Fire station site selection method and system based on optimal transmission theory

Abstract

The invention discloses a fire station site selection method and system based on an optimal transmission theory, and the method comprises the steps: building a multi-dimensional urban fire-fighting demand field, and building a three-dimensional quantitative index system which comprises a fire risk core evaluation factor, space population density and traffic accessibility; layered planning logic of high-risk area priority coverage, dense population area response guarantee and traffic reachability correction is realized, fire station site selection is abstracted into a probability measurement matching problem of a rescue capability field and a fire protection demand field, and a Wasserstein distance is introduced to measure a distribution gap between the rescue capability field and the fire protection demand field. The systematic balance of the coverage range and the response speed of the fire station is realized by minimizing the'transportation cost '(namely the response time of the fire fighting truck), and uncertainty factors in the site selection process are reasonably processed by introducing description of probability distribution, so that a site selection model which meets the actual fire-fighting planning requirements and also meets the site selection requirements is formulated. And a fire station site selection and distribution scheme of resource optimization configuration can be realized.

Description

Technical Field

[0001] This invention belongs to the field of fire station site selection technology, and relates to a fire station site selection method and system based on optimal transmission theory. Background Technology

[0002] Urban expansion presents numerous significant challenges to urban fire safety planning. On one hand, large buildings and densely populated areas created during urban development can easily amplify the impact of fires. Furthermore, the narrow passageways and complex routes in old urban areas and urban villages greatly hinder firefighting efforts. Simultaneously, the expansion of urban space and population has led to a significant shift in high-risk fire zones, necessitating a redistribution of urban fire resources. Therefore, fire safety planning must not only consider existing fire-fighting centers but also integrate with the city's own development plans to achieve foresight and predictability. This means that before conducting urban fire safety planning, it is necessary to collect historical fire data and information on influencing factors to predict the future spatial and temporal distribution of urban fire risks, thereby guiding fire departments to formulate more scientific planning schemes.

[0003] On the other hand, traditional fire station site selection methods are not rigorous enough, easily leading to problems such as excessively large station responsibility areas and unreasonable allocation of fire resources, which greatly hinders the service capacity of urban fire and rescue systems. my country's "Urban Fire Station Construction Standards" sets a standard response time of 5 minutes for fire stations, requiring them to reach the edge of their responsibility area within 5 minutes of receiving an alarm, and delineates the responsibility area of ​​ordinary fire stations to be 4 to 7 square kilometers. However, in actual fire planning, these two provisions are poorly operable and have considerable arbitrariness. Furthermore, the rise of high urbanization has meant that previous fire station layouts failed to consider current urban development issues, such as traffic congestion during rush hours, excessive urban building density, and the continuous emergence of densely populated areas. Therefore, urban fire authorities need to consider the rationality of the current regional fire station layout and the necessity of setting up new stations in a timely manner. However, how to combine the future development of the local city and the complexity of urban fire rescue, and incorporate many influencing factors under the current urban new normal into the urban fire service system to systematically plan the layout of municipal fire stations, has become a current research challenge. In particular, the current urban population density, frequent fires, and considerable uncertainty in travel time and fire service demand pose significant challenges to the medium- and long-term planning of fire departments.

[0004] Existing research on modeling methods and solution algorithms for fire station site selection specifically includes:

[0005] (1) Single-objective modeling method:

[0006] Maximum coverage model: The goal is to maximize coverage demand points while ensuring fairness, for example by setting a response time threshold to determine the coverage area of ​​fire stations.

[0007] Graph theory-based methods: Fire stations, demand points, and their reachability relationships are abstracted into points, edges, and relationships. The central point of the graph is then determined using the adjacency matrix, serving as the fire station. P-median model: This model optimizes efficiency by minimizing the average distance from demand points to fire stations, for example, by minimizing the total transportation cost through facility location calculations.

[0008] (2) Multi-objective optimization modeling method:

[0009] Some studies have attempted to combine coverage and response time for fire station location selection, but most of them use simple methods such as weighted summation to integrate the objectives, failing to build a systematic collaborative model and failing to quantify the impact of factors such as traffic and building density.

[0010] (3) Uncertainty handling methods:

[0011] Stochastic programming: It uses probability distributions to characterize uncertainties (such as the probability of a fire or traffic congestion) and establishes an expected value model to solve the problem.

[0012] Robust programming: Assuming that the uncertain parameters fluctuate within a certain set, find the robust solution in the worst case.

