Forest fire spreading space-time reverse deduction method based on cellular automaton

Abstract

The invention relates to the technical field of emergency management, and discloses a forest fire spreading space-time reverse deduction method based on a cellular automaton, and the method comprises the following steps: S1, completing the construction of an eight-direction forest fire spreading speed equation based on CA in combination with a king-hair correction forest fire spreading speed and a Kataburn gradient correction factor; s2, defining a cellular shape, a neighborhood, a combustion state and a local state transition rule, and completing the design of a CA-based forest fire spread space-time reverse deduction model; and S3, building an inverse travel time fire spreading network by using the forest fire model and a Di jkstra optimization algorithm so as to realize the fire point estimation method based on MTT. According to the technical scheme of the invention, through improving the accuracy of fire prediction and prevention and control, the safety of a power grid project is enhanced, the method adapts to special terrains and climates in the southwest region, the data fusion and model verification capability is improved, the application field is expanded, and the technical progress is promoted.

Description

Technical Field

[0001] The invention relates to the technical field of emergency management, and in particular to a spatiotemporal reverse deduction method of forest fire spread based on cellular automata. Background Art

[0002] Forest fire is a disaster that is difficult to extinguish and causes serious damage to forest resources and the ecological environment. Studying the laws of forest fires and assessing fire losses are important bases for formulating firefighting strategies and implementing fire fighting commands, and are of great significance for reducing forest fire losses. With the rapid development of power grid projects in the southwest region, the threat posed by forest fires to power grid security has become increasingly prominent.

[0003] Traditional forest fire prediction and prevention methods often have the following problems: most of them focus on the spread of forest fires, without deducing the specific location and direction of the fire point; the spread of forest fires is mostly calculated using a single model (mathematical model, physical model), with low accuracy and reliability; they are not very targeted, and do not combine specific terrain characteristics or conduct deduction and impact analysis for specific scenarios. Summary of the invention

[0004] In view of the shortcomings of the prior art, the present invention provides a spatiotemporal reverse deduction method for forest fire spread based on cellular automata, which solves the problem that the prior art is not perfect in predicting and preventing and controlling forest fires.

[0005] To achieve the above objectives, the present invention is implemented by the following technical scheme: a method for temporal and spatial reverse deduction of forest fire spread based on cellular automata, comprising the following steps:

[0006] S1: Combine the Wang-Mao modified forest fire spread speed and the Kataburn slope correction factor to complete the construction of the eight-direction forest fire spread speed equation based on CA;

[0007] S2: Define the cell shape, neighborhood, burning state and local state transition rules, complete the design of the CA-based forest fire spread spatiotemporal reverse deduction model, and realize the spatiotemporal retrospective simulation of forest fires extending inward from the fire boundary;

[0008] S3: Using the forest fire model and Dijkstra optimization algorithm, the inverse travel time fire spread network is constructed, thereby realizing the fire point estimation method based on MTT.

[0009] Preferably, the S1 further comprises:

[0010] S101: First, the formula for forest fire spread rate of the Wang-Mao modified model is given:

[0011] R=R0·K w ·K s ·Kf

[0012] R0=a·T+b·V+c·(100-RH)-d

[0013] In the formula, R represents the speed of forest fire spread; K w is the wind speed adjustment factor, K s is the slope adjustment factor; K f is the combustible adjustment factor; R0 represents the initial spreading speed; a, b, c, d are the correction coefficients of R0, T is the temperature, V is the wind force level, and RH is the relative humidity.

[0014] K w and K s Programming, that is, K w =e 0.1783v·cosθ ; The following formula is obtained:

[0015]

[0016] In the formula, v represents wind speed, θ represents the angle between wind direction and burning direction; g represents slope coefficient, which is 1 for upslope and -1 for downslope; is the slope angle.

[0017] S102: Based on the Wang-Mao modified model, the formula for forest fire spread speed in different terrains and wind directions is obtained:

[0018]

[0019] R 左平坡 =R0·K f ·e 0.1783v·cos(θ+90°)

[0020] R 右平坡 =R0·K f ·e 0.1783v·cos(θ-90°)

[0021]

[0022] In the formula, R 上坡 , R 下坡 , R 左平坡 , R 右平坡 , R 风方向 Indicates the forest fire spread speed in five directions obtained by combining different wind directions and terrains;

[0023] S103: Incorporate the forest fire spread speed formula into the CA model:

[0024] For the 8-neighborhood CA model, the spreading speed of the central cell in the 8 neighborhood directions needs to be solved separately, as shown in the figure above. According to the 8-neighborhood model, the wind speed adjustment factor and slope adjustment factor can be updated to the following calculation formula:

[0025] K w =e 0.1783v·cos(nd-wd)

[0026]

[0027] Where nd represents the direction of the neighborhood cell, wd represents the wind direction; H cen represents the height of the central cell, H nei represents the height of the neighborhood cell, and d represents the center distance between two cells.

[0028] S104: Construct the forest fire spread speed formula of the CA model combustion cell:

[0029]

[0030] In the formula, R IN represents the burning speed inside the central cell, and the rest are the speeds of spreading to the eight surrounding cells; the factor K of the forest fire spreading speed w and K s The following processing needs to be done according to the CA model;

[0031] In the cellular space, a central cell has eight neighboring cells in eight directions. The K w Derivation formula:

[0032] K w =e 0.1783v·cos(β-θ)

[0033] Where v represents wind speed; θ represents wind direction, which can be any number between 0° and 360°; β represents the direction of the neighborhood cell, which can be 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°.

[0034] In the cellular space, the slope adjustment factor K s It is used to express the influence of the slope between the central cell and the adjacent cells on the speed of forest fire spread. In the forest fire spread model, each cell has a certain elevation value and side length, and the slope angle can be calculated using the elevation difference and horizontal distance between the cell centers. Combined with the Wang-Mao modified model, the K suitable for the CA model of the present invention is given. s Derivation formula:

[0035]

[0036] In the formula, H i,j and Hk,l They represent the height of the center of the burning cell (i, j) and the adjacent cell (k, l), respectively, and assume that the terrain inside the cell is flat, and are equal to the height of the center of the cell. L represents the side length of the cell, the horizontal distance between two directly adjacent cells is L, and the horizontal distance between adjacent cells in the diagonal direction is α is used to mark uphill and downhill. When , α = -1, indicating that the current slope is flat or downhill, which has an inhibitory effect on the spread of forest fire; when When α=1, it means the current situation is uphill, which promotes the spread of forest fire.

