﻿ 基于RBF神经网络的柴油机控制模型辨识方法
 舰船科学技术  2022, Vol. 44 Issue (7): 118-121    DOI: 10.3404/j.issn.1672-7649.2022.07.023 PDF

Research on identification method of diesel engine control model based on RBF neural network
WU Yue, WU Jie-chang, CHANG Guang-hui, LIU Shu-yong
College of Power Engineering, Naval University of Engineering, Wuhan 430033, China
Abstract: For electronic governor of diesel engine design and development of model-based modeling problem need to solve the high real-time capability of model, the modeling method for diesel engine based on RBF neural network were studied. Under the environment of Matlab/Simulink, the identification model and the algorithm are designed. For PA6 diesel engine as an example for the model identification test, shows that the method has the advantages of high approximation accuracy and short response speed.
Key words: model of diesel     system identification     RBF neural network
0 引　言

1 船用柴油机外特性及动力学方程描述

 ${M}_{e}={M}_{i}{\eta }_{m}=\frac{{H}_{u}{g}_{c}{\eta }_{i}{\eta }_{m}}{\tau \pi } 。$ (1)

 ${\eta }_{i}={a}_{0}({({N}_{d}-{N}_{d0})}^{2}+{a}_{1}^{2}{(\alpha -{\alpha }_{0})}^{2})+{a}_{2}。$ (2)

 $\alpha =\frac{{G}_{tr}}{{G}_{f}{L}_{0}}，$ (3)

 ${G}_{f}=\frac{{g}_{c}\cdot {N}_{d}}{30\tau }，$ (4)

${G}_{tr}$ 为柴油机吸气流量，是柴油机转速和进气气体状态的函数，表达式为：

 ${G}_{tr}=\frac{i\cdot {V}_{s}\cdot {N}_{d}\cdot {p}_{3}\cdot {\eta }_{v}}{120\cdot R\cdot {T}_{i}} 。$ (5)

 ${\eta }_{v}=a{N}_{d}^{2}+b{N}_{d}+c 。$ (6)

 $\frac{{{\text{π}} I}_{e}}{30}\cdot \frac{{{\rm{d}}N}_{d}}{{\rm{d}}{\rm{t}}}={M}_{e}-{M}_{B}-{M}_{f1} ，$ (7)
 ${N}_{d}=\frac{30}{{{\text{π}} I}_{e}}\int {(M}_{e}-{M}_{B}-{M}_{f1}){\rm{d}}t 。$ (8)

2 RBF神经网络的柴油机模型辨识 2.1 基本原理

RBF神经网络为具有单隐藏层的3层前馈网络，网络结构相对较为简单。其3层前馈网络结构中， $X={[{x}_{1},{x}_{2},\cdots ,{x}_{n}]}^{{\rm{T}}}$ 为网络的输入向量，网络的径向基向量为 $H=[{h}_{1},{h}_{2},\cdots ,{h}_{m}]$ ，其中 ${h}_{j}$ 为高斯基函数：

 ${h}_{j}=\mathrm{exp}\left(-\frac{{‖X-{C}_{j}‖}^{2}}{2{b}_{j}^{2}}\right)(j=\mathrm{1,2},\cdots ,m) 。$ (9)

 ${y}_{m}\left(k\right)={W}^{{\rm{T}}}H，$ (10)

 $E\left(k\right)=y\left(k\right)-{y}_{m}\left(k\right) ，$ (11)

 $\begin{split} {w}_{j}\left(k\right)=&{w}_{j}\left(k-1\right)+\eta \left(y\left(k\right)-{y}_{m}\left(k\right)\right){h}_{j} +\\ &\alpha ({w}_{j}\left(k-1\right)-{w}_{j}\left(k-2\right))，\end{split}$ (12)
 $\Delta {b}_{j}=\left(y\left(k\right)-{y}_{m}\left(k\right)\right){w}_{j}{h}_{j}\frac{{‖X-{C}_{j}‖}^{2}}{{b}_{j}^{3}} ，$ (13)
 ${b}_{j}\left(k\right)={b}_{j}\left(k-1\right)+\eta \Delta {b}_{j}+\alpha ({b}_{j}\left(k-1\right) -{b}_{j}\left(k-2\right)) ，$ (14)
 $\Delta {c}_{ji}=\left(y\left(k\right)-{y}_{m}\left(k\right)\right){w}_{j}{h}_{j}\frac{{x}_{j}-{c}_{ji}}{{b}_{j}^{2}} ，$ (15)
 ${c}_{ji}\left(k\right)={c}_{ji}\left(k-1\right)+\eta \Delta {c}_{ji}+\alpha ({c}_{ji}\left(k-1\right) -{c}_{ji}\left(k-2\right)) 。$ (16)

2.2 基于RBF神经网络柴油机模型设计 2.2.1 柴油机外特性辨识原理

 ${F}_{r}=\frac{{g}_{c}-{g}_{c0}}{{g}_{cH}-{g}_{c0}} 。$ (17)

 ${M}_{e}=f({F}_{r},{N}_{d}) ，$ (18)

 ${\Delta M}_{e}\left(k\right)={M}_{e0}\left(k\right)-{\hat{M}}_{e}\left(k\right) ，$ (19)

 ${\hat{M}}_{e}\left(k\right)={W}^{{\rm{T}}}H ，$ (20)

 ${\Delta M}_{e}\left(k\right)={M}_{e0}\left(k\right)-{W}^{{\rm{T}}}H=E\left(k\right) 。$ (21)

2.2.2 柴油机机理模型与辨识模型设计

 图 1 RBF神经网络辨识结构图 Fig. 1 RBF neural network identification structure diagram

 图 2 在线辨识原理图 Fig. 2 Online-identification schematic diagram

2.3 神经网络参数设置实验

3 仿真实验 3.1 RBF神经网络离线辨识实验

 图 3 预测扭矩与仿真扭矩曲线图 Fig. 3 Curves of predicted torque and simulated torque

 图 4 预测扭矩误差曲线图 Fig. 4 Curve of prediction torque error

 图 5 预测转速与仿真转速曲线图 Fig. 5 Curve of predicted speed and simulated speed

3.2 RBF神经网络在线辨识实验

 ${F}_{r}=0.25\;{\rm{sin}}\left(0.314{t}_{s}\right)+0.7。$ (22)

 图 6 预测扭矩误差曲线图 Fig. 6 Curve of prediction torque error

 图 7 预测转速与仿真转速曲线图 Fig. 7 Curve of predicted speed and simulated speed

 图 8 预测转速误差曲线图 Fig. 8 Curve of prediction speed error
4 结　语

RBF神经网络系统辨识方法可对不同被辨识对象进行辨识建模，这与通过分析柴油机内部机理从而建立模型的方式相比，有着更加便捷、高效的特点，更为非线性、时变“黑箱”系统的逼近问题提供了解决方案。辨识建立的柴油机模型具有仿真精确度高、实时性强的优点，可应用于电子调速器的设计、调试，也可为实船训练系统提供模型基础。

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