Optimization design of dolphin-inspired AUV shape based on Kriging surrogate model

doi:10.3785/j.issn.1006-754X.2026.05.164

Chinese Journal of Engineering Design

2026, Vol. 33

Issue (2): 204-212 DOI: 10.3785/j.issn.1006-754X.2026.05.164

Optimization Design

Optimization design of dolphin-inspired AUV shape based on Kriging surrogate model

Jun TANG¹(

),Dongxu QIU¹(

),Yuanhui XIE²

^1.School of Mechanical and Electrical Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China
^2.Intelligent Manufacturing College, Ganzhou Polytechnic, Ganzhou 341000, China

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Abstract

Aiming at the contradiction between low resistance and large volume in the shape design of autonomous underwater vehicles (AUVs), an optimization design method taking dolphins as bionic objects is explored to enhance the hydrodynamic performance and mission payload capacity of AUVs. Firstly, nine segments of Myring-type curves were used to parameterize and fit the dolphin contour, thereby establishing a three-dimensional AUV geometric model. Based on the Reynolds-averaged Navier-Stokes (RANS) equation and the standard k-ε model, the total resistance and envelope volume of the initial AUV were obtained through computational fluid dynamics (CFD) simulation. Subsequently, the optimal Latin hypercube sampling method was utilized to generate sample points, and Kriging surrogate models describing the mapping relationship between the total resistance and envelope volume of the AUV and design variables were constructed. Finally, with the objectives of minimizing total resistance and maximizing envelope volume, the Pareto optimal solution set was solved using NSGA-II (non-dominated sorting genetic algorithm-II). After optimization, the total resistance of the AUV decreased by 5.74% and the envelope volume increased by 5.87% at a navigation speed of 2 m/s. Flow field simulation analysis indicated that the optimized shape flattened the pressure gradient at the AUV tail, reducing the pressure difference resistance by 12.56%. At the same time, the velocity gradient at the AUV tail decreased, effectively inhibiting boundary layer separation. The resistance composition showed that the reduction in pressure difference resistance was the main reason for the decrease in total resistance. The horizontal stability index G_H>0 indicated that the optimized AUV had dynamic stability. The multi-objective optimization method that integrates parametric modeling, CFD simulation, Kriging surrogate model and NSGA-II provides a reference for the shape optimization of underwater vehicles.

Key words： autonomous underwater vehicle (AUV) bio-inspired design computational fluid dynamics (CFD) Kriging surrogate model multi-objective optimization

Received: 24 July 2025 Published: 28 April 2026

CLC:

U 662.2

Corresponding Authors: Dongxu QIU E-mail: 9120060030@jxust.edu.cn;347943350@qq.com

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Cite this article:

Jun TANG,Dongxu QIU,Yuanhui XIE. Optimization design of dolphin-inspired AUV shape based on Kriging surrogate model. Chinese Journal of Engineering Design, 2026, 33(2): 204-212.

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https://www.zjujournals.com/gcsjxb/10.3785/j.issn.1006-754X.2026.05.164 OR https://www.zjujournals.com/gcsjxb/Y2026/V33/I2/204

基于Kriging代理模型的仿海豚AUV外形优化设计

针对自主水下航行器（autonomous underwater vehicle, AUV）外形设计中低阻力与大容积之间的矛盾，探索以海豚为仿生对象的优化设计方法，以提升AUV的水动力性能与任务载荷能力。首先，采用9段Myring型曲线对海豚轮廓进行参数化拟合，建立AUV三维几何模型，并基于雷诺平均纳维-斯托克斯（Reynolds-averaged Navier-Stokes, RANS）方程和标准 $k$ - $ε$ 模型，通过CFD（computational fluid dynamics，计算流体力学）仿真获取初始AUV的总阻力与包络体积。随后，利用最优拉丁超立方抽样法生成样本点，构建描述AUV总阻力、包络体积与设计变量映射关系的Kriging代理模型。最后，以最小化总阻力和最大化包络体积为目标，采用NSGA-II（non-dominated sorting genetic algorithm-II，二代非支配排序遗传算法）求解Pareto最优解集。优化后的AUV在2 m/s航速下的总阻力降低了5.74%，包络体积增大了5.87%。流场仿真分析表明：优化外形使AUV尾部的压力梯度趋于平缓，压差阻力降低了12.56%；同时，AUV尾部的速度梯度减小，有效抑制了边界层分离。阻力构成显示压差阻力降低是AUV总阻力下降的主要原因。水平面稳定性指数G_H>0，表明优化后的AUV具有动稳定性。融合参数化建模、CFD仿真、Kriging代理模型与NSGA-II的多目标优化方法，为水下航行器的外形优化提供了参考。

