Towards the uncertainty quantification of semi-empirical formulas applied to the added resistance of ships in waves of arbitrary heading

The present paper examines a semi-empirical framework for the estimation of added resistance in arbitrary wave heading under consideration of uncertainty quantification. In this respect, the calibration of the formula’s parameter vector is conducted based on particle swarm optimization as well as a database of model test results comprising 25 different ships and around 1100 samples. In the first iteration, the minimization of reducible systematic uncertainty is of interest and the effect of four objective functions on prediction accuracy is evaluated. Moreover, two different parameter combinations were obtained for blunt (CB≥0.70) and slender-type ships. Conversely, the irreducible statistical uncertainty, i.e. the inherent noise of the experimental data, is taken into account by a quantile regression procedure. Applying this approach, a 90% prediction interval for the formula’s estimates is implemented using the skewed version of the superior loss function in the previous iteration. The practical relevance of an uncertainty estimate for the prediction of the added resistance is emphasized in the final part, in which the proposed approach is validated in regular waves against model test data and other well-established prediction methods. In general, the validation studies suggest satisfactory performance and reliability of the adapted semi-empirical formulation.