CN105243186A - Cellular automaton based diffusion simulation method - Google Patents
Cellular automaton based diffusion simulation method Download PDFInfo
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Abstract
The present invention discloses a cellular automaton based diffusion simulation method. The method comprises the following steps: step 1, constructing a two-dimensional cellular automaton; step 2, constructing a diffusion pattern operational mechanism; step 3, constructing a diffusion simulation real-time dynamic control mechanism; and step 4, developing an integrated GUI modeling and simulation platform. According to the method of the present invention, the two-dimensional cellular automaton is adopted to perform modeling and simulation of various diffusion processes, a method framework is provided from the aspects of construction of the cellular automaton, setting of a cellular local dynamic rule, setting of a diffusion pattern and the like, and an integrated GUI platform for the implementation of the method framework is provided, thereby realizing real-time dynamic simulation of various diffusion processes.
Description
Technical field
The present invention relates to the two-dimentional dynamic similation of diffusion phenomena, particularly relate to the diffusion simulation method based on cellular automaton.
Background technology
Diffusion refers to that material, momentum, energy or information etc. are along with the migration of time is from a region to the phenomenon of other zone-transfer, propagation, as the diffusion of pollutant in the media such as air, water body, soil.Diffusion phenomena are complex processes of a temporal and spatial orientation, its complicacy is presented as that diffusion process affects by each combined factors such as diffusate, dispersive medium, diffusion conditions and regional environments, there is randomness, dynamic, non-linear, emerging in large numbers property, the complex characteristics such as evolutive, therefore, be difficult to carry out effective real time dynamic simulation with traditional macromodel to it.The analogy method great majority of current employing are the governing equation groups based on its statistical property deterministic process, adopt numerical computation method solving equation group again, the drawback of the method is that accuracy is not high, adaptability is strong, model structure and calculation of complex, is difficult to realize real time dynamic simulation truly simultaneously.
Summary of the invention
The object of the invention is to for above-mentioned defect of the prior art, a kind of diffusion simulation method based on cellular automaton is provided, the method emerges in large numbers the macroscopic appearance in whole space by local dynamic station between cellular and its neighborhood rule, can the compound movement process of modeling effort object better.
For achieving the above object, present invention employs following technical scheme, a kind of diffusion simulation method based on cellular automaton, carry out as follows:
Step one, the structure of two dimensional cellular automaton:
In MATLAB software, define two-dimensional matrix as cellular space, each element of matrix represents a cellular, and its 8 adjacent elements represent cellular neighbours, and element value is cellular state.By adopting the form parallel computation state transition function of matrix difference after structure transposed matrix, realize the quick renewal of all cellular state.Above-mentioned structure realizes by designing corresponding parameter and inputting MATLAB program by GUI modeling and simulation platform, arranges cellular basic parameter:
Cellspacelengthcolumns: the length (matrix columns) that cellular space is set;
Cellspacewidthrows: wide (matrix line number) that cellular space is set;
Seedpositionrow: the line number that diffusion source locations corresponds to cellular space is set;
Seedpositioncolumn: the columns that diffusion source locations corresponds to cellular space is set;
Seedsize: the size that diffuse source is set;
Seeddensity: the intensity that diffuse source is set;
Emergencydiffusion: define instantaneous disposable release diffusion way;
Continuousdiffusion: definition continuation repeatedly discharges diffusion way, and arranges continued emissions number of times;
MultiCASeed: add multiple diffuse source, arranges row (row) and the row (column) of diffuse source position respectively;
If non-point source, then at non-pointsourceparameters: the basic parameter arranging non-point source;
Importanon-pointsourcepicture: import the picture comprising non-point source region;
Definenon-pointsource: definition non-point source region basic parameter.