[0013] (4) Application of spatial analysis techniques:

[0014] GIS-based spatial analysis methods (such as Thiessen polygons and buffer analysis) have been used to delineate fire station responsibility areas, but they only consider geometric distances and do not integrate multi-dimensional data such as fire risk and population density, thus lacking dynamic adaptability.

[0015] Since the 1950s, numerous scholars have conducted extensive research on the site selection problem of urban fire stations, focusing on modeling methods (including deterministic programming, stochastic programming, and robust programming) and solution algorithms (such as heuristic algorithms), greatly enriching the theoretical research on urban fire station site selection planning. In recent years, the research focus of experts and scholars at home and abroad has gradually shifted to fire planning problems that meet practical needs, but existing research still has the following main shortcomings, which urgently need to be explored and resolved.

[0016] (1) The lack of a fairness and efficiency balance model

[0017] In traditional research, fire station site selection planning models are mostly extensions of single modeling ideas such as maximum coverage and P-median coverage. The core objective of the maximum coverage model is to pursue fairness in service to demand areas, while the P-median coverage model focuses on the efficiency of service to demand areas. However, in the actual fire station layout decision-making process, a reasonable balance needs to be achieved between fairness and efficiency in fire service, and current research on fire station site selection based on a combination of these two properties is extremely rare.

[0018] (2) Challenges in constructing a collaborative fire service model

[0019] The site selection and allocation of fire stations based on collaborative firefighting services is currently a mainstream research trend. In actual fire and rescue scenarios, multiple key factors need to be considered collaboratively, such as fire truck coverage and fire response time coverage, while also accurately characterizing numerous factors affecting fire and rescue services, including traffic conditions and fire truck types. However, due to the complex interactions among these factors, organically integrating them into a collaborative fire station site selection model has always been a research challenge. Especially when the research objective expands to be applicable to actual fire protection planning, or even the delineation of collaborative firefighting responsibility zones for municipal fire stations, higher demands are placed on the practicality and adaptability of the model, and existing research progress in this area still falls short of meeting practical needs.

[0020] (3) Limitations of uncertainty handling methods

[0021] Current research on the uncertain fire station site selection problem mainly focuses on modeling based on stochastic programming or robust programming. The effectiveness of stochastic programming methods is easily limited by the amount of sample data; when sample data is insufficient, it is difficult to accurately characterize the distribution characteristics of uncertain factors, thus affecting the model's prediction accuracy. Robust programming methods, on the other hand, can lead to overly conservative optimal site allocation schemes, potentially overestimating fire budget costs and resulting in unreasonable resource allocation. Although the objective function of distributed robust optimization models shows that its modeling approach can effectively avoid dependence on the precise distribution of uncertain variables and alleviate the conservatism of robust optimization, demonstrating significant feasibility in characterizing the uncertain fire station site allocation problem, research on fire station site allocation modeling based on this approach remains quite scarce. This results in a lack of more effective methods and models to support the practical handling of uncertain problems. Summary of the Invention

[0022] The purpose of this invention is to address the problem in the existing technology that fire station coverage and response speed cannot be reasonably balanced, and that many influencing factors under the new normal of urban development are not fully considered, resulting in unreasonable allocation of fire resources and lagging service capabilities of urban fire and rescue systems. This invention provides a fire station site selection method and system based on optimal transmission theory.

[0023] To achieve the above objectives, the present invention employs the following technical solution:

[0024] A fire station site selection method based on optimal transmission theory includes the following steps:

[0025] Constructing an urban fire demand field, which includes constructing a spatial fire risk field and calculating the population density and traffic accessibility within the spatial fire risk field;

[0026] Construct a fire station rescue capability field, distribute the urban fire demand field as a probability measure μ, distribute the fire station rescue capability field as a probability measure ν, define the total cost of dispatching resources from the fire station rescue capability field to the urban fire demand field as the service response time of the fire truck, calculate the optimal transmission scheme T for dispatching resources from the fire station rescue capability field to the urban fire demand field with Wasserstein distance as the objective function, and determine the final location of the fire station.

[0027] A further improvement of the present invention is that:

[0028] The constructed space fire risk field includes:

[0029] Discretize the center of the fire risk area to determine the set of coordinates of the center of the fire risk area.

[0030] The entropy weight-TOPSIS combined model is used to evaluate the center C of each risk region. i Risk level;

[0031] Based on the center C of each risk area i We construct a progressive coverage model based on risk levels to obtain a continuous expression of the risk field.

[0032] The population density within the calculated fire risk area includes:

[0033] D(r)=D0e (-βr)

[0034] Where D(r) represents the population density at a distance r from the center; D0 represents the theoretical density or core area density at the center (r=0); β represents the density decay coefficient, β>0, which reflects the rate at which density decreases with distance, and the larger the value of β, the faster the density decreases; r represents the distance to the center.

