This thesis introduces a new optimization algorithm for simulation-based design of systems with multi-modal, nonlinear, black box objective functions. The algorithm extends the recently introduced adaptive multi-modal optimization by incorporating surrogate modeling features similar to response surface methods (RSM). The resulting optimization algorithm has reduced computational intensity and is therefore well-suited for optimization of expensive black box objective functions. The algorithm relies on an adaptive and multi-resolution mesh to obtain an initial estimation of the objective function surface. Local surrogate models are then constructed to represent the objective function and to generate additional trial points in the vicinity of local minima discovered. The steps of mesh refinement and surrogate modeling continue until convergence criteria are met. An important property of this algorithm is that it produces progressively accurate surrogate models around the local minima; these models can be used for post-optimization studies such as sensitivity and tolerance analyses with minimal computational effort. This algorithm is suitable for optimal design of complex engineering systems and enhances the design cycle by enabling computationally affordable uncertainty analysis. The mathematical basis of the algorithm is explained in detail. The thesis also demonstrates the effectiveness of the algorithm using comparative optimization of several multi-modal objective functions. It also shows several practical applications of the algorithm in the design of complex power and power-electronic systems.

This thesis introduces a new optimization algorithm for simulation-based design of systems with multi-modal, nonlinear, black box objective functions. The algorithm extends the recently introduced adaptive multi-modal optimization by incorporating surrogate modeling features similar to response surface methods (RSM). The resulting optimization algorithm has reduced computational intensity and is therefore well-suited for optimization of expensive black box objective functions. The algorithm relies on an adaptive and multi-resolution mesh to obtain an initial estimation of the objective function surface. Local surrogate models are then constructed to represent the objective function and to generate additional trial points in the vicinity of local minima discovered. The steps of mesh refinement and surrogate modeling continue until convergence criteria are met. An important property of this algorithm is that it produces progressively accurate surrogate models around the local minima; these models can be used for post-optimization studies such as sensitivity and tolerance analyses with minimal computational effort. This algorithm is suitable for optimal design of complex engineering systems and enhances the design cycle by enabling computationally affordable uncertainty analysis. The mathematical basis of the algorithm is explained in detail. The thesis also demonstrates the effectiveness of the algorithm using comparative optimization of several multi-modal objective functions. It also shows several practical applications of the algorithm in the design of complex power and power-electronic systems.

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Design denotes the transformation of an identified need to its physical embodiment in a traditionally iterative approach of trial and error. Conceptual design plays a prominent role but an almost infinite number of possible solutions at the outset of design necessitates fast evaluations. The traditional practice of empirical databases loses adequacy for novel concepts and an ever increasing system complexity and resource scarsity mandate new approaches to adequately capture system characteristics. Contemporary concerns in atmospheric science and homeland security created an operational need for unconventional configurations. Unmanned long endurance flight at high altitudes offers a unique showcase for the exploration of new design spaces and the incidental deficit of conceptual modeling and simulation capabilities. The present research effort evolves around the development of an efficient and accurate optimization algorithm for high aspect ratio wings subject to natural frequency constraints. Foundational corner stones are beam dimensional reduction and modal perturbation redesign. Local and global analyses inherent to the former suggest corresponding levels of local and global optimization. The present approach departs from this suggestion. It introduces local level surrogate models to capacitate a methodology that consists of multi level analyses feeding into a single level optimization. The innovative heart of the new algorithm originates in small perturbation theory. A sequence of small perturbation solutions allows the optimizer to make incremental movements within the design space. It enables a directed search that is free of costly gradients. System matrices are decomposed based on a Timoshenko stiffness effect separation. The formulation of respective linear changes falls back on surrogate models that approximate cross sectional properties. Corresponding functional responses are readily available. Their direct use by the small perturbation based optimizer ensures constitutive laws and eliminates a previously necessary optimization at the local level. The great economy of the developed algorithm makes it suitable for the conceptual phase of aircraft design.