CN102254106A - City extension simulating method based on cellular automata - Google Patents

City extension simulating method based on cellular automata Download PDF

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CN102254106A
CN102254106A CN2011102274233A CN201110227423A CN102254106A CN 102254106 A CN102254106 A CN 102254106A CN 2011102274233 A CN2011102274233 A CN 2011102274233A CN 201110227423 A CN201110227423 A CN 201110227423A CN 102254106 A CN102254106 A CN 102254106A
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neighbours
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王海军
张文婷
贺三维
何青青
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Wuhan University WHU
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Abstract

The invention discloses a city extension simulating method based on a cellular automaton. In the city extension simulating method, the iterative process of the tradition cellular automaton is improved, the cell neighbor space is layered, and neighbors in all directions and other factors influencing cell transformation are showed in a matrix form. The city extension predicting method disclosed by the invention has remarkable advantages: firstly, the method is superior to the traditional point-by-point cell judgment method, and the prediction efficiency is increased remarkably; in addition, the matrix form is introduced to the iterative process, thus the distance factor of a city extension system is simplified, and the attribute judgment of a central cell is simplified, and the simulation result is totally consistent to that of the traditional traversing method.

Description

A kind of city expansion analogy method based on cellular automaton
Technical field
The present invention relates to city expansion simulation field, relate in particular to the city expansion analogy method of a kind of employing based on cellular automaton.
Background technology
Cellular automaton (cellular automata is called for short CA) is that a kind of time, space and state all disperse, and has powerful spatial modeling ability and arithmetic capability, can simulate the dynamic system with space-time characteristic [1], and extensively applied to the simulation that the city is expanded.But cellular automaton causes the standard cellular automaton to adopt the mode of " traversal " cellular unit all the time in iterative process with characteristic and " from top to bottom " operating mechanism thereof of simple local rule Simulation of Complex phenomenon [2]This kind alternative manner simple possible, be convenient to move on computers, but when cellular quantity is big, adopt the mode inefficiency of traversal, and be not easy to consider distance factor, when taking geographical phenomenon into account and be subjected to many-sided factor affecting, also acquire a certain degree of difficulty, influenced the popularization that the ingot automaton model is used.And city system dynamic evolution process has the complicacy of height, and be subjected to multifactorial influences such as nature, society, economy, culture, politics, the introducing of a large amount of factor factors and distance factor makes and utilizes the inefficiency problem of cellular automaton simcity expansion more obvious.
The iterative process of tradition cellular automaton is specific as follows:
If cellular space
Figure 502382DEST_PATH_IMAGE001
, wherein,
Figure 2011102274233100002DEST_PATH_IMAGE002
Be cellular space size,
Figure 879005DEST_PATH_IMAGE003
Expression the iRow, the jThe cellular of row, Cellular next moment state representation in center is
Figure 716511DEST_PATH_IMAGE005
, wherein
Figure 2011102274233100002DEST_PATH_IMAGE006
,
Figure 971037DEST_PATH_IMAGE007
Be the discrete time,
Figure 2011102274233100002DEST_PATH_IMAGE008
,
Figure 210389DEST_PATH_IMAGE009
For cellular exists
Figure 757914DEST_PATH_IMAGE006
,
Figure 145033DEST_PATH_IMAGE007
State constantly,
Figure 2011102274233100002DEST_PATH_IMAGE010
Be neighbours [1]Then be in size
Figure 452517DEST_PATH_IMAGE002
The cellular space in, the judgement that utilizes traditional cellular Automation Model to finish a step-length need be carried out
Figure 343113DEST_PATH_IMAGE002
Inferior
Figure 819794DEST_PATH_IMAGE011
Functional operation is to judge next moment state of each cellular, and therefore when cellular quantity was big, iteration efficient was lower.
The list of references that relates in the literary composition is as follows:
[1] Zhou Chenghu, Sun Zhanli, Xie Yichun. geographical cellular automaton research [M]. Beijing: Science Press, 1999.
[2] Li Xia, Ye Jiaan, Liu Xiaoping etc. geographical simulation system: cellular automaton and multiple agent [M]. Beijing: Science Press, 2007.
Summary of the invention
At the deficiency that has inefficiency in the prior art based on the city expansion analogy method of traditional cellular automaton, the iterative process that the present invention is directed to traditional cellular automaton is improved, layering is carried out in cellular neighbours space, the neighbours that represent each orientation with the form of matrix influence the factor factor of cellular conversion with other, and provide a kind of based on expansion analogy method in the city improved cellular automaton of above-mentioned matrix operation, high efficiency.
In order to solve the problems of the technologies described above, the present invention adopts following technical scheme:
A kind of city expansion analogy method based on the improved cellular automaton of matrix may further comprise the steps:
S1 is according to the city simulation drawing, urban land is divided into industrial land, merchant takes six types of ground, residential land, water body, road and unused lands, marks off according to city planning and plans the key area;
