DIMENSIONALITY REDUCTION IN DESIGN OPTIMIZATION

Abstract

The engineering design of complex free-form surfaces such as turbine blades and ship hulls presents significant challenges due to the intricate geometries involved. This study investigates the application of dimensionality reduction techniques to optimize the design process of such surfaces, with a focus on enhancing computational efficiency and maintaining high design quality. We propose a novel approach that integrates geometric moments with Karhunen-Loeve Expansion (KLE) to form a reduced-dimensional design space that retains essential shape characteristics while reducing computational demands. Our methodology leverages the collection of geometric moments to enrich the latent space representation, which is crucial for capturing the physical and geometric nuances of the designs. By employing this approach, we aim to address the curse of dimensionality often encountered in engineering optimization tasks. The findings suggest that incorporating geometric moments noticeably improves the quality of the resultant design space by maintaining variance and enhancing the validity of the designs without extensive computational resources. This research not only contributes to the academic field by providing a feasible solution to a common problem in engineering design but also suggests practical applications in optimizing design processes across various industries.