[0035] The calculation of traffic accessibility includes:

[0036] Construct a traffic accessibility correction model:

[0037]

[0038] Among them, L j Therefore, C i Centered on, with v is the shortest path length around the radius; j This represents the average speed of the fire truck passing through this section of road; ξ is the obstacle penalty factor, ξ = 1 when the road is passable, and ξ >> 1 when the road is impassable.

[0039] Constructing urban fire protection demand sites:

[0040] S j =ω R ·R j +ω P ·P j +ω V ·V j

[0041] Among them, R j Indicates the fire risk value; P j V represents the impact of population density; j Indicates accessibility; ω R ω P ω V These are the weights for fire risk, population density, and accessibility, respectively, ω R +ω P +ω V =1.

[0042] The construction of the fire station's rescue capability field includes:

[0043]

[0044] In the formula, d ij R represents the distance from demand point i to fire station j; j This indicates that fire station j can provide complete fire services within this radius, and the fire service capacity is denoted as 1; D represents the maximum coverage radius, which is a constant.

[0045] The calculation of the optimal transmission scheme T using Wasserstein distance as the objective function to determine the final location of the fire station includes:

[0046] Based on field theory, a continuous model is constructed to obtain a linear expression for the fire station site selection problem;

[0047] By introducing entropy regularization to select a unique solution, the linear expression of the fire station site selection problem is regularized to obtain the optimal transportation problem expression:

[0048]

[0049] Where C represents the response time of the fire truck; P represents the optimal transmission scheme for transmitting the fire truck response represented by vector a to the fire distribution represented by vector b; a represents the quantity of the initial state of the distribution at x, and b represents the quantity of the final state of the distribution at y.

[0050] Introduce Lagrange multipliers f and g to construct the Lagrange function;

[0051] The SinkHorn iterative algorithm is introduced to solve the Lagrange function and obtain the optimal transmission scheme T.

[0052] A fire station site selection system based on optimal transmission theory includes:

[0053] The urban fire demand field acquisition module is used to construct an urban fire demand field, which includes constructing a spatial fire risk field and calculating the population density and traffic accessibility within the spatial fire risk field.

[0054] The fire station rescue capability field acquisition module is used to construct the fire station rescue capability field. It distributes the urban fire demand field as a probability measure μ and the fire station rescue capability field as a probability measure ν. The total cost of dispatching resources from the fire station rescue capability field to the urban fire demand field is defined as the service response time of the fire truck. The optimal transmission scheme T for dispatching resources from the fire station rescue capability field to the urban fire demand field is calculated with Wasserstein distance as the objective function, and the final location of the fire station is determined.

[0055] A terminal device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program as steps of any of the methods described in this invention.

[0056] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of any of the methods described in this invention.

[0057] Compared with the prior art, the present invention has the following beneficial effects:

[0058] This invention discloses a fire station site selection method based on optimal transport theory. It constructs a multi-dimensional urban fire demand field and establishes a three-dimensional quantitative index system including core fire risk assessment elements, spatial population density, and traffic accessibility. This achieves a hierarchical planning logic of "prioritizing coverage in high-risk areas → ensuring response in densely populated areas → adjusting for traffic accessibility." The method abstracts fire station site selection as a probabilistic measurement matching problem between the "rescue capacity field" and the "fire demand field," introducing Wasserstein distance to measure the distribution gap between the two. By minimizing "transportation costs" (i.e., fire truck response time), a systematic balance between fire station coverage and response speed is achieved. By introducing a probability distribution description, uncertainties in the site selection process are reasonably handled, thus formulating a fire station site allocation scheme that meets actual fire planning needs and achieves optimal resource allocation. Attached Figure Description

[0059] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0060] Figure 1 This is a flowchart illustrating the construction process of urban fire protection demand sites according to the present invention;

[0061] Figure 2 This is a graph showing the decrease in fire risk value as a function of distance according to the present invention.

[0062] Figure 3 This is a heat map of urban fire protection demand intensity according to the present invention;

[0063] Figure 4 This is a heat map of the urban fire station rescue capabilities according to the present invention. Detailed Implementation

[0064] 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.

[0065] 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.

[0066] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0067] In the description of the embodiments of the present invention, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the present invention. Furthermore, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0068] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0069] In the description of the embodiments of the present invention, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in the present invention according to the specific circumstances.