[0037] The K in the above cellular space w and K s Combined with the above, we can obtain the eight-direction forest fire spread velocity equation of the burning cell extending to the neighborhood and the internal burning velocity equation:

[0038]

[0039] In the formula, v represents wind speed; θ represents wind direction; β max Take R NW , R N , R NE , R W , R E , R SW , R S and R SE The β value corresponding to the maximum spreading rate.

[0040] S105: The improved forest fire spread velocity equation obtained by combining the Kataburn slope correction factor is as follows:

[0041]

[0042] In the formula, R a represents the uphill spreading speed, is the uphill angle, R k represents the downhill spreading speed, α represents the downhill speed, and is calculated using the uphill spreading speed with the same angle.

[0043] When the slope angles of the uphill and downhill slopes are equal, the calculation formula of the slope correction factor is as follows:

[0044]

[0045] In the formula, is the downhill spreading rate, φ a is the uphill spreading rate, is the upslope angle, and α is the downslope angle (α<0°). In this formula, the distance along the slope is taken as the fire spread distance, which is in line with the actual situation.

[0046] Preferably, the CA model construction step in S2 includes:

[0047] S201: Constructing the cellular Moore neighborhood:

[0048] In the Moore neighborhood, the neighboring cells of a cell include the 4 direct neighboring cells on the top, bottom, left, and right, and the secondary neighboring cells on the 4 diagonal directions of the top left, top right, bottom left, and bottom right. The coordinates of the center cell are represented as (i, j), the coordinates of the cells directly adjacent to the center cell are represented as (i-1, j), (i, j-1), (i, j+1), (i+1, j), and the coordinates of the cells on the diagonal direction of the center cell are represented as (i-1, j-1), (i-1, j+1), (i+1, j-1), (i+1, j+1)

[0049] S202: Cell state definition:

[0050]

[0051] In the formula, represents the state of cell (i, j) at time t, Δt is the time interval, and f represents the state transition rule of the cell. For the forest fire spread reverse simulation model, the state of the cell at the current moment is determined by its own state at the previous moment and the states of the eight surrounding cells.

[0052] When designing the cellular combustion state, it is necessary to consider the combustion state of the cell in reverse time, that is, from the fire gradually extinguishing to the burning state, and then to the state before combustion. The cellular state used in the model of the present invention is defined as follows:

[0053] (1)

[0054] This state indicates that the cell (i, j) is in a state of gradually extinguishing at time t, with a spreading speed of zero and no ability to spread outward.

[0055] (2)

[0056] This state indicates that the cell (i, j) is in a state of complete combustion at time t, the spreading speed is not zero, and it has the ability to spread to the surroundings.

[0057] (3)

[0058] This state indicates that the cell (i, j) is in the initial combustion state at time t, the spreading speed is zero, and it has no ability to spread outward.

[0059] (4)

[0060] This state indicates that the cell (i, j) is in an unburned state at time t. Whether the cell can burn depends on whether the type of combustible material to which the cell belongs is combustible and whether the surrounding cells have the ability to spread outward.

[0061] S203: The cell state transition rule definition includes the following steps:

[0062] S2031:S T 3→S T 2

[0063] The state of cell (i, j) at time t is S T 3, is in a state of gradual extinguishing. In the reverse simulation process, the cell (i, j) changes from S T 3 to S T 2. Need to go through Where L is the cell side length, R max is the maximum fire spread rate. That is, from time t to time t-Δt, Convert to S T 2. From the gradual extinguishing state to the complete combustion state.

[0064] S2032:S T 2→S T 1

[0065] The state of cell (i, j) at time t is S T 2, in the complete combustion stage. In the reverse simulation process, the cell (i, j) changes from S T 2 to S T 1. If the time interval Δt is still used, the time for the cell to gradually change from the initial combustion to the complete combustion state is too short. Since the local cell has a large side length and area, the internal combustion time should be longer. Considering the spread rate inside the cell, assuming that the combustion starts inside the cell with its center as the center of the circle, the time it takes for the burning area to be equal to the cell area is the cell from S T 2 to S T 1 time consumed. If the cell side length is L and the area is L 2 , we can get L 2 =πr 2 , where r is the combustion distance inside the cell. From this we can get r = R IN ·Δt1, then the cell (i,j) from S T 2 to S T The time interval of 1 is That is, from time t back to time t-Δt, Convert to S T 1. Return from complete combustion to initial combustion state.

[0066] S2033:S T 1→S T 0

[0067] The state of cell (i, j) at time t is S T 1, in the initial combustion stage. In the reverse simulation process, the cell (i, j) changes from S T 1 to S T 0, it is necessary to consider the surrounding S T The cumulative effect of the heat generated by the neighboring cells of 2 on the cell (i, j) is expressed as Indicates that the initial value is 1, and the specific calculation is as follows:

[0068]

[0069] In the formula, when the cell (i, j) is S T 2 to S T 1 o'clock, order

[0070] Every time you pass The cumulative influence of the surrounding cells is updated at the same time. Here, the influence of the cells directly adjacent to cell (i, j) and the cells on the diagonal on cell (i, j) is related to the distance between the cells. The distance between the directly adjacent cells (i-1, j), (i, j-1), (i, j+1), (i+1, j) is L, and the distance between the diagonal cells (i-1, j-1), (i-1, j+1), (i+1, j-1), (i+1, j+1) is

[0071] When satisfied When , the state of cell (i,j) changes, that is, Convert to S T 0, returning from the initial combustion stage to the unburned state.

[0072] S204: The specific steps of implementing the reverse simulation of forest fire spread based on the CA model include:

[0073] S2041: The start time of the simulation is recorded as T start , the end time is T end , the current time of the model operation is recorded as t, T start The fire boundary at time is recorded as P, and T is initialized start The forest fire cell space within the range of P at any time is denoted as A, where T start >T end ;

[0074] S2042: Initialize the state of the cell on the fire boundary P to S T 0, and then change the state to S T The state of the neighboring cells of the cell with value 0 is initialized to S T 2. The state values ​​of the remaining cells in the forest fire cell space A are initialized to S T 3;

[0075] S2043: The status in A is S T After a time interval of Δt1, the internal state of the cell (i, j) of 2 changes, as shown in S T 2 to S T 1. At the same time,

[0076] S2044: The status in A is S T 1 cell (i, j) is affected by the surrounding state S T 2, update the cell (i, j) according to the formula in step S4033. When , the state of cell (i, j) is changed from S T 1 to S T 0;

[0077] S2045: Since the ignition state is S during the forward spread of the forest fire T The cell (i, j) with a value of 0 requires the fully burned cell to provide heat transfer, so when When , the state adjacent to cell (i, j) in A is S T The cell state of 3 is updated to S T 2, where 0<ξ<1;

[0078] S2046: Repeat steps S2043 and S2045 until t≤T is satisfied end .

