High-strength district multi-element coupling mathematical modeling and quantitative evaluation method for urban resilience

Abstract

The application discloses a high-strength block multi-element coupling mathematical modeling and quantitative evaluation method for urban resilience, relates to the technical field of fire emergency, and comprises the following steps: step S1: selecting a grid side length according to a high-strength block type; step S2: calculating a single-grid basic area index; step S3: expanding each grid of a building horizontal bottom layer into a vertical total scale, and converting a total building area of the grid calculated according to a building function into a negative index of evacuation pressure; step S4: calculating an evacuation index based on a road network topological feature; step S5: constructing an evaluation matrix of each grid by using the negative index of evacuation pressure and the evacuation index, determining the weight of each index by using an entropy weight method, and dividing a safety level according to an integrated safety score of each unit cell and an average value of integrated safety scores of all grids. S i The method can accurately reflect the vertical population agglomeration characteristics of high-rise buildings, and realize accurate quantification and scientific and objective evaluation of the connection level of evacuation channels.

Description

Technical Field

[0001] This application relates to the field of fire emergency technology, and in particular to a mathematical modeling and quantitative evaluation method for high-intensity urban areas with multi-factor coupling for urban resilience. Background Technology

[0002] With the continuous acceleration of urbanization, urban land resources are becoming increasingly scarce. High-intensity areas (such as core business districts, high-density residential areas, and integrated industrial parks) have become the mainstream form of modern urban development. These areas concentrate the city's main economic, cultural, and residential functions, and carry a large population and social wealth. Their safe and stable operation is of great importance.

[0003] High-density urban areas are characterized by high building density, high population concentration, complex road networks, high evacuation pressure, and highly integrated functions. In the event of sudden safety incidents such as fires or earthquakes, high-density urban areas are far more prone to large-scale casualties and property damage compared to ordinary urban areas. Therefore, after construction, these areas require safety and stability assessments during operation to promptly establish a comprehensive safety guarantee system.

[0004] Currently, existing mathematical modeling and quantitative assessment methods for high-intensity urban resilient areas, which involve multi-factor coupling, mostly use planar population density as the core assessment indicator. This involves dividing the assessment area into grids and calculating the ratio of the total population within each grid cell to the grid's planar area to measure population concentration and thus assess evacuation pressure. However, this method has significant technical flaws. Firstly, it only considers planar population density without taking into account the vertical agglomeration characteristics of high-rise buildings, treating them the same as single-story or low-rise buildings. This fails to accurately reflect the actual population distribution in high-intensity areas, leading to a severe disconnect between assessment results and actual evacuation scenarios, making it difficult to accurately identify high-risk areas within high-intensity zones. Secondly, existing assessment methods often focus on single-indicator assessments or use subjective weighting to determine the weights of each indicator, lacking a systematic characterization of the coupling relationship between "buildings-population-road network-refuge," resulting in low assessment accuracy and high subjectivity. This makes it difficult to provide scientific and accurate decision-making basis for safety planning and fire emergency response in high-intensity areas, and fails to meet the refined and objective needs of high-intensity areas for safety assessment.

[0005] Meanwhile, existing assessment methods lack precise grid-scale indicators, making it impossible to quantitatively assess the accessibility of evacuation routes. They often employ macro-grid assessment methods, which fail to reflect the connectivity of evacuation routes in individual grid units and make it difficult to accurately locate bottleneck areas in evacuation, further reducing the practicality and relevance of the assessment results.

[0006] The information disclosed in the background section is intended only to enhance the understanding of the overall background of the invention and should not be construed as an admission or in any way implying that such information constitutes prior art known to those skilled in the art. Summary of the Invention

[0007] This application provides a mathematical modeling and quantitative assessment method for high-intensity areas with multi-factor coupling, which is oriented towards urban resilience, to address the above-mentioned technical problems. This method can accurately reflect the vertical population agglomeration characteristics of high-rise buildings, achieve accurate quantification of the connectivity level of evacuation channels, and make the assessment scientific and objective. It is especially suitable for safety assessment of high-intensity areas, thereby helping to ensure the safe and stable operation of the core urban area. The accuracy of the assessment results relative to the simulation results can reach 88-96%.

[0008] This application provides a mathematical modeling and quantitative assessment method for high-intensity urban resilient areas with multi-factor coupling, including the following steps: Step S1: Select the grid side length according to the high-intensity area type, divide the high-intensity area into full-coverage grids, collect multi-source spatial data of the high-intensity area, project the collected multi-source spatial data onto the same coordinate system, and perform spatial association matching with grid cells to extract multi-source spatial data within each grid range and complete single grid data initialization. Step S2: Calculate the basic area index of a single grid: the cell area of ​​grid i. A cell The proportion of the building base area of ​​grid i to R build,i The proportion of road network area in grid i, R road,i The percentage of refuge coverage area in grid i R shelter,i ; Step S3: Expand each grid on the horizontal ground floor of the building to a vertical total scale, and calculate the total building area of ​​the grid according to the building function. Where m is the total number of building function types. For grid i Inner k The ground floor area of ​​a functional building, Let be the average number of floors of the k-th functional building within grid i; for buildings with residential function type . =1.0, Commercial / Office Building =1.2, Buildings with public service functions =0.8; Calculate the total building area of ​​the high-intensity area Calculate the population density per unit building area in high-intensity areas based on population changes over time. ,in, P total This represents the total population of the high-intensity area. γPopulation coefficient for that period γ The values ​​are: residential 0.9 at night, residential 0.3 during the day, office 0.8 during the day, office 0.1 at night, and commercial 0.95 during the day and 0.05 at night. This is used to calculate the actual population within the grid. ,in A floor,i Given the total building area of ​​the high-intensity zone in grid i; calculate the vertically corrected population density of grid i. ,in A cell Grid cell area; A build,i This represents the sum of the ground floor area of ​​all buildings within grid i, with a value range of [0,1]. F i Let i be the arithmetic mean of the number of building floors within grid i. D pop,i After performing extreme value normalization, we obtain ,Will Converted to negative exponent of evacuation pressure ; Step S4: Calculate the evacuation index based on road network topology characteristics; Step S5: Construct an evaluation matrix for each grid using the negative evacuation pressure index and evacuation indicators, determine the weight of each indicator using the entropy weight method, and calculate the comprehensive safety score for each cell. S i and the average of all grid-based integrated security scores Based on the comprehensive security score of each cell S i and the average of all grid-based integrated security scores Classify security levels.

