## 4 Case Study
### Comparison Results of Passenger Flow Prediction  
To test and verify the performance of the ARMA-RBFNN algorithm, the original passenger flow data from the Xinjiekou, Pin'anli, Xisi and Lingjinghutong stations of Beijing Line 4 were collected from 7:00 to 9:00 on weekdays for one month. This paper takes 3-4 s as the interval period to process the passenger flow data by using the change-point  
Figure 5: Distribution of passenger flow changes under different days: (**a**) passenger flow entering stations on different days; (**b**) passenger flow leaving stations on different days. Figure 6: Simulation modeling of passenger activity. algorithm. As shown in Figure 8, the change-point algorithm can search for the passenger flow data with change points; here, we use the Xinjiekou station as an example. After the change-point algorithm processing, wavelet functions are used to denoise the passenger flow data, including Haar wavelet, db wavelet, sym wavelet and coif wavelet. A variety of wavelet decomposition levels are used for denoising. The signal-to-noise ratio (SNR) is calculated by four kinds of wavelet functions and their changes under different decomposition levels, which are shown in Tables 2 and 3. Table 2 shows that the larger the signal-to-noise ratio, the better the denoising effect. When the decomposition level of db wavelet function is 4, the signal-to-noise ratio is at its largest. Therefore, the wavelet function of db4 can be used to denoise the passenger flow data for embarking on the train. Similarly, as shown in Table 3, it can be observed that the wavelet function of db5 is used to denoise the passenger flow data for disembarking from the train. The condition of using the ARMA algorithm is a stable time series; the stability of passenger flow when entering/leaving the station should be tested before using ARMA. As shown in Figures 9 and 10, the value and characteristics of the autocorrelation function and partial autocorrelation function are calculated and analyzed training both embarking and disembarking states. Figures 9 and 10 demonstrate that the autocorrelation function decreases from 1.0 to 0.0 and fluctuates nearby. The fluctuation amplitude gradually decreases. The partial autocorrelation function decays from 1.0 to 0.0 and oscillates at 0.0 and nearby, infinitely close to 0.0. Both of them are tailing and belong to stable time series, which satisfies the applicability conditions of the ARMA algorithm. In this section, the rank of the ARMA model is determined based on AIC criterion. According to experimental calculation, when \(p\) = 2, \(q\) = 3, AIC obtains the minimum value. Thus, the rank of the ARMA model is determined as ARMA (2, 3). Then, the selection and performance of the RBFNN algorithm's parameters are shown in Figure 11. Finally, the performance of ARMA-RBFNN is compared with other deep learning models in the datasets. Figure 9: Visualization for the stability test of passenger flow entering the station. Specifically, some commonly used time series prediction models (i.e., LSTM variation ([PERSON], [PERSON] and Tang [55]) and MQ-RNN ([PERSON] et al. [56]) are selected as benchmark models. The benchmark models are detailed as follows. First, the LAG-LSTM parameters are set as learning rate = 0.002, batch size = 80, pervious time steps = 14 and time delay = 5. The dimension of the hidden state is set as 12. The dropout is 0.2 ([PERSON], [PERSON] and [PERSON] [55]). Next, MQ-RNN is constructed as a simple combination of state and control variables as input data for the standard RNN network. The parameters are set as \(h_{t}\in\mathbb{R}^{12}\) and N = 14 ([PERSON] et al. [56]). In order to evaluate the performance of different algorithms, the Mean Absolute Percentage Error (MAPE) is selected as the evaluation index. As the ARMA-RBFNN algorithm predicts the passenger flow, it is necessary to evaluate the performance of this method as follows (see Figure 12 and Table 4).