基于图论及改进A*算法的屋面设备检修动线设计智能分析

doi:10.11996/JG.j.2095-302X.2026010216

摘要/Abstract

摘要：

在屋面工程设计中，设备检修动线的合理性直接影响检修效率与安全性，传统设计方法常依赖经验判断，难以在设计阶段充分评估动线设计的合理性。针对此问题，提出了一种基于图论及改进A*算法结合的混合算法，并结合建筑信息模型(BIM)技术，开发了一种基于该算法的屋面设备检修动线智能分析设计工具，通过数字化模型进行动线分析，弥补传统设计的不足。首先，采用碰撞检测与八叉树算法将屋面转化为带有权重的等效网格图；然后采用改进A*算法优化检修路径，综合考虑设备碰撞体积和空间限制，计算最优检修动线并评估动线区域深化设计合理性；最后，使用以该算法为基础的检修动线智能分析设计工具对实际项目进行实验。实验结果表明，该算法不仅能够精准揭示设计中可能存在的空间冲突和不合理布局，为优化设计提供数据支持，提高了设计的合理性和可操作性，且比传统人工设计效率提高了5倍以上。目前基于该算法的智能分析工具已在上海建工四建集团的多项实际项目中使用。

关键词: 屋面检修, BIM, 动线优化, A*算法, 图论, 八叉树算法

Abstract:

In roof engineering design, the rationality of equipment maintenance circulation routes directly impacts maintenance efficiency and safety. Traditional design methods often rely on empirical judgment, making it difficult to sufficiently evaluate the rationality of these routes during the design phase. To address this, a hybrid algorithm combining graph theory with an improved A* algorithm was developed. Integrated with Building Information Modeling (BIM) technology, an intelligent analysis and design tool for roof equipment maintenance circulation routes was created to address the shortcomings of traditional design via digital model-based route analysis. First, the roof was converted into a weighted equivalent grid map using collision detection and an octree algorithm. Next, an improved A* algorithm was employed to optimize the maintenance paths, comprehensively considering equipment collision volumes and spatial constraints to calculate the optimal maintenance circulation route and evaluate the rationality of detailed route-area design. Finally, the intelligent analysis and design tool based on this algorithm was tested on an actual project. Experimental results demonstrated that the algorithm accurately revealed potential spatial conflicts and irrational layouts, providing data to support design optimization, and enhanced design rationality and operability; it also improved efficiency by more than five times compared with traditional manual design. The intelligent analysis tool based on this algorithm is currently in use in several projects by the Shanghai Construction (No.4) Group Co., Ltd.

Key words: roof maintenance, BIM, route optimization, A* algorithm, graph theory, octree algorithm

中图分类号:

何瑞琦, 曹盈, 许璟琳, 余芳强. 基于图论及改进A*算法的屋面设备检修动线设计智能分析[J]. 图学学报, 2026, 47(1): 216-222.

HE Ruiqi, CAO Ying, XU Jinglin, YU Fangqiang. Intelligent analysis of design about roof equipment inspection paths based on graph theory and improved A* algorithm[J]. Journal of Graphics, 2026, 47(1): 216-222.

图/表 13

图1 技术路线图

Fig. 1 Technology roadmap

图2 屋面等效网格计算流程

Fig. 2 Roof equivalent grid computation workflow

图3 网格计算时间图(横轴为网格数量的对数，竖轴为计算时间的对数)

Fig. 3 Mesh computing time graph (with the number of mesh elements on the logarithmic x-axis and computation time on the logarithmic y-axis)

图4 屋面BIM模型

Fig. 4 Roof BIM model

图5 网格扩展后的长方体体元(下方红色立方体为网格在三维空间中的展现形式)

Fig. 5 Cuboid voxel units after grid expansion (the red cube is the representation of the grid in 3D space)

图6 屋面等效网格图(绿色为普通网格，红色为高权重网格)

Fig. 6 Roof equivalent grid graph (green represents ordinary grids, red indicates high-weight grids)

表1 算法性能对比表

Table 1 Algorithm performance comparison table

参数组合	构件阈值	单元尺寸/mm	耗时/min	碰撞检测误差率/%
C1	10	300	128	0.12
C2	10	600	75	0.35
C3	10	1 200	41	1.22
C4	30	300	106	0.09
C5	30	600	63	0.28
C6	30	1 200	35	0.95
C7	50	300	92	0.07
C8	50	600	55	0.21
C9	50	1 200	29	0.78

图7 八叉树算法计算流程

Fig. 7 Octree algorithm computation workflow

图8 八叉树算法示意图(红色对勾处为八叉树中满足碰撞要求的一支)

Fig. 8 Octree algorithm schematic diagram (the red mark indicates a branch that meets collision requirement)

图9 考虑通行体积的设备检修动线计算流程

Fig. 9 Equipment maintenance inspection route calculation workflow considering navigable volume

图10 项目A中某设备最优检修路线(绿色为最优路径中普通网格，红色为最优路径中障碍物网格)

Fig. 10 Optimal maintenance route for equipment in project A (green is the normal grid in the optimal path, and red is the obstacle grid in the optimal path)

图11 项目A中某设备实际检修空间

Fig. 11 Actual maintenance space for equipment in project A

表2 算法性能对比表(以较远检修设备为例)

Table 2 Algorithm performance comparison table (Taking remotely located maintenance equipment as an example)

项目	屋面面积/m²	网格划分 (大小/数量)	障碍密度	算法路径长度/m	人工路径长度/m	算法转折/次数	人工转折/次数	算法耗时/min	人工耗时/h
A	2 400	0.2 m×0.2 m/60 000	0.12	218.4	283.6	9	21	28	10.0
B	4 300	0.2 m×0.2 m/107 500	0.28	419.7	491.3	12	25	40	14.0
C	1 850	0.2 m×0.2 m/46 250	0.35	193.2	242.3	14	22	15	6.5

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