## 3 Computational Model of Interior Aerodynamic Noise  
### Statistical Energy Analysis Model  
When the high-speed maglev train is running, a huge fluctuating pressure is generated on the train surface, which in turn generates a large amount of aerodynamic noise inside the maglev train. The fluctuating pressure on the train surface has high and wide frequency characteristics, and the structure of the train body is very complex. Thus, the dynamic response of the body panels, windows, door, etc. caused by the fluctuating pressure on the train surface is very complex. The statistical energy analysis is a statistical method for analyzing random noise in a wide frequency range. It analyzes the transfer level of the average vibration energy of dense modes from a statistical point of view. This method is suitable for complex systems with high frequency and high modal density, which can effectively predict the dynamic response of the complex engineering structural systems under the high frequency broadband random excitation [23; 24]. Statistical energy analysis is mainly based on the statistics of modal density, internal loss factor, and coupling loss factor of each subsystem, and calculates the vibration energy transmission between subsystems in the form of power flow. The core of statistical energy analysis is the power flow balance equation. Assuming that the main energy flow between subsystems is caused by structural resonance or acoustic mode, when the vibration power flows from one subsystem to another linked subsystem, the power loss and flow law are shown in Figure 6.  
Generally, the subsystem is defined as a finite area with the same resonant modal performance, and the average modal energy depends on the balance between the external input energy, energy loss, and energy exchange. Therefore, the power balance equations between two subsystems are:  
\[P_{1}=\omega\eta_{1}E_{1}+\omega\eta_{12}n_{1}\bigg{(}\frac{E_{1}}{n_{1}}- \frac{E_{2}}{n_{2}}\bigg{)} \tag{10}\]  
\[P_{2}=\omega\eta_{2}E_{2}+\omega\eta_{21}n_{2}\bigg{(}\frac{E_{2}}{n_{2}}- \frac{E_{1}}{n_{1}}\bigg{)} \tag{11}\]  
If the system has \(m\) subsystems, the m power balance equation will be generated, written in matrix form as:  
\[\omega \begin{bmatrix}\eta_{11}n_{1}&-\eta_{12}n_{1}&\cdots&-\eta_{1m}n_{1}\\ -\eta_{21}n_{2}&\eta_{22}n_{2}&\cdots&-\eta_{2m}n_{1}\\ \vdots&\vdots&\ddots&\vdots\\ -\eta_{m1}n_{2}&-\eta_{m2}n_{2}&\cdots&\eta_{mm}n_{m}\\ \end{bmatrix}\begin{bmatrix}E_{1}/n_{1}\\ E_{2}/n_{2}\\ \vdots\\ E_{m}/n_{m}\\ \end{bmatrix} = \begin{bmatrix}P_{1}\\ P_{2}\\ \vdots\\ P_{m}\\ \end{bmatrix}  \tag{12}\]  
Figure 6: Statistical energy analysis model of two subsystems. \[\eta_{ii}=\eta_{i}+\sum_{j=1,j\
eq i}^{m}\eta_{ij} \tag{13}\]  
where \(\omega\) is the center frequency within the bandwidth, \(P_{i}\) is the external input power of subsystem \(i\), \(\eta_{ij}\) is the coupling loss factor from subsystem \(i\) and from subsystem \(j\), \(\eta_{i}\) is the internal loss factor of subsystem \(i\), \(n_{i}\) is the modal density of subsystem \(i\), and \(E_{i}\) is the energy of subsystem \(i\). For the conservation coupling system, the transmission power between the coupling systems meets the reciprocity principle, thus there are:  
\[n_{i}\eta_{ij}=n_{i}\eta_{ji} \tag{14}\]  
Then, the power flow balance equation can be rewritten as:  
\[\omega \begin{bmatrix}\eta_{11}&-\eta_{21}&\cdots&-\eta_{m1}\\ -\eta_{12}&\eta_{22}&\cdots&-\eta_{m2}\\ \vdots&\vdots&\ddots&\vdots\\ -\eta_{1m}&-\eta_{2m}&\cdots&\eta_{mm}\end{bmatrix}\begin{bmatrix}E_{1}\\ E_{2}\\ \vdots\\ E_{m}\end{bmatrix} = \begin{bmatrix}P_{1}\\ P_{2}\\ \vdots\\ P_{m}\end{bmatrix}  \tag{15}\]  
This formula is the power flow balance equations of the statistical energy analysis method. The power flow balance equations include the basic parameters of statistical energy analysis (i.e., modal density, internal loss factor, coupling loss factor) and external input power.