[0009] Preferably, step S4 includes the following steps: Step S41: Calculate the sparse reachability index of grid i ,in A i The value range is [0,1]; d i Let be the road network distance from the geometric center of grid i to the nearest shelter, obtained through road network topology shortest path analysis. d 0 The evacuation tolerance distance threshold is set at 300m to 500m. Step S42: Calculate the scale connectivity of grid i: ,in, C i The value range is [0,1]; N i Let i be the set of eight neighboring grids; wij The road weighting coefficient is 1.0 for main roads, 0.8 for secondary roads, and 0.6 for local roads, used to distinguish the evacuation capacity of different roads; L ij Let i be the length of the connecting path between grid i and its neighboring grid j; n N This represents the total number of neighboring grids; for an eight-neighbor grid, the value is 8. L This represents the side length of a single grid cell.

[0010] Preferably, step S5 includes the following steps: Step S51: Construct the original evaluation matrix: Where n is the total number of grid cells, R build,1 R build,2 …, R build,n R represents the percentage of the building footprint area in grids 1, 2, ..., n. road,1 R road,2 …, R road,n This represents the proportion of road network area in grids 1, 2, and n. 1, 2…, n For grids 1, 2 to n, the negative exponent of evacuation pressure is represented. R shelter,1 , R shelter,2 ,… R shelter,n This represents the percentage of refuge coverage area for grids 1, 2 to n. A 1 , A 2 ,… A n For grids 1, 2 to n, the evacuation reachability index is used. C 1 , C 2 ,… C n The connectivity of grids 1, 2 to n; Step S52: Normalize each index of the original evaluation matrix according to the following formula: ,in x ij These are the original indicator values. For the j-th evaluation index in the i-th grid, the normalized index value is: min( x j ), max( x j ) are the minimum and maximum values ​​of the j-th indicator, respectively; Step S53: Determine the weights of each indicator using the objective weighting entropy weight method; Step S54: Calculate the overall security score for mesh i: ,in, w j For the first j The weight of each indicator, where m is the total number of building function types. The j-th evaluation index value is the normalized value for the i-th grid; the overall safety score for the region is calculated as the average of the comprehensive safety scores of all grids. Where n is the total number of grid cells, S i For grid i The grid-based comprehensive security score; Step S55: Mesh i Comprehensive Security Score S i Classification: Security level; Basic security level; The level is unsafe. The average of all grid-based comprehensive security scores Classification: A value ≥0.7 indicates a safety level; 0.7 > A value of ≥0.4 indicates a basic safety level. A value <0.4 indicates an unsafe level; The safety level is: smooth road network, sufficient refuge, low evacuation pressure, which can serve as a benchmark area for safety optimization in high-intensity areas; The basic safety level is: meeting basic evacuation and refuge needs, with some areas that can be optimized, and is a key area for safety improvement in high-intensity areas; The area is classified as unsafe due to its dense population, congested road network, and insufficient refuge facilities. It requires key rectification efforts and is a high-intensity area requiring focused monitoring, guidance, and safety control.

[0011] Preferably, step S53 includes the following steps: Step S531: Calculate the weight of the j-th index in the i-th grid. ;in For the j-th normalized index of the i-th grid; Step S532: Calculate the entropy value of the j-th index. ; Step S533: Calculate the weight of the j-th indicator And satisfy in w j Let be the weight of the j-th indicator.

[0012] Preferably, step S2 includes the following steps: Step S21: Calculate the area of ​​the grid cells in grid i. ,inL The grid side length; Step S22: Calculate the proportion of the building footprint area of ​​grid i. ,in A build,i This represents the sum of the ground floor area of ​​all buildings within grid i, with a value range of [0,1]. Step S23: Calculate the area ratio of grid i. , where A road,i This is the sum of the areas of all roads within grid i, with values ​​ranging from [0,1]. Step S24: Calculate the refuge coverage area of ​​grid i. ,in, A cover,i Based on the shelter as the center, according to the evacuation tolerance distance threshold d After performing buffer analysis, the area overlapping with grid i is in the range of [0,1].

[0013] Preferably, step S3 includes the following steps: Step S31: Expand each grid of the building's horizontal base layer to a vertical total scale, and calculate the total building area of ​​the grid based on the building's function. Where m is the total number of building function types. Let be the ground floor area of ​​the k-th functional building within grid i. Let be the average number of floors of the k-th functional building within grid i; for buildings with residential function type . =1.0, Commercial / Office Building =1.2, Buildings with public service functions =0.8; Step S32: Calculate the total building area of ​​the high-intensity zone ,in A floor,i The total building area of ​​the high-intensity zone in grid i; Step S33: Calculate the population density per unit building area in high-intensity areas ,in, P total The population of the high-intensity area is represented by the population coefficient for that time period. γ The values ​​are as follows: 0.9 for residential buildings at night, 0.3 for residential buildings during the day, 0.8 for office buildings during the day, 0.1 for office buildings at night, and 0.95 for commercial buildings during the day and 0.05 for commercial buildings at night. Step S34: Calculate the actual population size within grid i ; Step S35: Calculate the vertically corrected population density of grid i: ; Step S36: To eliminate dimensional differences between grids, for Dpop,i The standardized population density index is obtained by performing extreme value normalization. ,in, The value range is [0,1]; min(D pop ) , max(D pop ) The minimum and maximum values ​​for the vertically corrected population density of this area; Because higher population density means greater safety, Converted to negative exponent of evacuation pressure .