Step 2, the operating mechanism structure of dispersal pattern:
The diffusion process of various different mode is simulated by providing the combination that arranges of diffuse source, diffusion way and coefficient of diffusion.Diffuse source is the seed cellular in cellular automaton, by the operation to corresponding element assignment in two-dimensional matrix, can arrange the position of one or more diffuse source, shape, size, intensity.Diffusion way has two kinds: the diffusion (continuous_diffusion) after the diffusion (emergency_diffusion) after instantaneous disposable release and continuation repeatedly discharge, and realizes its operation by the call back function writing timer.Coefficient of diffusion is the ratio that cellular state carries out to its 8 neighbours directions spreading, and designs corresponding parameters input control and arranges, can realize constant direction by its setting, non-constant direction or not specified diffusion.The setting of basic diffusion parameter:
Up: coefficient of diffusion is upwards set;
Down: downward coefficient of diffusion is set;
Left: coefficient of diffusion is left set;
Right: coefficient of diffusion is to the right set;
Upleft: the coefficient of diffusion to the upper left corner is set;
Upright: the coefficient of diffusion to the upper right corner is set;
Downleft: the coefficient of diffusion that inferior horn is left set;
Downright: the coefficient of diffusion to the lower right corner is set;
If there is turbulent flow, then DIFFUSION IN TURBULENCE parameter is set;
Addturbulent: add turbulent model;
Turbulentarea: turbulent flow size and position are set after clicking;
Topleftpositionrow: the line number that turbulent region top left corner apex position is corresponding is set;
Topleftpositioncolumn: the columns that turbulent region top left corner apex position is corresponding is set;
Length (columns): the length (columns) that turbulent region is set;
Width (rows): the width (line number) that turbulent region is set;
Importpattern: import turbulent diffusivity matrix.
Diffusion times and interval time are arranged:
Executingtimes: the number of times that diffusion runs is set;
Repeatinterval: the time interval arranging adjacent twice diffusion, unit is: second.
Step 3, the real-time Dynamic controlling mechanism of diffusion simulations:
Utilize the timer object that MATLAB provides, realize the process control such as real-time graph display, beginning, time-out, continuation, stopping of simulation process.Realization mechanism is: create an example timer, by needing the userdata of the parameter read-in timer used in the parameters of cellular automaton and dispersal pattern and other simulation processes, using it as data exchange interface in whole simulation process.During beginning, start timer, in its call back function, run the diffusion way of setting and show diffusion result in real time.As suspended, then current state being kept at userdata, during continuation, after newly setting being read in, in previous status, continuing simulation.During stopping, then delete this example timer, for simulating removing internal memory next time.Be implemented as follows:
1. from userdata, read diffusion way and judge, if instantaneous disposable diffusion, then performing call back function emergencydiffusion, if be continuation diffusion, then performing call back function continuousdiffusion;
2. function starts to perform, and reads cellular diffusion parameter from userdata;
3. read in cellular space matrix current_cellspace;
4. build the transposed matrix (spaceup, spacedown, spaceleft, spaceright, spaceupleft, spaceupright, spacedownleft, spacedownright) in 8 directions;
5. the parallel renewal of cellular state is realized according to the transfer function of 8 direction coefficient of diffusion, transposed matrix and matrix differential configuration:
newspace＝space+(up*(spaceup-space)+down*(spacedown-space)+left*(spaceleft-space)+right*(spaceright+(-space))+upleft*(spaceupleft-space)+upright*(spaceupright-space)+downleft*(spacedownleft-space)+downright*(spacedownright-space))；
6. judge whether to there is turbulent flow, if existed, then read the turbulent region diffusion coefficient matrix in the size of turbulent region and upper left position (tposition) thereof and userdata; Build 8 direction transposed matrixs (tspaceup, tspacedown, tspaceleft, tspaceright, tspaceupleft, tspaceupright, tspacedownleft, tspacedownright) of turbulent region; Then the parallel renewal of turbulent region cellular state is realized:
tnewspace＝tspace+(tup.*(tspaceup-tspace)+tdown.*(tspacedown-tspace)+tleft.*(tspaceleft-tspace)+tright.*(tspaceright-tspace)+tupleft.*(tspaceupleft-tspace)+tupright.*(tspaceupright-tspace)+tdownleft.*(tspacedownleft-tspace)+tdownright.*(tspacedownright-tspace))
By the matrix assignment after renewal to turbulent region in cellular space:
newspace(tposition(1)：tposition(1)+tr-1，tposition(2)：tposition(2)+tc-1)＝tnewspace；
7. preserve the state value of diffusion each cellular rear;
8. calculate current diffusion times and preserve;
9. the newspace matrix gray-scale map obtained is presented at the window of software, and under picture is stored in computing machine specified path;
10. the data after renewal are stored in userdata, for diffusion next time;
11. if instantaneous disposable diffusion, then directly enter and spread next time; If continuation diffusion, then need to read from userdata to continue diffusion times, the concentration that the concentration obtaining cellular seed is set to setting enters and spreads, until complete lasting diffusion times next time.
