## 3 Simulation Studies and Results
### Evaluation of LSTM Predictive Model Performance  
The raw data is collected in a 1-s interval. At each monitoring point, the noise data was examined for two weeks with two 1-week-long monitoring periods to get eight 1-s interval data sets. The monitoring data of 60 s per minute is averaged and combined to obtain 1-min interval data sets. A similar average operation was applied to get the 10-min interval and 30-min interval data sets. For each data set, 80% of the data in the chronological order was used for training, and the last 20% of the data was exploited to test model performance. Figure 6 exemplifies the RMSE and MAE of predicted noise value and actual observations on the test data sets.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multirow{2}{*}{**ADF Test Result**} & \multicolumn{5}{c}{**Test Critical Values**} \\ \cline{3-6}  & & **1\% Level** & **5\% Level** & **10\% Level** \\ \hline
01\_a & \(-18.62\) & & & & & \\
02\_a & \(-24.82\) & & & & & \\
03\_a & \(-13.76\) & & & & & \\
04\_a & \(-24.09\) & & \(-3.43\) & \(-2.86\) & \(-2.57\) \\
01\_b & \(-14.78\) & & & & & \\
02\_b & \(-17.33\) & & & & & \\
03\_b & \(-13.64\) & & & & & \\
04\_b & \(-23.07\) & & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 6: Stationary tests for noise time series of different sampling points and monitoring periods.  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Monitoring Point** & **Average** & **Maximum** & **Minimum** & **Standard Deviation** & **Quartile 1** & **Quartile 2** & **Quartile 3** \\ \hline
01 & 1.39 & 36.7 & \(-0.5\) & 0.79 & 2.6 & 0.7 & 0.7 \\
02 & 0.13 & \(-6.3\) & 0.9 & \(-0.06\) & 0.1 & 0.1 & 0.1 \\
03 & 1.02 & 4.3 & 1.4 & 0.3 & 0.8 & 2.5 & 0.6 \\
04 & 0.59 & \(-5\) & 0.2 & \(-0.32\) & 1.4 It can be observed in Figure 6 that the LSTM network predicts the noise level with RMSE and MAE ranging between 1.77-3.20 dB(A) and 1.41-1.95 dB(A) in 1-s interval data sets respectively. Also, it forecasts the noise level to range between 0.71-1.64 dB(A) and 0.46-1.15 dB(A) in 1-min interval data sets for RMSE and MAE respectively while the noise level prediction by the LSTM network in 10-min interval data sets for RMSE and MAE ranges between 0.48-0.93 dB(A) and 0.31-0.69 dB(A) respectively. Lastly, the next level prediction made by the LSTM network in 30-min interval data sets for RMSE and MAE vary between 1.14-2.38 dB(A) and 0.73-1.57 dB(A) respectively.  
Intuitively, the prediction results are fairly good based on the results of the above four groups of noise data in the LSTM model. For different monitoring points and different periods, the models behave differently. In general, the larger the time interval, the better the model performance, because the randomness of the noise is weakened as the time interval becomes larger. However, due to insufficient data volume, the number of records in the 30-min interval data set is limited, and the network is not trained enough to perform well.  
Considering the visualization of the data (too many drawing points may cause the image to appear messy), we used 10-min interval datasets throughout a monitoring day to compare the observation values and prediction values obtained by the LSTM model. As is displayed in Figure 7, the predicted values are fitted to the fluctuations of the actual values.  
Figure 6: Model performance on different time interval datasets: (**a**) 1-s interval; (**b**) 1-min interval; (**c**) 10-min interval; (**d**) 30-min interval.