[0014] Preferably, the multi-source spatial data includes: road network vector data, building vector data, population data, refuge vector data, and land use data.

[0015] Preferably, the same coordinate system is CGCS2000_3_Degree_GK_cm_117E.

[0016] The beneficial effects that this application can produce include: 1) This method proposes a vertical population density model based on building area weighting. By coupling the building base area with the average number of floors, it achieves vertical dimension correction of population density. This solves the shortcomings of traditional planar density, which cannot reflect the agglomeration of high-rise buildings and cannot combine agglomeration to obtain the dispersal capacity. It can realistically depict the population distribution and evacuation pressure differences in high-intensity areas, significantly improve the assessment accuracy, provide core technical support for the accurate identification of safety risks in high-intensity areas, and improve the safety of people in high-intensity areas.

[0017] 2) This method constructs a grid-scale connectivity index based on road network topology characteristics and combines it with the evacuation accessibility index to form a dual spatial index system of "accessibility-connectivity". This achieves accurate quantification of evacuation convenience and road network smoothness, makes up for the lack of refined spatial analysis in existing evaluation methods, and can accurately locate evacuation bottleneck areas in high-intensity areas, providing a scientific basis for evacuation route optimization.

[0018] 3) This method constructs a six-item evaluation index system encompassing four dimensions: buildings, population, road network, and refuge. It employs the entropy weight method to achieve objective weighting, avoiding biases caused by subjective scoring. This makes the evaluation results more scientific, objective, and reproducible, adapting to the refined and standardized needs of safety assessment in high-intensity areas and providing a reliable quantitative basis for safety planning in high-intensity areas.

[0019] 4) This method forms a complete technical process of "grid construction - index calculation - comprehensive evaluation - implementation optimization". The evaluation results are quantifiable and implementable, and can directly provide accurate decision-making basis for urban planning, fire emergency management and safety control in high-intensity areas, effectively improve the safety guarantee capability of high-intensity areas, reduce safety risks and ensure the stable operation of the core urban area. Attached Figure Description

[0020] Figure 1 A schematic diagram of the process for high-intensity area multi-factor coupling mathematical modeling and quantitative evaluation method for urban resilience in at least one embodiment provided in this application; Figure 2 A schematic diagram of the precise grid division of the study area in Embodiment 2 provided in this application; a is a 50m×50m grid; b is an 80m×80m grid; c is a 100m×100m grid; Figure 3 The diagram shows a comparison between vertically corrected population density and traditional planar population density in Embodiment 2 of this application; a represents low-rise buildings; b represents multi-story buildings; c represents high-rise buildings; d represents super high-rise buildings. As can be seen from the figure, the traditional planar population density is overly concentrated, and there is no population density projection result in the surrounding grid. However, the vertically corrected population density provided in this application takes into account the functional type of the buildings and accurately projects the population of high-rise buildings with different functions onto multiple grids.

[0021] Figure 4 The diagram shows the spatial distribution of the comprehensive safety score in the study area in Embodiment 2 of this application. As can be seen from the diagram, the method provided in this application can cover different functional grid areas of the study area and accurately divide each functional grid. Detailed Implementation

[0022] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0023] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0024] Technical means not detailed in this application and not used to solve the technical problems of this application are all set according to common general knowledge in the field, and multiple common general knowledge setting methods can achieve the same result. See Figures 1-4 The mathematical modeling and quantitative assessment method for high-intensity urban resilient areas with multi-factor coupling provided in this application includes the following steps: Step S1: Construct a high-intensity patch mesh base and preprocess the data. Step S11: Obtain the boundaries of high-intensity areas (such as area red lines and street boundaries). Use a square grid, selecting the grid side length according to the high-intensity area type, to perform full coverage division, ensuring no grid cells are omitted or overlapped. Specifically, for high-intensity areas classified as core business districts / high-density residential areas, use a 50m×50m grid (adapting to high-density, high-population-density characteristics and improving assessment accuracy); for high-intensity areas classified as industrial parks / comprehensive commercial areas, use an 80m×80m grid; for high-intensity areas classified as city-level high-intensity areas, use a 100m×100m grid. Number each grid according to row priority. , where n is the total number of grid cells.

[0025] Step S12: Collect multi-source spatial data for the high-intensity area, including: road network vector data (including main roads, secondary roads, and branch roads), building vector data (including base outline, number of floors, and building function), population data (resident population raster / instantaneous population statistics), refuge vector data (including location, service radius, and capacity), and land use data; project the collected multi-source spatial data onto the same coordinate system (e.g., CGCS2000_3_Degree_GK_cm_117E), and perform spatial correlation matching with grid cells to extract the road network area, building base area, population-related data, and refuge coverage area within each grid, completing the single grid data initialization and providing accurate data support for subsequent assessments.

[0026] Step S2: Calculate the various indices of the base area of ​​a single grid. Step S21: Calculate the area of ​​a single grid cell: Calculate the planar area of ​​a single grid cell based on the grid edge length. The calculation formula is as follows: ,in A cell For the area of ​​the grid cell, L This represents the grid side length. It provides the basis for the subsequent quantitative calculation of various indicators.

[0027] Step S22: Calculation of Building Footprint Area Ratio: This quantifies the horizontal density of building development within the grid, directly reflecting the horizontal characteristics of high-intensity building clusters. The calculation formula is as follows: , where R build,i The percentage of the building's base area in grid i. Abuild,i It is the sum of the ground floor area of ​​all buildings within grid i, and its value ranges from [0,1].

