CN113033035B - Dynamic simulation method, system and device for pollutant diffusion area - Google Patents
Dynamic simulation method, system and device for pollutant diffusion area Download PDFInfo
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Abstract
The invention discloses a dynamic simulation method, a dynamic simulation system and a dynamic simulation device for a pollutant diffusion area, wherein the method comprises the steps of selecting a habitat to be estimated, acquiring satellite data of the habitat area, and constructing an initial sample area set based on the satellite data; an accessible set of contaminants over time is constructed based on historical contaminant information for the habitat. Because a functional relation can be established between the speed set at each point in the area and the position information of the point, the speed set at the representative point can predict the speed sets at all points in the area through convex combination by utilizing the obtained convex combination coefficient; and adding a time factor to estimate the range of the forest fire in the inhabited area which can dynamically spread along with the time. The present invention introduces differential inclusion to better predict the spread of a fire in different directions over time. Meanwhile, the invention introduces the idea of finite element, and solves the problem that the calculated amount of the speed set at all points in the region is too large in the actual prediction calculation work.
Description
Technical Field
The invention relates to the technical field of computational mathematics, in particular to a dynamic simulation method, a dynamic simulation system and a dynamic simulation device for a pollutant diffusion area.
Background
Natural disasters frequently occur on a global scale, and cause great damage to the living environment and the natural ecosystem of human beings, wherein annual forest fires are particularly destructive disasters for human beings and other organisms, large-scale fires such as forest fires are difficult to extinguish manually, and habitats for protecting human beings and animals are required to be effectively established and isolated in order to suppress the disasters. Therefore, how to construct the fire isolation zone at the minimum speed becomes a central part of the current research on the related work of controlling forest fires. In order to protect habitats of human beings and wild animals from natural disasters, a fire isolation belt needs to be constructed at the highest speed possible, and the construction of the isolation belt is premised on predicting the speed and direction of fire spread as accurately as possible.
Existing strategies for controlling fire spread show that many algorithms are run with habitats that meet the convex set properties and default fire spread rates that remain constant in all directions, but in reality many habitats are non-convex, and these masking strategies are not generally feasible.
Disclosure of Invention
In view of the above-mentioned drawbacks of the prior art, the present invention provides a method, a system and a device for dynamically simulating a pollutant diffusion area, so as to solve the deficiencies of the prior art.
In order to achieve the above object, the present invention provides a dynamic simulation method for a pollutant diffusion area, comprising:
step 1, selecting a habitat to be estimated, acquiring satellite data of the habitat area, and constructing an initial sample area set based on the satellite data;
step 2, constructing a reachable set of forest fires based on historical fire information of the habitat;
and 3, based on a finite element thought, selecting effective discrete representative points in the habitat area to triangulate the whole area, and dividing the area into a plurality of small triangular areas with convex set properties. The discrete representative points are the vertexes of the small triangle areas, and each small triangle area is a convex set, so the convex combination coefficient can be obtained by using the three vertexes of the small triangle area and the simultaneous convex combination formula of all the discrete points in the small triangle.
Step 4, predicting the speed set of all points in the small triangular area by using the speed sets at the three vertexes on the small triangular area by using the convex combination coefficient obtained in the step 3; the set of velocities at all points in the entire region can thus be predicted using a limited number of sets of velocities representing discrete points. Thus, a differential inclusion propagation discrete model is established. The differential comprises a model for estimating the speed of each position point in the whole inhabitation area in each direction;
and 5, adding a time factor, and estimating the dynamic spreading range of the reachable set of the forest fire in the inhabited area along with time.
Furthermore, the satellite data of the habitat area at least comprises habitat longitude and latitude data, earth surface temperature data, earth surface day and night temperature difference data, earth surface sulfide data, earth surface vegetation data and earth surface infrared remote sensing image data.
