A Short-term Prediction of Air Traffic Flow Based on a Wavelet-optimized GRU-ARMA Model
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摘要: 空中交通流量短时预测是空中交通管理的基础，是有效缓解交通拥堵问题的前提。为提高空中交通流量短时预测的精度，减小空中交通管制员的工作压力，提出了基于小波优化GRU-ARMA的空中交通流量短时预测方法。在传统预测方法的基础上，通过小波变换对原始流量数据进行多尺度分解，提取不同频率交通流量的细节特征，对原始流量数据进行预处理。同时，根据小波变换，在低频处将频率细分作为趋势项，高频处将时间细分作为噪声项。其中，趋势项反映了空中交通流量随时间演化的整体趋势性，噪声项反映了随机因素对空中交通流量的综合影响。使用门控循环单元（GRU）神经网络模型预测趋势项，自回归滑动平均模型（ARMA）模型预测噪声项；将趋势项和噪声项的预测值叠加，得到最终的短时流量预测值。误差分析表明，该方法在每个预测点上的误差保持在2%左右，预测效果稳定；而直接采用原始流量数据进行预测的GRU、BiLSTM、CNN-LSTM神经网络模型及单一的ARMA模型，每个点的预测误差在5%~37.14%之间。与GRU、BiLSTM、CNN-LSTM神经网络模型相比，该模型的预测精度分别提高了3.02%，5.39%，5.05%。Abstract: A short-term prediction of air traffic flow is important for air traffic management, and effectively reduce traffic congestion.To improve the accuracy of the short-term prediction and reduce the workload of air traffic controllers, a wavelet-optimized GRU-ARMA based model is proposed.Based on traditional prediction methods, the originaldata of air traffic flow is decomposed by multi-scale wavelet transform. The detailed features of traffic flow with different frequenciesare extracted. Moreover, by using wavelet transform, component at low frequencies is subdivided as trend term, and time at high frequencies as noise term.Among them, the trend term represents the overall evolution trends of air traffic flow over time, while the noise term describes the comprehensive influences of random factors on air traffic flow. The gated recurrent unit (GRU) neural network and the autoregressive moving average (ARMA) model are used to predict the trend and noise terms, respectively.The prediction values of trend and noise terms are superimposed to obtain the final value of short-termprediction. An error analysis shows that the method maintains a stable prediction of about 2% at each prediction point. In contrast, the models that directly use raw traffic data for prediction (i.e. GRU, BiLSTM, CNN-LSTM neural network models) and the single ARMA model have prediction errors ranging from 5% to 37.14%.Compared to the GRU, BiLSTM and CNN-LSTM neural network models, the prediction accuracy of the proposed model is increased by 3.02%, 5.39% and 5.05%, respectively.
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图 2 基于小波优化GRU-ARMA模型的空中交通流量短时预测流程
Figure 2. Short term air traffic flow frediction process based on Wavelet-Optimized GRU-ARMA model
图 8 小波优化GRU-ARMA预测结果
Figure 8. Prediction results of the wavelet-optimized GRU-ARMA model
表 1 不同分解层数信噪比对比
Table 1. Comparison of different decomposition layers of signal-to-noise ratio
小波基函数 分解层数 信噪比 bior2.2 3 24.195 0 4 24.175 6 5 24.174 6 db3 3 21.701 3 4 21.663 6 5 21.639 2 sym4 3 22.383 5 4 22.336 5 5 22.332 5 
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表 2 不同置信区间对应的临界ADF值
Table 2. Corresponding critical ADF value under different confidence intervals
置信区间 临界ADF值 99% -3.430 9 95% -2.861 8 90% -2.566 9
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表 3 5种模型的评价指标
Table 3. Evaluation indexes of four models
预测模型 评价指标 RMSE MAE MAPE/% 小波优化GRU-ARMA 1.338 0.958 1.74 GRU 3.234 2.542 4.76 BiLSTM 4.996 3.958 7.13 CNN-LSTM 4.601 3.667 6.79 ARMA 5.208 3.33 6.04
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