[0028] Step S23: Calculation of Road Network Area Ratio: The formula for calculating the supply level of evacuation routes within the quantitative grid is as follows: , where R road,i For the area ratio of grid i road network, A road,i This represents the sum of the areas of all roads (including lanes and sidewalks) within grid i, with a value range of [0,1]. Obtaining the supply level can accurately reflect the evacuation capacity of high-intensity areas.

[0029] Step S24: Calculation of Escape Coverage Area Ratio: Quantifying the coverage level of escape services within the grid directly relates to the ability to ensure personnel escape during sudden safety incidents in high-intensity areas. The calculation formula is as follows: ,in R shelter,i Percentage of area covered by grid-based refuge. A cover,i Based on the shelter as the center, according to the evacuation tolerance distance threshold d After performing buffer analysis, the area overlapping with grid i is in the range of [0,1].

[0030] Step S3: Calculate the vertically corrected population density (core step) Step S31: Calculate the total building area of ​​the grid: Expand each grid of the horizontal ground floor of the building to the vertical total scale, and calculate the total building area of ​​the grid: A floor,i For grid i, the total building area F i It is the arithmetic mean of the number of building floors within grid i, which truly reflects the population space carried by the building and accurately adapts to the core characteristics of high-density high-rise building agglomeration in the area.

[0031] If it is necessary to differentiate building functions, a functional floor area ratio correction factor should be introduced. β k ( k (For building function type), the calculation formula is adjusted as follows: ,in Let be the ground floor area of ​​the k-th functional building within grid i. Let be the average number of floors of the k-th functional building within grid i, where the building function type is residential. =1.0, Commercial / Office Building =1.2, Buildings with public service functions =0.8, with correction coefficients set for each building type, enabling classified calculations for different functional areas in high-intensity, multi-functional zones. This coefficient uses residential buildings as the benchmark. =1.0, adjusted according to specific functions and traffic flow to better adapt and improve the accuracy of population accounting.

[0032] Step S32: Calculate the total building area of ​​the high-intensity zone The calculation formula is: The total building carrying capacity of the entire high-intensity area is summarized to provide a benchmark for population allocation during the assessment.

[0033] Step S33: Calculate the population density per unit building area in high-intensity areas The calculation formula is: ,in P total The total population of high-intensity areas is represented by the permanent resident population for residential buildings and the on-duty population for commercial / office buildings. The population density per unit building area in high-intensity areas is used as the core benchmark for the even distribution of population in building space, accurately reflecting the vertical agglomeration characteristics of the population in high-intensity areas.

[0034] In fire-fighting scenarios, to accurately estimate the number of people to be evacuated during the day and night, and to adapt to the characteristics of high-intensity population tidal flow in high-intensity areas, a time-based population coefficient is added. γ High-intensity areas, population density per unit building area The calculation formula is adjusted as follows: Among them, the population coefficient of the time period γ The values ​​are: 0.9 for residential buildings at night, 0.3 for residential buildings during the day, 0.8 for office buildings during the day, 0.1 for office buildings at night, and 0.95 for commercial buildings during the day and 0.05 at night.

[0035] Step S34: Calculate the actual population within the grid: The calculation formula is as follows: ,in P i Let represent the actual population in grid i. Based on the building area allocation, the total number of people actually accommodating within the grid is obtained, accurately reflecting the population concentration level at the grid scale in high-intensity areas.

[0036] Step S35: Calculate the vertically corrected population density: The calculation formula is as follows: ,in The population density of grid i is vertically corrected; the actual population per unit grid area (including vertical dimension) is used as the core indicator for assessing the evacuation pressure of high-intensity areas, thus solving the problem that traditional planar density cannot reflect the agglomeration of high-rise buildings.

[0037] Step S36: Standardization and Reverse Processing: To eliminate dimensional differences between meshes, the following steps are performed: D pop,i Perform extreme value normalization: ,in The standardized population density index has a value range of [0,1]. min(D pop ) , max(D pop ) The minimum and maximum values ​​for vertically adjusted population density in this area are determined; since higher population density generally indicates lower safety, [the following values ​​are used]. Converted to the negative exponent of evacuation pressure, the calculation formula is: ,in The larger the size, the less pressure there is in evacuation, which is suitable for the needs of safety assessments in high-intensity areas.

[0038] Step S4: Calculate key evacuation indicators based on road network topology characteristics Step S41: Calculate the evacuation accessibility index: The calculation formula is as follows: ,in A i is the sparse reachability index for grid i, with a value range of [0,1]. d i This is the road network distance from the geometric center of grid i to the nearest shelter, obtained through road network topology shortest path analysis (such as Dijkstra's algorithm). d 0 The evacuation tolerance distance threshold is set at 300m to 500m, which meets fire safety regulations and is suitable for the evacuation needs of high-intensity areas. An exponential decay model characterizes the relationship between evacuation distance and accessibility, aligning with the psychological and physiological characteristics of people evacuating in high-intensity areas, and accurately quantifies the ease of evacuation from the grid to refuge sites.

[0039] Step S42: Calculate grid-scale connectivity: ,in C i Let be the connectivity of the evacuation channels in grid i, with a value range of [0,1]. N i Let i be the set of eight neighboring grids; w ij The road weighting coefficient is 1.0 for main roads, 0.8 for secondary roads, and 0.6 for local roads, used to distinguish the evacuation capacity of different roads; L ij Let i be the length of the connecting path between grid i and its neighboring grid j; n N The total number of neighboring grids is 8 for eight-neighborhood; L is the side length of a single grid.

