A Method for Predicting Air Traffic Flow Based on a Combined GA, RBF, and Improved Cao Method
-
摘要: 针对传统空中交通流量预测方法精度不足、时效性差的问题，考虑空中交通流量时间序列的混沌特征，在相空间重构理论的基础上，研究了结合遗传算法（GA）、径向基（RBF）神经网络与改进Cao方法的空中交通流量预测方法。为降低传统Cao方法人为参数选择引入的误差，提高相空间重构精度，通过判定虚假邻近点，以及迭代比较嵌入维度离差和可接受偏差，确定重构相空间嵌入维度值的选择标准，进而得到重构后的空中交通流量时间序列数据；为提升径向基神经网络预测精度并降低参数误差，使用遗传算法优化RBF神经网络的中心矢量、加权系数和输出层阈值，再通过最优系数标定后的神经网络对重构后的时间序列进行预测；利用实际空中交通流量数据进行仿真以验证方法的有效性，并结合最大Lyapunov指数和预测结果分析了预测的时效性以及时间尺度对精度影响。结果显示：①改进后的预测方法具有更好的非线性拟合能力，提高了交通流量时间序列的预测精度；②以5 min时间间隔预测为例，相比传统RBF神经网络，改进方法的平均绝对误差、均方误差以及平均绝对百分比误差分别降低了19.44%、34.78%和27.21%；③相比反向传播（BP）神经网络和长短期记忆（LSTM）神经网络，所提方法的平均绝对误差分别降低了36.20%和16.10%，运行速度分别提高了27.42%和35.00%。综上所述，所提方法能更好地解析系统的混沌特性，提升空中交通流量预测精度与速度。Abstract: Considering the chaotic characteristic of air traffic flow time series data, a prediction model based on the phase space reconstruction theory is proposed to improve the accuracy and effectiveness of previous air traffic flow prediction methods, which combines genetic algorithm (GA), radial basis function (RBF) neural network (NN) and improved Cao method. First, to reduce the error introduced by the human in the traditional Cao method and improve the accuracy of phase space reconstruction, the criteria for determining the dimension of the reconstructed phase space is developed by identifying false neighboring points and iteratively comparing the deviation of the embedded dimension with its acceptable limits. In this way, reconstructed air traffic flow time series data is developed. Secondly, to improve the prediction accuracy of the traditional RBF neural network, GA is employed to optimize center vectors, weight coefficients, and output layer thresholds of the neural network. Then, the reconstructed time series are predicted by the calibrated RBF neural network with optimal coefficients. Finally, the proposed method is verified using the observed air traffic flow data, the effectiveness of the prediction is evaluated, and the influence of the time scale on the accuracy is analyzed by incorporating the maximal Lyapunov exponent and the quality of the prediction. Study results show that ①the proposed method fits the nonlinear data well and improves the accuracy of traffic flow prediction. ②Taking the prediction with a 5-min time interval as the instance, compared with the traditional RBF neural network, the mean absolute errors (MAE), mean square errors (MSE) and mean absolute percentage error (MAPE) is reduced by 19.44%, 34.78%, and 27.21%, respectively. ③Compared with the back propagation (BP) neural network and the long short-term memory (LSTM) neural network model, the MAE of the proposed method is reduced by 36.20% and 16.10%, respectively, and the response speed is increased by 27.42% and 35.00%. In summary, the proposed method can explain the intricate chaotic properties of the system and improves the accuracy and efficiency of air traffic flow prediction.
-
图 3 嵌入维度为8的x三维重构吸引子
Figure 3. Embedded x -3d reconstruction attractor with dimension 8
图 4 嵌入维度为14的x三维重构吸引子
Figure 4. Embedded x -3d reconstruction attractor with dimension 14
图 10 4种预测方法预测效果与运行时间对比
Figure 10. Comparison of prediction effect and operation time of four prediction methods
表 1 最大Lyapunov指数
Table 1. Maximum Lyapunov exponent
时间尺度/min 时间延迟/mi 嵌入维度 改进后嵌入维度 最大Ly指数 3 3 3 6 0.001 5 5 6 4 7 0.008 2 7.5 5 6 8 0.010 3 10 4 5 7 0.021 4 12 3 4 5 0.034 2 15 3 3 4 0.083 7 
下载: 导出CSV
-
[1] PACKARD N H, CRUTCHFIELD J P, FARMER J D. Geometry from a time series[J]. Physics Review Letters, 1980, 45 (9): 712-713. doi: 10.1103/PhysRevLett.45.712 [2] LI S, XU X, MENG L. Flight conflict forecasting based on chaotic time series[J]. Transactions of Nanjing University of Aeronautics and Astronautics, 2012, 29(4): 388-394. [3] 王超, 郑旭芳, 王蕾. 交汇航路空中交通流的非线性特征研究[J]. 西南交通大学学报, 2017, 52(1): 171-178. https://www.cnki.com.cn/Article/CJFDTOTAL-XNJT201701024.htmWANG C, ZHENG X F, WANG L. Research on nonlinear characteristics of air traffic flows on converging air routes[J]. Journal of Southwest Jiaotong University, 2017, 52(1): 171-178. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-XNJT201701024.htm [4] 杨阳. 空中交通流量短期预测方法研究[D]. 天津: 中国民航大学, 2017.YANG Y. Research on short term forecasting method of air traffic flow[D]. Tianjin: Civil Aviation University of China, 2017. (in Chinese) [5] 王飞. 空中交通流非线性分形特征[J]. 