# Optimization of Buoy Shape for Wave Energy Converter Based on Particle Swarm Algorithm
###### Abstract  
In order to improve the wave energy capture rate of the buoy of a wave energy generation device, this paper proposes a multi-degree of freedom method to optimize the shape of the buoy with maximum wave energy capture. Firstly, a multi-degree of freedom wave energy converter was designed, and the buoy shape was defined using a B-spline curve to generate the shape vector; then, a numerical model of the multi-degree of freedom wave energy converter was established and numerical calculations were carried out using AQWA/WEC-Sim software; on this basis, the particle swarm optimization algorithm was introduced to find the buoy shape corresponding to the maximum wave energy capture. Finally, the optimization of the buoy shape was in irregular waves. The results show that as the wave energy capture increased, the buoy shape tended to be flatter, with a smaller taper, and the optimal buoy shape had a better motion response than the conventional cone buoy. Eventually, the correctness of the buoy shape optimization method was verified through experimental testing. particle swarm optimization; wave energy converter; buoy-shape; multi-degree of freedom; B-spline curve +
Footnote †: journal: Applied sciences  
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which is important for improving the efficiency of primary energy conversion. Therefore, buoy shape optimization has become one of the hot topics in WEC primary energy conversion research. In terms of primary energy conversion, this study can be broadly based on the definition of buoy geometry, numerical calculation methods, and the selection of optimization algorithms. For example, buoy geometry is defined using B-spline surfaces [4; 5; 6; 7], Bezier curves [8], specific shapes such as rectangles and wedges [9; 10], changing the outer diameter and bottom shape of the buoy [11], using polar equations in polar coordinates [12], and changing other parameters while keeping the buoy volume constant [13]. A complex buoy shape is also defined by a central line and multiple cubic B-spline curves [14]. In terms of numerical calculation methods, there are joint simulations by AQWA/WEC-Sim boundary element methods [15; 16; 17] for numerical calculations. [PERSON] et al. [18] used AQWA to calculate hydrodynamic data for different buoy shapes, followed by MATLAB codes to obtain output power and efficiency. Similarly, the hydrodynamic data were calculated by AQWA software and then the design of experiments method was applied by Minitab software [19] to determine the optimum geometry. The Taguchi design and response surface design methods [20; 21] were used to develop a shape optimization process, also using computational fluid dynamics software for viscous hydrodynamic calculations [10; 22]. In terms of optimization using metaheuristic algorithms, in previous studies, genetic algorithms have been used to develop multi-objective problems [23; 24]. [PERSON] et al. [25] used five metaheuristic algorithms to achieve the optimal value of WEC power output under damping. [PERSON] et al. [6] used the genetic algorithm and the particle swarm optimization algorithm (PSO) to propose different geometry definition methods adapted to different optimization algorithms. [PERSON] et al. [26] proposed a PSO-based heuristic framework for solving nonlinear continuous maximum coverage position models. [PERSON] et al. [27] proposed the effect of buoy volume on power capture based on a differential evolutionary algorithm. [PERSON] et al. [14] used a genetic algorithm combined with a neural network to determine optimal buoy shape, and the implementation of a neural network greatly reduced the computation time. [PERSON] et al. [28] proposed a buoy shape optimization method based on an annual average power prediction model by combining a multi-island genetic algorithm and a power prediction model.