A ship hull form optimization is conducted for KCS focusing on the shape of bow and stern. Shape of the hull form is expressed in a radial basis function to facilitate its deformation during the course of optimization. Optimization of stern focuses mainly on improvement of the quality of the wake to increase propulsion efficiency potentially, while the bow optimization aims at the reduction of total resistance. In the optimization, a Kriging model is constructed to replace actual hydrodynamic performances of the ship by a model based on Latin hypercube sampling. Multi-island genetic algorithm and non-dominated sorting genetic algorithm-II are employed in the optimization to prevent pre-mature termination at local optimal solution rather than global optimal solution. As a result, the total resistance of KCS at service speed is reduced by 1.36% and the wake object function (WOF), proposed by MARIN, is reduced by 10.2%. The method coordinated in this study could be applied in ship hull optimization problem for other hydrodynamic performances.


Nowadays shipping industry plays a more important role than ever before in international transportation. With the increase of attention to environment protection, greenhouse gas emission has to be reduced as well in ship transportation. The international maritime organization, IMO, at her 75th meeting of Marine Environment Protection Committee (MEPC) has presented that the energy efficiency design index (EEDI) "phase 3" requirements of container ships will enter into force at date of 1 April 2022. In order to meet the EEDI requirement, further reduction of ship resistance is still a topic for all of the ship designers, since ship resistance is a great concern of fuel consumption and closely related to the greenhouse gas emission. Design of optimal hull form is the origin of resistance reduction. Based on this consideration, construction of a ship hull optimization system is an urgent task. Generally, ships usually look like a slender cylinder, variation of the cross-section mainly lies in the bow and stern parts. In this study, we will integrate a system for optimization of the bow and stern to minimize ship resistance and improve the wake behind the stern to make the flow incident to the propeller more uniform and gaining a more higher propulsion efficiency. With the development of CFD simulation, hydrodynamic ship performances, such as resistance, propulsion and etc., are more likely predicted by numerical simulation, and tests performed in towing tank are becoming a final confirmation of a design. In this way, today's ship design is more and more relied on numerical simulation, and such a design of ship hull is known as simulation-based design, i.e. SBD, which consists of three components, namely, geometry expression of the ship hull, performance prediction by simulation, and searching strategy for the hull form with optimal performance. Simulation based design in seeking for optimal hull form with reduced resistance is becoming a common practice in ship design. Sharma, Kim, Storch, Hopman and Erikstad (2011) reviewed the application of computer technology in methodology, modeling and the integration of ship design system and analysis involved. Tahara, Tohyama and Katsui (2006) conducted a development of SBD by integrating computer-aided design (CAD) for hull geometry, CFD for performance simulation, and an optimizer module into a system. At the same time, Harries (2006) practiced resistance reduction and capacity increase for a medium-size container carrier by means of adjusting the shape of sectional area curve in terms of morphing approach, and received a good result. Hyunyul Kim and Chi Yang (2009) also focused on the sectional area curve of hull, and the hull form is interpolated by means of radial basis functions, i.e. RBF, and performed optimization to minimize resistance for KCS in terms of their in-house so-called practical design-oriented CFD tool, namely SSF. Recently, Nazemian and Ghadimi (2021) also applied RBF-morph technique in resistance minimization for a trimaran hull at two design speeds, and received a reduction of resistance by 6.77% at low speed, and by 1.55% at high speed. Kim, Choi and Chun (2016) devised a parametric modification function to perform deformation of the ship hull expressed as B-spline surface, and received reduction of wave making resistance by 7.5% for KCS, reduction of viscous pressure resistance coefficient by 6.2% for KVLCC2. Liu, Wang and Wan (2018) applied the free-form deformation method, FFD, to perform deformation of the hull form of KCS in minimization of resistance at whole speed range. Zhao, Wang, Jia, Xie (2021) chose an ocean-going trawler as parent ship and used FFD to deform the bulbous bow Lackenby method to deform the hull. As a result, the resistance under the trawling and design conditions optimized by NSGA-II and T-search were reduced by 8.5% and 11.8%. On the other hand, with respect to the wake behind stern, Duy, Hino, Suzuki (2017) applied their in-house tool, SURF, for simulation of the stern flow fields behind a container ship stern with various transom configurations. In reality, a design should take a balance between some performances contradicted with each other. On this respect, Gammon (2011) presented a Multi-Objective Genetic Algorithm (MOGA) to perform optimization of resistance, seakeeping and stability at the same time, and applied it to a fishing vessel to derive her optimal principal dimensions and hull offsets. Zakerdoost and Ghassemi (2018) performed a multi-disciplinary and multi-level optimization for a hull-propeller system considering lifetime fuel consumption (LFC) and energy efficiency design index (EEDI) as objectives. On the optimization strategy, Campana, Liuzzi, Lucidi, Peri, Piccialli, Pinto (2009) applied particle swarm optimization strategy to perform heave optimization for a containership with a new method, GO, and the heave performance was significantly improved. Zakerdoost, Ghassemi and Ghiasi (2013) applied an evolution strategy to minimize total resistance for a standard Wigley hull. Finally, Lu, Chang, Yin and Li (2018) performed a concurrent local optimization of the bow and stern for KCS through the whole speed range, and received an average resistance reduction of about 4%. Through the short survey of ship hull optimization practice, we can see that there is still no unified system. The geometry expression of hull form could be CAD platform, RBF or B-spline based, the simulation tool for performance prediction could be different in-house tools, and commercial tools, and optimization strategy could be different algorithm. In addition, objective of the optimization could be single, say resistance, or multiple, such as resistance and capacity.

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