关键词： 自主水下航行器, 仿生设计, 计算流体力学, Kriging代理模型, 多目标优化

Fig.1 Simplified geometric model of dolphin-inspired AUV

Fig.2 Shape contour of dolphin-inspired AUV

参数	初始值	上限	下限	备注
$d 1$ /mm	60	40	80	曲线1的高度
$a 1$ /mm	100	80	120	曲线1的长度
$n 1$	2	1	3	曲线1的饱和度
$d 2$ /mm	60	40	80	曲线2的高度
$a 2$ /mm	100	80	120	曲线2的长度
$n 2$	2	1	3	曲线2的饱和度
$d 3$ /mm	180	160	200	曲线3的高度
$a 3$ /mm	440	340	540	曲线3的长度
$n 3$	2	1	3	曲线3的饱和度
$a 4$ /mm	960	800	1 200	曲线4的长度
$n 4$	3	1	5	曲线4的饱和度
$d 5$ /mm	60	40	80	曲线5的高度
$n 5$	2	1	3	曲线5的饱和度
$d 6$ /mm	40	30	50	曲线6的高度
$n 6$	2	1	3	曲线6的饱和度
$n 7$	3	1	5	曲线7的饱和度
$d 8$ /mm	200	100	300	曲线8的高度
$a 8$ /mm	200	160	240	曲线8的长度
$n 8$	2	1	3	曲线8的饱和度
$n 9$	2	1	3	曲线9的饱和度

Table 1 Initial value and range of design variables

Fig.3 Calculation domain and boundary conditions

Fig.4 Relationship between total resistance of AUV and number of grids

Fig.5 Grid division around AUV

Fig.6 Comparison of simulated and predicted values of total resistance of AUV

Fig.7 Comparison of simulated and predicted values of envelope volume of AUV

Fig.8 Optimization process of NSGA-II

Fig.9 Pareto optimal solution set for multi-objective optimization of AUV shape

参数	初始方案	优化方案B	优化方案C
$d 1$ /mm	60	40.33	40.41
$a 1$ /mm	100	81.18	80.24
$n 1$	2	2.99	2.99
$d 2$ /mm	60	77.51	77.76
$a 2$ /mm	100	119.54	119.53
$n 2$	2	1.04	1.04
$d 3$ /mm	180	164.58	171.35
$a 3$ /mm	440	344.08	345.31
$n 3$	2	2.95	2.77
$a 4$ /mm	960	1 198.23	1 198.31
$n 4$	3	2.67	2.66
$d 5$ /mm	60	79.80	79.82
$n 5$	2	1.83	1.46
$d 6$ /mm	40	30.27	34.46
$n 6$	2	2.48	2.68
$n 7$	3	4.97	4.97
$d 8$ /mm	200	299.44	281.37
$a 8$ /mm	200	191.52	196.49
$n 8$	2	2.98	2.99
$n 9$	2	1.56	1.71
总阻力/N	18.63	17.39	17.48
包络体积/ $d m 3$	91.68	97.06	97.81

Table 2 Comparison of initial design and optimized design of AUV shape

Fig.10 Sensitivity analysis result for total resistance of AUV

Fig.11 Sensitivity analysis result for envelope volume of AUV

Fig.12 Pressure contour plots of AUV before and after optimization

Fig.13 Velocity contour plots of flow field around AUV before and after optimization

Table 3 Comparison of simulation value and predicted value of total resistance of optimized AUV

阻力类型

初始

方案

优化

方案B

变化量

变化率/

%

压差阻力/N

10.19

8.91

-1.28

-12.56

摩擦阻力/N

8.44

8.65

+0.21

+2.49

总阻力/N

18.63

17.56

-1.07

-5.74

Table 4 Comparison of total resistance composition of AUV before and after optimization

Fig.14 Comparison of total resistance of AUV before and after optimization at different navigation speeds

水动力系数	数值
$Y v'$	-0.247 553
$N v'$	-0.007 264
$Y r'$	-0.016 574
$N r'$	-0.021 381

Table 5 Hydrodynamic coefficients of AUV


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