Step 4, develop integrated GUI modeling and simulation platform:
Realize the optimum configurations of various different mode diffusion process simulation, real-time graph display and the function such as process control by GUI modeling and simulation platform, the function that each functional areas realize and concrete operations as follows,
1. set timer and time showing district comprise:
The viewing area of TimerParameterSet setting area and ExecuteTimes and CurrentTime;
Timestoexecute: the number of times that diffusion runs is set;
Repeatinterval: the time interval that adjacent twice diffusion is set, unit is second;
ExecuteTimes: the number of times of display executed diffusion;
CurrentTime: the current date and time of Display control computer.
2. cellular automaton optimum configurations district comprises:
Basic parameter setting, basic diffusion parameter setting, DIFFUSION IN TURBULENCE optimum configurations, default value button, parameter testing button.Wherein,
(1) basic parameter is arranged:
Cellspacelengthcolumns: the length (matrix columns) that cellular space is set;
Cellspacewidthrows: wide (matrix line number) that cellular space is set;
Seedpositionrow: the line number that diffusion source locations corresponds to cellular space is set;
Seedpositioncolumn: diffusion source locations is set corresponding to the columns in cellular space;
Seedsize: the size that diffuse source is set;
Seeddensity: the intensity that diffuse source is set;
Emergencydiffusion: define instantaneous disposable release diffusion way;
Continuousdiffusion: definition continuation repeatedly discharges diffusion way, selects pop-up window after this option, input continued emissions number of times;
MultiCASeed: add multiple diffuse source, and the row and column of diffuse source position is set respectively in row and column of pop-up window;
Non-pointsourceparameters: the basic parameter that non-point source is set;
Importanon-pointsourcepicture: import the picture comprising non-point source region;
Definenon-pointsource: definition non-point source region.
(2) basic diffusion parameter is arranged:
Up: coefficient of diffusion is upwards set;
Down: downward coefficient of diffusion is set;
Left: coefficient of diffusion is left set;
Right: coefficient of diffusion is to the right set;
Upleft: the coefficient of diffusion to the upper left corner is set;
Upright: the coefficient of diffusion to the upper right corner is set;
Downleft: the coefficient of diffusion that inferior horn is left set;
Downright: the coefficient of diffusion to the lower right corner is set.
(3) DIFFUSION IN TURBULENCE optimum configurations:
Addturbulent: add turbulent model;
Turbulentarea: turbulent flow size and position are set after clicking;
Topleftpositionrow: the line number that turbulent region top left corner apex position is corresponding is set;
Topleftpositioncolumn: the columns that turbulent region top left corner apex position is corresponding is set;
Length (columns): the length (columns) that turbulent region is set;
Width (rows): the width (line number) that turbulent region is set;
Importpattern: import turbulent diffusivity matrix.
3. simulation process control zone:
Start: bring into operation diffusion simulations;
Pause: suspend diffusion, modifiable parameter after suspending;
Continue: continue diffusion, if Parameters variation, continues diffusion according to new argument;
Stop: stop diffusion simulations;
Exit: exit software.
4. diffusion pattern viewing area: this region comprises the display window of a diffusion pattern and multi-usage window (can be used for show selected turbulent model or for defining non-point source).
Compared to prior art, advantage of the present invention is: the present invention adopts two dimensional cellular automaton to carry out the modeling and simulation of various diffusion process, from the structure of cellular automaton, cellular local dynamic station rule is arranged, dispersal pattern is arranged etc., and aspect provides a method frame, simultaneously for the realization of the method framework provides an integrated GUI platform, thus realize the real time dynamic simulation of various diffusion process.