Further, step 2 constructs a reachable set of forest fires based on the historical fire information of the habitat, and specifically includes: the sulfur concentration of the habitat is high, the surface temperature is high, the day-night temperature difference is smaller than a certain threshold value, and finally the fire area of the habitat in a certain time period is calculated to be used as an accessible set.
Further, the step 3 triangulates the whole habitat area by using a limited number of discrete representative points, and then predicts the speed sets at all points of the whole habitat area by using the speed sets at the limited number of representative points. The method specifically comprises the following steps:
initializing a habitat area, and selecting n discrete points in the habitat area, wherein the point set is x = (x) 1 ,x 2 ,…,x n ) Here, a point x is defined k The set of velocities at is F (x) k ) K is more than or equal to 1 and less than or equal to n; then m discrete representative points x are selected i I is more than or equal to 1 and less than or equal to m, and m is less than or equal to n. Triangulation of the habitat area is performed.
Further, the step 4 predicts the speed set at each point in the whole inhabitation area by using the speed sets at the m discrete representative points, and establishes a differential inclusion spread discrete model. The differential includes the speed of each position point in the whole habitat area in each direction estimated in the model, and specifically includes: selecting the most effective m discrete representative points x in the inhabitation region i I is more than or equal to 1 and less than or equal to m, triangulating the whole area by using the m discrete representative points to obtain p small triangular areas d with the convex set property, and collecting the small triangular areas as
d＝(d 1 ,d 2 ,d 3 ,...,d p ),
Using the vertex on the small triangle area and the coordinate convex combination formula of all discrete points in the small triangle area, x i Is a point within the qth small triangular area, x q1 ,x q2 ,x q3 Three vertexes of the small triangular area are shown, and the specific formula is as follows:
calculating convex combination coefficient alpha 1 ，α 2 ，α 3 . Since the discrete points in the small triangle can be represented by convex combination of three vertices on the small triangle region, and so on, the velocity set at the discrete points in the small triangle can also be represented by convex combination prediction of the velocity set at the three vertices on the small triangle region. The formula is as follows:
further, the step 5 adds a time factor to estimate a range within which the forest fire in the habitat can reach dynamic spreading over time, and specifically comprises the following steps: and solving a speed set of each fire point on the initial reachable boundary of the forest fire, introducing a time factor, calculating the motion tracks of each fire point on the boundary of the initial forest fire in different directions, solving the motion tracks of all the fire points after the time t, and then solving a union set of the motion tracks to obtain a new reachable set, namely a new range in which the forest fire spreads after the time t.
The invention also provides a dynamic simulation system for a pollutant diffusion area, which comprises:
the area set acquisition module is used for selecting a habitat to be estimated, acquiring satellite data of the habitat area and constructing an initial sample area set based on the satellite data;
the reachable set acquisition module is used for constructing a reachable set of the forest fire based on the historical fire information of the habitat;
the region dividing module is used for selecting a limited number of discrete representative points to triangulate the whole habitat region based on a finite element thought, dividing the whole region into a plurality of small triangular regions, wherein each small triangular region is a convex set, and the discrete representative points are vertexes of the small triangular regions.
The fire speed forecasting module uses three vertexes on the small triangular area and all discrete points in the small triangular area to simultaneously obtain a convex combination coefficient by using a convex combination formula, and the speed set can be expressed as a function related to the discrete points. The above steps have already established a differential inclusion propagation discrete model.
And the fire spreading estimation module estimates the reachable set of the forest fire in the inhabited area to dynamically spread along with time by adding a time factor.
An apparatus comprising a memory, a processor and a computer program stored in the memory and executable on the processor, the processor implementing the steps of the method as described above when executing the computer program.
The invention has the beneficial effects that:
the invention introduces a mathematical model of differential inclusion to simulate a forest fire spread model, and the differential inclusion is introduced to better predict the spread range of the fire in different directions over time.
