We propose and analyse an optimization method that uses a machine learning approach to solve multi-objective, constrained propeller optimization problems. The method uses an online learning strategy where explainable supervised classifiers learn the location of the Pareto front and advise search strategies. The classifiers are trained with orthogonal features that capture geometric variation in radial distribution of pitch, skew, camber and chordlength. Based on orthogonal features, the classifiers predict whether or not a design lies on the Pareto front. If the design is predicted to lie on the Pareto front, the method verifies this with an evaluation. If the design is predicted to not lie on the Pareto front with a high confidence level, then the design is ignored. This skipped evaluation reduces the computational effort of optimization. The method is demonstrated on a cavitating, unsteady flow case of the Wageningen B-4 70 propeller with P/D = 1.0 operating in the Seiun-Maru wake. Compared to the classical Non-dominated Sorting Genetic Algorithm — III (NSGA-III) the optimization method is able to reduce 30% of evaluations per generation while reproducing a comparable Pareto front. Trade-offs between suction side, pressure side, tip-vortex cavitation and efficiency are identified from the Pareto front. The non-elitist NSGA-III search algorithm in conjunction with the explainable supervised classifiers also find very diverse solutions. Among the solutions, a design with no pressure side cavitation, low suction side cavitation and reasonable tip-vortex cavitation is found.

This paper introduces a machine learning approach for optimizing propellers. The method aims to improve the computational cost of optimization by reducing the number of evaluations required to find solutions. This is achieved by directing the search towards design clusters with good performance, i.e. high propulsive efficiency and low cavitation. Three types of clusters are expected. The first cluster constitutes designs with performance of interest, i.e. high efficiency and low cavitation. The second cluster constitutes designs with performance not of interest, i.e. low efficiency and high cavitation. The third cluster constitutes designs whose performance cannot be estimated with the Boundary Element Methods (BEM) that we use in this study. In simple cases with single objective optimization to maximize efficiency, these clusters can be identified a-priori with unsupervised classifiers provided that orthogonally independent parameters are used as demonstrated in this paper. For multi-objective constrained optimization, to maximize efficiency and minimize cavitation, for example, supervised classifiers may be required to learn the clusters. Classical design variables such as chordlength, pitch, skew, rake, thickness distribution and camber of hydrofoils cannot be used to identify these clusters because of multicollinearity. Thus, a new orthogonal parametric model is proposed where the parameters are directly derived from the propeller blade mesh. As the blade surface mesh is used as boundary conditions to solve the governing equations, the orthogonal parameters are expected to have a stronger correlation with performance predictions of BEM or Computational Fluid Dynamics (CFD) than classical design variables. We demonstrate that design clusters with good performance can be identified with few BEM evaluations. Furthermore, the method synergizes explainable supervised and unsupervised learning to advice search algorithms and quickly guide them to lucrative regions in the design space. However, reducing the cost of optimization results in a trade-off with completeness of the search; this is also investigated in this paper. The method is demonstrated on a simple fully wetted flow case of the benchmark Wageningen B-4 70 propeller with P/D=1.0, as the geometry and open-water curves are readily accessible allowing back of the envelope verification and validation of our results.