# Noise Prediction Using Machine Learning with Measurements Analysis
## 3 Results and Discussion  
To use the GBM model for future Leq value prediction on the 125 Hz frequency band, time characteristics and historical Leq were used as the input data. There were 12 sensor data, which were recorded every 10 s (sampling time = 10 s) with an average sample of 875,000. As the training time was too long, the sampling time was lengthened in order to reduce the amount of training data. Sensor 8 was used as a sampling example and used the previous two minutes of data to make predictions at different sampling times; the results are shown in Figure 12.  
The X-axis in Figure 12 is the R\({}^{2}\)[30], which represents the degree of curve fit between the predicted value and the actual value (sensor 8 at 125 Hz in August). The R\({}^{2}\) value is distributed in the range of 0-1, and values closer to 1 indicate better prediction performance; otherwise, the prediction performance worsens. The Y axis is the RMSE [31]. Here, the higher the value indicates a worse prediction result; otherwise, the convergence is smaller. We found that a sampling time of 1 min and 30 s had a higher R\({}^{2}\) and the best prediction performance; in addition, the RMSE was below 1 dBA. However, the R\({}^{2}\) value of the 30 s sampling time was very close to those of 1 min and better, but the calculation requires double the time to complete. Thus, in the subsequent experimental design, the sampling time was adjusted to 1 min. Next, according to the frequency of harmful Leq levels at 125 Hz, a 21-dimensional feature prediction task was performed for the Leq for 12 sensors at this frequency in August. The features included the previous one minute and the previous two minutes of each frequency Leq value; the prediction results are shown in Figure 13.  
In Figure 13, the X-axis represents the R\({}^{2}\). The Y-axis represents the RMSE and the prediction results of 12 sensors at 125 Hz; R\({}^{2}\) > 0.7 represents sensors 10, 8, and 3, among which sensor 3 had the largest R\({}^{2}\) value and the smallest RMSE value. This indicates that input characteristics and Leq values are highly influence. In addition, the RMSE values of the 12 sensors were all below 1 dBA, indicating that the difference between the predicted Leq values and the actual Leq values was minute. Therefore, the R\({}^{2}\) value was mainly used as an indicator to judge the quality of the prediction results. Observing the prediction results of sensor 1, not only was the R\({}^{2}\) only 0.0643, but the RMSE was within 0.75 dBA and the input features were almost unrelated to the Leq values. Figure 12: Different sampling times vs. predicted effect. However, we added multiple linear regression (MLR) experiments to compare noise prediction results with the proposed approach, as shown in Figures 14a and 15a. This shows that GBM outperforms MLR in terms of both index, R\({}^{2}\), and RMSE while using the full 21 dimensions at 125 Hz. As shown in Figure 14b, the results clearly show that the GBM algorithm achieved higher R\({}^{2}\) and showed a good grasp of the trend and reference value of noise fluctuations at each sensor, thus it was more effectively and accurate than MLR in this task. This result also shows that although the working environment was relatively stable, a very simple prediction model may not work well. This explains why we used the GBM prediction model for this problem in the NSRRC. Figure 14: (**a**) Performance of multiple linear regression (MLR) method. (**b**) Combine MLR and gradient boosting model (GBM). Figure 13: Predicted effect at 125 Hz for different sensors. Furthermore, we compared three different input features set with 21, 16, and five dimensions, respectively, to investigate the impact of input factors. The conditions are shown in Table 1, and the prediction results in Figure 15a-c. Then, we clearly found more dimensions were better in terms of R\({}^{2}\). Then, it was easily found that the input 21-dimensional data had better performance, as shown in Figure 15d.