## 6 Empirical Research
### Empirical Results and Analysis
Therefore, if this method is chosen, determining how to eliminate invalid data without referencing real values or other prediction methods becomes a critical challenge. The prediction for a 15 min period of one day will be changed into the consecutive days based on the data in 9:00-9:15 from 22 May 2017 to 30 May 2017; these two methods are used to predict 100 times per day. The prediction results are sorted from small to large and the corresponding data of the 50% quantile is selected as the final prediction data, as shown in Figure 9.  
Figure 8: AR05 traffic demand prediction and error during 9:00–9:15 22 May 2017 (BP After). The error performance parameters of the above prediction results are compared on a daily basis, as shown in Figure 6.0 It can be seen that the performance of the probability density prediction method (red line) is significantly better than that of the BP neural network prediction method (blue line) over an extended period of time. We will select another day from 22 May 2017 to 30 May 2017, such as May 23 rd. The probability density prediction method and BP neural network prediction method are used to predict the traffic demand in the morning peak of 07:45:00-11:29:59 every 15 min. Finally, corresponding to these two methods, 15 probabilistic prediction results are obtained, and the probability density distribution is shown in Figure 6.1  
Figure 6.2 AR05 traffic demand prediction error analysis of two prediction methods. Figure 6.3 AR05 traffic demand prediction and error in 9:00-9:15 from 22 May 2017 to 30 May 2017. Figure 6.4 AR05 traffic demand probability density distribution during 07:45:00–11:29:59 23 May 2017. The 15 probabilistic prediction results are compared with the deterministic prediction results obtained by the BP neural network prediction method. As shown in Figure 12, it can be found that the accuracy of the probability prediction method under a continuous time condition is also better than that of the BP neural network prediction method. We compare the 15 probabilistic predictions, 15 BP predictions and the sector's airspace capacity (35 flights/15 min). As shown in Figure 13, according to the balance between the deterministic predictions and the sector's airspace capacity, the interventional flow control measures should be taken during 09:15:00-09:29:59, 09:45:00-09:59:59, and 11:00:00-11:14:59. In fact, compared with more accurate probabilistic prediction results, air traffic flow management measurements should be appropriately intervened to avoid overload, because the flow demand is always at the limit of capacity during 08:45:00-09:29:59. By contrast, traffic demand is far less than sector's airspace capacity during 11:00:00-11:14:59, so there is no need to intervene in air traffic flow management measurements. Figure 6.5 AR05 traffic demand prediction and error during 07:45:00–11:29:59 22 May 2017. Figure 6.6 The comparison of AR05 traffic demand prediction results during 07:45:00–11:29:59 22 May 2017. From the further comparison in Figure 13, because the BP neural network prediction method is limited by the prediction scale, the accuracy of the prediction result is not as good as the probabilistic prediction method when the prediction scale is larger or numerous data samples. That is, the prediction results during the peak hours of flight operations are more accurate. The probabilistic prediction results accurately predict sector traffic overload during 09:00:00-09:14:59, which is conducive to the air traffic management department taking measures to ease congestion in advance. However, the probabilistic prediction results show that the traffic demand does not exceed the capacity, thus avoiding false alarms problem caused by BP neural network predictions method during 07:45:00-07:59:59 and 11:00:00-11:14:59.