﻿ 基于高维优化的RBF神经网络螺旋桨性能预测
 舰船科学技术  2022, Vol. 44 Issue (5): 54-58    DOI: 10.3404/j.issn.1672-7649.2022.05.011 PDF

Performance prediction of propeller based on high-dimensional optimization RBF neural network
ZHU Jian-ping, LIU Xiao-xiao, WANG Guan-nan, YANG Sheng, LIU Yuan-hao, HAO Si-jia
Rongcheng College, Harbin University of Science and Technology, Weihai 264300, China
Abstract: The hydrodynamic performance of the underwater robot is determined by the thrust of the propeller-type underwater propeller. In order to predict the open water performance of the propeller quickly and accurately, an open water performance estimator model which is based on RBF neural network needs to be established. The network size is adjusted by using several types of propeller open water simulation values as training samples.On this basis, the connection weights between the networks have been adjusted, and the network parameters have also been optimized. After achieving the learning accuracy requirements through continuous iterative optimization, a high-dimensional optimized neural network open water performance estimator is finally obtained. By comparing and analyzing the open water coefficient predicted by the RBF neural network propeller open water performance estimator model and the open water coefficient simulated by CDF, the result shows that the gap between them is small. Therefore, the RBF neural network open water performance estimator model can meet the requirements of accuracy and rapidity of prediction, and can also be used as one of the effective prediction methods of propeller open water coefficient.
Key words: propeller     RBF neural network     performance prediction
0 引　言

1 RBF神经网络螺旋桨敞水性能估计器模型 1.1 RBF神经网络螺旋桨敞水性能估计器模型的建立

RBF神经网络是一种前反馈式神经网络，主要包括输入层、隐藏层、及输出层3层网格结构[4]。RBF径向基神经网络的隐节点之间采用中心向量与输入模式之间的距离来作为函数的自变量，并快速使用径向基函数作为一个激活函数。接着对网络规模进行调整，广义逆动态地调整各网络间的连接权重，进行网络参数的优化，进而构建一种高维优化的神经网络估计器，最终达到输出敞水能参数误差小于预先设置的学习精度，或者在达到预先设定的学习次数时，停止整个神经网络的学习训练过程，神经网络结构示意图如图1所示。

 图 1 螺旋桨估计器RBF神经网络结构图 Fig. 1 RBF neural network structure diagram of propeller estimator

1）构建隐含层神经元宽度

 ${\delta _j} = {\delta _{\min }} + \left( {{\delta _{\max }} - {\delta _{\min }}} \right) \bullet rand\left( {} \right)\;\;j = 1,2, \cdots , \cup ,$ (1)

${\boldsymbol{X}} = {\left( {x_1^{\rm{T}},x_2^{\rm{T}}, \cdots ,x_M^{\rm{T}}} \right)^{\rm{T}}} \in {\Re ^{M \times n}}$ 表示训练集的输入集， ${{\boldsymbol{x}}_q} = {\left( {{x_{q1}},{x_{q2}}, \cdots ,{x_{qn}}} \right)^{\rm{T}}} \in {\Re ^{1 \times n}}$ 为输入级的第q个输入样本，M为训练集样本规模；令 $Y \in {\Re ^{M \times 1}}$ 为训练集的期望输出，建立RBF神经网络螺旋桨估计器：

2）构成RBF单元

3）计算输入层X下隐含层的输入H

 ${\phi _j}\left( x \right) = \exp \left( { - \dfrac{{\parallel x - {\mu _j}{\parallel ^2}}}{{2\delta _j^2}}} \right),j = 1,2, \cdots ,k_{sise}^i，$ (2)
 $H = {\left( {\begin{array}{*{20}{c}} {{\phi _{11}}}& \ldots &{{\phi _{1M}}} \\ \vdots & \ddots & \vdots \\ {\phi k{{_{sise}^i}_1}}& \cdots &{{\phi _{k_{sise}^iM}}} \end{array}} \right)^{\rm{T}}}，$ (3)
 $\begin{gathered} {\phi _{jq}} = \exp \left( { - \dfrac{{\parallel {x_q} - \mu _j^i{\parallel ^2}}}{{2\delta _j^2}}} \right),q = 1,2, \cdots ，\hfill \\ M\;and\;j = 1,2, \cdots ,k_{sise}^i。\hfill \\ \end{gathered}$ (4)

4）广义逆计算出各网格之间的连接权重 ${W_i}$

 ${{\boldsymbol{H}}^ + } = {\left( {{{\boldsymbol{H}}^{\rm{T}}}{\boldsymbol{H}} + \lambda I} \right)^{ - 1}}{{\boldsymbol{H}}^{\rm{T}}}，$
 ${W_i} = {{\boldsymbol{H}}^ + }Y。$

1.2 RBF神经网络训练

1.3 RBF神经网络螺旋桨敞水性能估计器模型训练结果

 图 2 某型号螺旋桨敞水系数 Fig. 2 Open water coefficient of special type propeller
2 螺旋桨CFD敞水性能仿真计算 2.1 构造螺旋桨几何模型

 图 3 管螺旋经 Fig. 3 Spiral diameter of catheter propeller
2.2 控制方程

1）连续性方程

2）动量守恒方程

 $\left\{ {\begin{array}{*{20}{c}} {\rho \dfrac{{{\rm{d}}u}}{{{\rm{d}}t}} = \rho {f_x} - \dfrac{{\partial p}}{{\partial x}} + \mu {\nabla ^2}u}，\\ {\rho \dfrac{{{\rm{d}}v}}{{{\rm{d}}t}} = \rho {f_y} - \dfrac{{\partial p}}{{\partial y}} + \mu {\nabla ^2}v} ，\\ {\rho \dfrac{{{\rm{d}}w}}{{{\rm{d}}t}} = \rho {f_z} - \dfrac{{\partial p}}{{\partial z}} + \mu {\nabla ^2}w} 。\end{array}} \right.$ (5)

2.3 建立计算域

 图 4 螺旋桨流体计算域 Fig. 4 Fluid computing domain of propeller
2.4 网格划分

 图 5 螺旋桨网格 Fig. 5 Propeller grid

 图 6 螺旋桨网格 Fig. 6 Propeller grid
2.5 设置边界条件

 ${V_A} = JnD$ (6)
2.6 计算结果验证

 图 7 RBF预测与CFD仿真结果对比图 Fig. 7 Comparison chart between the prediction of RBF and the simulation result of CFD
3 结　语

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