[0070] The present invention will now be described in further detail with reference to the accompanying drawings:

[0071] See Figure 1 This invention discloses a fire station site selection method based on optimal transmission theory, aiming to construct a novel fire station site selection model that can effectively balance the fairness and efficiency of fire services. This model fully considers the synergistic effects of multiple factors such as fire truck coverage, fire response time coverage, traffic conditions, and fire truck types. By introducing a probability distribution description, it rationally handles uncertainties in the site selection process, thereby formulating a fire station site allocation scheme that meets actual fire planning needs and achieves optimal resource allocation, providing more scientific and practical theoretical support for urban fire planning.

[0072] This embodiment is mainly based on the following considerations:

[0073] (1) Fire protection demand site construction method considering multiple factors

[0074] It includes an integrated process for fire risk quantification (TOPSIS entropy weight method), population density modeling (Clark model), traffic accessibility correction (road network travel time model), and a method for spatial risk field continuity based on normal distribution.

[0075] (2) Fire station site selection model based on optimal transmission theory

[0076] The location problem is defined as the optimal transport problem between probabilistic measures. A modeling framework with Wasserstein distance as the objective function and fire truck response time as the transfer cost is used to achieve a balance between fairness and efficiency.

[0077] (3) Solution scheme for discrete problem of location selection - continuous distribution - sampling.

[0078] Breaking away from traditional discrete modeling methods for location selection problems, this approach employs continuous modeling based on field theory, followed by sampling techniques to transform the continuous distribution into a discrete one. This ensures accurate modeling while optimizing solution efficiency, achieving precise and rapid solutions.

[0079] Specifically, this embodiment discloses a fire station site selection method based on optimal transmission theory, which includes the following steps:

[0080] Step 1: Construction of Urban Firefighting Demand Sites

[0081] Step 1.1: Analysis of Factors Affecting Fire Risk

[0082] Fire risk can be viewed as the probability of a fire occurring under conditions of uncertainty and the potential consequences (such as damage to life, property, or the environment). Therefore, this embodiment defines fire risk as the product of the probability of a fire occurring and the severity of its consequences. To support this definition, fire risk assessment must incorporate two types of indicators: indicators that directly affect the probability of a fire occurring and indicators that directly determine the severity of the disaster consequences. The quantitative indicator system constructed in this embodiment is shown in Table 1.

[0083] Table 1 Quantitative Index System for Fire Risk Assessment

[0084]

[0085] Based on the above indicator analysis, for cities, following the principle of "prioritizing coverage of high-risk areas → ensuring response in densely populated areas → adjusting for traffic accessibility," the process for constructing urban fire demand sites is as follows: Figure 1 As shown.

[0086] Step 1.2: Construction of the Space Fire Risk Field

[0087] The core of constructing an urban spatial fire risk field is to establish a continuous mapping from geographic space to risk level. Normalization ensures that risk values ​​have a unified dimension, facilitating spatial analysis and fire station site selection. The construction of this risk field involves the following key steps:

[0088] Step 1: Decoupling the Fire Risk Area Center

[0089] The urban geospatial space is divided into m discrete risk assessment units, with buildings or grids as the basic units, to determine the set of center coordinates of the risk areas. This process requires consideration of urban land use, building density, and the distribution of historical fire hotspots, prioritizing the geometric center of high-risk functional areas as the assessment node.

[0090] Step 2: Risk Quantification Based on TOPSIS-Entropy Weight Method

[0091] For each risk center C i The fire risk level was assessed using the entropy weight-TOPSIS combined model, and the specific process is as follows:

[0092] (1) Construction of indicator system: Select the core fire risk assessment elements and indicators shown in Table 1 to form the feature vector X. i =[x i1 ,x i2 ,...,x in ].

[0093] (2) Data standardization: The normalization method is used to eliminate dimensions, and the formula is:

[0094]

[0095] (3) Entropy weighting method: Calculate the index weight w using entropy value. j This reflects the contribution of data dispersion to risk:

[0096]

[0097] (4) TOPSIS overall evaluation:

[0098] Step 1: Calculate the weighted normalization matrix

[0099] Step 2: Determine the ideal solution V + and negative ideal solution V - ;

[0100] Step 3: Calculate the Euclidean distance

[0101] Step 4 Risk Score The value range is [0,1], and the larger the value, the higher the risk.

[0102] Step 3: Construct a progressive covering model to make the space continuous.