西南交通大学学报, 2019, 54(6): 1147-1154. https://www.cnki.com.cn/Article/CJFDTOTAL-XNJT201906004.htmWANG F. Nonlinear fractal characteristics of air traffic flow[J]. Journal of Southwest Jiaotong University, 2019, 54 (6): 1147-1154. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-XNJT201906004.htm [6] 丛玮. 空中交通多尺度行为模式识别方法研究[D]. 南京: 南京航空航天大学, 2016.CONG W. Research on the recognition method of multi-scale behavior patterns in air traffic management[D]. Nanjing: Nanjing University of Aeronautics and Astronautics, 2016. (in Chinese) [7] 杨阳, 王超. 空中交通流扇区内飞行流量优化预测管理[J]. 计算机仿真, 2017, 34(9): 74-78.YANG Y, WANG C. Forecasting and management of flight in air traffic flow sector[J]. Computer Simulation, 2017, 34(9): 74-78. (in Chinese) [8] 王超, 朱明, 赵元棣. 基于改进加权一阶局域法的空中交通流量预测模型[J]. 西南交通大学学报, 2018, 53(1): 206-213.WANG C, ZHU M, ZHAO Y D. Air traffic flow prediction model based on improved adding-weighted one-rank local-rejion method[J]. Journal of Southwest Jiaotong University, 2018, 53(1): 206-213. (in Chinese) [9] 王飞, 韩翔宇. 基于分形插值的空中交通流量短期预测[J]. 航空学报, 2022, 43(9): 513-520.WANG F, HAN X Y. Short-term prediction of air traffic flow based on fractal interpolation[J]. Acta Aeronautica et Astronautica Sinica, 2022, 43(9): 513-520. (in Chinese) [10] 潘志毅. 基于灰色神经网络的空中交通流量预测方法[J]. 微计算机信息, 2011, 27(9): 163-164.PAN Z Y. Air traffic flow forecast method based on grey neural network[J]. Microcomputer Information, 2011, 27(9): 163-164. (in Chinese) [11] 崔德光, 吴淑宁, 徐冰. 空中交通流量预测的人工神经网络和回归组合方法[J]. 清华大学学报(自然科学版), 2005 (1): 96-99.CUI D G, WU S N, XU B. Air traffic flow forecasts based on artificial neural networks combined with regression methods[J]. Journal of Tsinghua University(Science and Technology), 2005(1): 96-99. (in Chinese) [12] ZHANG Z, ZHANG A, SUN C, et al. Research on air traffic flow forecast based on ELM non-iterative algorithm[J]. Mobile Networks and Applications, 2021(26): 425-439. [13] LIN Y, ZHANG J, LIU H. Deep learning based short-term air traffic flow prediction considering temporal-spatial correlation[J]. Aerospace Science and Technology, 2019(93): 105-113. [14] YANG Z, WANG Y, LI J, et al. Airport arrival flow prediction considering meteorological factors based on deep-learning methods[J]. Complexity, 2020(1): 1-11. [15] TAKENS F. Detecting strange attractors in fluid in turbulence[J]. Lecture Notes in Mathematics, 1981(898): 361-381. [16] 张玉梅. 交通流时间序列的分析与应用[M]. 北京: 科学出版社, 2019.ZHANG Y M. Analysis and application of traffic flow time series[M]. Beijing: Science Press, 2019. (in Chinese) [17] KENNEL M B, BROWN R, ABARBANEL H D I. Determining embedding dimension for phase-space reconstruction using a geometrical construction[J]. Physical Review A, 1992 (45): 3403-3411. [18] CAO L. Practical method for determining the minimum embedding dimension of a scalar time series[J]. Physica D: Nonlinear Phenomena, 1997, 110(1/2): 43-50. [19] 张敏. 基于RBF神经网络的短时交通流预测研究[D]. 兰州: 兰州理工大学, 2021.ZHANG M. Research on short-term traffic flow forecasting based on RBF neural network[D]. Lanzhou: Lanzhou University of Technology, 2021. (in Chinese) [20] 张玉梅, 曲仕茹, 温凯歌. 基于混沌和RBF神经网络的短时交通流量预测[C]. 2007全国控制科学与工程博士生学术论坛, 上海: 中国机械工程学会, 2007.ZHANG Y M, QU S R, WEN K G. A short-term traffic flow forecasting method based on chaos and RBF neural network[C]. 2007 National Control Science and Engineering Doctoral Academic Forum, Shanghai: Chinese Mechanical Engineering Society, 2007. (in Chinese) [21] 刘凌, 李志成, 张莹. 面向双关节机械臂的参数可调RBF神经网络控制[J]. 西安交通大学学报. 2021. 55(4): 1-7. https://www.cnki.com.cn/Article/CJFDTOTAL-XAJT202104001.htmLIU L, LI Z C, ZHANG Y. A RBF network control with adjustable parameters for 2-yoint robot manipulators[J]. Journal of Xi'An Jiaotong University, 2021, 55(4): 1-7. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-XAJT202104001.htm [22] 张勇. 交通流的非线性分析、预测和控制[D]. 北京: 北京交通大学, 2011.ZHANG Y. Nonlinear characteristics analysis, predication and control of traffic flow[D]. Beijing: Beijing Jiaotong University, 2011. (in Chinese) [23] 张海龙, 闵富红, 王恩荣. 关于Lyapunov指数计算方法的比较[J]. 南京师范大学学报(工程技术版), 2012, 12(1): 5-9. https://www.cnki.com.cn/Article/CJFDTOTAL-NJSE201201004.htmZHANG H L, MIN F H, WANG E R. The comparison for Lyapunov exponents calculation methods[J]. Journal of Nanjing Normal University(Engineering and Technology Edition). 2012, 12(1): 5-9. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-NJSE201201004.htm -
点击查看大图
图(10) / 表(1)
计量
- 文章访问数: 480
- HTML全文浏览量: 182
- PDF下载量: 20
- 被引次数: 0