[0079] Preferably, the ignition point estimation step in S3 includes:

[0080] S301: Establish fire spread model:

[0081] A fire spread model is established based on the Wang-Mao modified forest fire spread speed, and the cell position is marked with one-dimensional coordinates. The fire spread rate from the central cell to the surrounding cells is calculated according to the eight directions of the Moore neighborhood. The spread rate from the central cell to the neighboring cells is shown in the figure above. The eight-directional spread rates calculated by the fire spread model and the distance between the nodes are used to construct the inverse travel time network of forest fires.

[0082] S302: Construct a reverse fire spread network. The fire travel time calculation formula of the node is as follows:

[0083]

[0084] Where, t ij represents the travel time from the center of cell i to the center of cell j; d ik represents the distance from the center of cell i to the boundary of cell i in direction k; R ik represents the spreading rate of cell i in the k direction; d jl represents the distance from the center of cell j to the boundary of cell j in direction l; R jl represents the spreading rate of cell j in the direction of l, where k and l are the directions of the Moore neighborhood.

[0085] Since the purpose is to estimate the location of the fire point from the known fire boundary, it is necessary to exchange the fire travel time between nodes to obtain the fire spread network with respect to the inverse travel time.

[0086] S303: Select n points from the fire boundary, perform inverse travel time simulation on each boundary point, calculate the MTT from the point to other cells within the fire range, and use the n groups of MTT to calculate the MTT standard deviation of all cells within the fire range. The specific steps include:

[0087] S3031: Let the final fire boundary be P, initialize the area within P as the forest fire cell space A, and let the total number of cells in A be m.

[0088] S3032: Calculate the fire spread speed in the cell neighborhood and construct the inverse travel time network graph G[m][8], assuming that in the initial state each cell is only connected to the eight surrounding neighboring cells.

[0089] S3033: Select n points on P, and for each point i, use the Dijkstra heap optimization algorithm to perform MTT simulation, and perform n times for n boundary points. The specific steps include:

[0090] S30331: Let the boundary point i be the starting point start, define mtt[m] as the shortest distance from the starting point start to all nodes, initialize mtt[start] = 0, and the distance to other nodes is infinite INF. Use visit[m] to mark whether the node has been visited, and initialize all values ​​to False;

[0091] S30332: define a pq heap to store the travel time and node coordinates of visited nodes, sort the data in pq according to the travel time from small to large, and update [mtt[start], start] to pq;

[0092] S30333: Select the node u with the smallest corresponding travel time from the unvisited nodes of pq, and set visit[u] = True;

[0093] S30334: Update the value of mtt[m] for all points v directly adjacent to u, that is, mtt[v]=min{dis[v], mtt[u]+G[u][v]}. If mtt[u]+G[u][v]<mtt[v] and visit[v]=False are satisfied, update [mtt[v], v] to pq.

[0094] S30335: Loop through steps S60333 and S60334 until pq is empty, and return the result mtt[m].

[0095] S3034: Calculate the MTT mean value formula as follows

[0096]

[0097] In the formula, mean[j] represents the MTT mean value of cell j.

[0098] S3035: Calculate the MTT standard deviation formula as follows:

[0099]

[0100] In the formula, std[j] represents the MTT standard deviation of cell j.

[0101] The present invention provides a spatio-temporal reverse deduction method for forest fire spread based on cellular automata, which has the following beneficial effects:

[0102] 1. Through the spatio-temporal reverse deduction method for forest fire spread based on cellular automata, the present invention can more accurately simulate the fire spread process, thereby achieving accurate prediction of the fire starting position and spread path, which helps relevant departments take effective prevention and control measures before or in the initial stage of the fire, reducing the losses caused by the fire.

[0103] 2. The present invention incorporates the layout of power grid projects into the deduction scope, can analyze the potential threats of fires to power grid facilities, and optimize the layout and fire prevention measures of power grid facilities accordingly, which helps reduce the risk of fires to power grid safety and ensure the stable operation of the power grid in extreme situations such as fires.

[0104] 3. The present invention fully considers the complex terrain and climate conditions in the southwestern region. By adjusting the parameters and rules of the cellular automata model, it makes it closer to the actual situation, making the deduction results more accurate and reliable, which helps formulate targeted fire prevention and control strategies.

[0105] 4. The present invention combines multiple data such as satellite remote sensing and meteorological monitoring to verify and optimize the deduction results, which not only improves the accuracy of the model, but also provides rich data support for subsequent research. At the same time, through comparative analysis with actual fire cases, the deduction method can be continuously optimized to enhance its application effect in practice.

[0106] 5. The present invention is not only applicable to the field of forest fire prevention and control, but can also be expanded to other fields such as urban planning and environmental protection. Through continuous exploration and practice, it can promote the development and progress of space-time deduction technology and provide more technical support and innovative ideas for related fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0107] Figure 1 It is a flow chart of the deduction method of the present invention. DETAILED DESCRIPTION

[0108] The following will be combined with the drawings in the specification of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0109] Example:

[0110] Please refer to the attached Figure 1 The embodiment of the present invention provides a method for temporal and spatial reverse deduction of forest fire spread based on cellular automata, comprising the following steps:

[0111] S1: Combining the Wang-Mao modified forest fire spread speed and the Kataburn slope correction factor, the eight-direction forest fire spread speed equation based on CA is constructed. In the cellular automaton model, the forest area is discretized into grids, and each grid represents a cell. According to the terrain characteristics of the southwest region (such as the Sichuan Basin, Hengduan Mountains, Yunnan-Guizhou Plateau, etc.), different cell states (such as trees, fires, open spaces, etc.) are set, and the influence of terrain on fire spread (such as slope, wind direction, etc.) is considered. S1 further includes:

[0112] S101: First, the formula for forest fire spread rate of the Wang-Mao modified model is given:

[0113] R=R0·K w ·K s ·K f

[0114] R0=a·T+b·V+c·(100-RH)-d

[0115] In the formula, R represents the speed of forest fire spread; K wis the wind speed adjustment factor, K s is the slope adjustment factor; K f is the combustible adjustment factor; R0 represents the initial spreading speed; a, b, c, d are the correction coefficients of R0, T is the temperature, V is the wind force level, and RH is the relative humidity.

