# A Network-Based Method to Analyze EMI Events of On-Board Signaling System in Railway
## 2 Network-Based Modeling Framework and Method
### Approach of the Network Modeling  
In this subsection, we aim to introduce the step-by-step approach and definitions applied in the EN model. The model construction is divided into several parts, including the definition and representation of the node, the definition and form of the edge, the model expression and simplification, and the procedure. Detailed descriptions are as follows:  
1. The definition and representation of the node  
The node is the basic unit of the network. It can represent the EMC elements and sensitive components in the target system. In other words, each node in the EN model, which has a consistent one-to-one match with the EMC elements and system functional structure, has a specific function and meaning. Thus, the attributes or characteristic parameters of the nodes can be obtained through calculation, simulation, or measurements, such as the amplitude, frequency, transfer function, and the module function. Based on the above definition, the node form can be determined in Table 1.  
Figure 4: The framework of the EMC network model. There are two kinds of EM disturbance nodes in the running scenario of the high-speed railway. One is the radiated disturbance node and the other is the conducted disturbance node. The attributes of the source node can be represented by waveforms in standards or the parameters measured on-site. Besides, two virtual nodes are designed, which are the radiation and conduction coupling nodes. There are two advantages, on the one hand, the virtual node can be used to determine the coupling relationship between the disturbance source and the module nodes. On the other hand, it can reduce the complexity of the network by reducing the cross among the connection edges from the disturbance nodes to the module nodes. 2. The definition and form of the edge  
Considering the coupling process of the EM disturbance in the EMC network domain, the connection relationship between the disturbance source and equipment is divided into two types, namely, the conduction and radiation coupling connections correspond to the coupling nodes in Table 1. Additionally, to address the connection in the system structure network domain, such as signal connection and physical connection, the form of the edge are designed in Table 2.  
3. The model simplification and expression  
Based on the definition of the node and edge in the EN model, if the results of the network achieve an acceptable level, the process is stopped and the model is analyzed in the next step. Otherwise, the model should be simplified by several times until there are no repetition and conflict between the nodes and edges. After the work above, the expression can be given with the format as:  
\[ \begin{split} EN&=G(V,E,A_{v},A_{c})\\ &=\left\{\begin{array}{c}A_{v}=\{A_{v}(1),A_{v}(2),\cdots,A_{v} (n),\cdots,A_{v}(N)\},n=1,2,\ldots,N\\ A_{e}=\{A_{e}(1),A_{e}(2),\cdots A_{e}(m),\cdots,A_{v}(M)\},m=1,2,\ldots,M\\ v_{i},v_{j}\in V,i\leq N,e_{ij}\in E,j\leq N\end{array}\right.\end{split}  \tag{2}\] \begin{table}
\begin{tabular}{c c c c} \hline
**No.** & **Node** & **Form** & **EMC Elements** \\ \hline
1 & Disturbance node & & Radiation source \\
2 & Disturbance node & & & Conduction source \\
3 & Virtual node 1 & & & Radiation coupling \\
4 & Virtual node & & & Conduction coupling \\
5 & Module node & & & Equipment \\ \hline \end{tabular} 1  
\end{table} 
Table 1: The form of the node. \begin{table}
\begin{tabular}{c c c} \hline
**Edge** & **Form** & **Explanation** \\ \hline Physical connection & & & Contact by metal (ground) \\ Coupling connection a 1 & & & Conduction coupling \\ Coupling connection b 2 & & & Radiation coupling \\ Signal connection & & & Wire transmission (unidirectional or bidirectional) \\ \hline \end{tabular}
\end{table} 
Table 2: The form of the edge.