# Research on Short-Term Traffic Flow Combination Prediction Based on CEEMDAN and Machine Learning
## 4 Combined Model Construction and Case Analysis Based on CEEMDAN and Machine Learning
### Case Studies
#### 4.2.2 Data Preprocessing  
The authors selected a time series of traffic flows for five consecutive days, as shown in Figure 5. It can be seen from the traffic flow time series curve chart that the traffic flow data do not form a gentle curve but fluctuate significantly with time changes. The traffic flow suddenly increased or decreased at some time points, showing strong randomness. At the same time, the trends of the traffic flows were similar over the course of the days, showing the cyclical nature of traffic flows.  
For the existing traffic flow data, CEEMDAN was used for decomposition, and the white noise of 500 sets of standard deviations of 0.2 was added. The decomposition result is shown in Figure 6. As can be seen in Figure 6, the original traffic flow was decomposed into eight well-performing component sequences, which show the frequency and amplitude changes of the traffic flow sequence. In the figure, from top to bottom, the frequency of the component sequence gradually decreases, and the amplitude gradually decreases. IMF\({}_{1}\) has the largest fluctuation and shortest period, and IMF\({}_{8}\) has the smallest fluctuation, the longest period, and a certain degree of stationarity.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Time** & **Traffic Flow/Vehicle** & **Time** & **Traffic Flow/Vehicle** \\ \hline
7 October 2019 00:00:00 & 43 & 7 October 2019 01:05:00 & 38 \\
7 October 2019 00:05:00 & 47 & 7 October 2019 01:10:00 & 41 \\
7 October 2019 00:10:00 & 42 & 7 October 2019 01:15:00 & 38 \\
7 October 2019 00:15:00 & 40 & 7 October 2019 01:20:00 & 36 \\
7 October 2019 00:20:00 & 43 & 7 October 2019 01:25:00 & 38 \\
7 October 2019 00:25:00 & 45 & 7 October 2019 01:30:00 & 42 \\
7 October 2019 00:30:00 & 38 & 7 October 2019 01:35:00 & 39 \\
7 October 2019 00:35:00 & 40 & 7 October 2019 01:40:00 & 36 \\
7 October 2019 00:45:00 & 36 & 7 October 2019 01:45:00 & 36 \\
7 October 2019 00:50:00 & 36 & 7 October 2019 01:50:00 & 36 \\
7 October 2019 00:55:00 & 43 & 7 October 2019 01:55:00 & 40 \\
7 October 2019 01:00:00 & 38 & 7 October 2019 02:00:00 & 38 \\ \hline \end{tabular}
\end{table}
Table 1: Partial traffic flow data.  
In order to measure the decomposition effect of CEEMDAN, the reconstruction error after the decomposition of traffic flow was calculated. Figure 7 shows the reconstruction error. As can be seen in the figure, the maximum reconstruction error does not exceed 6 \(\times\) 10\({}^{-14}\). The reconstruction error is extremely small and not enough to have an impact on the prediction results and can be ignored.  
In order to accurately predict the sequence of different traffic flow components, the PE values of each IMF component obtained from the decomposition analysis were calculated. In the calculation of the PE values, the embedded dimension m and the delay time \(\tau\) affected the sizes of the PE values. The embedded dimension m was 6 and the delay time \(\tau\) was 1. The calculation results for each IMF component are shown in Table 2 and Figure 8.  
Figure 5: Five-day traffic flow time series curve.  
Figure 6: CEEMDAN decomposition of traffic flow time series graph.  
and IMF\({}_{7}\) are between 0.3 and 0.5, indicating that the randomness and complexity of these three components are not high, and they are regarded as intermediate-frequency components. The permutation entropy value of IMF8 is between 0 and 0.1, indicating that the randomness and complexity of the component sequence are weak, and it is listed as a low-frequency component. The classification of the component sequences provided a basis for the construction of the subsequent combined models.