[0116] K w and K s Programming, that is, K w =e 0.1783v·cosθ ; The following formula is obtained:

[0117]

[0118] In the formula, v represents wind speed, θ represents the angle between wind direction and burning direction; g represents slope coefficient, which is 1 for upslope and -1 for downslope; is the slope angle.

[0119] S102: Based on the Wang-Mao modified model, the formula for forest fire spread speed in different terrains and wind directions is obtained:

[0120]

[0121] R 左平坡 =R0·K f ·e 0.1783v·cos(θ+90°)

[0122] R 右平坡 =R0·K f ·e 0.1783v·cos(θ-90°)

[0123]

[0124] In the formula, R 上坡 , R 下坡 , R 左平坡 , R 右平坡 , R 风方向 Indicates the forest fire spread speed in five directions obtained by combining different wind directions and terrains;

[0125] S103: Incorporate the forest fire spread speed formula into the CA model:

[0126] For the 8-neighborhood CA model, the spreading speed of the central cell in the 8 neighborhood directions needs to be solved separately, as shown in the figure above. According to the 8-neighborhood model, the wind speed adjustment factor and slope adjustment factor can be updated to the following calculation formula:

[0127] K w =e 0.1783v·cos(nd-wd)

[0128]

[0129] Where nd represents the direction of the neighborhood cell, wd represents the wind direction; H cen represents the height of the central cell, H nei represents the height of the neighborhood cell, and d represents the center distance between two cells.

[0130] S104: Construct the forest fire spread speed formula of the CA model combustion cell:

[0131]

[0132] In the formula, R IN represents the burning speed inside the central cell, and the rest are the speeds of spreading to the eight surrounding cells; the factor K of the forest fire spreading speed w and K s The following processing needs to be done according to the CA model;

[0133] In the cellular space, a central cell has eight neighboring cells in eight directions. The K w Derivation formula:

[0134] K w =e 0.1783v·cos(β-θ)

[0135] Where v represents wind speed; θ represents wind direction, which can be any number between 0° and 360°; β represents the direction of the neighborhood cell, which can be 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°.

[0136] In the cellular space, the slope adjustment factor K s It is used to express the influence of the slope between the central cell and the adjacent cells on the speed of forest fire spread. In the forest fire spread model, each cell has a certain elevation value and side length, and the slope angle can be calculated using the elevation difference and horizontal distance between the cell centers. Combined with the Wang-Mao modified model, the K suitable for the CA model of the present invention is given. s Derivation formula:

[0137]

[0138] In the formula, H i,j and H k,l They represent the height of the center of the burning cell (i, j) and the adjacent cell (k, l), respectively, and assume that the terrain inside the cell is flat, and are equal to the height of the center of the cell. L represents the side length of the cell, the horizontal distance between two directly adjacent cells is L, and the horizontal distance between adjacent cells in the diagonal direction is α is used to mark uphill and downhill. When , α = -1, indicating that the current slope is flat or downhill, which has an inhibitory effect on the spread of forest fire; when When α=1, it means the current situation is uphill, which promotes the spread of forest fire.

[0139] The K in the above cellular space w and K s Combined with the above, we can obtain the eight-direction forest fire spread velocity equation of the burning cell extending to the neighborhood and the internal burning velocity equation:

[0140]

[0141] In the formula, v represents wind speed; θ represents wind direction; β max Take R NW , R N , R NE , R W , R E , R SW , R S and R SE The β value corresponding to the maximum spreading rate.

[0142] S105: The improved forest fire spread velocity equation obtained by combining the Kataburn slope correction factor is as follows:

[0143]

[0144] In the formula, R a represents the uphill spreading speed, is the uphill angle, R k represents the downhill spreading speed, α represents the downhill speed, and is calculated using the uphill spreading speed with the same angle.

[0145] When the slope angles of the uphill and downhill slopes are equal, the calculation formula of the slope correction factor is as follows:

[0146]

[0147] In the formula, is the downhill spreading rate, φ a is the uphill spreading rate, is the upslope angle, and α is the downslope angle (α<0°). In this formula, the distance along the slope is taken as the fire spread distance, which is in line with the actual situation.

[0148] Specifically, by combining the Wang-Mao modified forest fire spread speed and the Kataburn slope correction factor, this method effectively constructs an eight-direction forest fire spread speed equation based on cellular automata, which not only improves the accuracy of forest fire spread simulation, but also enhances the model's ability to be applied under complex terrain conditions. By carefully considering the effects of different slopes and wind directions, the model can more realistically reflect the diffusion characteristics of forest fires in different geographical environments. This precise velocity equation provides a solid theoretical foundation for subsequent time-space reverse deduction, making fire retrospective analysis more scientific and reliable, and providing strong support for fire management and emergency response decisions.

[0149] S2: Define the cell shape, neighborhood, burning state and local state transition rules, complete the design of the CA-based forest fire spread spatiotemporal reverse deduction model, and realize the spatiotemporal retrospective simulation of forest fires extending inward from the fire boundary. The CA model steps constructed in S2 include:

[0150] S201: Constructing the cellular Moore neighborhood:

[0151] In the Moore neighborhood, the neighboring cells of a cell include the 4 direct neighboring cells on the top, bottom, left, and right, and the secondary neighboring cells on the 4 diagonal directions of the top left, top right, bottom left, and bottom right. The coordinates of the center cell are represented as (i, j), the coordinates of the cells directly adjacent to the center cell are represented as (i-1, j), (i, j-1), (i, j+1), (i+1, j), and the coordinates of the cells on the diagonal direction of the center cell are represented as (i-1, j-1), (i-1, j+1), (i+1, j-1), (i+1, j+1)

[0152] S202: Cell state definition:

[0153]

[0154] In the formula, represents the state of cell (i, j) at time t, Δt is the time interval, and f represents the state transition rule of the cell. For the forest fire spread reverse simulation model, the state of the cell at the current moment is determined by its own state at the previous moment and the states of the eight surrounding cells.