Meanwhile, the invention introduces the idea of finite element, divides the fire spreading area into a plurality of small triangle areas, and because the small triangle areas are convex sets, three vertexes on the small triangle areas and a point coordinate convex combination formula of all points in the small triangle areas can be combined to obtain convex combination coefficients. And then predicting the velocity set at all points in the small triangle area by using the velocity set at the three vertexes of the small triangle by using the convex combination coefficients. The vertices of all the small triangular areas form a limited number of discrete representative points, the speed sets at the limited number of discrete points are used for predicting the speed sets at all the points in the whole area, and the problem that in actual prediction calculation work, only the limited points can be used for prediction, and the prediction effect is poor is solved.
In addition, the method for dividing the region solves the problem that the region is non-convex by using a triangulation method, each small triangle region divided by the triangulation method is convex, and all point sets in the small triangles can be predicted by performing convex combination on three vertexes of the small triangles.
The conception, the specific structure and the technical effects of the present invention will be further described with reference to the accompanying drawings to fully understand the objects, the features and the effects of the present invention.
Drawings
FIG. 1 is a schematic diagram of the present invention for selecting n discrete points within a habitat area.
FIG. 2 is a schematic diagram of the triangulation of a limited number of discrete points within a habitat area of the present invention.
FIG. 3 is a schematic view of the inside and outside of a triangle after triangulation of the fire point of the present invention.
Fig. 4 is an algorithm flow diagram of the present invention.
Fig. 5 is a data flow diagram of the present invention.
Fig. 6 is an application architecture diagram of the present invention.
Detailed Description
The key point of the invention is to establish a discrete model contained by differential based on finite element thought and design a numerical simulation method of fire area change dynamics based on Minkowski addition. Specifically, the habitat area selected and predicted is firstly divided into limited small areas, the area dividing method is a triangulation method, the problem that the area is non-convex is solved, and all small triangular areas divided by triangulation are convex, so that all point sets in the small triangles can be predicted by convex combination of three vertexes of the small triangles. And establishing the propagation speed of each position point in the region in each direction based on the differential inclusion. And finally, simulating a model capable of gathering dynamic spreading of the forest fire by using Minkowski addition. For convenience of explanation, the invention selects forest fires as a specific example of pollutant diffusion; based on finite element thought, selecting a limited number of most representative discrete points in the region to triangulate the region, establishing a point coordinate convex combination formula of the representative points and all points in the region to obtain convex combination coefficients, wherein each small triangular region after triangulation is a convex set. Because a functional relation can be established between the speed set at each point in the area and the position information of the point, the speed set at the representative point can predict the speed sets at all points in the area through convex combination by utilizing the obtained convex combination coefficient; and adding a time factor to estimate the range of the forest fire in the inhabited area which can dynamically spread along with the time. The present invention introduces differential inclusion to better predict the spread of a fire in different directions over time. Meanwhile, the invention introduces the idea of finite element, and solves the problem that the calculated amount of the speed set at all points in the region is too large in the actual prediction calculation work.
The specific technical scheme of the invention is as follows:
1. mathematical noun interpretation
The differentiation comprises: the general differential equation is defined as follows:
let x be a set of n location points x = (x) 1 ,x 2 ,x 3 ,…,x n ) The rate of change (speed) of x
Is completely determined by x, its variation model can be represented by the following differential equation:
plus an initial condition x (t) 0 )＝x 0 We can find out the different states of the point x along with the time to build the prediction model of the point x.
The control system theory introduces a control factor on the basis, so that the change track of the point x can be manually controlled, and a control model is changed into a control model
Where U (-) is a governing equation, U is a set of a series of governing equations, the evolution of the change at point x depends not only on x itself, but also on a governing factor, U = (U =) 1 ,u 2 ,…,u m ). By adjusting the governing equations, the model can be developed towards the direction we expect. Equation (3) is written as a differential contained shapeThe formula is as follows:
where F (x) is the set of all possible rates of change (velocities) for x, written as follows:
here, the
Is the varying velocity under the constraint u at point x and this velocity vector is only one of all allowable velocity vectors. In summary, the solution of differential inclusion is a set of mapping of sets, and by using this, the invention introduces the differential inclusion into a fire spread model to simulate the trajectory of fire spread at a certain speed in different directions at the same time.
