The article herein presents a statistical calibration study of the approximate power method of Holtrop and Mennen focused on adapting the method to vessels characterized as "full" hull forms and low design and operating speeds and, thus, low Froude numbers. The fitting of the method is done by adjusting the constants, coefficients, and components of the method's equations by a systematic variation process controlled by genetic algorithms. The database that the method is calibrated against is consisted by model test results from modern (built between 2010 and 2016) bulk carriers and tankers, the KVLCC2, and the method follows a multistage approach, calibrating first the model for the prediction of total resistance and applying the selfpropulsion equations afterward. The uncertainty of the new improved method is assessed and modeled with a nonlinear regression equation to enable the use of the calibrated method in the early ship design and optimization process.

1. Introduction

One of the most important aspects of the design and study of vessels and ocean structures is the prediction of resistance and, thus, powering requirements for a range of operational speeds. Given the constant societal and legislative pressure for the reduction of the carbon footprint of shipping and maritime activities, the accurate and reliable powering prediction from an early stage and tightly integrated within the process itself as the respective optimization studies is imperative. Although towing tank model testing has been since early times the most reliable method for power predictions, because of its high cost and demand for a fixed and given geometry it can be used only in the basic design stage when the design parameters related to the vessel's hull geometry are fixed and serves as a final validation and benchmark to be used afterward in the conclusion of the shipbuilding process during sea trials. On the other hand, the last decade has seen the exponential growth of computational fluid dynamic solvers that solve Reynolds Averaged Navier Stokes equations over the hull form in finite volume approaches (Schneekluth & Bertram 1998; Specialist Committee on CFD 2014). Although originally the computational cost was penalizing its application in early design stages, the advances in computing hardware and software allowed the integration of Computational Fluid Dynamics (CFD) in the early ship hull form design and optimization (Specialist Committee on CFD 2014). Such methods, however, can be used in applications where variables such as the principal particulars have been fixed or have a small variance, with the focus being on the variation in local geometry and topological characteristics that have a significant effect on local flow phenomena (Specialist Committee on CFD 2014). However, when the application in question is a global optimization study, where there is a large variance in principal particulars (vessel's dimensions) and structural and cargo arrangements, there is an apparent need for a large number of optimization variants and, thus, evaluations (usually in the order of thousands). The application of CFD in such cases is impractical as the optimization algorithm will eventually require hundreds of thousands computational hours even in high-performance computers; therefore, empirical or statistical methods are better suited. The most prominent of these is the approximate power prediction method by Holtrop and Mennen (1982) together with its revision (Holtrop 1984). Although this methodology provides sufficient accuracy, the statistical sample of the hull forms on which it is based dates back to the 1970s and 1980s. Such hulls, although roughly similar, have some distinct deviations from modern commercial vessels. In the article presented herein, the authors attempt to make a calibration of the Holtrop and Mennen methodology via a systematic variation with the use of genetic algorithms. The calibration is based on a statistical sample of model test results of low Froude number (Fn) full hull forms (with Cb greater than 0.7) of modern commercial bulk carriers and tankers, and its focus is on the integration of the new coefficients in a holistic methodology for the optimization of large bulk carriers. The uncertainty of the new coefficients is also taken into account based on the sea trial results of an expanded statistical sample.

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