[0155] When designing the cellular combustion state, it is necessary to consider the combustion state of the cell in reverse time, that is, from the fire gradually extinguishing to the burning state, and then to the state before combustion. The cellular state used in the model of the present invention is defined as follows:

[0156] (1)

[0157] This state indicates that the cell (i, j) is in a state of gradually extinguishing at time t, with a spreading speed of zero and no ability to spread outward.

[0158] (2)

[0159] This state indicates that the cell (i, j) is in a state of complete combustion at time t, the spreading speed is not zero, and it has the ability to spread to the surroundings.

[0160] (3)

[0161] This state indicates that the cell (i, j) is in the initial combustion state at time t, the spreading speed is zero, and it has no ability to spread outward.

[0162] (4)

[0163] This state indicates that the cell (i, j) is in an unburned state at time t. Whether the cell can burn depends on whether the type of combustible material to which the cell belongs is combustible and whether the surrounding cells have the ability to spread outward.

[0164] S203: The cell state transition rule definition includes the following steps:

[0165] S2031:S T 3→S T 2

[0166] The state of cell (i, j) at time t is S T 3, is in a state of gradual extinguishing. In the reverse simulation process, the cell (i, j) changes from S T 3 to S T 2. Need to go through Where L is the cell side length, R max is the maximum fire spread rate. That is, from time t to time t-Δt, Convert to S T 2. From the gradual extinguishing state to the complete combustion state.

[0167] S2032:S T 2→S T 1

[0168] The state of cell (i, j) at time t is S T 2, in the complete combustion stage. In the reverse simulation process, the cell (i, j) changes from S T 2 to S T1. If the time interval Δt is still used, the time for the cell to gradually change from the initial combustion to the complete combustion state is too short. Since the local cell has a large side length and area, the internal combustion time should be longer. Considering the spread rate inside the cell, assuming that the combustion starts inside the cell with its center as the center of the circle, the time it takes for the burning area to be equal to the cell area is the cell from S T 2 to S T 1 time consumed. If the cell side length is L and the area is L 2 , we can get L 2 =πr 2 , where r is the combustion distance inside the cell. From this we can get r = R IN ·Δt1, then the cell (i,j) from S T 2 to S T The time interval of 1 is That is, from time t back to time t-Δt, Convert to S T 1. Return from complete combustion to initial combustion state.

[0169] S2033:S T 1→S T 0

[0170] The state of cell (i, j) at time t is S T 1, in the initial combustion stage. In the reverse simulation process, the cell (i, j) changes from S T 1 to S T 0, it is necessary to consider the surrounding S T The cumulative effect of the heat generated by the neighboring cells of 2 on the cell (i, j) is expressed as Indicates that the initial value is 1, and the specific calculation is as follows:

[0171]

[0172] In the formula, when the cell (i, j) is S T 2 to S T 1 o'clock, order

[0173] Every time you pass The cumulative influence of the surrounding cells is updated at the same time. Here, the influence of the cells directly adjacent to cell (i, j) and the cells on the diagonal on cell (i, j) is related to the distance between the cells. The distance between the directly adjacent cells (i-1, j), (i, j-1), (i, j+1), (i+1, j) is L, and the distance between the diagonal cells (i-1, j-1), (i-1, j+1), (i+1, j-1), (i+1, j+1) is

[0174] When satisfied When , the state of cell (i,j) changes, that is, Convert to S T 0, returning from the initial combustion stage to the unburned state.

[0175] S204: The specific steps of implementing the reverse simulation of forest fire spread based on the CA model include:

[0176] S2041: The start time of the simulation is recorded as T start , the end time is T end , the current time of the model operation is recorded as t, T start The fire boundary at time is recorded as P, and T is initialized start The forest fire cell space within the range of P at any time is denoted as A, where T start >T end ;

[0177] S2042: Initialize the state of the cell on the fire boundary P to S T 0, and then change the state to S T The state of the neighboring cells of the cell with value 0 is initialized to S T 2. The state values ​​of the remaining cells in the forest fire cell space A are initialized to S T 3;

[0178] S2043: The status in A is S T After a time interval of Δt1, the internal state of the cell (i, j) of 2 changes, as shown in S T 2 to S T 1. At the same time,

[0179] S2044: The status in A is S T 1 cell (i, j) is affected by the surrounding state S T 2, update the cell (i, j) according to the formula in step S4033. When , the state of cell (i, j) is changed from S T 1 to S T 0;

[0180] S2045: Since the ignition state is S during the forward spread of the forest fire T The cell (i, j) with a value of 0 requires the fully burned cell to provide heat transfer, so when When , the state adjacent to cell (i, j) in A is S T The cell state of 3 is updated to S T 2, where 0<ξ<1;

[0181] S2046: Repeat steps S2043 and S2045 until t≤T is satisfied end ;

[0182] Specifically, by defining the cell shape, neighborhood, burning state and local state transition rules, the design of the spatiotemporal reverse deduction model of forest fire spread based on CA was completed. This design enables the model to realize the spatiotemporal retrospective simulation of forest fires starting from the fire boundary and expanding inward, greatly improving the efficiency of forest fire behavior analysis and fire investigation. The model can reproduce the historical process of fire spread in detail, helping researchers and firefighters understand the development dynamics of fires, so as to formulate more effective fire prevention and control strategies. In addition, this reverse deduction technology can also be used for training and education to enhance the relevant personnel's understanding and response capabilities of forest fire behavior.

[0183] S3: Using the forest fire model and Dijkstra optimization algorithm, the inverse travel time fire spread network is constructed to realize the fire point estimation method based on MTT. The algorithm simulates the inverse process of fire spread, that is, reversely deduce the starting position and spread path of the fire from the end state of the fire. By continuously adjusting the cell state and spread rules, the deduction results are consistent with the actual fire situation. The fire point estimation steps in S3 include:

[0184] S301: Establish fire spread model:

[0185] A fire spread model is established based on the Wang-Mao modified forest fire spread speed, and the cell position is marked with one-dimensional coordinates. The fire spread rate from the central cell to the surrounding cells is calculated according to the eight directions of the Moore neighborhood. The spread rate from the central cell to the neighboring cells is shown in the figure above. The eight-directional spread rates calculated by the fire spread model and the distance between the nodes are used to construct the inverse travel time network of forest fires.

[0186] S302: Construct a reverse fire spread network. The fire travel time calculation formula of the node is as follows:

[0187]

[0188] In the formula, t ij represents the travel time from the center of cell i to the center of cell j; d ik represents the distance from the center of cell i to the boundary of cell i in direction k; R ik represents the spreading rate of cell i in the k direction; d jl represents the distance from the center of cell j to the boundary of cell j in direction l; R jl represents the spreading rate of cell j in the direction of l, where k and l are the directions of the Moore neighborhood.