[0040] Based on the topological characteristics of the road network, the connectivity level of the road network surrounding the grid is quantified, which accurately reflects the smoothness of the evacuation channels of each grid unit in the high-intensity area, and provides support for the identification of evacuation bottlenecks.

[0041] Step S5: Calculate the evaluation matrix and construct the overall score Step S51: Construct the original evaluation matrix: Summarize all individual indicators of all grids to construct an n x m original evaluation matrix, where rows represent grid cells and columns represent evaluation indicators for each grid cell. The matrix expression is:

[0042] Where n is the total number of grid cells, R build,1 R build,2 ..., R build,n R represents the percentage of the building footprint area in grids 1, 2, ..., n. road,1 R road,2 ..., R road,n This represents the proportion of road network area in grids 1, 2, and n. 1, 2……, n For grids 1, 2 to n, the negative exponent of evacuation pressure is represented. R shelter,1 , R shelter,2 , ... R shelter,n This represents the percentage of refuge coverage area for grids 1, 2 to n. A 1 , A 2 , ... A n For grids 1, 2 to n, the evacuation reachability index is used. C 1 , C 2 , ... C n The connectivity of grids 1, 2 to n is represented by the following elements: building base area ratio, road network area ratio, standardized reverse population density, refuge coverage area ratio, evacuation accessibility index, and connectivity of the corresponding grid. This enables a safety assessment of the core dimensions of each grid in high-intensity coverage areas, thereby improving the accuracy of the assessment results.

[0043] Step S52: Normalization of each index in the original evaluation matrix: The calculation formula is as follows: ,in x ij These are the original indicator values. The normalized index value, min( x j max() x j) represent the minimum and maximum values ​​of the j-th indicator, respectively. A uniform extreme value normalization process is performed on all indicators within the original evaluation matrix to eliminate dimensional differences, ensure the comparability of each indicator, and provide an accurate basis for the comprehensive score.

[0044] Step S53: Determining Indicator Weights Using the Entropy Weight Method: The entropy weight method, which involves objective weighting, is used to determine the weights of each indicator. This method avoids the bias in assessment results caused by subjective weight setting and can objectively and accurately allocate the weights of each indicator, thereby effectively improving the objectivity and accuracy of safety assessment results for high-intensity areas. Specifically, it includes the following steps: Step S531: Calculate the weight of the indicators : ;in, For the i-th grid and the j-th evaluation index, the standardized index value after normalization is given. Step S532: Calculate the index entropy value: ; Step S533: Calculate the indicator weights: And satisfy in w j Let be the weight of the j-th indicator.

[0045] Step S54: Calculate the overall safety score S i The calculation formula is: ;in For the i-th grid and the j-th evaluation index, the normalized index value is used; the overall regional safety score is the average of the comprehensive safety scores of all grids. The calculation formula is: , where n is the total number of grids, to achieve a comprehensive quantitative assessment of the safety level of high-intensity areas.

[0046] The formula multiplies the normalized index with its corresponding weight and sums the results to obtain the comprehensive safety index of a single grid. The higher the score of the summed comprehensive safety index of the grid, the higher the safety level of the area and the stronger its emergency evacuation and refuge guarantee capabilities.

[0047] Step S55: Determine security levels: based on the comprehensive security score of individual grids. S i The grid security level is divided into three categories: With a safety rating, smooth road network, ample refuge areas, and low evacuation pressure, it can serve as a benchmark area for safety optimization in high-intensity areas. It is at the basic safety level, meeting basic evacuation and refuge needs, with some areas that can be optimized, and is a key area for safety improvement in high-intensity areas; The area is classified as unsafe due to its dense population, congested road network, and insufficient refuge facilities. It requires significant rectification and is a key area for high-intensity monitoring, traffic control, and safety management. The average comprehensive safety score across all grid areas is also considered. Similarly, it meets the above-mentioned grading evaluation criteria, that is... A value ≥0.7 indicates a safety level; 0.7 > A value of ≥0.4 indicates a basic safety level. A value <0.4 indicates an unsafe level; Step S6: Design Implementation Guide Based on the comprehensive safety score results and safety level classification, targeted safety optimization and supervision work will be carried out in high-intensity areas. Given the characteristics of these areas—high population density and important functions—safety assurance capabilities will be enhanced, specifically including: Step S61: Signage Design: Add eye-catching evacuation signs and directional signs in unsafe areas to strengthen crowd control, improve evacuation efficiency, and adapt to the characteristics of high-intensity areas with large population concentration and high evacuation pressure. Step S62: Evacuation route optimization: In areas with low connectivity of evacuation routes, connect dead-end roads, widen branch roads, optimize the road network structure, improve the traffic capacity of evacuation routes, and break through the evacuation bottleneck in high-intensity areas. Step S63: Refuge site design: In densely populated areas with insufficient refuge coverage, supplement small refuge spaces, reasonably reduce the service radius of refuge sites, improve refuge support capabilities, and meet the refuge needs of people in high-intensity areas during sudden security incidents.

[0048] This enables targeted, zoned, and intensive regional control, improving the precision of control and achieving better emergency response.

[0049] The present invention will be further described in detail below with reference to specific embodiments. High-intensity areas, as core urban areas, are directly related to the level of urban safety governance in terms of the accuracy of their safety assessments. This embodiment takes a typical high-intensity area (core business district) as the research object to verify the feasibility and practicality of the method.

[0050] This embodiment takes a core business district (high-intensity area) as the research object (hereinafter referred to as the research area), which covers an area of ​​approximately 2 km². 2 It is dominated by high-rise buildings, including commercial, office, and residential buildings, with a high population density (statistics show that the instantaneous population exceeds 35,000 during the day). The road network structure is complex. It is the core of the city's economy and the center of population gathering. Its safety level directly affects the overall safety and stability of the city, and it is urgent to optimize the safety guarantee system through scientific assessment methods.

