﻿ 基于SVR近似模型的潜水器外形优化
 舰船科学技术  2016, Vol. 38 Issue (12): 127-130 PDF

1. 南通航运职业技术学院, 江苏 南通 226010 ;
2. 吉宝(南通)重工有限公司工程部, 江苏 南通 226010

Optimization of submersible shape based on SVR surrogate
XIE Yun-fei1, SUN Jian-fei2
1. Nantong Shipping Vocational and Technical College, Nantong 226010, China ;
2. Keppel(Nantong) Industry Limited Company, Engineering Department, Nantong 226010, China
Abstract: CFD simulation software greatly improves the efficiency and accuracy of optimization design of submersible shape. However, during the optimization, optimization results usually requires a lot of iterations to be achieved. Fluid simulation software, such as fluent will take enormous time and cost during the optimization process. Therefore, this paper proposes a Support Vector Regression (SVR) to study the optimization of submersible shape. The process of building matamodel include:Latin Hypercube experimental design selected sample points, automatic division based ICEM submersible parametric modeling and grid-based computing. Particle Swarm Optimization (PSO) algorithm is adopted to obtain the optimum with a minimum resistance.
Key words: SVR     approximation model     computation of resistance     particle swarm optimization algorithm     submersible shape
0 引 言

1 SVR 近似模型

 $f(x) = {{w}^{\rm T}}\varphi ({x}) + b$ (1)

 $\begin{array}{l} {\rm{min}}\;\;\frac{1}{2}{{w}^{\rm T}}{w} + C\sum\limits_{i = 1}^n {({\xi _i} + \xi _i^*)}, \\ {\rm s}.{\rm t}.\;\;\left\{ {\begin{array}{*{20}{c}} {{y_i}-{{w}^{\text{，}}}\varphi ({{x}_i})-b \leqslant \varepsilon + {\xi _i}},\\ {{{w}^{\text{T}}}\varphi ({{x}_i}) + b-{y_i} \leqslant \varepsilon + \xi _i^*},\\ {{\xi _i},\xi _i^* \geqslant 0}{\text {。}} \end{array}} \right. \end{array}$ (2)

LSSVR 引入了线性最小二乘规则，上式中的不等式约束转化为了等式约束。LSSVR 可以用以下公式描述：

 $\begin{array}{l} {\rm{min }}\frac{1}{2}{{w}^{\text{T}}}{w} + \frac{1}{2}C\sum\limits_{i = 1}^n {e_i^2}, \\ {\rm s}.{\rm t}.{\rm{ }}{e_i} = {{\rm{y}}_i}-{{w}^{\text{T}}}\varphi ({{x}_i})-b,i = 1,2...n{\text {。}} \end{array}$ (3)
2 基于 SVR 近似模型的潜器外形优化流程 2.1 潜器外形

 图 1 流线形回转体 Fig. 1 Streamline body of rotation

 $y = \frac{{{D_0}}}{2}{\left[ {1-{{\left( {1-\frac{X}{{{L_H}}}} \right)}^{{x_2}}}} \right]^{1/{x_1}}},$ (4)

 $y = \frac{{{D_0}}}{2}{\left[ {1-{{\left( {X-{L_H}-{L_M}} \right)}^{{x_4}}}} \right]^{{x_3}}}{\text {。}}$ (5)

2.2 基于 SVR 近似模型的潜器阻力模型构建

 图 2 潜器网格模型 Fig. 2 Submersible grid model

16组参数下的阻力系数计算结果的汇总见表 1

 图 3 仿真结果与预测结果的关系 Fig. 3 Relationship between simulation and prediction results

 图 4 x1，x2 与潜器阻力系数的近似关系 Fig. 4 Approximate relationship betweenx1，x2 and drag coefficients

 图 5 x1，x4 与潜器阻力系数的近似关系 Fig. 5 Approximate relationship betweenx1，x4 and drag coefficients

 图 6 x1，x3 与潜器阻力系数的近似关系 Fig. 6 Approximate relationship betweenx1，x3 and drag coefficients

 图 7 x2，x3 与潜器阻力系数的近似关系 Fig. 7 Approximate relationship betweenx2，x3 and drag coefficients
2.3 优化求解

 图 8 粒子群寻优迭代过程图 Fig. 8 Iterative process of PSO

x1 = 0.441 6，x2 = 18.4，x3 = 7.353 2，x4 = 0.2，CR = 0.109 5。

3 结 语

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