基于图论的建筑风系统阻力自动化计算方法和工具研发

doi:10.11996/JG.j.2095-302X.2026020440

摘要/Abstract

摘要：

在建筑机电系统中，风系统的阻力计算是暖通空调设计与优化的关键环节。传统方法依赖人工识别最不利环路并逐段计算阻力，存在效率低、易出错等问题，难以适应复杂工程需求。随着建筑信息模型(BIM)技术的发展，基于Revit模型进行自动化分析已成为提升设计质量的重要手段。研究提出了一种基于图论的建筑风系统阻力自动化计算方法，以Revit MEP模型为基础，通过API接口提取风系统构件拓扑关系，并将其抽象为一张无向图，其中管件作为节点，管道作为边。利用广度优先搜索(BFS)算法从风机出发遍历整个风系统，识别所有连接风口，并构建以风机为根节点、风口为叶子节点的树状结构。在此基础上，采用自下而上的深度优先回溯策略，逐层计算各节点下游风量，并结合局部阻力系数与沿程阻力公式，完成每条路径的总阻力计算。最终，通过比较所有路径的阻力值，识别出最不利环路，实现风系统阻力的智能化、自动化分析。基于该方法开发了集成于Revit平台的自动化计算插件，并在上海某大型实验室项目中完成应用验证。案例中对144台风机进行了全回路复核，结果显示有28台风机原选型无法满足系统阻力要求，同时计算效率较传统人工方式提升约37倍。研究成果为风机选型、节能优化及后续运维管理提供了可靠的数据支持，具有良好的工程应用前景。

关键词: 风系统阻力计算, 图论, 最不利环路, 广度优先搜索, 建筑信息模型(BIM), 机电深化设计

Abstract:

In building mechanical and electrical systems, airflow resistance calculation of ventilation systems is a critical task in HVAC design and optimization. Traditional methods, which rely on manual identification of the most unfavorable loop and segment-by-segment resistance calculation, suffer from low efficiency and high error rates, making them inadequate for complex engineering demands. With the advancement of Building Information Modeling (BIM), automated analysis based on Revit models has become an important approach to improving design quality. A graph theory-based automated calculation method for airflow resistance in building ventilation systems was proposed. Based on Revit MEP models, the topological relationships of ventilation system components were extracted via the API and abstracted into an undirected graph, where fittings were represented as nodes and duct segments as edges. The Breadth-First Search (BFS) algorithm was employed to traverse the entire system from the fan, identifying all connected air terminals and constructing a tree structure with the fan as the root node and the terminals as leaf nodes. A bottom-up, depth-first backtracking strategy was then applied to calculate the downstream airflow at each node layer by layer. By integrating local resistance coefficients and frictional resistance formulas, the total resistance for each path was computed. The most unfavorable loop was automatically identified by comparing the resistance values of all paths, enabling an intelligent and automated analysis of the system’s airflow resistance. An automated calculation plugin integrated into the Revit platform was developed based on this method and validated in a large-scale laboratory project in Shanghai. The case study involved a comprehensive review of 144 fans, revealing that the original selection for 28 fans could not meet the system’s resistance requirements, while the calculation efficiency was improved by approximately 37 times compared to traditional manual methods. This research provided reliable data support for fan selection, energy-saving optimization, and subsequent operation and maintenance management, demonstrating strong potential for practical engineering applications.

Key words: airflow resistance calculation in ventilation systems, graph theory, most unfavorable loop, breadth-first search, building information modeling (BIM), MEP detailing design

中图分类号:

TU83

江凯, 许璟琳, 余芳强. 基于图论的建筑风系统阻力自动化计算方法和工具研发[J]. 图学学报, 2026, 47(2): 440-448.

JIANG Kai, XU Jinglin, YU Fangqiang. Development of a graph theory-based automated calculation method and tool for airflow resistance in building ventilation systems[J]. Journal of Graphics, 2026, 47(2): 440-448.

图/表 17

图1 技术路线图

Fig. 1 Technology roadmap

图2 机电管线图连接示意((a) 构件管道连接示意；(b) 主管接多支管分段示意)

Fig. 2 Electromechanical pipeline connection diagram ((a) Component pipeline connection diagram; (b) Main pipe connection with multiple branch pipes segmentation diagram)

图3 风机连接子图

Fig. 3 Fan connection sub-diagram

图4 风系统拓扑关系的树状表示

Fig. 4 Tree representation of wind system topology

图5 风机回路阻力计算流程

Fig. 5 Calculation process of wind turbine circuit resistance

图6 软件工具计算流程

Fig. 6 Software tool calculation process

图7 构件类型匹配

Fig. 7 Component type matching

图8 最不利回路三维视图显示

Fig. 8 3D view of the most unfavorable loop

图9 风机最不利环路计算书

Fig. 9 Calculation sheet for the most unfavorable loop of the wind turbine

图10 计算建筑机电管线模型示意图

Fig. 10 Schematic diagram of building electromechanical pipeline model

表1 最不利回路阻力计算结果

Table 1 Calculation results of the most unfavorable loop resistance

回路编号	总阻力损失
A-B	0.045 764
B-C	0.665 325
C-D	1.845 909
D-E	0.999 318
E-F	0.202 210
F-G	0.073 550
G-H	0.260 114
H-I	1.302 221
I-J	0.537 196
J-K	0.584 712
K-L	2.953 525×10^-15
L-M	0.496 909
M-N	0.033 618
N-O	0.000 207
O-P	0.000 207
总	7.047 260

表2 风机最不利环路计算效率对比

Table 2 Comparison of the calculation efficiency of the most unfavorable loop of the wind turbine

计算方式	拓扑连接确定方式	单次计算对象	单风机计算耗时/h	总工作量/ 人天
插件计算	基于模型数据自动识别	全回路	0.08	1.44
人工计算	查阅图纸模型手动判断	一条回路	3.00	54.00

图11 所选风机完整回路选中示意图

Fig. 11 Selected complete circuit diagram of the fan

图12 所选风机完整回路隔离视图

Fig. 12 Selected fan complete loop isolation view

图13 所选风机最不利环路

Fig. 13 The most unfavorable loop of the selected fan

图14 所选风机回路最长路径

Fig. 14 Longest path of the selected fan loop

图15 风管阻力计算书截图

Fig. 15 Screenshot of duct resistance calculation sheet

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