Design-space Dimensionality Reduction in Hydrodynamic Shape Optimization by Generalized Karhunen-Loève Expansion

An offline method to reduce the dimension of design spaces in hydrodynamic shape optimization is presented. The geometry based method (developed by the authors in earlier research) is extended, bringing physics based information into the design variability analysis. The generalized Karhunen-Lo` ve expansion is applied to a combined geometry and physics based design modification vector, embedded in a generalized (disjoint) Hilbert space. Design spaces are assessed in terms of Karhunen-Loève modes (eigenvectors) and associated variance (eigenvalues). The former are used as a basis to build a reduced-dimensionality representation of the shape modification, retaining the 95% of the original design variability. The method is demonstrated for the design-space dimensionality reduction of the DTMB 5415 bare hull. The dimensionality reduction is based on geometry, wave resistance coefficient, pressure distribution, and wave elevation at Fr = 0.25, evaluated by linear potential flow theory. Compared to the geometry based method, the current extension to combined geometry and physics based analysis improves the effectiveness of the design-space dimensionality reduction.