Metamodelagem da otimização de sistemas de engenharia na presença de incerteza

Abstract

This thesis explores the use of surrogate models to address uncertainties in the optimization of engineering systems, aiming to improve decision-making in complex problems and reduce computational costs. The research considers factors where external disturbances and uncertainties can impact the determination of optimal operating conditions. Generally, robust optimization seeks to minimize sensitivity to these variations, while reliability analysis focuses on preventing system failures, ensuring safe operation. This work employs Gaussian Process Regression, in a hybrid approach, to reduce the number of objective function evaluations in optimization under uncertainty, thereby improving efficiency without sacrificing solution quality. Furthermore, it integrates a stereographic projection method with an adaptive step size scheme for inverse reliability analysis. The effectiveness of the proposed methodology is demonstrated through its application to benchmark problems and structural engineering problems commonly used in the literature. Results demonstrate a reduction of at least 60% in the number of objective function evaluations for robustness and reliability-based optimization problems, using Pareto frontiers, compared to approaches without metamodels. Moreover, the proposed method exhibits robustness to parameter variations, maintaining solution quality within a maximum deviation of 1%.