Further, cellular automaton diffusion model of the present invention is that the change of the local dynamic station of diffusion process is carried out quantificational description with rational node transition rule, makes the time-spactial dynamic pattern in cellular space meet the dynamic change of survey region diffusion process.
Accompanying drawing explanation
Fig. 1 is that two dimensional cellular automaton forms process flow diagram.
Fig. 2 is Moore type cellular neighbours.
Fig. 3 is the diffusion process of cellular automaton diffusion model.
Fig. 4 is the setting of dispersal pattern.
Fig. 5 is the real-time control flow of diffusion simulations process.
Fig. 6 is GUI modeling and simulation platform development flow process.
Fig. 7 is GUI modeling and simulation platform software interface.
Fig. 8 is certain manufacturing district figure and grid chart.
Fig. 9 is quiet wind point source diffusion figure.
Figure 10 has the instantaneous discharge scatter diagram of wind point source.
Figure 11 has wind point source continued emissions scatter diagram.
Figure 12 is turbulent model.
Figure 13 is the diffusion source locations of turbulent model.
Figure 14 is the instantaneous diffusion process figure of turbulent model.
Figure 15 is the lasting diffusion process figure of turbulent model.
Embodiment
Below in conjunction with preferred embodiment and accompanying drawing thereof, technical solution of the present invention is further non-limitingly described in detail.
The present invention adopts two dimensional cellular automaton to build diffusion model, and it is formed as shown in Figure 1.Survey region is carried out rectangular node and divide the cellular space obtaining model, each rectangular node represents a cellular.Cellular neighbours adopt two-dimentional Moore type, and each cellular has 8 neighbours, as shown in Figure 2.Using the property value (such as material concentration) of studied diffusate (or momentum, energy etc.) as cellular state, build node transition rule such as formula:
{k∈[i-1，i，i+1]，l∈[j-1，j，j+1]，k，l≠i，j}
In above formula
represent cellular E
i, jin the state of t,
represent the cellular state of its Moore type neighbours.
represent the state coefficient of migration between t cellular and its neighbours, its value can be constant also can be function, reflect that the local dynamic station in various diffusion process between adjacent cellular is mutual, m ∈ on, under, left, the right side, upper left, lower-left, upper right, bottom right } represent 4 positive dirctions and direction, 4 oblique angles respectively.Cellular spatial framework according to above-mentioned model t just can calculate through node transition rule the cellular spatial framework being diffused into the t+1 moment, and the rest may be inferred, and its process as shown in Figure 3.
Construct the operating mechanism of various dispersal pattern, by what provide diffuse source, coefficient of diffusion, diffusion way, combination is set, simulate the diffusion of various pattern, as disposable point source or the release diffusion of source, face, continuation point source or the diffusion of source, face release constant direction, continuation point source or source, face discharge the diffusion of non-constant direction and non-determined direction (turbulent flow) diffusion etc.The setting of dispersal pattern is as accompanying drawing 4.
Construct the real-time Dynamic controlling mechanism of diffusion simulations, utilize the characteristic of timer object, real-time graph display and beginning, time-out, the continuation etc. of carrying out simulation process operate the real time and dynamic and the controllability that realize simulation process.Concrete simulation process controls in real time as accompanying drawing 5.
Develop integrated GUI modeling and simulation platform and realize the functions such as relative parameters setting, figure display and simulation process control.Platform development flow process is as accompanying drawing 6.Accompanying drawing 7 is seen at platform software interface, is divided into 4 functional areas: (1) set timer and time showing district; (2) model construction and operational factor setting area; (3) simulation process control zone; (4) graphical display area.GUI modeling and simulation platform operations provided by the invention is easy, and travelling speed is fast, can Real time dynamic display and control the simulation of various diffusion process, and analog result is rationally credible, for the research of various diffusion phenomena provides powerful.
For industrial park, North City of China air pollution diffusion.
1. construct cellular Automation Model
Fig. 8 is industrial park, North City of China, and wherein (a) is this regional satellite figure, the stress and strain model schematic diagram that (b) is this region.Whole region horizontal span is 12 kms, and longitudinal span is 8 kms, with 400 × 600 square net Research on partition regions, obtains the cellular space that each sizing grid is 20 × 20 square metres.In view of display needs, in Fig. 8 (b), each grid represents 20 × 20 cellulars.
