基于GA、RBF和改进Cao方法的空中交通流预测方法

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。 

A Method for Predicting Air Traffic Flow Based on a Combined GA,RBF, and Improved Cao Method

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.