Application of Radial Basis Functions for Partially-Parametric Modeling and Principal Component Analysis for Faster Hydrodynamic Optimization of a Catamaran

Abstract

The paper shows the application of a flexible approach of partially-parametric modelling on the basis of radial basis functions (RBF) for the modification of an existing hull form (baseline). Different to other partially-parametric modelling approaches, RBF functions allow defining sources which lie on the baseline and targets which define the intended new shape. Sources and targets can be corresponding sets of points, curves and surfaces. They are used to derive a transformation field that subsequently modifies those parts of the geometry which shall be subjected to variation, making the approach intuitive and quick to set up. Since the RBF approach may potentially introduce quite a few degrees-of-freedom (DoF) a principal component analysis (PCA) is utilized to reduce the dimensionality of the design space. PCA allows the deliberate sacrifice of variability in order to define variations of interest with fewer variables, then being called principal parameters (prinPar). The aim of combining RBFs and PCA is to make simulation-driven design (SDD) easier and faster to use. Ideally, the turn-around time within which to achieve noticeable improvements should be 24 h, including the time needed to set up both the CAD model and the CFD simulation as well as to run a first optimisation campaign. An electric catamaran was chosen to illustrate the combined approach for a meaningful application case. Both a potential and a viscous solver were utilized, namely, SHIPFLOW XPAN (SHF) and Neptuno (NEP), respectively. Rather than to compare the two codes in any detail the purpose of this was to study the efficacy of the proposed approach of combining RBF and PCA for solvers of different fidelity. All investigations were realized within CAESES, a versatile process integration and design optimisation environment (CAESES). It is shown that meaningful reductions of total resistance and, hence, improvements of energy efficiency can be realized within very few simulation runs. If a one-stop steepest descent is applied as a deterministic search strategy, for instance, some 10 to 12 CFD runs are needed to already identify better hulls, rendering turn-around times of a day of work and a night of number crunching a realistic option.