## 2 Reliability Modeling of the Natural Gas Supply Chain  
### Natural Gas Supply Chain Reliability Modeling Based on Minimal Cut Set  
The natural gas supply chain is composed of gas supply, gas transmission, and gas consumption. The actual natural gas system is a large and complex pipeline network structure formed by various connection methods. Due to the direct relationship between the gas transmission of the pipeline network and its physical topology, using the minimal cut set method to simplify the topology of the gas transmission through the pipeline is proposed in this paper.  
The reliability of a single pipeline or a simple pipeline network system is generally calculated by using an intuitive and clear logic block diagram for the established pipeline system model, and such a schematic diagram is shown in Figure 1. In this model, any unit in the minimal cut set is in normal working condition, and when all the component units in the minimal cut set fail, the minimal cut set will fail. This definition of the minimal cut set is associated with the reliability calculation of a parallel system, where the link connection form of the minimal cut set is used as an equivalent parallel structure.  
The set of minimal events that can lead to the occurrence of the top event is known as the minimal cut set. Any of the minimal cut sets can cause the system to fail, which is why they are connected in a series structure, and the equivalent diagram of it is shown in Figure 2.  
In this paper, a method for obtaining the network cut set by identifying the network concatenation set is proposed [15; 16]. In the context of the natural gas supply chain, this refers to the pipeline system that connects the gas source to the load at the end of the  
Figure 1: Schematic diagram of minimal cut set composition.  
transmission. Using graph theory, the gas-transmission path is decomposed and a search tree based on the decomposition results is constructed. The following steps are performed: (1) partitioning and numbering the pipelines in the gas-transmission network; (2) using the gas source point as the starting point and obtaining \(n\) adjacent gas-transmission lines in the next round of search, which are used as branches for the starting point of the current round; (3) continuing the search from the new branch, ensuring that the search result of the new round is inconsistent with the line number obtained from the previous search before it can be used as a new branch. This step is repeated until the search is completed.  
Due to the limited number of actual natural gas pipeline branches, all paths from the gas source point to the load point can be obtained by traversing the stations (i.e., nodes in the graph) in the supply chain. The search tree from the source point to the load point is a typical recursive structure, which can be represented by the connected set matrix \(T\), where the column number of the matrix represents the transmission line number and the number of rows represents the minimum set of connections in the pipeline system. Each row represents a minimum set of connections, and the elements of the matrix \(T_{ij}\) are 0-1 variables, where \"1\" indicates that the pipeline is in the set and \"0\" indicates that it is not included in the set [17; 18; 19].  
\[\mathbf{T}=\begin{bmatrix}T_{11}&T_{12}&\cdots&T_{1j}\\ T_{21}&T_{22}&\cdots&T_{2j}\\ \vdots&\vdots&\ddots&\vdots\\ T_{i1}&T_{i2}&\cdots&T_{ij}\end{bmatrix} \tag{1}\]  
When a column is a unit column vector, it indicates that the gas-transmission lines in this column form the minimal cut set of the network system. If the sum of \(n\) columns is a unit column vector, it means that they form the \(n\)-th order minimal cut set of the network system. However, the low-order minimal cut set should not be a subset of the high-order minimal cut set; otherwise, the high-order minimal cut set should be eliminated.