[0051] Example 1: Specific Implementation Steps for Safety Assessment of High-Intensity Areas Step 1: Grid base construction and data preprocessing in the study area 1.1 Grid Division: This study area is a core business district, a high-density, high-population-density, high-intensity area. A 50m × 50m square grid was selected for full coverage division, with a total number of grid units n = 800 (2000m × 2000m ÷ 2500m² / grid). The grid units were numbered according to row priority. This ensures that the differences in population concentration in high-rise buildings can be accurately captured.

[0052] 1.2 Data Collection and Preprocessing: The study area collected vector data of the road network (including 3 main roads, 8 secondary roads, and 15 branch roads), building vector data (a total of 120 buildings, including 40 residential buildings, 35 commercial buildings, and 45 office buildings, with 3 to 28 floors, reflecting the high-intensity area's high-rise building clustering characteristics), resident population data (12,000 people), instantaneous office / commercial population data (35,000 people, reflecting the high-intensity area's population tidal flow characteristics), refuge vector data (3 large refuges, with a service radius of 500m), and land use data. Project all data onto the CGCS2000_3_Degree_GK_CM_117E coordinate system, perform spatial correlation matching with grid cells, and extract data such as road network area, building base area, number of building floors, and refuge coverage area for each grid to complete the initialization of single grid data.

[0053] Step 2: Calculation of basic area index for a single grid 2.1 Grid cell area: .

[0054] 2.2 Building footprint area ratio: based on a grid For example, its building footprint area A build,100 =1200m 2 ,but R build,100 =1200÷2500=0.48, reflecting the horizontal characteristics of the grid building cluster, which is consistent with the characteristics of dense buildings in high-intensity areas.

[0055] 2.3 Road network area ratio: grid Internal road network area A road,100 = 450m 2 ,but R road,100 = 450 ÷ 2500 = 0.18, which reflects the supply level of the grid evacuation channels.

[0056] 2.4 Refuge Coverage Area Percentage: Grid Located within the buffer zone of a certain shelter, overlapping area Acover,100 =2500m 2 ,but R shelter,100 =2500÷2500=1.0, reflecting insufficient coverage of the grid's refuge service.

[0057] Step 3: Vertically Corrected Population Density Calculation 3.1 Total building area of ​​the grid: Grid It comprises two commercial buildings and one office building, with the commercial buildings having a footprint of 500 square meters each. 2 300m 2 The average number of floors is 12 and 10 respectively; the office building footprint is 400m². 2 Average number of floors: 18; Functional floor area ratio correction factor β Values: 1.2 for commercial areas and 1.2 for office areas. A floor,100 =(1.2×500×12)+(1.2×300×10)+(1.2×400×18)=19440m 2 It accurately reflects the building's load-bearing space in the vertical direction of the grid.

[0058] 3.2 Total Building Area of ​​the Study Area: The total building area of ​​the 800 grids is summarized to obtain... .

[0059] 3.3 Population density per unit building area: Instantaneous daytime population in the study area P total =35,000 people, population coefficient for the period γ =0.9 (primarily commercial and office space, consistent with the daytime population concentration characteristics of a high-intensity core business district), then ρ floor =(0.9×35000)÷1200000≈0.02625 people / m 2 .

[0060] 3.4 Grid-based real population: The population density of the grid accurately reflects the actual population concentration level of the grid, avoiding the deviation of traditional planar density.

[0061] 3.5 Vertically Corrected Population Density: D pop,100 =510÷2500=0.204 people / m 2 .

[0062] 3.6 Standardization and Reverse Processing: Calculations were performed on all grids in the study area. D pop The minimum value is 0.03 people / m 2 The maximum value is 0.35 people / m2 ,but , .

[0063] Step 4: Calculation of key evacuation indicators based on road network topology characteristics 4.1 Evacuation Accessibility Index: Grid Shortest distance from the geometric center to the nearest shelter via the road network Evacuation tolerance distance threshold ,but This reflects the ease of evacuation within the grid.

[0064] 4.2 Calculation of grid-scale connectivity index: Grid Eight-neighbor grid set N 100 There are 8 grids in total, with road weight coefficients. w ij The calculation uses 1.0 for main roads, 0.8 for secondary roads, and 0.6 for local roads. ,but This reflects the accessibility of the grid's evacuation routes.

[0065] Step 5: Construction of the evaluation matrix and calculation of the comprehensive score 5.1 Original Evaluation Matrix: R of 800 grids build,i R road,i , , R shelter,i , A i , C i Summarize and construct an original evaluation matrix of 800×6.

[0066] 5.2 Indicator Normalization Process: Extreme value normalization is performed on all indicators in the original evaluation matrix to eliminate dimensional differences.

[0067] 5.3 Determining Weights Using the Entropy Weight Method: The calculated weights for the six indicators are as follows: w 1 (Building footprint as a percentage of total area) = 0.15 w 2 (Road network area ratio) = 0.20 w 3 (Standardized inverse population density) = 0.25 w 4 (Percentage of area covered by refuge) = 0.18 w 5 (Evacuation Accessibility Index) = 0.12 w 6 (Connectivity) = 0.10, which satisfies the condition. Among them, the standardized reverse population density has the highest weight, which is suitable for the core characteristics of high-intensity population agglomeration in areas.

[0068] 5.4 Overall Security Score: Grid The normalized index values ​​are: 0.48, 0.18, 0.456, 1.0, 0.571, and 0.8.

[0069] It falls under the basic security level and requires localized optimization.

[0070] Overall safety score of the study area Overall, the area is at a basic safety level, while some local areas (23 grids with S<0.4) are at an unsafe level and require key optimization. This result accurately reflects the current security status of this high-intensity core business district and provides a clear direction for subsequent optimization.

