## 3 Construction of the Noise Prediction Model
### Prediction Model and Parameters  
Drawing on the theoretical framework of incoherent finite-line source radiation from Section 3.1, combined with Shanghai Maglev train field measurement data (Section 2.2) and aerodynamic simulation results (Section 2.3), established international methodologies for the exterior noise prediction of high-speed wheel-rail trains and Maglev systems were synthesized to develop an environmental noise prediction model for high-speed Maglev trains. The proposed model employs a five-segment line source equivalence approach, with the equivalent continuous A-weighted sound level \(L_{Aeq,T}\) at the reception points given by  
\[L_{Aeq,T}=10\log_{10}\left[\frac{1}{T}\left(\sum_{i}t_{eq,i}\cdot 10^{0.1L_{ p,i}}\right)+10^{0.1L_{b}}\right], \tag{13}\]  
where \(T\) is the evaluation time, \(L_{b}\) is the equivalent continuous A-weighted sound level of the background noise at the prediction point, \(t_{eq,i}\) is the equivalent passing time of train \(i\), and \(t_{eq,i}\) is calculated as follows:  
\[t_{eq,i}=\frac{L}{v}\Big{(}\sqrt{1+r^{2}/L^{2}}+r/L\Big{)}, \tag{14}\]  
where \(v\) is the train operating speed to be predicted, in m/s, and \(r\) is the distance from the predicted point to the line source. \(L_{p,i}\) is the equivalent continuous A-weighted sound level during passage of the \(i\)-th train. The formula is as follows:  
\[L_{p,i}=10\log_{10}\left[10^{0.1(L_{p,i}+C_{i})}+10^{0.1(L_{p,2i}+C_{i})}+10^{ 0.1(L_{p,i}+C_{i})}+10^{0.1(L_{p,i}+C_{i})}+10^{0.1(L_{p,i}+C_{i})}\right], \tag{15}\]  
where \(L_{p}\) is the noise source strength of train \(i\) at the reference point, which can be obtained from Section 3.2. \[C_{i}=C_{v,i}+C_{div,i}+C_{air,i}+C_{g,i}, \tag{16}\]  
where \(C_{v,l}\), \(C_{div,l}\), \(C_{air,l}\), and \(C_{g,i}\) are the speed correction, geometric divergence correction, air absorption correction, and ground correction of the \(i\)-th train, respectively. For speed correction, according to the fitting formula of the sound power level per unit length of the line source with the running speed, the calculation formula for \(C_{v,i}\) is as follows [11]:  
\[C_{v,i}=10\log_{10}(\
icefrac{{v}}{{v_{ref}}}), \tag{17}\]  
where \(v_{ref}\) is the reference speed, which is \(235\) km/h. Figure 13: Sound power levels of line sources vary with train operating speed. For the geometric divergence correction, the geometric divergence correction of the \(i\)-th train can be expressed as  
\[C_{div,i}=10\ \log_{10}\left(\frac{dr_{0}^{3}\Big{(}1+\sqrt{1+L^{2}/r_{0}^{2}} \Big{)}}{d_{0}r^{3}\Big{(}1+\sqrt{1+L^{2}/r^{2}}\Big{)}}\right), \tag{18}\]  
where \(d_{0}\) and \(d\) are the horizontal distances from the strong source reference point and predicted point, respectively, to the side of the car body, and \(r_{0}\) and \(r\) are the distances from the strong source reference point and predicted point, respectively, to the sound source. With air absorption attenuation, sound energy is generated during the heat energy dissipation process owing to the medium viscosity, heat conduction, and molecular relaxation absorption effect of sound waves in air. Sound absorption in air is related to the temperature, humidity, frequency, and propagation distance, and the atmospheric absorption correction of the \(i\)-th train can be uniformly expressed as  
\[C_{air,i}=-\alpha(r-r_{0}). \tag{19}\]  
In Equation (18), \(\alpha\) is the attenuation coefficient of air absorption, and Table 3 presents the attenuation coefficients of air absorption in the octave band under partial temperature and humidity conditions [22]. In general, the sound attenuation caused by air absorption is relatively small, with high-frequency sound waves experiencing greater absorption attenuation than low-frequency sound waves. The ground correction factors mainly include the correction \(C_{g,i}\) caused by ground reflection and ground attenuation correction \(C_{g,i,i}\) caused by interference between direct and reflected sound paths.