[0103] To achieve a continuous representation of the risk field, this embodiment employs a progressive coverage mechanism with distance decay and truncation constraints to extend risk assessment from a point to a surface. The specific derivation is as follows:

[0104] (1) Definition of attenuation rule and cutoff constraint

[0105] Let risk center C be set i The risk value is T i (T i (∈[0,1], the larger the value, the higher the fire risk at the center). For any point P in space, two types of distance thresholds are defined:

[0106] Cutoff distance When P and C i distance At that time, it was believed that C i The risk impact on P is zero;

[0107] Attenuation interval [0, d c ):when At that time, the risk contribution decreases exponentially with increasing distance, and the decay law is characterized by a normal distribution.

[0108] (2) Derivation of parameters of normal distribution

[0109] A normally distributed, symmetrical, and smooth decay curve better reflects the spatial patterns of risk diffusion. Let C... i The corresponding normal distribution is (with C) i Centered on the x-axis, with distance d as the x-coordinate, and symmetric about d = 0, its probability density function is:

[0110]

[0111] The extreme value of the normal distribution occurs when d = 0 (i.e., at the risk center). Let the extreme value be equal to T i We can deduce that:

[0112]

[0113] Furthermore, Substituting the density function, we obtain the risk decay formula (only applicable to 0 ≤ d < d). c (Interval):

[0114] φ i (d)=T i ·exp(-πTi 2 d 2 ).

[0115] (3) Calculation of risk value superposition of spatial points

[0116] For any point P in the urban space, traverse all risk centers C. i Its total risk value is the sum of the contributions of each center:

[0117]

[0118] Where: d i =d(PC) i (P) represents the distance from point P to the risk center C. i The Euclidean distance; m is the total number of risk centers.

[0119] Step 1.3: Overlay population density weights

[0120] After obtaining the spatial fire risk field, the impact of spatial population density on fire station site selection needs to be further considered. After aligning the population density data with the discrete assessment units of the fire risk field, the Clark negative exponential model is used to calculate the regional population density:

[0121] D(r)=D0e (-βr)

[0122] For each C i Where D(r) represents the population density at a distance r from the center; D0 represents the theoretical density or core area density at the center (r=0); β represents the density decay coefficient (β>0), reflecting the rate at which density decreases with distance. The larger the β value, the faster the density decreases. r represents the distance to the center. By normalizing the data to unify the dimensions, the population density value and the fire risk value become comparable.

[0123] Step 1.3 Traffic Accessibility Correction

[0124] This embodiment constructs a traffic accessibility correction model based on actual road network traffic efficiency, using the actual travel time of fire trucks as the core calculation standard. The specific formula is as follows:

[0125]

[0126] Where L j Therefore, C i Centered on, with v is the shortest path length around the radius; j This represents the average speed of the fire truck passing through this section of road; ξ is the obstacle penalty factor, ξ = 1 when the road is passable, and ξ >> 1 when the road is impassable.

[0127] The travel time tiers correspond to accessibility scores, with shorter travel times resulting in higher scores. The specific accessibility score piecewise function is as follows:

[0128]

[0129] Step 1.4, Urban Firefighting Demand Site

[0130] For each spatial point j, the formula S j =ω R ·R j +ω P ·P j +ω V ·V j Achieving fire risk value R j Population density impact value P j With accessibility V j The weighted superposition of ω. R ω P ω V The weights for fire risk, population density, and transportation accessibility are respectively, and can be dynamically adjusted according to regional characteristics, and ω R +ω P +ω V =1.

[0131] A randomized set of data is simulated, and the urban fire-fighting demand is visualized using a heat map. Figure 3 As shown.

[0132] Step 2: Construction of the fire station's rescue capability field

[0133] When fire stations provide fire services, the difficulty of the service is usually measured by the travel distance or time between the fire station and the service recipient. Therefore, this embodiment models the fire station's rescue capabilities using a scheme similar to step 1.2, employing a multi-layered, progressive coverage approach based on the needs of each point in space, comprehensively considering the fairness and efficiency of the fire station's services. (Note: f) j (d ij The formula () represents the rescue capability of fire station j at point i in space, and is calculated as follows:

[0134]

[0135] In the formula, d ij R represents the distance from demand point i to fire station j; j This indicates that fire station j can provide complete fire services within this radius, denoted as 1 for fire-fighting capacity; D represents the maximum coverage radius, which is a constant. On one hand, f j (d ijOn the one hand, setting the maximum coverage distance D to serve as many spatial locations as possible ensures the fairness of fire services; on the other hand, setting the ideal fire service distance ensures the efficiency of fire services.

[0136] Based on the above modeling and analysis of fire station rescue capabilities, if n fire stations are deployed in the city, their firefighting capabilities can work together to construct a rescue capability field within the urban space. (See [link to relevant documentation]). Figure 4 .

