## 3 Case Study: Analysis of Urban Pipeline Sensor Placement Optimization  
### System Clustering for Risk Level Classification  
The risk levels near inspection wells are divided into four categories: high risk, medium risk, low risk, and negligible risk. The key factors and statistical methods for classifying risk levels are listed in Table 1 below. In the study of optimizing gas leak detection sensor placement in urban gas pipeline networks, it is essential to consider a wide range of key facilities and environmental factors. The factors involved in this study include large buildings, government departments, various types of roads (pedestrian roads, factory roads, and urban roads), parallel pipelines, power cables, communication cables, heating pipes, railways, and utility poles. These factors, along with previously discussed key infrastructures, high-risk facilities, traffic elements, geographical and environmental factors, historical safety data, and population density and activity frequency, form a comprehensive analytical framework for assessing the installation priority and risk level of each node, as shown in Figure 7, which provides the GIS map of the gas pipeline layout and node locations. Figure 6: \(\beta\) Convergence plot. The presence of key buildings, such as large buildings and government departments, increases the potential impact of a leakage event since these locations typically gather large numbers of people and essential functions. Additionally, intersections of various types of roads, such as pedestrian roads, factory roads, and urban roads, are usually high-traffic areas with complex underground pipeline networks, making them relatively high-risk locations where the consequences of a leak could be widespread. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{5}{c}{(**a**)} \\ \hline Node & Large Buildings & \begin{tabular}{c} Government \\ Departments \\ \end{tabular}  & Urban Roads & Parallel Pipelines & Power Cables \\ \hline  
The dense layout of infrastructures such as parallel pipelines, power cables, communication cables, and heating pipes can complicate the underground environment, increasing the probability of damage to the pipeline network. The presence of railways and utility poles are also important factors to consider, especially railways, as their vibrations and heavy loads may have long-term physical impacts on underground pipelines. By combining these specific factors with geographical and environmental characteristics, historical accident data, and the frequency of socioeconomic activities, the risk levels and monitoring needs of each node can be more accurately assessed. This comprehensive analysis allows for the optimization of sensor placement strategies, effectively improving monitoring efficiency, reducing leakage risks, ensuring public safety, and minimizing environmental pollution. This approach is not only scientific and rational but also holds significant practical value in enhancing the safety management of urban gas pipeline networks. The data from Table 1 are analyzed through systematic clustering to classify the risk levels of each inspection well. In this study, a hierarchical clustering method is applied to classify 19 nodes in the urban gas pipeline network. The aim is to conduct a risk assessment and category classification based on the number of key facilities and potential safety hazards surrounding each node. First, various data points were collected for each node, including the presence of large buildings, government departments, different types of roads, parallel pipelines, power cables, and more. Each factor is represented in binary form, indicating whether it is present or absent. The clustering process involved multiple stages, where, in each stage, two clusters were merged based on their similarity or distance coefficient. These coefficients reflect the differences between clusters, with smaller coefficients indicating higher similarity between clusters.