Determining residuary resistance per unit weight of displacement with Symbolic Regression and Gradient Boosted Tree algorithms

Determining the residuary resistance per unit weight of displacement is one of the key factors in the design of vessels. In this paper, the authors utilize two novel methods – Symbolic Regression (SR) and Gradient Boosted Trees (GBT) to achieve a model which can be used to calculate the value of residuary resistance per unit weight, of displacement from the longitudinal position of the center of buoyancy, prismatic coefficient, length-displacement ratio, beam-draught ratio, length-beam ratio, and Froude number. This data is given as results of 308 experiments provided as a part of a publicly available dataset. The results are evaluated using the coefficient of determination (R2) and Mean Absolute Percentage Error (MAPE). Pre-processing, in the shape of correlation analysis combined with variable elimination and variable scaling, is applied to the dataset. The results show that while both methods achieve regression results, the result of regression of SR is relatively poor in comparison to GBT. Both methods provide slightly poorer, but comparable results to previous research focussing on the use of “black-box” methods, such as neural networks. The elimination of variables does not show a high influence on the modeling performance in the presented case, while variable scaling does achieve better results compared to the models trained with the non-scaled dataset.