[0137] Step 3: Fire station site selection problem based on optimal transmission theory

[0138] After obtaining the urban fire demand field and rescue capacity field, the fire station location problem can be described as transferring a discrete rescue distribution (source distribution) to another discrete demand distribution (target distribution). From the perspective of optimal transmission, this process can be abstracted as an optimal mapping problem between probability measures. The fire station rescue capacity field distribution is represented by probability measure μ, and the urban fire demand field distribution is represented by probability measure ν. The objective is to find an optimal transmission scheme T that minimizes the total cost ∫c(x,T(x))dμ(x) of dispatching resources from the fire station rescue capacity field to the urban fire demand field, where c(x,y) represents the resource transfer cost from location x to location y, defined as the service response time of the fire truck. By solving this optimization problem, the optimal location of the fire station can be determined, achieving the fastest fire station rescue response.

[0139] Step 3.1: This embodiment introduces the Wasserstein-1 distance (W1 distance for short) to measure the distribution gap between the urban fire demand field and the fire station rescue capacity field. Its mathematical definition is:

[0140]

[0141] Where Γ(μ,ν) represents all joint probability measures (transmission schemes) with marginal distributions of μ and ν, and c(x,y) is the cost function. Intuitively, the W1 distance characterizes the minimum "transportation cost" required to convert the probability measure μ into ν, and its geometric meaning can be understood as the "displacement mean" between probability distributions. In this embodiment, when the distributions of μ and v highly overlap, the W1 distance approaches 0, indicating that the fire station's rescue capability accurately meets the city's fire protection needs; when the distributions of the two differ significantly, the W1 distance increases, reflecting the "mismatch" between the fire station's rescue capability and the city's fire protection needs.

[0142] By transforming the location problem into a continuous problem, the continuous model can be used for mechanistic analysis using tools such as calculus and functional analysis. In this embodiment, optimal transport theory is used to transform the discrete resource scheduling problem into a convex optimization problem in a continuous space. This transformation avoids the combinatorial explosion of computational complexity in discrete scenarios and improves solution efficiency. At the same time, continuous modeling is naturally compatible with probability measure theory, allowing the uncertainty of fire occurrence to be incorporated into the model, providing a probabilistic interpretation.

[0143] Step 3.2: Solve the fire station site selection problem using the SinkHorn algorithm.

[0144] Because computers can only process discrete data, and the SinkHorn algorithm is designed for discrete distributions, this embodiment uses a sampling method to approximate continuous probability measures in order to increase computational efficiency.

[0145] A continuous probability distribution can be approximated by a linear combination of Dirac distributions. The Dirac distribution δ(xx) i () is an idealized point mass distribution, existing only at x = x i The value at point A is infinity, and the value at all other points is 0, with the integral normalized to 1. This is achieved through a finite number of sampling points. and weight Construct an approximate distribution Where, when N→∞ and the sampling point {x i When covering the support set of the target distribution, It converges to the true distribution p(x).

[0146] This embodiment assumes that the field distribution is discretized into n point sets, resulting in a position vector: x:=(x1,…,x n ),y:=(y1,…,y n After normalizing it, we can re-express it using (a,b):

[0147]

[0148] Where a represents the quantity of the initial state of the distribution at x, and b represents the quantity of the final state of the distribution at y.

[0149] In this embodiment, matrix C is used to represent the response time of the fire truck, i.e., C0 ij x represents i The fire truck arrived at the unit to measure y j The response time for carrying out firefighting tasks; using matrix P to represent the optimal transmission scheme for transmitting the fire truck response (represented by vector a) to the fire distribution location (represented by vector b), i.e., P ij x represents i Construction of P site ij When a fire station is located in the city, j The area coverage service is located here. Therefore, P1 is here.n =a,P T 1 n =b,P ij ≥0, where 1 n =[1,…,1] T ;

[0150] The optimal solution to the fire station site selection problem is expressed in the following optimization form:

[0151]

[0152] stP1 n =a,P T 1 n =b

[0153] Note that the above equation is a linear optimization problem, but the solution may not be unique. To address this issue, entropy regularization is introduced to select a unique solution. For entropy-regularized problems, the SinkHorn algorithm, which is simpler to describe than the simplex method, can be used to solve them. Furthermore, the SinkHorn algorithm is better suited for parallel computing on GPUs.

[0154] Define the peel function The rule is that if P has a number less than or equal to 0, then H(P) = -∞.