The SO2 that the pollution source in this district discharge every year is 1093.6t, SO2 concentration of emission is 82.8mg/m3.So, using the concentration of pollutant as the state of cellular, make the source strength 0.1 after quantizing represent the SO of 0.00068t
2, pollution source size is 9 (namely 3 × 3) cellulars; Model running 480 representatives pollute exhaust gas diffusion 1.
According to atmospheric diffusion principle, coefficient of diffusion spreads (similar molecular diffusion) and wind and turbulent flow factor by pollutant levels and determines:
wherein
represent the pollutant levels coefficient of migration between t cellular and its neighbours,
for concentration coefficient of diffusion,
for the coefficient of diffusion that wind determines,
for the coefficient of diffusion that turbulent flow determines, in formula
Represent 4 positive dirctions and direction, 4 oblique angles respectively.Coefficient of diffusion under different situation is different, so can simulate different diffusion situations by changing coefficient of diffusion.
To sum up, to arrange cellspacelengthcolumns be 600, cellspacewidthrows be 400, seedsize be 3, executingtimes is 1440.
2. the optimum configurations of different dispersal pattern and simulation
2.1 quiet wind point source emission diffusion simulations
In the calm situation of ideal, the diffusion of waste gas is only subject to the impact of concentration coefficient of diffusion.According to the isotropy of uniform dielectric, Pollutants Diffusion sub-circular.The coefficient of diffusion arranging 8 directions is:
Suppose that the coordinate of pollution source is arranged in (10 of Fig. 8 (b), 4) place, the position corresponding to cellular space is (200,500), as shown in Fig. 9 (a), respectively it is carried out to the diffusion simulations of instantaneous discharge mode and continued emissions pattern:
(1) select dispersal pattern to be instantaneous discharge emergencydiffusion, discharge number of times duration is 30 times, and pollution source concentration seeddensity is 1, and it is 1440 times that program runs executingtimes, and analog result is as Fig. 9 (b).
(2) dispersal pattern is selected to be continued emissions continuousdiffusion, discharge number of times duration is 1440 times, pollution source concentration seeddensity is 0.1, and it is 1440 times that program runs executingtimes, and analog result is as shown in Fig. 9 (c).
As can be seen from Fig. 9 (b) and Fig. 9 (c), under quiet wind or windless condition, along with the migration of time, pollute distribution and present circle, pollutant levels value is successively decreased from center toward both sides and is met Gaussian distribution, conform to the diffusion of pollutant under quiet wind condition, simultaneously due to continuation discharge, the concentration at Fig. 9 (c) center spreads the concentration of rear center apparently higher than the instantaneous discharge of Fig. 9 (b).
2.2 have wind point source emission diffusion simulations
When there being wind, need to consider coefficient of diffusion
with
namely the contaminated substrate concentration difference of diffusion process and wind carry the joint effect of diffusion.According to this ground in May, 2012 meteorological data, the coefficient of diffusion of May 2 to model on the 4th in May can be asked for respectively:
(1) coefficient of diffusion on May 2 is { 0.1787,0.084,0.084,0.084,0.0134,0.0134,0.0134,0.0134};
(2) coefficient of diffusion on May 3 is { 0.1045,0.084,0.1045,0.084,0.0134,0.0134,0.0134,0.0134};
(3) coefficient of diffusion on May 4 is { 0.1679,0.084,0.084,0.084,0.0134,0.0134,0.0134,0.0134}.
Suppose that certain steel plant is arranged in (10,1.5) place of Fig. 8 (b), the position corresponding to cellular space is (325,500).Arranging dry run number of times executingtimes is 1440 times, represents one day every 480 times.Respectively the instantaneous discharge mode of the pollutant had under landscape condition and continued emissions pattern are simulated according to the above-mentioned parameter asked for:
(1) select dispersal pattern to be instantaneous discharge emergencydiffusion, instantaneous discharge number of times duration is 40, and pollution source concentration seeddensity is 1, often runs 480 times and suspends, and click after amendment coefficient of diffusion and continue, result is as Figure 10.
