文章摘要
李阳,杨亚莉,钟卫军.基于DRNet的常微分方程模型逼近和序列预测方法[J].空军工程大学学报,2022,23(5):83-89
基于DRNet的常微分方程模型逼近和序列预测方法
DRNet for ODE model Approximation and Series Prediction
  
DOI:
中文关键词: 深度学习  密集残差网络  序列预测  模型逼近
英文关键词: deep learning  DenseResNet  series prediction  model approximation  ResNet
基金项目:国家自然科学基金(11902362);空军工程大学基础部研究生创新基金
作者单位
李阳,杨亚莉,钟卫军 1. 空军工程大学基础部西安7100512. 文昌航天发射场指挥控制中心海南文昌5713003. 宇航动力学国家重点实验室西安710043 
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中文摘要:
      针对残差网络预测精度偏低的问题,基于系统观测数据和相轨线的关系,提出密集残差网络的方法实现对自治系统的拟合逼近和序列的高精度预测。首先,为强化对数据内含“特征信息”的提取和流通使用,将神经网络各隐藏层的输入与之前各层输出拼接后作为本层的输入,形成密集连接模块;其次,为避免加大网络深度时出现的“退化”现象,引入残差机制,将密集连接模块的输入层与输出层相连,形成密集残差网络。最后,将密集残差网络应用于线性的单自由度系统振动模型和非线性的SEIRS模型、Logistic Volterra模型。结果表明,在规模为5 000和10 000的数据集上,密集残差网络对模型的拟合逼近效果和预测精度优于残差网络、反向传播神经网络和密集网络,特别是在非线性系统上的4项定量评价指标均优于对照模型,表现出密集残差网络对自治系统模型逼近和序列预测的高有效性;同时,在观测数据中加入5%的噪声后,密集残差网络表现出较好的抗干扰性。
英文摘要:
      In view of the low prediction accuracy of ResNet, a method of DenseResNet (DRNet) for approximation of autonomous systems and series prediction is proposed based on the relationship between observed data and the system phase trajectory. Firstly, in order to strengthen the extraction and the circulation of ‘feature information’ contained in the data, all the outputs of previous layers in each hidden layer of feedforward neural network are concatenated as an input of this layer to form a dense block. Secondly, to avoid the ‘degradation’ phenomenon occurs when the depth of neural network increases, the residual mechanism is introduced to connect the input layer and output layer of the dense block to form the DRNet. Finally, DRNet is applied to the linear model, Damped single degree of freedom system and nonlinear models, SEIRS model and Logistic Volterra model. The results show that DRNet outperforms the ResNet, Back Propagation Neural Network (BPNN) and DenseNet in terms of model approximation and prediction accuracy on both datasets of 5 000 and 10 000. According to the four evaluation indexes on the nonlinear models, DRNet has high effectiveness on autonomous systems. The DRNet also shows good noise immunity for its better performance on the data with 5% noise.
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