Linear reduced order method for design-space dimensionality reduction and flow-field learning in hull form optimization

Abstract In the earlier stage of hull form optimization design, a series of design variables is usually needed to control the hull shape, so as to find optimal hull forms with better performance. In the surrogate-based hydrodynamic performance optimization for ships, with the increase of the dimensionality of design space, the number of new sample hulls to construct surrogate model needs to be larger, which will bring a large amount of calculation. Through reduced order method, the dimensionality of the optimization design space can be reduced while keeping the deformation range of the original design space to a great extent, for instance, using the linear combination of a smaller number of bases to represent the deformation range. In addition, in the later stage of hull form optimization design, flow field results of the new sample hulls can be fully utilized to do the dimensionality reduction multi-physics field learning. In this paper, the principle of the Proper Orthogonal Decomposition method is used and briefly introduced, the steps of dimensionality reduction of the design space are shown then, and some important problems for the design-space dimensionality reduction in the specific field of hull form optimization, such as retainability of fixed control points, irrelevance of the relative order of data to dimensionality reduction results, and decision of the new design space range after dimensionality reduction, are deep analyzed. Furthermore, taking the resistance optimization of the modified Wigley ship as an example, the specific application and error analysis of the dimensionality reduction method for design-space dimensionality reduction in the earlier stage of hull form optimization and the multi-physics field learning in the later stage of hull form optimization are given, and the applicability and reliability of the method are demonstrated by analyzing the influence of mode order and sample number on reconstruction effect of the hull shape or flow field, and the prediction effect of flow field for not-in-the-database new hull form in detail. Results show that the linear dimensionality reduction method can reduce samples needed for optimization, thus reduce the amount of calculation for the surrogate-based hull form optimization, and be used for quick prediction of multi-physics fields of any new form in the design space. Furthermore, it can not only be applied to the sensitivity analysis or a Pareto frontier selection in comprehensive performance optimization of hull form based on CFD, but also be implemented in the real-time forecast of the flow field and influence analysis of the ship performance when adjusting the hull form (or hull appendages).