Research on the Multi-step Prediction of Volterra Neural Network for Traffic Flow
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摘要: 研究了VNNTF 神经网络(Volterra neural network trafficflow model,VNNTF) 交通流量混沌时间序列多步预测问题. 通过分析比较交通流量混沌时间序列相空间重构的嵌入维数和Volterra 离散模型之间的关系,给出了确定交通流量Volterra 级数模型截断阶数和截断项数的方法,并在此基础上建立了VNNTF 神经网络交通流量时间序列模型;设计了交通流量Volterra 神经网络的快速学习算法;最后,利用交通流量混沌时间序列对VNNTF 网络模型,Volterra 预测滤波器和BP 网络进行了多步预测实验,比较了多步预测结果的仿真图、绝对误差的柱状图以及归一化后的方均根;实验结果表明VNNTF 神经网络的多步预测性能明显优于Volterra 预测滤波器和BP 神经网络.Abstract: This paper studies multi-step prediction of traffic flow chaotic time series based on Volterra neural network traffic flow model (VNNTF). Firstly, by analyzing the relationship between the embedding dimension of phase space reconstruction of traffic flow chaotic time series and Volterra discrete model, we give the method to determine the truncation order and items of Volterra series. Secondly, based on the first step, we build the VNNTF neural networks model of chaos time series and design the fast learning algorithm of Volterra neural network traffic flow. Thirdly, we describe multi-step prediction experiments based on chaotic time series VNNTF traffic network model, Volterra prediction filter and BP networks. Finally, we compare the multi-step prediction simulation diagram with the absolute error histogram and normalized root mean square are compared. The experimental results show that the VNNTF neural network multi-step prediction performance is significantly better than those of the Volterra filter and BP neural network.
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[1] Xiao Z L, Jing X J, Cheng L. Parameterized convergence bounds for Volterra series expansion of NARX models. IEEE Transactions on Signal Processing, 2013, 61(20): 5026-5038 [2] Zhu Xiong-Yong, Zhou Jie, Tan Hong-Zhou. Method for eliminating LCD motion de-blurring model's pole. Acta Automatica Sinica, 2012, 38(5): 759-768 (朱雄泳, 周杰, 谭洪舟. 一种消除 LCD 运动图像去模糊模型极点的方法. 自动化学报, 2012, 38(5): 759-768) [3] Asyali M, Alc M. Obtaining Volterra kernels from neural networks. In: Proceedings of World Congress on Medical Physics and Biomedical Engineering 2006, IFMBE Proceedings. Berlin: Springer Berlin Heidelberg, 2007. 11-15 [4] Silveira D D, Gilabert P L, dos Santos A B, Gadringer M. Analysis of variations of volterra series models for RF power amplifiers. IEEE Microwave and Wireless Components Letters, 2013, 23(8): 442-444 [5] Ghasemi M, Tavassoli K M, Babolian E. Numerical solutions of the nonlinear Volterra-Fredholm integral equations by using homotopy perturbation method. Applied Mathematics and Computation, 2007, 188(1): 446-449 [6] Meng X Z, Chen L S. Permanence and global stability in an impulsive Lotka-Volterra n-species competitive system with both discrete delays and continuous delays. International Journal of Biomathematics, 2008, 1(2): 179-196 [7] Despotovic V, Goertz N, Peric Z. Nonlinear long-term prediction of speech based on truncated Volterra series. IEEE Transactions on Audio, Speech, and Language Processing, 2012, 20(3): 1069-1073 [8] Chen F D. Permanence and global attractivity of a discrete multispecies Lotka-Volterra competition predator-prey systems. Applied Mathematics and Computation, 2006, 182(1): 3-12 [9] Kobayakawa S, Yokoi H. Evaluation of prediction capability of Non-recursion type 2nd-order Volterra neuron network for electrocardiogram. In: Proceedings of the 15th International Conference on Neuro-Information Processing of the Asia Pacific Neural Network Assembly, Lecture Notes in Computer Science. Berlin, Heidelberg: Springer, 2009, 5507: 679-686 [10] Kang Ling, Wang Cheng, Jiang Tie-Bing. Hydrologic model of Volterra neural network and its application. Journal of Hydroelectric Engineering, 2006, 25(5): 22-26 (康玲, 王乘, 姜铁兵. Volterra神经网络水文模型及应用研究. 水力发电学报, 2006, 25(5): 22-26) [11] Rubiolo M, Stegmayer G, Milone D. Compressing arrays of classifiers using Volterra-neural network: application to face recognition. Neural Computing & Applications, 2013, 23(6): 1687-1701 [12] Yu J L, Yi Z, Zhou J L. Fcontinuous attractors of Lotka-Volterra recurrent neural networks with infinite neurons. IEEE Transactions on Neural Networks, 2010, 21(10): 1690-1695 [13] Jia Li, Yang Ai-Hua, Qiu Ming-Sen. Research on multi-signal based neuro-fuzzy Hammerstein-Wiener model. Acta Automatica Sinica, 2013, 39(5): 690-696 (贾立, 杨爱华, 邱铭森. 基于多信号源的神经模糊Hammerstein-Wiener 模型研究. 自动化学报, 2013, 39(5): 690-696) [14] Si Wei, Duan Zhe-Min, Wang Hai-Tao. Novel method based on projection of vectors in linear space to identify Volterra kernels of arbitrary orders. Application Research of Computers, 2008, 25(11): 3340-3342 (司伟, 段哲民, 王海涛. 基于线性空间投影的计算Volterra级数高阶核的方法. 计算机应用研究, 2008, 25(11): 3340-3342) [15] Li Peng-Hua, Chai Yi, Xiong Qing-Yu. Quantum gate Elman neural network and its quantized extended gradient back-propagation training algorithm. Acta Automatica Sinica, 2013, 39(9): 1511-1522 (李鹏华, 柴毅, 熊庆宇. 量子门Elman神经网络及其梯度扩展的量子反向传播学习算法. 自动化学报, 2013, 39(9): 1511-1522) [16] Zhao H Q, Zeng X P, He Z Y. Low-complexity nonlinear adaptive filter based on a pipelined bilinear recurrent neural network. IEEE Transactions on Neural Networks, 2011, 22(9): 1494-1507 [17] Wu Yu-Xiang, Wang Cong. Deterministic learning based adaptive network control of robot in task space. Acta Automatica Sinica, 2013, 39(9): 806-815 (吴玉香, 王聪. 基于确定学习的机器人任务空间自适应神经网络控制. 自动化学报, 2013, 39(9): 806-815) [18] Yakubov Y A. On nonlinear Volterra equations of convolution type. Differential Equations, 2009, 45(9): 1326-1336 [19] Murakami S, Ngoc P H A. On stability and robust stability of positive linear Volterra equations in Banach lattices. Central European Journal of Mathematics, 2010, 8(5): 966-984 [20] Bibik Y V. The second Hamiltonian structure for a special case of the Lotka-Volterra equations. Computational Mathematics and Mathematical Physics, 2007, 47(8): 1285-1294 [21] Yin L S, Huang X Y, Yang Z Y, Xiang C C. Prediction for chaotic time series based on discrete Volterra neural networks. In: Proceedings of the 3rd International Symposium on Neural Networks, Lecture Notes in Computer Science. Berlin, Heidelberg: Springer, 2006, 3972: 759-764
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