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| 基于平面密铺理论的最小灭火器配置点计算算法研究 |
| Research on the Calculation Algorithm for Optimal Fire Extinguisher Allocation Based on Planar Density Theory |
| 投稿时间：2025-04-22 修订日期：2025-12-08 |
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| 中文关键词: 平面密铺 数学模型 灭火器配置 算法 |
| 英文关键词:densely paved area mathematical modeling fire extinguisher placement optimization algorithm |
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| 中文摘要: |
| 针对传统灭火器配置点数量计算方法的实现，本文提出了一种基于平面密铺理论的数学建模方法和计算算法，将灭火器的最小配置数量计算建立数学模型，转化为以保护距离为半径的圆平面密铺覆盖给定平面矩形的问题。其次，分析了不同密铺方法的效率，给出三种不同密铺模型最小配置点数量的数学公式和计算方法。最后，为工程设计、消防管理提供了一种优化的方法，结合不同实例，利用matlab工具实例运行验证，实现了数学、消防工程与计算机科学的结合，对提高灭火器配置效率，降低人力和经济成本都有重要意义。研究结果表明：在某些狭长布局条件下，正方形布局有优势，大面积布局条件下，正六边形蜂窝状布局有优势，保护单元的长宽比数值关系，适用于不同方向的正六边形蜂窝状排列。 |
| 英文摘要: |
| Considering the limitations of traditional methods for calculating the number of fire extinguisher configuration points, this paper introduces a novel mathematical modeling approach and algorithm based on plane tiling theory. The problem of determining the minimum number of fire extinguishers is formulated as a mathematical model, which translates into covering a given rectangular area with circles whose radii correspond to the protection distance. We analyze the efficiency of various tiling methods and provide mathematical formulas and calculation methods for the minimum number of configuration points for three distinct tiling models. This study offers an optimized method for engineering design and fire management. Through practical examples and verification using MATLAB, we demonstrate the integration of mathematics, fire engineering, and computer science, significantly enhancing the efficiency of fire extinguisher configuration while reducing human and economic costs. Research findings indicate that square layouts are advantageous in narrow and elongated spaces, whereas regular hexagonal honeycomb layouts excel in large-area settings. The aspect ratio of the protection unit influences the optimal arrangement of hexagonal cells in different directions. |
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