Finite element method: the core ideas of the finite element method are 'numerical approximation' and 'discretization'. The continuous complex area is discretized into a plurality of simple basic units, and the solutions on the finite discrete simple areas are combined to approximate the solution on the whole continuous complex area. The invention is based on the thought of finite element, the prediction area is triangulated, the whole area is divided into a plurality of small triangular areas with convex set property, and the speed sets of all points in the whole area are predicted by using the speed sets of a small number of discrete representative points.
Triangulation: triangulation needs to meet two principles, and firstly, all small triangles obtained through division do not overlap with each other; and secondly, new points are not generated after the region is divided, one important property of the triangle subdivision is that at most one common edge of two adjacent small triangles in the region has at least one common vertex, and each divided small triangle is a convex set.
Minkowski addition: a method of summing two sets.
2. Preliminary preparation phase
2.1 generating region set Ω of habitat
Selecting a habitat to be predicted, acquiring earth surface satellite remote sensing data of the region from an NASA official website, and extracting longitude and latitude position information of the habitat. The location information of the habitat is rasterized to generate an area set Ω in a two-dimensional space.
2.2 Generation of reachable set of forest fires R
Satellite data related to habitat, such as earth surface temperature data, earth surface day-night temperature difference data, earth surface sulfide data, earth surface vegetation data, earth surface infrared remote sensing image data and the like, are acquired from national weather service and domestic wind and cloud series satellites. The extracted regional meteorological data is subjected to data mining and data filtering to obtain fire point data in the region, and the main basis for judging that a certain position is a fire point is as follows: the concentration of the sulfide at the place is high, the surface temperature is high, and the day and night temperature difference is less than a certain threshold value, and finally the fire area of the habitat in a certain time period is calculated to be used as an accessible set R in the project.
3. Pretreatment of habitat areas
3.1 initializing habitat area
A set of regions of the selected habitat is obtained according to step 2. In order to predict the spread of the fire, the invention sets that each position point x has a velocity set belonging to it. According to the definition contained in the differential:
the point x has an infinite number of velocity vectors in each direction to form its corresponding velocity set F (x). There are numerous location points x in the region Ω, and in order to optimize the algorithm, the present invention selects a velocity set corresponding to the discrete points represented in the region Ω to approximately solve the velocity set of the whole region, the present invention selects n discrete points in the habitat region, the point set is x = (x =) 1 ,x 2 ,x 3 ,…,x n ) Here, a point x is defined k The set of velocities at is F (x) k ) And k is more than or equal to 1 and less than or equal to n, and the running result in the computer program is shown in figure 1.
3.2 triangulating habitat areas
Selecting m discrete representative points x in inhabited region i I is more than or equal to 1 and less than or equal to m, and m is more than or equal to n/10. Triangulating the habitat area by using the m discrete points to obtain p small triangular areas d, and collecting the small triangular areas into a set
d＝(d 1 ,d 2 ,d 3 ,...,d p ),
The result of the computer program run is shown in fig. 2.
All the small triangles in the area after triangulation are not overlapped, new points are not added, and at most one common edge is directly arranged between the adjacent small triangles. Because each small triangle is convex and has the property of a convex set, all points in the whole habitat area can be predicted by using a limited discrete position point in the habitat area, so that the algorithm is simplified, and the calculation speed is increased.