[0189] Since the goal is to implement the function of estimating the ignition point location from the known fire boundary, it is necessary to exchange the fire travel time between nodes to obtain a fire spread network regarding the inverse travel time.

[0190] S303: Select n points from the fire boundary, perform inverse travel time simulation for each boundary point respectively, calculate the MTT from this point to other cells within the fire range, and calculate the standard deviation of MTT for all cells within the fire range using these n groups of MTT. The specific steps are as follows:

[0191] S3031: Denote the final fire boundary as P, initialize the area within P as the forest fire cell space A, and denote the total number of cells in A as m.

[0192] S3032: Calculate the fire spread speed of the cell neighborhood, construct an inverse travel time network graph G[m][8], assuming that each cell is only connected to its eight surrounding neighbor cells in the initial state.

[0193] S3033: Select n points on P. For each point i, perform MTT simulation using the Dijkstra heap optimization algorithm. This is executed n times for the n boundary points. The specific steps are as follows:

[0194] S30331: Denote the boundary point i as the starting point start, define mtt[m] as the shortest distance from the starting point start to all nodes, initialize mtt[start] = 0, and the distance to other nodes as infinity INF. Use visit[m] to mark whether a node has been visited, and initialize all values to False;

[0195] S30332: Define a pq heap to store the travel time and node coordinates of the visited nodes. The data in pq is sorted in ascending order according to the travel time, and update [mtt[start], start] to pq;

[0196] S30333: Select the node u with the minimum corresponding travel time from the unvisited nodes in pq, and set visit[u] = True;

[0197] S30334: Update the values of all points v directly adjacent to u in mtt[m], that is, mtt[v] = min{dis[v], mtt[u] + G[u][v]}. If mtt[u] + G[u][v] < mtt[v] and visit[v] = False are satisfied, update [mtt[v], v] to pq;

[0198] S30335: Loop through steps S60333 and S60334 until pq is empty, and return the result mtt[m]

[0199] The formula for calculating the MTT mean is as follows

[0200]

[0201] Where mean[j] represents the mean MTT of cell j.

[0202] S3035: The formula for calculating the MTT standard deviation is as follows:

[0203]

[0204] Where std[j] represents the MTT standard deviation of cell j.

[0205] Specifically, using the forest fire model and Dijkstra optimization algorithm, we completed the construction of the inverse travel time fire spread network and realized the fire point estimation method based on MTT (minimum travel time), which significantly improved the accuracy and efficiency of fire point positioning, provided key information for quickly and accurately extinguishing forest fires, and reduced the calculation time by optimizing the algorithm, ensuring that potential fire points can be quickly estimated in emergency situations, thereby guiding the rational allocation and dispatch of firefighting resources. In addition, accurate fire point estimation is also helpful for the determination of legal liability after the fire and the investigation of the cause of the fire, which is of great significance for preventing future fires.

[0206] In view of the technical problem to be solved by the present invention, namely, the inability of the traditional forest fire spread model to reversely simulate the fire spread process from the final boundary of the fire and the inaccurate judgment of the fire location, the following are some alternative solutions:

[0207] Alternative 1: Reverse analysis based on physical models

[0208] This approach attempts to reversely calculate the spread of a fire from its final boundary through complex physical models and reverse analysis methods. This approach is theoretically feasible, but it requires the establishment of a highly accurate physical model, and the reverse calculation process can be very complex, requiring high computing resources and time. In addition, the accuracy and reliability of the physical model will directly affect the results of the reverse analysis.

[0209] Alternative 2: Predictive models based on big data and machine learning

[0210] This approach uses a large amount of historical fire data and machine learning algorithms to train a model that can predict the spread and location of fires. By inputting the final boundaries of the fire and related meteorological, topographical and other data, the model can output the possible location of the fire. This method relies on the accumulation of big data and the optimization of machine learning algorithms, and has certain advantages in dealing with complex and changing fire situations. However, data acquisition and preprocessing can be a challenge, and the generalization ability of the model also needs to be continuously verified and improved in practical applications.

[0211] Alternative 3: Decision support based on expert systems

[0212] Expert systems use the knowledge and experience of domain experts to assist in determining the location and spread of fires through methods such as rule reasoning and decision trees. This method can respond quickly and provide certain decision support, but it relies on the knowledge and experience of experts and may have certain subjectivity and limitations. In addition, for complex and changeable fire situations, expert systems may not be able to provide accurate and comprehensive judgments.

[0213] Alternative 4: A comprehensive solution combining multiple technologies

[0214] This approach attempts to combine the advantages of the above-mentioned technologies to form a comprehensive solution. For example, physical models can be used for basic fire spread simulation, combined with big data and machine learning algorithms to predict and optimize the fire location, while expert systems are used for decision support and result verification. This approach can fully utilize the advantages of various technologies to improve the accuracy and reliability of fire spread simulation and fire location judgment. However, this may also increase the complexity of the solution and the difficulty of implementation.

[0215] In summary, although these alternatives can solve the technical problems to be solved by the present invention to a certain extent, they all have their own limitations and challenges. In contrast, the CA-based forest fire reverse simulation algorithm proposed in the present invention has higher accuracy, reliability and flexibility, and can better meet the needs of forest fire prevention and rescue and fire source tracing.

[0216] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for temporal and spatial reverse deduction of forest fire spread based on cellular automata, characterized in that: The following steps are involved: S1: Combine the Wang-Mao modified forest fire spread speed and the Kataburn slope correction factor to complete the construction of the eight-direction forest fire spread speed equation based on CA; S2: Define the cell shape, neighborhood, burning state and local state transition rules, complete the design of the CA-based forest fire spread spatiotemporal reverse deduction model, and realize the spatiotemporal retrospective simulation of forest fires extending inward from the fire boundary; S3: Using the forest fire model and Dijkstra optimization algorithm, the inverse travel time fire spread network is constructed, thereby realizing the fire point estimation method based on MTT.

