Simulation-based design of multi-modal systems

Abstract

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.