[0071] Step 6: Design Implementation Guidelines 6.1 Signage Design: In 23 unsafe grid areas (densely populated and under great evacuation pressure), 20 eye-catching evacuation signs and directional signs will be added to cover major intersections and building entrances to improve evacuation efficiency; 6.2 Evacuation route optimization: For 15 grid areas with evacuation route connectivity of less than 0.5, 3 dead-end side roads were opened up and 2 existing side roads were widened (from 4m to 6m) to solve the evacuation bottleneck in high-intensity areas; 6.3 Refuge site design: In the 8 grid areas with dense population and insufficient refuge coverage, 2 small refuge spaces (each accommodating 500 people) will be added to reduce the service radius of the surrounding refuge sites from 500m to 400m, improve the refuge support capacity, and adapt to the refuge needs of high-intensity areas with large population concentration.

[0072] Example 2: Comparative Verification of Different Mesh Sizes To verify the adaptability of the method provided by this invention to different types of high-intensity areas, safety assessments were conducted on the aforementioned study area using grid sizes of 50m, 80m, and 100m, respectively. The results are as follows: 1) 50m grid: This method offers the highest assessment accuracy, precisely capturing the micro-scale differences between high-rise buildings and population in high-intensity areas. The accuracy rate for identifying unsafe grid levels is 96%, which is calculated as 22 / 23*100%. Based on the method provided in this application, the number of unsafe grid levels is 23. Considering the grid division size and the typical engineering error ratio, the actual number of unsafe grid levels is reasonably inferred to be 22. This grid division requires a large amount of computation and is suitable for high-intensity areas with high precision requirements, such as core business districts and high-density residential areas. 2) 80m grid: This method balances assessment accuracy and computational efficiency, achieving a 92% accuracy rate for identifying unsafe grid levels. The accuracy rate is calculated as 21 / 23 * 100%. Based on the grid size and typical engineering error ratios, the actual number of unsafe grid levels is reasonably estimated to be 21. Suitable for medium-to-high intensity areas such as industrial parks and integrated commercial districts. 3) 100m grid: This method offers the highest computational efficiency, achieving an 88% accuracy rate in identifying unsafe grid levels. The accuracy rate is calculated as 20 / 23 * 100%. Based on the grid size and the typical engineering error ratio, the actual number of unsafe grid levels can be reasonably inferred to be 20. This method is suitable for regional-scale assessments of high-intensity urban areas.

[0073] Verification results show that the method provided by this invention can flexibly select the grid size according to the characteristics of different types of high-intensity areas, and has strong adaptability and practicality. It can meet the safety assessment needs of various high-intensity areas and provide technical support for the safety management of high-intensity areas of different scales and types.

[0074] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A mathematical modeling and quantitative assessment method for multi-factor coupling in high-intensity urban resilient areas, characterized in that: Includes the following steps: Step S1: Select the grid side length according to the high-intensity area type, divide the high-intensity area into full-coverage grids, collect multi-source spatial data of the high-intensity area, project the collected multi-source spatial data onto the same coordinate system, and perform spatial association matching with grid cells to extract multi-source spatial data within each grid range and complete single grid data initialization. Step S2: Calculate the basic area index of a single grid: the cell area of ​​grid i. A cell The proportion of the building base area of ​​grid i R build,i The proportion of road network area in grid i, R road,i The percentage of refuge coverage area in grid i R shelter,i ; Step S3: Expand each grid on the horizontal ground floor of the building to a vertical total scale, and calculate the total building area of ​​the grid according to the building function. Where m is the total number of building function types. For grid i Inner k The ground floor area of ​​a functional building, Let be the average number of floors of the k-th functional building within grid i; for buildings with residential function type . =1.0, Commercial / Office Building =1.2, Buildings with public service functions =0.8; Calculate the total building area of ​​the high-intensity area Calculate the population density per unit building area in high-intensity areas based on population changes over time. ,in, P total This represents the total population of the high-intensity area. γ Population coefficient for that period γ The values ​​are: residential 0.9 at night, residential 0.3 during the day, office 0.8 during the day, office 0.1 at night, and commercial 0.95 during the day and 0.05 at night. This is used to calculate the actual population within the grid. ,in A floor,i Given the total building area of ​​the high-intensity zone in grid i; calculate the vertically corrected population density of grid i. ,in A cell Grid cell area; A build,i This represents the sum of the ground floor area of ​​all buildings within grid i, with a value range of [0,1]. F i Let i be the arithmetic mean of the number of building floors within grid i. D pop,i After performing extreme value normalization, we obtain ,Will Converted to negative exponent of evacuation pressure ; Step S4: Calculate the evacuation index based on road network topology characteristics; Step S5: Construct an evaluation matrix for each grid using the negative evacuation pressure index and evacuation indicators, determine the weight of each indicator using the entropy weight method, and calculate the comprehensive safety score for each cell. S i and the average of all grid-based integrated security scores Based on the comprehensive security score of each cell S i and the average of all grid-based integrated security scores Classify security levels.

2. The method for multi-factor coupled mathematical modeling and quantitative evaluation of high-intensity urban resilient areas according to claim 1, characterized in that, Step S4 includes the following steps: Step S41: Calculate the sparse reachability index of grid i ,in A i The value range is [0,1]; d i Let be the road network distance from the geometric center of grid i to the nearest shelter, obtained through road network topology shortest path analysis. d 0 The evacuation tolerance distance threshold is set at 300m to 500m. Step S42: Calculate the scale connectivity of grid i: ,in, C i The value range is [0,1]; N i Let i be the set of eight neighboring grids; w ij The road weighting coefficient is 1.0 for main roads, 0.8 for secondary roads, and 0.6 for local roads, used to distinguish the evacuation capacity of different roads; L ij Let i be the length of the connecting path between grid i and its neighboring grid j; n N This represents the total number of neighboring grids; for an eight-neighbor grid, the value is 8. L This represents the side length of a single grid cell.

