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 哈尔滨工程大学学报  2019, Vol. 40 Issue (2): 240-246  DOI: 10.11990/jheu.201803054 0

### 引用本文

ZHANG Zhigang, HE Guanghua, WANG Zhengke. Application of genetic algorithm in reduction of wave drift forces on the multiple floating bodies[J]. Journal of Harbin Engineering University, 2019, 40(2), 240-246. DOI: 10.11990/jheu.201803054.

### 文章历史

Application of genetic algorithm in reduction of wave drift forces on the multiple floating bodies
ZHANG Zhigang , HE Guanghua , WANG Zhengke
School of Naval Architecture and Ocean Engineering, Harbin Institute of Technology, Weihai, Weihai 264209, China
Abstract: To protect floating structures at sea, this study aims to reduce the wave drift force acting on multiple floating bodies by controlling the dimensions of these bodies and the wave-approach angle of the structure based on real-coded genetic algorithm (GA). To accurately calculate the wave drift force acting on the floating structure, a numerical model that uses a combination of wave interaction theory and higher-order boundary element method is introduced. Computation results show that the wave drift forces not only on the entire structure but also on each body can be reduced with the optimized parameters obtained by GA. Moreover, the wave height around the floating structure can be improved significantly, thereby reducing the occurrence possibility of deck slamming and green water. The reduction of the wave drift force on the entire structure is strongly related to the wave height on the weather side and leeside of the structure.
Keywords: genetic algorithm    multiple floating bodies    wave drift force    wave-approach angle    wave interaction theory    higher-order boundary element method    deck slam

1 数学模型及数值方法 1.1 四柱结构模型

 Download: 图 1 四柱结构的计算模型 Fig. 1 The notations of the four-column structure
1.2 波漂移力

 $\varPhi \left( {x, y, z;t} \right) = \operatorname{Re} \left[{\frac{{g{\zeta _0}}}{{{\text{i}}\omega }}\phi \left( {x, y, z} \right)\exp \left( {{\text{i}}\omega t} \right)} \right]$ (1)

 $\begin{gathered} {\phi ^n}\left( p \right) = \psi _I^n\left( p \right) + {\psi ^n}\left( p \right) = \hfill \\ \left( {\phi _I^n\left( p \right) + \sum\limits_{k = 1, k \ne n}^4 {{\psi ^{kn}}\left( p \right)} } \right) + {\psi ^n}\left( p \right) = \hfill \\ \sum\limits_{m =- \infty }^\infty {\left[{\left( {\alpha _m^n + \sum\limits_{k = 1, k \ne n}^4 {A_m^{kn}} } \right){{\text{J}}_m}\left( {{k_0}{r_n}} \right) + {\text{A}}_m^n{\text{H}}_m^{\left( 2 \right)}\left( {{k_0}{r_n}} \right)} \right]} \cdot \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;{Z_0}\left( z \right)\exp \left( { -{\text{i}}m{\theta _n}} \right) \hfill \\ \end{gathered}$ (2)

 $A_m^{kn} = \sum\limits_{l =-\infty }^\infty {A_l^k{\text{H}}_{l-m}^{\left( 2 \right)}\left( {{k_0}{L_{kn}}} \right){\alpha _{no}}\exp \left( {-{\text{i}}\left( {l - m} \right)} \right)}$ (3)
 $\alpha _m^n = {\alpha _m}\exp \left( {-{\text{i}}{k_0}\left( {{x_{on}}\cos \beta + {y_{on}}\sin \beta } \right)} \right)$ (4)

Kashiwagi等[13]采用朗斯基矩阵推导出了波漂移力的表达式。本文采用同样的方法，利用式(2)可以计算得到四柱结构中第n个浮体的波漂移力：

 $\begin{gathered} \frac{{F_x^n - {\text{i}}F_y^n}}{{\rho g\zeta _0^2r}} = \hfill \\ \frac{{\text{i}}}{{2{C_0}Kr}}\sum\limits_{m = - \infty }^\infty {\left[ {2A_m^nA_{m + 1}^{n*} + \left( {\alpha _{m + 1}^{n*} + \sum\limits_{k = 1,k \ne n}^4 {A_{m + 1}^{kn*}} } \right)A_m^n + } \right.} \hfill \\ \;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\left. {\left( {\alpha _m^n + \sum\limits_{k = 1,k \ne n}^4 {A_m^{kn}} } \right)A_{m + 1}^{n*}} \right] \hfill \\ \end{gathered}$ (5)
 ${C_0} = \frac{{{k_0}}}{{K + \left( {k_0^2-{K^2}} \right)h}}$ (6)
1.3 遗传算法

 Download: 图 2 遗传算法流程 Fig. 2 The Flow process of the genetic algorithm

 $P\left( i \right) = \frac{{F_{\max }^2-{F^2}\left( i \right)}}{{N \cdot F_{\max }^2-\sum\limits_{i = 1}^N {{F^2}\left( i \right)} }}$ (7)

2 数值模拟结果与分析 2.1 数值模型的验证

 Download: 图 3 1号圆柱浮体的波漂移力 Fig. 3 The wave drift forces acting on cylinder 1
 Download: 图 4 每个圆柱浮体的波漂移力方向 Fig. 4 The direction of the wave drift forces acting on each cylinder

 Download: 图 5 点A处的波高与相位 Fig. 5 The wave height and phase at point A

 Download: 图 6 四柱结构总的波漂移力 Fig. 6 The wave drift force acting on the whole structure
2.2 优化结果

 Download: 图 7 两参数优化前后四柱结构总的波漂移力 Fig. 7 The wave drift force acting on the original structure and on the optimized structure with two-parameters optimization

 Download: 图 8 优化前后四柱结构总的波漂移力 Fig. 8 The wave drift force acting on the original structure and on the optimized structure

 Download: 图 9 优化前后每个圆柱浮体的波漂移力 Fig. 9 The wave drift forces acting on each cylinders with the optimized parameters

 Download: 图 10 优化过程中的目标函数精英值 Fig. 10 The elite of optimized objective F in the optimization process

 Download: 图 11 优化过程中3个典型种群中的个体 Fig. 11 The individuals in three typical generations
2.3 波漂移力与波面分布的关系

 Download: 图 12 优化前每个圆柱浮体两侧的波剖面 Fig. 12 The wave profile in the two sides of the original cylinders

 Download: 图 13 优化后每个圆柱浮体两侧的波剖面 Fig. 13 The wave profile in the two sides of the optimized cylinders
3 结论

1) 本文建立的数值模型可以准确地模拟海上多浮体间的波浪干涉现象。

2) 本文建立的基于实数编码的遗传算法优化模型可以有效地实现多浮体波漂移力的优化。

3) 优化后，不仅实现了四柱结构的总波漂移力的有效减小，而且每个浮体的波漂移力及其周围的波浪场也得到了明显改善。

4) 浮体波漂移力的减小与其迎浪侧和背浪侧波高差和相位差的改善密切相关。

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