## 1 Introduction  
Underground pipeline networks, serving as the \"supply stations\" for urban energy consumption, play a vital role in optimizing urban planning, construction, and management. Not only do they meet residents' living needs, but they also reduce resource consumption, mitigate environmental pollution, and enhance ecological benefits, thus promoting urban sustainability and fostering comprehensive urban development and social progress. However, due to the concealed nature of underground pipeline projects and the difficulty in directly visualizing their benefits, the management methods and levels of underground pipeline networks have lagged behind urban planning and construction management. There is a prevalent tendency to prioritize surface engineering over underground facilities and to emphasize the approval process while neglecting subsequent supervision [1]. Facing various challenges in underground pipeline construction, including the efficient integration and management of vast underground pipeline data in cities and the accurate classification of the geometric morphology, semantic information, and temporal information of pipeline networks, scholars have been continuously exploring more effective data models to meet the complex spatial data representation and processing requirements [2]. Whether it is hybrid data models [3], relational data models [4], or object-oriented data models [5], all aim to find a universally applicable data model. Scholars such as [PERSON] [6; 7; 8; 9] have studied how to construct a three-dimensional model of an urban underground pipe network. [PERSON] and other scholars [10; 11; 12] realized the rapid modeling of a 3D fine model of an underground pipe network by designing different rule models. The underground pipeline network forms a complex urban underground network space, characterized by intersecting lines and intricate connections. It includes various types and sizes of points and accessories, as well as pipelines composed of different textures and materials. From a geometric perspective, understanding the expression of underground pipeline construction and management in three-dimensional space is crucial. This not only involves accurately reflecting the physical world in a virtual environment but also relates to the effectiveness of underground facility maintenance and planning. By abstracting the underground pipeline into nodes and polylines and embedding them into a three-dimensional coordinate system, we can clearly demonstrate the precise positions of each facility and their spatial relationships. This abstraction covers spatial location information for points and ancillary facilities such as manholes and valve chambers, as well as their attribute information, providing a foundation for the management and operation of the underground pipeline network [13]. In the three-dimensional model, underground pipelines are no longer simple line segments, but complex structures composed of multiple polyline segments. These polyline segments are connected in a predetermined order according to certain rules, forming a complex network structure. In this network, nodes and ancillary objects connect various polyline segments, serving as the core elements of the overall pipeline network. Through this structural design, the 3D model of the underground pipeline network not only reflects the extension and distribution of the pipelines in space but also clearly demonstrates the topological relationships and dynamic features such as facility changes. The temporal characteristics of underground pipelines refer to the changes that occur in the pipeline system over time during its usage and operation. These changes encompass various aspects such as aging, deterioration, maintenance, renewal, and expansion. In comparison to temporal characteristics, the changes in the geometric and semantic features are more independent. For instance, within different timeframes of usage, the semantic features of the network may remain unchanged, while its spatial positioning may have altered.