﻿ 无人潜水器主体多学科多目标设计优化
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 哈尔滨工程大学学报  2019, Vol. 40 Issue (4): 858-864  DOI: 10.11990/jheu.201803113 0

### 引用本文

LI Jianing, LIU Feng, YAO Jingzheng, et al. Multidisciplinary and multi-objective design optimization of main body of unmanned underwater vehicle[J]. Journal of Harbin Engineering University, 2019, 40(4), 858-864. DOI: 10.11990/jheu.201803113.

### 文章历史

1. 哈尔滨工程大学 经济管理学院, 黑龙江 哈尔滨 150001;
2. 哈尔滨工程大学 船舶工程学院, 黑龙江 哈尔滨 150001

Multidisciplinary and multi-objective design optimization of main body of unmanned underwater vehicle
LI Jianing 1, LIU Feng 2, YAO Jingzheng 2, DU Shixin 2, LIANG Xu 2
1. College of Economics and Management, Harbin Engineering University, Harbin 150001, China;
2. College of Shipbuilding Engineering, Harbin Engineering University, Harbin 150001, China
Abstract: To improve the overall performance and design efficiency of an unmanned underwater vehicle, this study considered one part of the vehicle's main body as the research object in investigating the analysis method of form resistance and pressure hull, and designing the parametric analysis process.Development of structural and resistance analysis software was conducted.Automatic computation and analysis based on parameterization was performed, and on this basis, sample points of the shape resistance and pressure-resistant structure were analyzed.Furthermore, a resistance and structural analysis model was constructed based on an approximate model.A multidisciplinary and multi-objective optimization model was established to optimize the second-generation non-dominated sorting genetic algorithm, and some plans were selected for comparison with the initial plan.The optimization results were obvious, thereby providing the basis for the main body design of the unmanned underwater vehicle.
Keywords: unmanned underwater vehicle    main body    parametric analysis    shape resistance    pressure hull    approximate model    optimization solution

1 外形阻力分析模型 1.1 阻力求解方法

 $\partial \left( {{{\bar u}_i}} \right)/\partial {x_i} = 0$ (1)
 $\begin{array}{l} \partial \left( {{\rho _i}{{\bar u}_i}} \right)/\partial t + {\rho _j}{{\bar u}_j}({\partial _i}{{\bar u}_i}/\partial {x_j}) = \\ \rho {{\bar F}_i} - \frac{{\partial \bar p}}{{\partial {x_i}}} + \frac{\partial }{{\partial {x_j}}}\left( {\mu \frac{{\partial {{\bar u}_i}}}{{\partial {x_j}}} - \rho \overline {u_i^\prime } \overline {u_j^\prime } } \right) \end{array}$ (2)

 $\frac{{\partial \left( {\rho k} \right)}}{{\partial t}} + \frac{{\partial \left( {\rho k{u_i}} \right)}}{{\partial {x_i}}} = \frac{\partial }{{\partial {x_j}}}\left( {{\mathit{\Gamma }_k}\frac{{\partial k}}{{\partial {x_j}}}} \right) + {G_k} - {Y_k}$ (3)
 $\frac{{\partial \left( {\rho \omega } \right)}}{{\partial t}} + \frac{{\partial \left( {\rho \omega {u_i}} \right)}}{{\partial {x_i}}} = \frac{\partial }{{\partial {x_j}}}\left( {{\mathit{\Gamma }_\omega }\frac{{\partial \omega }}{{\partial {x_j}}}} \right){\rm{ + }}{G_\omega } - {Y_\omega } + {D_\omega }$ (4)

1.2 基于STAR-CCM+的外形阻力分析

 Download: 图 1 潜水器外形 Fig. 1 Exterior map of submersible

 Download: 图 2 计算域网格与边界条件设置 Fig. 2 Calculation area network grid and boundary conditions

1.3 外形阻力参数化分析流程

 Download: 图 3 外形参数化分析流程 Fig. 3 Parametric analysis process of shape

2 耐压结构分析模型 2.1 耐压结构非线性分析方法

 $\Delta {{\rm{ \mathsf{ λ} }}_i} = \Delta {{\rm{ \mathsf{ λ} }}_0}, \Delta u_i^N = \Delta {{\rm{ \mathsf{ λ} }}_0}v_0^N$ (1)

1)内部结点应力为：

 ${I^N} = \int_V {{\beta ^N}} :\sigma {\rm{d}}V;{K^{NM}} = \partial {I^N}/\partial {u^M}$ (2)

2)检查平衡方程：

 $R_i^N = \left( {{{\rm{ \mathsf{ λ} }}_0} + \Delta {{\rm{ \mathsf{ λ} }}_i}} \right){P^N} - {I^N}$ (3)

 ${K^{NM}}\{ v_i^M;c_i^M\} = \{ {P^N};R_i^N\}$ (4)