[0155] The optimal transmission problem after regularization becomes:

[0156] It can be proven that the solution to this problem is unique, and that the optimal solution P is found when ∈→0. ∈ It will converge to the set of solutions to the original problem that has the largest droplet.

[0157] Introducing Lagrange multipliers f and g, we construct the Lagrange function:

[0158]

[0159] Differentiate:

[0160]

[0161] The optimal solution is obtained by simplification:

[0162]

[0163] remember as well as Therefore, the optimal solution can be written as:

[0164] P = diag(u)Kdiag(v),

[0165] Where, diag(u) is a matrix whose diagonal elements are the values ​​corresponding to vector u, i.e.

[0166] Since P∈U(a,b), u,v satisfy diag(u)Kdiag(v)1 n =a,diag(v)K T diag(u)1 n =b, rewritten as element-wise multiplication.

[0167] u⊙(Kv)=a,v⊙(K T v)=b,

[0168] Here, ⊙ represents element-wise multiplication.

[0169] To solve the above equation, SinkHorn uses an iterative algorithm, first initializing v. (0) =1 n Then use iterative After iterative solving and convergence, the optimal transmission plan is:

[0170]

[0171] The method disclosed in this embodiment has the following advantages:

[0172] (1) Construction of multi-dimensional urban fire protection demand field

[0173] Establish a three-dimensional quantitative indicator system that includes core fire risk assessment elements (land use, building density, number of historical fires, distribution of high-risk sources), spatial population density, and traffic accessibility. Quantify risk levels using the TOPSIS entropy weight method, and dynamically adjust the demand field by combining the Clark negative exponential model and road network traffic efficiency to achieve a hierarchical planning logic of "prioritizing coverage of high-risk areas → ensuring response in densely populated areas → adjusting for traffic accessibility".

[0174] (2) Addressing modeling based on optimal transmission theory

[0175] The selection of fire station sites is abstracted as a probabilistic measurement matching problem between "rescue capacity field" and "fire demand field". Wasserstein distance is introduced to measure the distribution gap between the two. By minimizing "transportation cost" (fire truck response time), a systematic balance between fairness (coverage) and efficiency (response speed) is achieved.

[0176] (3) Engineering solution of SinkHorn algorithm

[0177] To address the demands of discrete data processing in computers, a linear combination of Dirac distributions is used to approximate a continuous probability measure. Entropy regularization transforms the original problem into a convex optimization problem with a unique solution. The SinkHorn iterative algorithm is introduced to solve for the optimal transfer matrix, improving computational efficiency and adapting to GPU parallel computing.

[0178] This method breaks through the traditional discrete entity enumeration evaluation paradigm, integrates physical field theory, and constructs a spatially continuous representation system for fire rescue capabilities: it abstracts discrete fire station entities as "field sources," and uses a custom field strength function to characterize the effectiveness radiation capability, achieving a two-way mapping between "network topology and spatial effectiveness"; after multi-source field strength superposition and normalization, it integrates local rescue capabilities into a global potential energy distribution. It also combines optimal transmission theory to realize the transformation from continuous field optimization to discrete site selection.

[0179] By transforming the location problem into a continuous problem, the continuous model can be used for mechanistic analysis using tools such as calculus and functional analysis. In this embodiment, optimal transport theory is used to transform the discrete resource scheduling problem into a convex optimization problem in a continuous space. This transformation avoids the combinatorial explosion of computational complexity in discrete scenarios and improves solution efficiency. At the same time, continuous modeling is naturally compatible with probability measure theory, allowing the uncertainty of fire occurrence to be incorporated into the model, providing a probabilistic interpretation.

[0180] This embodiment also discloses a fire station site selection system based on optimal transmission theory, including:

[0181] The urban fire demand field acquisition module is used to construct an urban fire demand field, which includes constructing a spatial fire risk field and calculating the population density and traffic accessibility within the spatial fire risk field.

[0182] The fire station rescue capability field acquisition module is used to construct the fire station rescue capability field. It distributes the urban fire demand field as a probability measure μ and the fire station rescue capability field as a probability measure v. The total cost of dispatching resources from the fire station rescue capability field to the urban fire demand field is defined as the service response time of the fire truck. The optimal transmission scheme T for dispatching resources from the fire station rescue capability field to the urban fire demand field is calculated with Wasserstein distance as the objective function, and the final location of the fire station is determined.

[0183] A schematic diagram of a terminal device according to an embodiment of the present invention. The terminal device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps in the various method embodiments described above. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the various device embodiments described above.

[0184] The computer program can be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention.