2. The method for reversely deducing the spatiotemporal spread of forest fires based on cellular automata according to claim 1, characterized in that: Said S1 further comprises: S101: First, the formula for forest fire spread rate of the Wang-Mao modified model is given: R=R0·K w ·K s ·K f R0=a·T+b·V+c·(100-RH)-d In the formula, R represents the speed of forest fire spread; K w is the wind speed adjustment factor, K s is the slope adjustment factor; K f is the combustible adjustment factor; R0 represents the initial spreading speed; a, b, c, d are the correction coefficients of R0, T is the temperature, V is the wind force level, and RH is the relative humidity. K w and K s Programming, that is, K w =e 0.1783v·cosθ ; The following formula is obtained: In the formula, v represents wind speed, θ represents the angle between wind direction and burning direction; g represents slope coefficient, which is 1 for upslope and -1 for downslope; is the slope angle. S102: Based on the Wang-Mao modified model, the formula for forest fire spread speed in different terrains and wind directions is obtained: R 左平坡 =R0·K f ·is 0.1783v·cos(θ+90°) R 右平坡 =R0·K f ·is 0.1783v·cos(θ-90°) In the formula, R 上坡 , R 下坡 , R 左平坡 , R 右平坡 , R 风方向 Indicates the forest fire spread speed in five directions obtained by combining different wind directions and terrains; S103: Incorporate the forest fire spread speed formula into the CA model: For the 8-neighborhood CA model, the spreading speed of the central cell in the 8 neighborhood directions needs to be solved separately, as shown in the figure above. According to the 8-neighborhood model, the wind speed adjustment factor and slope adjustment factor can be updated to the following calculation formula: K w =e 0.1783v·cos(nd-wd) Where nd represents the direction of the neighborhood cell, wd represents the wind direction; H cen represents the height of the central cell, H nei represents the height of the neighborhood cell, and d represents the center distance between two cells. S104: Construct the forest fire spread speed formula of the CA model combustion cell: In the formula, R IN represents the burning speed inside the central cell, and the rest are the speeds of spreading to the eight surrounding cells; the factor K of the forest fire spreading speed w and K s The following processing needs to be done according to the CA model; In the cellular space, a central cell has eight neighboring cells in eight directions. The K w Derivation formula: K w =e 0.1783v·cos(β-θ) Where v represents wind speed; θ represents wind direction, which can be any number between 0° and 360°; β represents the direction of the neighborhood cell, which can be 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°. In the cellular space, the slope adjustment factor K s It is used to express the influence of the slope between the central cell and the adjacent cells on the speed of forest fire spread. In the forest fire spread model, each cell has a certain elevation value and side length, and the slope angle can be calculated using the elevation difference and horizontal distance between the cell centers. Combined with the Wang-Mao modified model, the K suitable for the CA model of the present invention is given. s Derivation formula: In the formula, H i,j and H k,l They represent the height of the center of the burning cell (i, j) and the adjacent cell (k, l), respectively, and assume that the terrain inside the cell is flat, and are equal to the height of the center of the cell. L represents the side length of the cell, the horizontal distance between two directly adjacent cells is L, and the horizontal distance between adjacent cells in the diagonal direction is α is used to mark uphill and downhill. When , α = -1, indicating that the current slope is flat or downhill, which has an inhibitory effect on the spread of forest fire; when When α=1, it means the current situation is uphill, which promotes the spread of forest fire. The K in the above cellular space w and K s Combined with the above, we can obtain the eight-direction forest fire spread velocity equation of the burning cell extending to the neighborhood and the internal burning velocity equation: In the formula, v represents wind speed; θ represents wind direction; β max Take R NW , R N , R NE , R W , R E , R SW , R S and R SE The β value corresponding to the maximum spreading rate. S105: The improved forest fire spread velocity equation obtained by combining the Kataburn slope correction factor is as follows: In the formula, R a represents the uphill spreading speed, is the uphill angle, R k represents the downhill spreading speed, α represents the downhill speed, and is calculated using the uphill spreading speed with the same angle. When the slope angles of the uphill and downhill slopes are equal, the calculation formula of the slope correction factor is as follows: In the formula, is the downhill spreading rate, φ a is the uphill spreading rate, is the upslope angle, and α is the downslope angle (α<0°). In this formula, the distance along the slope is taken as the fire spread distance, which is in line with the actual situation.