(2) select dispersal pattern to be continued emissions continuousdiffusion, continued emissions number of times duration is 1440, and pollution far stronger seeddensity is 0.1, often runs 480 times and suspends, and click after amendment coefficient of diffusion and continue, result is as Figure 11.
Result figure under two kinds of patterns, in figure, the evolving path in damage zone is north-northwest-north, the evolving path is by the impact of actual wind direction, very fast with wind direction contamination in the same way under wind action, in diffusion process, pollutant moves towards the direction identical with wind direction, meets the Diffusion Law of pollutant under the meteorological condition of May 2 to May 4.
Diffusion simulations under 2.3 turbulent models
Suppose that this manufacturing district affects by atmospheric turbulence, then except considering concentration coefficient of diffusion, also to consider and, be all that air flowing drives Pollutants Diffusion under both of these case, its coefficient of diffusion is determined by wind speed, wind direction.
First importpattern loads Turbulent Flow Field pattern, as shown in figure 12, includes turbulent flow and flow to and flow velocity two parameters in the Turbulent Flow Field of loading.Suppose that the position of pollution source is coordinate in Fig. 8 (1,2) place, the position in corresponding cellular space is (300,50), as shown in figure 13.Under turbulent model, respectively the instantaneous discharge mode of pollutant and pollutant continued emissions pattern are simulated:
(1) select dispersal pattern to be instantaneous discharge emergencydiffusion, instantaneous discharge number of times duration is 40, and pollution source concentration seeddensity is 1, and run 1440 times, result is as Figure 14
(2) select dispersal pattern to be continued emissions continuousdiffusion, continued emissions number of times duration is 1440, and pollution far stronger seeddensity is 0.1, and run 1440 times, result is as Figure 15
Turbulent flow tendency in conjunction with field of turbulent flow in Figure 12 can be found out, consistent with the turbulent motion residing for instantaneous pollution source in the tendency of Figure 14 Pollutants Diffusion, in Figure 15, in continued emissions pattern, the spread condition of pollutant is consistent with the turbulent flow tendency in the field of turbulent flow region at pollution source.
It is pointed out that above-mentioned preferred embodiment is only and technical conceive of the present invention and feature are described, its object is to person skilled in the art can be understood content of the present invention and implement according to this, can not limit the scope of the invention with this.All equivalences done according to Spirit Essence of the present invention change or modify, and all should be encompassed within protection scope of the present invention.
Claims (1)
1., based on a diffusion simulation method for cellular automaton, it is characterized in that carrying out as follows:
Step one, structure two dimensional cellular automaton: with MATLAB software for platform, definition two-dimensional matrix is as cellular space, and each element of matrix represents a cellular, and its 8 adjacent elements represent cellular neighbours, and element value is cellular state;
Step 2, the operating mechanism of structure dispersal pattern: simulate the diffusion process of various different mode by providing the combination that arranges of diffuse source, diffusion way and coefficient of diffusion;
Step 3, the real-time Dynamic controlling mechanism of structure diffusion simulations: the timer object utilizing MATLAB software platform to provide, realizes the process control such as real-time graph display, beginning, time-out, continuation, stopping of simulation process;
Step 4, develop integrated GUI modeling and simulation platform: utilize GUI modeling and simulation platform realize various different mode diffusion process simulation optimum configurations, real-time graph display and process control.
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| CN109359431B (en) * | 2018-11-30 | 2022-12-20 | 中国航空工业集团公司沈阳飞机设计研究所 | Simulation method for material surface pitting in flowing seawater |
| CN111986064A (en) * | 2020-08-26 | 2020-11-24 | 山东大学 | Water pollution rapid tracing method and system |
| CN111986064B (en) * | 2020-08-26 | 2023-11-03 | 山东大学 | Rapid tracing method and system for water pollution |
| CN114970388A (en) * | 2022-05-12 | 2022-08-30 | 河海大学 | Site ground surface pollution diffusion method with self-adaptive time step |
| CN114970388B (en) * | 2022-05-12 | 2023-07-25 | 河海大学 | Site surface pollution diffusion method with self-adaptive time step |
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