2个方向的分量是PNRN，2个方向的位移分量是viNciN

3)将矢量($\tilde v_i^N$; 1)缩放，代入到($\tilde c_i^N$; ρi)(其中ρi=RiNPN/$\overline {{P^2}}$)，得到：

 $\left\{ {\left( {0; - {\rho _i}} \right) + {\rm{ }}\left( {\tilde c_i^N;{\rho _i}} \right) + \mu \left( {\tilde v_i^N;1} \right)} \right\}:\left( {\tilde v_0^N;1} \right) = 0$ (5)

4)下一次迭代：

 $\left\{ \begin{array}{l} \Delta u_{i + 1}^N = \Delta u_i^N + c_i^N + \mu v_i^N\\ \Delta {{\rm{ \mathsf{ λ} }}_{i + 1}} = \Delta {{\rm{ \mathsf{ λ} }}_i} + \mu ;i = i + 1 \end{array} \right.$ (6)

2.2 耐压壳结构有限元分析

 Download: 图 4 有限元模型与坐标系方向 Fig. 4 Finite element model and coordinate direction

 Download: 图 5 耐压壳整体网格划分及环肋网格划分 Fig. 5 Block grid division of pressure resistant shell and ring ribbed grid division

2.3 耐压壳体参数化分析流程

3 耐压壳体分析模型的建立 3.1 响应面模型

 $\hat y\left( x \right) = {a_0} + \sum\limits_{i = 1}^n {{b_i}{x_i}} + \sum\limits_{i = 1}^n {{c_{ii}}x_i^2} + \sum\limits_{ \le i \ne j \le n}^n {{d_{ij}}{x_i}{x_j}}$ (7)

 ${R^2} = 1 - \left( {\sum\limits_{i = 1}^n {{{\left( {{y_i} - {{\hat y}_i}} \right)}^2}} /\sum\limits_{i = 1}^n {{{\left( {{y_i} - {{\bar y}_i}} \right)}^2}} } \right)$ (8)

3.2 外形近似模型

 Download: 图 6 Rx预测值与计算值对比 Fig. 6 Comparison of forecast and calculated values for Rx

3.3 耐压壳体近似模型

 Download: 图 7 σmax预测值与计算值对比 Fig. 7 Comparison of forecast and calculated values for σmax
 Download: 图 8 Pcr预测值与计算值对比 Fig. 8 Comparison of forecast and calculated values for Pcr

4 优化模型的建立 4.1 第2代非支配排序遗传算法

1)初始种群的赋予的同时，进行排序种群的排序，此代种群为P0，其是随机产生的，初始种群进行选择、交叉与变异，进一步产生新种群，即Q0种群，令t=0；

2)构造新种群，对于Rt进行非劣排序，得到非劣前端F1F2，…；

3)按拥挤比较操作pn对所有Fi进行排序，将最优秀的N个个体组成种群Pt+1

4)对种群Pt+1执行选择、交叉和变异，进一步得到种群Qt+1

5)若满足优化条件，则计算程序终止，若不满足，则令t=t+1，并返回至2)重新执行。

4.2 优化模型

 $\left\{ \begin{array}{l} M = {M_f}({x_2}, {x_3}, {x_4}, {\rho _f}, {t_f}) + {M_N}({y_1}, \cdots {y_5}, {\rho _N})\\ \Delta = {\Delta _f}({x_2}, {x_3}, {x_4}, {t_f}) + {\Delta _N}({y_1}, \cdots {y_5}, {\rho _N}) \end{array} \right.$ (9)

 $\left\{ \begin{array}{l} {\rm{max}}:\{ V;{P_{cr}}\} \\ {\rm{min}}:\{ M;{R_x}\} \\ {\rm{s}}{\rm{.t}}:\{ {\sigma _{{\rm{max}}}} \le \left[ \sigma \right]\\ DV:\begin{array}{*{20}{c}} {{x_2}, {x_3}, {x_4};}\\ {{y_1}, {y_2}, {y_3}, {y_4}, {y_5}} \end{array} \end{array} \right.$ (10)

 $\left[ \sigma \right] = 0.85{\sigma _s}$ (11)

5 优化求解

 Download: 图 9 Pareto解集 Fig. 9 Pareto solution

6 结论

1)通过针对STAR-CCM+和Abaqus进行的二次开发实现了外形阻力、耐压壳体的参数化分析，可避免设计过程中频繁的模型修改，实现了设计效率的提高；

2)采用二阶响应面拟合得到分析模型具有极高的精度，进一步将分析模型模型引入到主体结构优化模型，在满足了工程需要的同时，降低了计算成本、提高了设计效率；

3)基于NSGA-II对于优化模型进行优化求解得到了Pareto解集，选取其中的2个方案与初始方案进行对比，结果表明：2个优化方案均实现了优化，且各自在不同性能的提升方面效果明显。

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