Nonlinear methods for design-space dimensionality reduction in shape optimization

In shape optimization, design improvements significantly depend on the dimension and variability of the design space. High dimensional and variability spaces are more difficult to explore, but also usually allow for more significant improvements. The assessment and breakdown of design-space dimensionality and variability are therefore key elements to shape optimization. A linear method based on the principal component analysis (PCA) has been developed in earlier research to build a reduced-dimensionality design-space, resolving the 95% of the original geometric variance. The present work introduces an extension to more efficient nonlinear approaches. Specifically the use of Kernel PCA, Local PCA, and Deep Autoencoder (DAE) is discussed. The methods are demonstrated for the design-space dimensionality reduction of the hull form of a USS Arleigh Burke-class destroyer. Nonlinear methods are shown to be more effective than linear PCA. DAE shows the best performance overall.