3.3 solving the convex combination coefficient
The method is mainly realized by simulating a dynamic spreading model of the forest fire based on some mathematical principles, and a speed set of fire points in each direction is required to be obtained in order to simulate the dynamic process of fire spreading. Therefore, the strategy adopted by the invention is to carry out convex combination on a limited number of initially selected position points in the region to predict the velocity set at the fire point with dynamically changing position, solve the convex combination coefficient by a simultaneous equation set, and then predict the velocity set at the fire point in the region by using the solved convex combination coefficient. The specific mathematical operation process is as follows:
after the habitat is triangulated, to determine which small triangle the fire point X belongs to, for example, to determine whether X is inside the small triangle Δ ABC, an equal area determination method may be used, as shown in the following figure, if the point X is outside the small triangle Δ ABC, the sum of the areas of the triangles consisting of the point X and the point A, B, C is greater than the area of the triangle consisting of the point A, B, C, and the geometric visualization is as shown in fig. 3.
Establishing corresponding inequality, as formula (6)
| S(ΔABC)<S(ΔABX)+S(ΔACX)+S(ΔBCX) | (6) |
If point X is inside the small triangle Δ ABC, the sum of the areas of the triangles consisting of point X and point A, B, C, respectively, is equal to the area of the triangle consisting of point A, B, C, establishing the corresponding equation, as shown in equation (7) below:
| S(ΔABC)＝S(ΔABX)+S(ΔACX)+S(ΔBCX) | (7) |
if the equation is established, the small triangle where the fire point X is located is determined to be delta ABC, convex combination is performed by using three vertexes A, B, C of the small triangle to represent the fire point X, and the convex combination coefficient sum is 1, so that an equation set can be simultaneously established to obtain the convex combination coefficient.
The vertexes A, B and C of the small triangle are respectively (x) a ,y a ),(x b ,y b ),(x c ,y c ) The coordinates of the point X are (X, y). The following system of equations is associated:
construction of an augmented matrix, e.g. formula (9)
Increase and demandUnique solution of the wide matrix to obtain the convex combination coefficient alpha 1 ,α 2 ,α 3
3.4 convex combination of velocity sets for other fire points in the predicted region
In step 3.3, the fire point X has been solved for in triangle Δ ABC and convex combination coefficients representing point X by convex combination with the three vertices A, B, C of the small triangle are found. Since the velocity set F (X) corresponding to the fire point X is a set of functions related to X, the velocity set corresponding to the fire point X can be convex combination predicted by using the velocity sets F (a), F (B), and F (C) corresponding to the three vertices A, B, C of the small triangle, and the predicted value is:
by analogy, the velocity sets at other fire points in the habitat can also be subjected to convex combination prediction by using the velocity sets at the three vertexes of a certain small triangle in the habitat. And obtaining the speed set at each fire point and adding a time factor to calculate the spreading track of the fire.
4. Dynamic change track of disaster area is simulated based on Minkowski addition
The final purpose of the invention is to simulate the dynamic spreading model of the disaster area, establish the discrete model of the speed set in the whole area of the habitat by the three steps, and simulate the process of the dynamic change of the fire in the habitat area along with the time by adding the time factor.
4.1 computing the set of velocities at fire points in a region based on convex combinations
With this method, the convex combination of velocity sets in equation (8) can be calculated:
thereby estimating the velocity set at each fire point within the habitat area. First, the small triangles of the habitat area omega to which the fire points belong are determined, and then the fire points are usedAnd (3) carrying out convex combination on the speed sets at the vertexes of the subordinate small triangles to estimate the speed set of the fire points, and calculating new areas where the fire points reach after the time t passes by the speed sets of the fire points in the reachable set of the forest fire, namely solving a new reachable set of the forest fire, thereby establishing a fire dynamic spreading model of the habitat.