3. The method for multi-factor coupled mathematical modeling and quantitative evaluation of high-intensity urban resilient areas according to claim 1, characterized in that, Step S5 includes the following steps: Step S51: Construct the original evaluation matrix: Where n is the total number of grid cells, R build,1 R build,2 …, R build,n R represents the percentage of the building footprint area in grids 1, 2, ..., n. road,1 R road,2 …, R road,n This represents the proportion of road network area in grids 1, 2, and n. 1, 2…, n For grids 1, 2 to n, the negative exponent of evacuation pressure is represented. R shelter,1 , R shelter,2 ,… R shelter,n This represents the percentage of refuge coverage area for grids 1, 2 to n. A 1 , A 2 ,… A n For grids 1, 2 to n, the evacuation reachability index is used. C 1 , C 2 ,… C n The connectivity of grids 1, 2 to n; Step S52: Normalize each index of the original evaluation matrix according to the following formula: ,in x ij These are the original indicator values. For the j-th evaluation index in the i-th grid, the normalized index value is: min( x j ), max( x j ) are the minimum and maximum values ​​of the j-th indicator, respectively; Step S53: Determine the weights of each indicator using the objective weighting entropy weight method; Step S54: Calculate the overall security score for mesh i: ,in, w j For the first j The weight of each indicator, where m is the total number of building function types. The j-th evaluation index value is the normalized value for the i-th grid; the overall safety score for the region is calculated as the average of the comprehensive safety scores of all grids. Where n is the total number of grid cells, S i For grid i The grid-based comprehensive security score; Step S55: Mesh i Comprehensive Security Score S i Classification: Security level; Basic security level; The level is unsafe. The average of all grid-based comprehensive security scores Classification: A value ≥0.7 indicates a safety level; 0.7 > A value of ≥0.4 indicates a basic safety level. A value <0.4 indicates an unsafe level; The safety level is: smooth road network, sufficient refuge, low evacuation pressure, which can serve as a benchmark area for safety optimization in high-intensity areas; The basic safety level is: meeting basic evacuation and refuge needs, with some areas that can be optimized, and is a key area for safety improvement in high-intensity areas; The area is classified as unsafe due to its dense population, congested road network, and insufficient refuge facilities. It requires key rectification efforts and is a high-intensity area requiring focused monitoring, guidance, and safety control.

4. The method for multi-factor coupled mathematical modeling and quantitative evaluation of high-intensity urban resilient areas according to claim 3, characterized in that, Step S53 includes the following steps: Step S531: Calculate the weight of the j-th index in the i-th grid. ;in For the j-th normalized index of the i-th grid; Step S532: Calculate the entropy value of the j-th index. ; Step S533: Calculate the weight of the j-th indicator And satisfy in w j Let be the weight of the j-th indicator.

5. The method for multi-factor coupled mathematical modeling and quantitative evaluation of high-intensity urban resilient areas according to claim 1, characterized in that, Step S2 includes the following steps: Step S21: Calculate the area of ​​the grid cells in grid i. ,in L The grid side length; Step S22: Calculate the proportion of the building footprint area of ​​grid i. ,in A build,i This represents the sum of the ground floor area of ​​all buildings within grid i, with a value range of [0,1]. Step S23: Calculate the area ratio of grid i. , where A road,i This is the sum of the areas of all roads within grid i, with values ​​ranging from [0,1]. Step S24: Calculate the refuge coverage area of ​​grid i. ,in, A cover,i Based on the shelter as the center, according to the evacuation tolerance distance threshold d After performing buffer analysis, the area overlapping with grid i is in the range of [0,1].

6. The method for multi-factor coupled mathematical modeling and quantitative evaluation of high-intensity urban resilient areas according to claim 5, characterized in that, Step S3 includes the following steps: Step S31: Expand each grid of the building's horizontal base layer to a vertical total scale, and calculate the total building area of ​​the grid based on the building's function. Where m is the total number of building function types. Let be the ground floor area of ​​the k-th functional building within grid i. Let be the average number of floors of the k-th functional building within grid i; for buildings with residential function type . =1.0, Commercial / Office Building =1.2, Buildings with public service functions =0.8; Step S32: Calculate the total building area of ​​the high-intensity zone ,in A floor,i The total building area of ​​the high-intensity zone in grid i; Step S33: Calculate the population density per unit building area in high-intensity areas ,in, P total The population of the high-intensity area is represented by the population coefficient for that time period. γ The values ​​are as follows: 0.9 for residential buildings at night, 0.3 for residential buildings during the day, 0.8 for office buildings during the day, 0.1 for office buildings at night, and 0.95 for commercial buildings during the day and 0.05 for commercial buildings at night. Step S34: Calculate the actual population size within grid i ; Step S35: Calculate the vertically corrected population density of grid i: ; Step S36: To eliminate dimensional differences between grids, for D pop,i The standardized population density index is obtained by performing extreme value normalization. ,in, The value range is [0,1]; min(D pop ) , max(D pop ) The minimum and maximum values ​​for the vertically corrected population density of this area; Because higher population density means greater safety, Converted to negative exponent of evacuation pressure .

7. The method for multi-factor coupled mathematical modeling and quantitative evaluation of high-intensity urban resilient areas according to claim 1, characterized in that, Multi-source spatial data includes: road network vector data, building vector data, population data, refuge vector data, and land use data.

8. The method for multi-factor coupled mathematical modeling and quantitative evaluation of high-intensity urban resilient areas according to claim 1, characterized in that, The same coordinate system is CGCS2000_3_Degree_GK_cm_117E.

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