3. The method for reversely deducing the spatiotemporal spread of forest fires based on cellular automata according to claim 1, characterized in that: The CA model steps constructed in S2 include: S201: Constructing the cellular Moore neighborhood: In the Moore neighborhood, the neighboring cells of a cell include the 4 direct neighboring cells on the top, bottom, left, and right, and the secondary neighboring cells on the 4 diagonal directions of the top left, top right, bottom left, and bottom right. The coordinates of the center cell are represented as (i, j), the coordinates of the cells directly adjacent to the center cell are represented as (i-1, j), (i, j-1), (i, j+1), (i+1, j), and the coordinates of the cells on the diagonal direction of the center cell are represented as (i-1, j-1), (i-1, j+1), (i+1, j-1), (i+1, j+1) S202: Cell state definition: In the formula, represents the state of cell (i, j) at time t, Δt is the time interval, and f represents the state transition rule of the cell. For the forest fire spread reverse simulation model, the state of the cell at the current moment is determined by its own state at the previous moment and the states of the eight surrounding cells. When designing the cellular combustion state, it is necessary to consider the combustion state of the cell in reverse time, that is, from the fire gradually extinguishing to the burning state, and then to the state before combustion. The cellular state used in the model of the present invention is defined as follows: (1) This state indicates that the cell (i, j) is in a state of gradually extinguishing at time t, with a spreading speed of zero and no ability to spread outward. (2) This state indicates that the cell (i, j) is in a state of complete combustion at time t, the spreading speed is not zero, and it has the ability to spread to the surroundings. (3) This state indicates that the cell (i, j) is in the initial combustion state at time t, the spreading speed is zero, and it has no ability to spread outward. (4) This state indicates that the cell (i, j) is in an unburned state at time t. Whether the cell can burn depends on whether the type of combustible material to which the cell belongs is combustible and whether the surrounding cells have the ability to spread outward. S203: The cell state transition rule definition includes the following steps: S2031:S T 3→S T 2 The state of cell (i, j) at time t is S T 3, is in a state of gradual extinguishing. In the reverse simulation process, the cell (i, j) changes from S T 3 to S T 2. Need to go through Where L is the cell side length, R max is the maximum fire spread rate. That is, from time t to time t-Δt, Convert to S T 2. From the gradual extinguishing state to the complete combustion state. S2032:S T 2→S T 1 The state of cell (i, j) at time t is S T 2, in the complete combustion stage. In the reverse simulation process, the cell (i, j) changes from S T 2 to S T 1. If the time interval Δt is still used, the time for the cell to gradually change from the initial combustion to the complete combustion state is too short. Since the local cell has a large side length and area, the internal combustion time should be longer. Considering the spread rate inside the cell, assuming that the combustion starts inside the cell with its center as the center of the circle, the time it takes for the burning area to be equal to the cell area is the cell from S T 2 to S T 1 time spent. If the cell side length is L and the area is L 2 , we can get L 2 =πr 2 , where r is the combustion distance inside the cell. From this we can get r = R IN ·Δt1, then the cell (i,j) from S T 2 to S T The time interval of 1 is That is, from time t back to time t-Δt, Convert to S T 1. Return from complete combustion to initial combustion state. <h2 style=";text-align:left;direction:ltr">S2033:S<h2 style=";text-align:left;direction:ltr"> T <h2 style=";text-align:left;direction:ltr"> 1→S<h2 style=";text-align:left;direction:ltr"> T <h2 style=";text-align:left;direction:ltr"> 0 The state of cell (i, j) at time t is S T 1, in the initial combustion stage. In the reverse simulation process, the cell (i, j) changes from S T 1 to S T 0, it is necessary to consider the surrounding S T The cumulative effect of the heat generated by the neighboring cells of 2 on the cell (i, j) is expressed as Indicates that the initial value is 1, and the specific calculation is as follows: In the formula, when the cell (i, j) is S T 2 to S T 1 o'clock, order Every time you pass The cumulative influence of the surrounding cells is updated at the same time. Here, the influence of the cells directly adjacent to cell (i, j) and the cells on the diagonal on cell (i, j) is related to the distance between the cells. The distance between the directly adjacent cells (i-1, j), (i, j-1), (i, j+1), (i+1, j) is L, and the distance between the diagonal cells (i-1, j-1), (i-1, j+1), (i+1, j-1), (i+1, j+1) is When satisfied When , the state of cell (i,j) changes, that is, Convert to S T 0, returning from the initial combustion stage to the unburned state. S204: The specific steps of implementing the reverse simulation of forest fire spread based on the CA model include: S2041: The start time of the simulation is recorded as T start , the end time is T end , the current time of the model operation is recorded as t, T start The fire boundary at time is recorded as P, and T is initialized start The forest fire cell space within the range of P at any time is denoted as A, where T start >T end ; S2042: Initialize the state of the cell on the fire boundary P to S T 0, and then change the state to S T The state of the neighboring cells of the cell with value 0 is initialized to S T 2. The state values ​​of the remaining cells in the forest fire cell space A are initialized to S T 3; S2043: The status in A is S T After a time interval of Δt1, the internal state of the cell (i, j) of 2 changes, as shown in S T 2 to S T 1. At the same time, S2044: The status in A is S T 1 cell (i, j) is affected by the surrounding state S T 2, update the cell (i, j) according to the formula in step S4033. When the state of cell (i,j) is changed from S T 1 to S T 0; S2045: Since the ignition state is S during the forward spread of the forest fire T The cell (i, j) with a value of 0 requires the fully burned cell to provide heat transfer, so when When , the state adjacent to cell (i, j) in A is S T The cell state of 3 is updated to S T 2, where 0<ξ<1; S2046: Repeat steps S2043 and S2045 until t≤T is satisfied end。 4. The method for reversely deducing the spatiotemporal spread of forest fires based on cellular automata according to claim 1, characterized in that: The ignition point estimation step in S3 includes: S301: Establish fire spread model: A fire spread model is established based on the Wang-Mao modified forest fire spread speed, and the cell position is marked with one-dimensional coordinates. The fire spread rate from the central cell to the surrounding cells is calculated according to the eight directions of the Moore neighborhood. The spread rate from the central cell to the neighboring cells is shown in the figure above. The eight-directional spread rates calculated by the fire spread model and the distance between the nodes are used to construct the inverse travel time network of forest fires. S302: Construct a reverse fire spread network. The fire travel time calculation formula of the node is as follows: Where, t ij represents the travel time from the center of cell i to the center of cell j; d ik represents the distance from the center of cell i to the boundary of cell i in direction k; R ik represents the spreading rate of cell i in the k direction; d jl represents the distance from the center of cell j to the boundary of cell j in direction l; R jl represents the spreading rate of cell j in the direction of l, where k and l are the directions of the Moore neighborhood. Since the purpose is to estimate the location of the fire point from the known fire boundary, it is necessary to exchange the fire travel time between nodes to obtain the fire spread network with respect to the inverse travel time. S303: Select n points from the fire boundary, perform inverse travel time simulation on each boundary point, calculate the MTT from the point to other cells within the fire range, and use the n groups of MTT to calculate the MTT standard deviation of all cells within the fire range. The specific steps include: S3031: Let the final fire boundary be P, initialize the area within P as the forest fire cell space A, and let the total number of cells in A be m. S3032: Calculate the fire spread speed in the cell neighborhood and construct the inverse travel time network graph G[m][8], assuming that in the initial state each cell is only connected to the eight surrounding neighboring cells. S3033: Select n points on P, and for each point i, use the Dijkstra heap optimization algorithm to perform MTT simulation, and perform n times for n boundary points. The specific steps include: S30331: Let the boundary point i be the starting point start, define mtt[m] as the shortest distance from the starting point start to all nodes, initialize mtt[start] = 0, and the distance to other nodes is infinite INF. Use visit[m] to mark whether the node has been visited, and initialize all values ​​to False; S30332: define a pq heap to store the travel time and node coordinates of visited nodes, sort the data in pq according to the travel time from small to large, and update [mtt[start], start] to pq; S30333: Select the node u with the smallest corresponding travel time from the unvisited nodes of pq, and set visit[u] = True; S30334: Update the value of mtt[m] for all points v that are directly adjacent to u, i.e., mtt[v] = min{dis[v], mtt[u] + G[u][v]}. If mtt[u] + G[u][v] < mtt[v] and visit[v] = False, update [mtt[v], v] to pq; S30335: Loop through steps S60333 and S60334 until pq is empty, and return the result mtt[m] S3034: Calculate the MTT mean formula as follows In the formula, mean[j] represents the MTT mean of cell j. S3035: Calculate the MTT standard deviation formula as follows: In the formula, std[j] represents the MTT standard deviation of cell j.

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