The concrete implementation is as follows:
(1) In the initial set of forest fires, data in the set is boundary longitude and latitude information of a fire range at a certain position in the habitat at the time 0 (the observation starting time is set as the time 0). Calculating the diffusion locus of the boundary of the disaster-affected area requires calculating the velocity set of all the points on the boundary, however, the boundary has an infinite number of position points and an infinite number of velocity sets. The method adopted by the invention is that the speed set of each point on each line segment on the boundary of the initial set of forest fires is used for representing the speed set of each point on the line segment, and because all points on the line segment belonging to a certain small triangle of the habitat are linearly related, only the fire points at the end points can be selected as representative points. The concrete implementation is as follows: and (3) bringing the line segment end points on the reachable set boundary of the forest fire into the speed set discrete model established in the steps 1, 2 and 3, and carrying out convex combination on the speed sets corresponding to a limited number of discrete points on the region omega to represent the speed set at the corresponding point between the two end points of the line segment on the boundary of the disaster-affected region.
(2) The line segments on the boundary of the disaster-affected area are not necessarily all contained in a small triangle after the omega triangulation of the area. There are certain situations as follows: two end points of a certain line segment on the boundary of the disaster area belong to different small triangles in the area omega, and at the moment, all the speed sets of the line segment on the boundary of the disaster area cannot be represented by convex combination of three vertexes of the same small triangle. In this case, it is necessary to segment the line segment, only the portion completely belonging to the same small triangle is taken out as a new line segment, and the three vertices of the small triangle are used for performing convex combination to predict the velocity set at the two end points of the new line segment. And by analogy, solving the speed set of each fire point on the boundary of the forest fire area.
4.2 calculating the dynamic change process of the disaster area along with the time
The method comprises the steps of already calculating a speed set of each fire point on the boundary of the initial reachable R (0) of the forest fire, introducing a time factor kt, calculating the motion area of each side on the polygonal boundary of the initial set of the forest fire by utilizing Minkowskiaddition, calculating the motion areas of all sides after the time t, and then summing the motion areas to obtain a new reachable set R (t) which is the new range of the forest fire spreading after the time t.
The invention also provides a device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the method when executing the computer program.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (8)
1. A method for dynamic simulation of a pollutant diffusion zone, comprising:
step 1, selecting a habitat to be estimated, acquiring satellite data of the habitat area, and constructing an initial sample area set based on the satellite data;
step 2, constructing an initial reachable set R (0) of the forest fire based on the historical fire information of the habitat;
step 3, selecting a limited number of discrete representative points to triangulate the habitat area based on a finite element thought, and dividing a plurality of small triangular areas with convex set properties; establishing a convex combination formula of point coordinates of three vertexes on the small triangular area and all points in the small triangular area to obtain convex combination coefficients;
step 4, predicting the speed set of all points in the small triangular area by using the speed sets of the three vertexes on the small triangular area by using the convex combination coefficient obtained in the step 3; thereby predicting a set of velocities at all points within the entire region using the set of velocities at the finite number of discrete representative points; thus, a differential including spread discrete model is established;
and 5, adding a time factor, and estimating the range of the forest fire in the inhabited area, which can be dynamically spread along with time.
2. The method of claim 1, wherein the satellite data of the habitat area comprises at least habitat latitude and longitude data, surface temperature data, surface diurnal temperature difference data, surface sulfide data, surface vegetation data, and surface infrared remote sensing image data.
3. The method for dynamically simulating a pollutant diffusion area according to claim 1, wherein the step 2 is to construct a reachable set of forest fires based on historical fire information of the habitat, and specifically comprises the following steps: the sulfur concentration of the habitat is high, the surface temperature is high, the day-night temperature difference is smaller than a certain threshold value, and finally the fire area of the habitat in a certain time period is calculated to be used as an accessible set.
