antenna Stiffened Structures (SWASS) in future commercial and military aircraft calls for the development of an airworthiness certification procedure. The first step of this procedure is to provide a computationally low-cost method for modeling waveguide antenna arrays on the scale of an aircraft skin panel using a multi-fidelity model. Weather detection radar for the Northrop Grumman X-47 unmanned air system is considered as a case study. COMSOL Multiphysics is used for creating high-fidelity waveguide models that are imported into the MATLAB Phased Array Toolbox for large-scale array calculations using a superposition method. Verification test cases show that this method is viable for relatively accurate modeling of large SWASS arrays with low computational effort. Additionally, realistic material properties for carbon fiber reinforced plastic (CFRP) are used to create a more accurate model. Optimization is performed on a 12-slot CFRP waveguide to determine the waveguide dimensions for the maximum far-field gain and separately for the maximum critical buckling load. Using the two separate optima as utopia points, a multi-objective optimization for the peak far-field gain and critical buckling load is performed, to obtain a balance between EM performance and structural strength. This optimized waveguide is then used to create a SWASS array of approximately the same size as an aircraft wing panel using the multi-fidelity modeling method that is proposed. This model is compared to a typical conventional weather radar system, and found to be well above the minimum mission requirements. / Master of Science

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<p>Practical design problems in engineering and science involve the evaluation of expensive black-box functions, the optimization of multiple—often conflicting—targets, and the integration of data generated by multiple sources of information, e.g., numerical models with different levels of fidelity. If not properly handled, the complexity of these design problems can lead to lengthy and costly development cycles. In the last years, Bayesian optimization has emerged as a powerful alternative to solve optimization problems that involve the evaluation of expensive black-box functions. Bayesian optimization has two main components: a probabilistic surrogate model of the black-box function and an acquisition function that drives the optimization. Its ability to find high-performance designs within a limited number of function evaluations has attracted the attention of many fields including the engineering design community. The practical relevance of strategies with the ability to fuse information emerging from different sources and the need to optimize multiple targets has motivated the development of multi-fidelity modeling techniques and multi-objective Bayesian optimization methods. A key component in the vast majority of these methods is the Gaussian process (GP) due to its flexibility and mathematical properties.</p> <p><br></p> <p>The objective of this dissertation is to develop new approaches in the areas of multi-fidelity modeling and multi-objective Bayesian optimization. To achieve this goal, this study explores the use of linear and non-linear compositions of GPs to build probabilistic models for Bayesian optimization. Additionally, motivated by the rationale behind well-established multi-objective methods, this study presents a novel acquisition function to solve multi-objective optimization problems in a Bayesian framework. This dissertation presents four contributions. First, the auto-regressive model, one of the most prominent multi-fidelity models in engineering design, is extended to include informative mean functions that capture prior knowledge about the global trend of the sources. This additional information enhances the predictive capabilities of the surrogate. Second, the non-linear auto-regressive Gaussian process (NARGP) model, a non-linear multi-fidelity model, is integrated into a multi-objective Bayesian optimization framework. The NARGP model offers the possibility to leverage sources that present non-linear cross-correlations to enhance the performance of the optimization process. Third, GP classifiers, which employ non-linear compositions of GPs, and conditional probabilities are combined to solve multi-objective problems. Finally, a new multi-objective acquisition function is presented. This function employs two terms: a distance-based metric—the expected Pareto distance change—that captures the optimality of a given design, and a diversity index that prevents the evaluation of non-informative designs. The proposed acquisition function generates informative landscapes that produce Pareto front approximations that are both broad and diverse.</p>