Development of a graph theory-based automated calculation method and tool for airflow resistance in building ventilation systems

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

Abstract

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

CLC Number:

TU83

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.

Figures/Tables 17

Fig. 1 Technology roadmap

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

Fig. 3 Fan connection sub-diagram

Fig. 4 Tree representation of wind system topology

Fig. 5 Calculation process of wind turbine circuit resistance

Fig. 6 Software tool calculation process

Fig. 7 Component type matching

Fig. 8 3D view of the most unfavorable loop

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

Fig. 10 Schematic diagram of building electromechanical pipeline model

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

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

Fig. 11 Selected complete circuit diagram of the fan

Fig. 12 Selected fan complete loop isolation view

Fig. 13 The most unfavorable loop of the selected fan

Fig. 14 Longest path of the selected fan loop

Fig. 15 Screenshot of duct resistance calculation sheet

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