# A Machine Learning Model for Predicting Noise Limits of Motor Vehicles in UNECE R51 Regulations
## 4 Prediction of Acceleration Noise Limits by Using the Proposed BPNN Model
### Prediction of Noise Limits for Future Revision of UNECE Regulations  
In this section, according to the development trend of noise limits defined in UNECE R51 regulations, the proposed BPNN model is employed to predict the new noise limits of motor vehicles for the future revisions of UNECE regulations. By using its migration ability, shifting one unit of values from the original noise limits backwards, that is, the proposed BPNN model updates the noise limits specified in the second to seventh as inputs to replace those from first to sixth in the regulations, and they are used to predict the noise limits for the next eighth revision of the regulations.  
The predicted values of these noise limits of all vehicle categories are shown in Table 6. To better express the trend and law of the future noise limits, a change rate (CR) can be determined by  
\[CR=\frac{CNL_{n+1}-CNL_{n}}{CNL_{n}}\times 100\%\quad(n=1,\,2,\,3,\,4,\,5,\,6, \,7) \tag{8}\]  
where, \(CNL_{n}\) is noise limits with revision number \(n\) standing for different versions of UNECE regulations. According to the CR with revision number 7, there are two scenarios, either positive or negative:  
(1) The negative rate of change indicates that the vehicle noise limits are becoming stricter, which is conducive to the popularisation and promotion of new automotive technology on vehicle vibration control and noise reduction. It is in line with the development theme of traffic noise control in an urban city, but the cost of noise control would be high.  
(2) On the contrary, a positive rate of change indicates that automotive noise limits become looser, which is not conducive to provide better automobile products. In such four cases in M1, M2 and N1 categories, the existing noise limits are suggested being maintained reasonably, and it also suggests the current noise limits are already very strict.  
Large fluctuations in the rate of change mainly occur in such a category of vehicles with higher current noise limits than others. The objective of next revision of the regulations on noise limits will focus on reducing the noise limits of these categories of vehicle, such as N2 and N3, sharing technologies to reduce vibrations and noises on all categories of vehicles, and improving the quality of automobile products.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Categories of Vehicle**} & \multicolumn{2}{c}{**Current Noise Limits**} & \multicolumn{2}{c}{**Predicted Noise Limits for Next**} \\  & & **with Revision Number 7** & **Revision (Revision Number 8)** & **CR** \\ \hline \multirow{3}{*}{M1} & 1 & 68 & 69.14 & 1.68\% \\  & 2 & 69 & 69.40 & 0.58\% \\  & 3 & 71 & 69.83 & \(-\)1.65\% \\ \hline \multirow{3}{*}{M2} & 1 & 69 & 69.89 & 1.28\% \\  & 2 & 71 & 69.95 & \(-\)1.48\% \\  & 3 & 72 & 69.59 & \(-\)3.34\% \\  & 4 & 72 & 69.82 & \(-\)3.03\% \\ \hline \multirow{3}{*}{M3} & 1 & 73 & 70.45 & \(-\)3.49\% \\  & 2 & 76 & 72.23 & \(-\)4.97\% \\  & 3 & 77 & 72.26 & \(-\)6.15\% \\ \hline \multirow{3}{*}{N1} & 1 & 69 & 69.19 & 0.27\% \\  & 2 & 71 & 69.16 & \(-\)2.59\% \\ \hline \multirow{3}{*}{N2} & 1 & 74 & 69.57 & \(-\)5.99\% \\  & 2 & 75 & 70.73 & \(-\)5.70\% \\ \hline \multirow{3}{*}{N3} & 1 & 76 & 70.63 & \(-\)7.07\% \\  & 2 & 77 & 73.03 & \(-\)5.15\% \\ \cline{1-1}  & 3 & 79 & 73.75 & \(-\)6.64\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: Predicted values by using the proposed BPNN model.