﻿ 基于平流层风场预测的浮空器轨迹控制<sup>*</sup>
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Trajectory control of aerostat based on prediction of stratospheric wind field
LI Kui, DENG Xiaolong, YANG Xixiang, HOU Zhongxi
College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China
Received: 2018-09-12; Accepted: 2018-11-08; Published online: 2018-11-27 12:00
Foundation item: Natural Science Foundation of Hunan Province, China (2018JJ3590, 2018JJ3587)
Corresponding author. YANG Xixiang.E-mail:nkyangxixiang@163.com
Abstract: The stratospheric wind environment has an important influence on the aerostat design and trajectory control. Taking the wind field data from 2005 to 2010 in Changsha as an example, this paper firstly uses the proper orthogonal decomposition (POD) method to reduce order of the wind field data, and then uses the Fourier series and BP neural network algorithm to predict the stratospheric wind field. The prediction accuracy of the two models is compared and analyzed. Finally, the dynamic model and height control model of the near-space aerostat are established, and the influence of the two wind field prediction models on the trajectory control of the aerostat is analyzed. The research results show that the prediction model based on the BP neural network is more accurate and more reliable than the Fourier prediction model, and it can provide a better reference value for the flight trajectory control of the aerostat.
Keywords: proper orthogonal decomposition (POD) method     Fourier series     BP neural network algorithm     wind field prediction     near-space aerostat

1 平流层风场预测模型

POD方法是风场建模中常用的一种方法，本文在采用POD方法对风场数据进行降阶处理的基础上，分别采用Fourier级数与BP神经网络算法对风场进行预测，风场预测模型原理如图 1所示。

 图 1 风场预测模型原理图 Fig. 1 Schematic of wind field prediction model
1.1 基于POD方法的风场降阶模型

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 图 2 东西方向风场POD模态的相对和累积模态能量 Fig. 2 Relative and cumulative modal energy of east-west wind field POD modes

 图 3 南北方向风场POD模态的相对和累积模态能量 Fig. 3 Relative and cumulative modal energy of north-south wind field POD modes
 图 4 POD降阶模型 Fig. 4 POD reduced order model
1.2 基于Fourier级数的风场预测模型

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 图 5 Fourier级数拟合 Fig. 5 Fourier series fitting

 图 6 基于Fourier风场预测 Fig. 6 Prediction of wind field based on Fourier
1.3 基于BP神经网络的风场短期预测模型

BP神经网络模型一般分为3层前馈网或3层感知器：输入层、中间层(也称隐含层)和输出层。主要特点：各层神经元只与相邻层神经元相连接，同层的内神经元彼此独立没有连接，同时各层神经元之间也不存在反馈连接，从而构成了层次分明的前馈型神经网络系统[9-10]，BP神经网络拓扑结构如图 1中虚线框图所示。

BP算法的实质是将一组输入、输出问题转化成非线性映射问题，并通过梯度下降算法迭代求解权值[11-13]。平流层风场短期预测中，对于输出层有

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 图 7 基于BP神经网络预测系数 Fig. 7 Prediction of coefficients based on BP neural network

 图 8 基于BP神经网络风场预测 Fig. 8 Prediction of wind field based on BP neutral network
2 风场预测误差分析

 图 9 风场预测误差 Fig. 9 Wind field prediction errors

2种风场预测方法采取的POD降阶阶数一致，降阶模型导致的误差也一致，因此风场预测精度与投影系数的拟合程度有直接的关系。分别将2种预测模型的拟合系数与实际投影系数进行比较分析，以第1阶POD模态的投影系数为例，如图 10图 11所示。相对于Fourier级数拟合误差，基于BP神经网络所获取的系数拟合误差范围更小，误差值的分布更加平整、均匀，说明采用BP神经网络算法的系数拟合程度更高，可信度更强。

 图 10 Fourier级数拟合误差 Fig. 10 Fourier series fitting errors
 图 11 BP神经网络预测误差 Fig. 11 Prediction errors of BP neural network
3 动力学建模

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4 飞行仿真与分析

 图 12 五天风场预测 Fig. 12 Wind field prediction for 5 days

 图 13 工作流程图 Fig. 13 Diagram of work process

 图 14 竖直方向运动状态 Fig. 14 Motion state in vertical direction

 图 15 水平方向运动状态 Fig. 15 Motion state in horizontal direction
5 结论

1) 以长沙地区为例，选取海拔高度10~30 km五年风场数据，采用了一种对平流层风场数据进行降阶处理的POD方法，在此基础上，分别采用了Fourier级数与BP神经网络算法对平流层风场进行预测。

2) 对2种模型的预测精度进行了比较分析，通过建立临近空间浮空器的动力学模型和高度调控模型，分析了2种风场预测模型对浮空器轨迹控制的影响。

3) 相对于Fourier预测模型，基于BP神经网络预测模型的预测预测误差波动的范围更小，误差值的分布更加平整、均匀，预测精度更高，可信度更强，能够更好地为浮空器飞行轨迹控制提供参考价值。

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#### 文章信息

LI Kui, DENG Xiaolong, YANG Xixiang, HOU Zhongxi

Trajectory control of aerostat based on prediction of stratospheric wind field

Journal of Beijing University of Aeronautics and Astronsutics, 2019, 45(5): 1008-1018
http://dx.doi.org/10.13700/j.bh.1001-5965.2018.0538