[0185] The terminal device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The terminal device may include, but is not limited to, a processor and a memory.

[0186] The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0187] The memory can be used to store the computer program and / or module. The processor implements various functions of the terminal device by running or executing the computer program and / or module stored in the memory and calling the data stored in the memory.

[0188] If the modules / units integrated into the terminal device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0189] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A fire station site selection method based on optimal transmission theory, characterized in that, Includes the following steps: Constructing an urban fire demand field, which includes constructing a spatial fire risk field and calculating the population density and traffic accessibility within the spatial fire risk field; Construct a fire station rescue capability field, distribute the urban fire demand field as a probability measure μ, distribute the fire station rescue capability field as a probability measure v, define the total cost of dispatching resources from the fire station rescue capability field to the urban fire demand field as the service response time of the fire truck, calculate the optimal transmission scheme T for dispatching resources from the fire station rescue capability field to the urban fire demand field with Wasserstein distance as the objective function, and determine the final location of the fire station.

2. The fire station site selection method based on optimal transmission theory according to claim 1, characterized in that, The constructed space fire risk field includes: Discretize the center of the fire risk area to determine the set of coordinates of the center of the fire risk area. The entropy weight-TOPSIS combined model is used to evaluate the center C of each risk region. i Risk level; Based on the center C of each risk area i We construct a progressive coverage model based on risk levels to obtain a continuous expression of the risk field.

3. The fire station site selection method based on optimal transmission theory according to claim 2, characterized in that, The population density within the calculated fire risk area includes: D(r)=D0e (-βr) Where D(r) represents the population density at a distance r from the center; D0 represents the theoretical density or core area density at the center (r=0); β represents the density decay coefficient, β>0, which reflects the rate at which density decreases with distance, and the larger the value of β, the faster the density decreases; r represents the distance to the center.

4. The fire station site selection method based on optimal transmission theory according to claim 3, characterized in that, The calculation of traffic accessibility includes: Construct a traffic accessibility correction model: Among them, L j Therefore, C i Centered on, with v is the shortest path length around the radius; j ξ represents the average speed of the fire truck passing through this section of road; ζ is the obstacle penalty factor, ζ = 1 when it is passable, and ξ >> 1 when it is impassable.

5. The fire station site selection method based on optimal transmission theory according to claim 4, characterized in that, Constructing urban fire protection demand sites: S j =ω R ·R j +oh P ·P j +oh V ·V j Among them, R j Indicates the fire risk value; P j V represents the impact of population density; j Indicates accessibility; ω R ω P ω V These are the weights for fire risk, population density, and accessibility, respectively, ω R +ω P +ω V =1.

6. The fire station site selection method based on optimal transmission theory according to claim 1, characterized in that, The construction of the fire station's rescue capability field includes: In the formula, d ij R represents the distance from demand point i to fire station j; j This indicates that fire station j can provide complete fire services within this radius, and the fire service capacity is denoted as 1; D represents the maximum coverage radius, which is a constant.

7. The fire station site selection method based on optimal transmission theory according to claim 1, characterized in that, The calculation of the optimal transmission scheme T using Wasserstein distance as the objective function to determine the final location of the fire station includes: Based on field theory, a continuous model is constructed to obtain a linear expression for the fire station site selection problem; By introducing entropy regularization to select a unique solution, the linear expression of the fire station site selection problem is regularized to obtain the optimal transportation problem expression: Where C represents the response time of the fire truck; P represents the optimal transmission scheme for transmitting the fire truck response represented by vector a to the fire distribution represented by vector b; a represents the quantity of the initial state of the distribution at x, and b represents the quantity of the final state of the distribution at y. Introduce Lagrange multipliers f and g to construct the Lagrange function; The SinkHorn iterative algorithm is introduced to solve the Lagrange function and obtain the optimal transmission scheme T.

8. A fire station site selection system based on optimal transmission theory, characterized in that, include: The urban fire demand field acquisition module is used to construct an urban fire demand field, which includes constructing a spatial fire risk field and calculating the population density and traffic accessibility within the spatial fire risk field. The fire station rescue capability field acquisition module is used to construct the fire station rescue capability field. It distributes the urban fire demand field as a probability measure μ and the fire station rescue capability field as a probability measure ν. The total cost of dispatching resources from the fire station rescue capability field to the urban fire demand field is defined as the service response time of the fire truck. The optimal transmission scheme T for dispatching resources from the fire station rescue capability field to the urban fire demand field is calculated with Wasserstein distance as the objective function, and the final location of the fire station is determined.

9. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1-7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-7.

Images