## 3 Construction of the Noise Prediction Model
### Equivalent Source Strength  
Based on the simulation results of the flow field described in Section 2.3, the exterior noise prediction of the high-speed Maglev train was implemented using a five-segment incoherent line source equivalent model. The sound sources were equivalently modeled as finite-length incoherent line sources with intermediate directivity, where the sound power levels \(L_{w1}\), \(L_{w2}\), \(L_{w3}\), \(L_{w4}\), and \(L_{w5}\) correspond to the front positive-pressure zone, streamlined head section, middle carriage section, streamlined tail section, and rear negative-pressure zone, respectively. Computational validation confirmed the optimal positioning of line source segments at the rail level (0 m height) on the vehicle side, with the horizontal distance between \(R\) and the vehicle side defined as \(d\). Figure 11 provides a schematic of the equivalent acoustic source model for the high-speed Maglev train noise prediction. Figure 11: Schematic of the high-speed Maglev train noise prediction equivalent acoustic source model. Reference standards ISO 3095-2013 [18] and HJ 2.4-2021 [11] define the position 25 m from the centerline of the guideway and 3.5 m above the guideway surface as the reference measurement point of the source intensity. The equivalent continuous A-weighted sound level during the train passing time at this position is called the noise source intensity. When sound sources \(S_{1}\)-\(S_{5}\) act alone, the noise source intensity is \(L_{p1}\)-\(L_{p5}\). As the noise source intensity obtained in a real train test is the result of the joint action of all sound sources, to improve the accuracy of the environmental noise prediction model of the Maglev train, \(L_{p1}\)-\(L_{p5}\) should be separated. According to Equation (8), the SPL at the reception point generated by the combined effect of five uniform finite-length line source segments with intermediate directivity is expressed as  
\[L_{p}(t) = 10\log_{10}\left(\frac{d(1-M_{0}^{2})^{3}}{4\pi}\right)+ \tag{11}\] \[10\log_{10}\left( \begin{array}{c}\frac{v_{0}t-\frac{L}{2}+l_{1 }}{\int\limits_{v_{0}t-\frac{L}{2}}^{t}}\frac{10^{0.1L_{\text{\tiny{at}}}}}{ \left(\sqrt{x^{2}+(1-M_{0}^{2})\cdot r_{1}^{2}}-M_{0}x\right)^{3}}\text{d}x+ \int\limits_{v_{0}t-\frac{L}{2}}^{v_{0}t-\frac{L}{2}}\frac{10^{0.1L_{\text{ \tiny{at}}2}}}{\left(\sqrt{x^{2}+(1-M_{0}^{2})\cdot r_{2}^{2}}-M_{0}x\right)^{ 3}}\text{d}x+\\ \int\limits_{v_{0}t+\frac{l_{3}}{2}}^{v_{0}t+\frac{l_{3}}{2}}\frac{10^{0.1L_{ \text{\tiny{at}}3}}}{\left(\sqrt{x^{2}+(1-M_{0}^{2})\cdot r_{3}^{2}}-M_{0}x \right)^{3}}\text{d}x+\int\limits_{v_{0}t+\frac{l_{3}}{2}}^{v_{0}t+\frac{l_{3} }{2}+l_{4}}\frac{10^{0.1L_{\text{\tiny{at}}4}}}{\left(\sqrt{x^{2}+(1-M_{0}^{2} )\cdot r_{4}^{2}}-M_{0}x\right)^{3}}\text{d}x+\\ \int\limits_{v_{0}t+\frac{L}{2}}^{v_{0}t+\frac{L}{2}}\frac{10^{0.1L_{\text{ \tiny{at}}5}}}{\left(\sqrt{x^{2}+(1-M_{0}^{2})\cdot r_{5}^{2}}-M_{0}x\right)^{ 3}}\text{d}x\end{array} \right).\]  
The total length of the five-segment line source is denoted as \(L\), where \(l_{1}\)-\(l_{5}\) represent the lengths of the line source segments, that is, \(L=l_{1}+l_{2}+l_{3}+l_{4}+l_{5}\), where \(l_{2}=l_{4}=7\) m, \(l_{3}=65\) m, and the sum of the three segments provides a total vehicle length of 79 m. As can be seen from Figure 12, there is a good linear relationship between the length of the line source and the speeds of \(l_{1}\) and \(l_{5}\), where \(l_{1}=57.15-0.18\cdot v\), \(l_{5}=35.00+0.38\cdot v\), and \(v\) is the train operating speed to be predicted in m/s. Designating the reference measurement position as \(R\), the instantaneous SPL \(L_{p,R}(t_{i})\) of the Shanghai Maglev train pass-by noise at \(R\) were measured with 0.1 s time intervals based  
Figure 12: Line source lengths vary with train operating speed. on the full-scale test data from Section 2.2. Using Equation (11), the predicted instantaneous SPL \(\widetilde{L}_{p,R}(t_{i})\) at \(R\) can be calculated when specific values are assigned to the sound power levels per unit length \(L_{w1}\)-\(L_{w5}\).