Data-Driven Prediction of Added Wave Resistance in Regular Head Waves at the Early Stage of Ship Design Using Multivariable Regression and Monte Carlo Sampling

This paper presents a data-driven empirical method for predicting the added wave resistance in regular head waves i the early stages of ship design. The proposed approach is based on a multivariable nonlinear regression model using nondimensional hull parameters (L/B, B/T, block coefficient), the Froude number, and the relative wavelength (λ/L). The model was developed using experimental data from multiple towing tank studies, consisting of over 1,000 measurements of cargo ships with various hulls. The framework combines least-squares regression with GRG optimisation, Monte Carlo sampling of nonlinear exponents, iterative elimination of statistically insignificant variables, and overfitting control. The resulting model demonstrates good predictive performance (R² = 0.93, r = 0.96, RRMSE = 15.7%) while remaining computationally efficient and easy to implement. An agreement analysis based on the Bland–Altman methodology and the concordance correlation coefficient confirms strong agreement between the predicted and experimental values, with no significant mean bias. The model also accurately reproduces the characteristic overall shape of the added wave resistance curve. Unlike more detailed methods that require fuller information on the hull form, the proposed model uses only nondimensional parameters that are typically available at the early stage of parametric design. This model is therefore intended to support preliminary assessments and comparisons of design variants within the range of hull forms and operating conditions represented in the experimental dataset, rather than to replace high-fidelity methods when detailed hull geometry is available.