4. The method according to claim 1, wherein step 3 is based on finite element concept, and triangulates the whole habitat area with a finite number of discrete representative points, specifically:
initializing a habitat area, and selecting n discrete points in the habitat area, wherein the point set is x = (x) 1 ,x 2 ,x 3 ,...，x n ) Here, a point x is defined k The set of velocities at is F (x) k ) K is more than or equal to 1 and less than or equal to n; then m discrete representative points x are selected i I is more than or equal to 1 and less than or equal to m, m is more than or equal to n, the habitat area is triangulated by the m discrete representative points to obtain p small triangular areas d, and the small triangular areas are collected into a set
d＝(d 1 ，d 2 ，d 3 ，...，d p )。
5. The pollutant diffusion zone dynamic simulation method of claim 1, wherein, the step 4 predicts the velocity set at each point in the whole inhabited zone by using the velocity sets at a finite number of discrete representative points, and establishes a differential inclusion spread discrete model; the differential includes the speed of each position point in the whole habitat area in each direction estimated in the model, and specifically includes: selecting the most effective m discrete representative points x in the inhabitation region i I is more than or equal to 1 and less than or equal to m, m is more than or equal to n/10, the whole area is triangulated by the m discrete representative points to obtain p small triangular areas d with the property of convex set, and the small triangular area set is d = (d) 1 ，d 2 ，d 3 ，...，d p ) Using a convex combination formula of coordinates of the vertices of the small triangular areas and all discrete points in the small triangular areas, x i Is a point within the qth small triangular area, x q1 ，x q2 ，x q3 Three vertexes of the small triangular area are shown, and the specific formula is as follows:
α 1 *x q1 +α 2 *x q2 +α 3 *x q3 ＝x i (1)
wherein: x is the number of i ∈x，x i in d q ，1≤i≤n，1≤q≤p；
Calculating convex combination coefficient alpha 1 ，α 2 ，α 3 (ii) a Because the discrete points in the small triangle are represented by convex combination of three vertexes on the small triangle area, by analogy, the speed set at the discrete points in the small triangle can also be represented by convex combination prediction of the speed sets at the three vertexes on the small triangle area; the formula is as follows:
wherein, f (x) q1 )、f(x q2 )、f(x q3 ) Respectively represent x q1 ，x q2 ，x q3 The known velocity set at these three vertices;
representing the set of velocities f (x) from three vertices q1 )、f(x q2 )、f(x q3 ) Reconstructing the resulting point x i The approximate velocity set of (a).
6. A method as claimed in claim 1, wherein said step 5 adds a time factor to estimate the range of the forest fire dynamic spreading over time in the habitat area, and comprises: and solving a speed set of each fire point on the initial reachable boundary of the forest fire, introducing a time factor, calculating the motion tracks of each fire point on the boundary of the initial forest fire in different directions, solving the motion tracks of all the fire points after the time t, and then solving a union set of the motion tracks to obtain a new reachable set, namely a new range in which the forest fire spreads after the time t.
7. A pollutant diffusion zone dynamic simulation system, comprising:
the area set acquisition module is used for selecting a habitat to be estimated, acquiring satellite data of the habitat area and constructing an initial sample area set based on the satellite data;
the reachable set acquisition module is used for constructing a reachable set of forest fires based on the historical fire information of the habitat;
the region dividing module is used for selecting a limited number of discrete representative points to triangulate the whole habitat region based on a finite element thought, dividing the whole region into a plurality of small triangular regions, wherein each small triangular region is a convex set, and the discrete representative points are vertexes of the small triangular regions;
the fire speed prediction module is used for solving a convex combination coefficient by using a simultaneous convex combination formula of three vertexes on the small triangular region and all points in the small triangular region, and by analogy, the speed set at the three vertexes on the small triangular region is used for carrying out convex combination prediction on the speed sets at all discrete points in the small triangular region by using the solved convex combination coefficient as a function related to the discrete points; establishing a differential including spread discrete model to predict a speed set of the fire point in each direction;
and the fire spread estimation module estimates the range of the forest fire reachable set dynamically spreading along with time in the habitat area by adding time factors and utilizing a threshold Kefski addition.
8. A pollutant diffusion zone dynamic simulation apparatus comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor when executing the computer program implements the steps of the method of any one of claims 1 to 6.
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