The definition of S2 land used cellular attribute layer:
S2-1 definition land used cellular is apart from road distance attribute layer
Figure 2011102274233100002DEST_PATH_IMAGE012
:
Calculate the distance of each unused land cellular respectively apart from one-level road and secondary road
Figure 366313DEST_PATH_IMAGE013
,
Figure 2011102274233100002DEST_PATH_IMAGE014
, and definition land used cellular is apart from the road distance attribute
Figure 726756DEST_PATH_IMAGE015
, wherein,
Figure 2011102274233100002DEST_PATH_IMAGE016
Be sign of operation, can determine according to different cities Characteristics of Development and condition; Be cellular space size; Right simultaneously
Figure 643077DEST_PATH_IMAGE017
Carry out normalization and obtain the land used cellular apart from road distance attribute layer
Figure 739209DEST_PATH_IMAGE012
The planning limitation attribute layer of S2-2 definition unused land cellular
Figure 2011102274233100002DEST_PATH_IMAGE018
--:
Figure 139228DEST_PATH_IMAGE019
Wherein,
Figure 2011102274233100002DEST_PATH_IMAGE020
Expression is in the cellular space the iRow, the jThe cellular of row,
Figure 942099DEST_PATH_IMAGE004
S3 definition unused land cellular exists Neighbours' matrix constantly
Figure 851335DEST_PATH_IMAGE021
:
Figure 2011102274233100002DEST_PATH_IMAGE022
Wherein,
rRadius for neighbours' scope; ,
Figure 709493DEST_PATH_IMAGE025
Represent the in neighbours' scope respectively Row, the
Figure 2011102274233100002DEST_PATH_IMAGE027
The cellular of row,
Figure 2011102274233100002DEST_PATH_IMAGE028
,
Figure 143886DEST_PATH_IMAGE029
Figure 2011102274233100002DEST_PATH_IMAGE030
Expression
Figure 152293DEST_PATH_IMAGE006
Constantly
Figure 205700DEST_PATH_IMAGE020
Place's cellular
Figure 733895DEST_PATH_IMAGE031
Figure 2011102274233100002DEST_PATH_IMAGE032
Individual neighbours' cellular,
Figure 152238DEST_PATH_IMAGE033
, Expression
Figure 631630DEST_PATH_IMAGE006
Constantly Place's cellular
Figure 120697DEST_PATH_IMAGE031
Figure 772258DEST_PATH_IMAGE032
Individual neighbours' cellular, from top to bottom
Figure 508920DEST_PATH_IMAGE024
Increase successively, from left to right Increase successively;
Figure 452922DEST_PATH_IMAGE035
For
Figure 478647DEST_PATH_IMAGE008
Increase the extended matrix on border,
Figure 745680DEST_PATH_IMAGE008
For the unused land cellular exists
Figure 131531DEST_PATH_IMAGE006
State constantly;
Figure 1 shows that neighbours' position view, Figure 2 shows that to be in the center cellular
Figure 534831DEST_PATH_IMAGE020
Neighbours' matrix of position, the upper left corner
Figure 2011102274233100002DEST_PATH_IMAGE036
S4 is right
Figure 731457DEST_PATH_IMAGE006
Moment neighbours' matrix
Figure 174202DEST_PATH_IMAGE021
Carry out the iteration of a step-length, obtain the unused land cellular and exist
Figure 911214DEST_PATH_IMAGE007
State constantly
Figure 372282DEST_PATH_IMAGE037
, wherein,
Figure 2011102274233100002DEST_PATH_IMAGE038
The representing matrix computing;
S5 is according to neighbours' matrix
Figure 989077DEST_PATH_IMAGE021
, calculate the transition probability that the unused land cellular is converted into urban land :
Figure 2011102274233100002DEST_PATH_IMAGE040
Wherein, Represent the distance of some neighbours' matrixes apart from the center cellular,
Figure 2011102274233100002DEST_PATH_IMAGE042
Expression tThe set of all neighbours' matrixes constantly, lExpression the lIndividual neighbours' cellular,
Figure 772466DEST_PATH_IMAGE043
,
Figure 2011102274233100002DEST_PATH_IMAGE044
,
Figure 45315DEST_PATH_IMAGE045
Being sign of operation, is any computing in addition subtraction multiplication and division or other complex calculation, can determine according to different cities Characteristics of Development and condition;
S6 works as
Figure 2011102274233100002DEST_PATH_IMAGE046
The time,
Figure 961188DEST_PATH_IMAGE047
, unused land is converted into construction land; Otherwise,
Figure 2011102274233100002DEST_PATH_IMAGE048
, unused land does not transform; Wherein,
Figure 977685DEST_PATH_IMAGE049
Decide by urban development speed.
Adopt the conversion of map algebraically distance of obstacle among the above-mentioned steps S2-1, calculate the distance of each land used cellular respectively apart from one-level road and secondary road
Figure 475663DEST_PATH_IMAGE013
,
Compared with prior art, the present invention has following advantage and beneficial effect:
The inventive method is improved at the iterative process of traditional cellular automaton, and layering is carried out in cellular neighbours space, represents that with the form of matrix the neighbours in each orientation influence the factor factor of cellular conversion with other.Expansion Forecasting Methodology in city of the present invention has significant advantage, and at first, this method is better than the mode that cellular is judged in traditional pointwise, has significantly improved forecasting efficiency; In addition, introduced matrix in iterative process, simplified the difficulty of considering the distance factor in the expanding system of city and having simplified center cellular property determine, analog result and traditional traversal method are in full accord.
Description of drawings
Fig. 1 is mole type neighbours position views;
Fig. 2 is neighbours' matrix synoptic diagram;
Fig. 3 is the simcity synoptic diagram in certain city;
Fig. 4 be embodiment apart from the attribute synoptic diagram, wherein, figure (a) be among the embodiment each cellular apart from the one-level road apart from the attribute synoptic diagram, scheme (b) be among the embodiment each cellular apart from secondary road apart from the attribute synoptic diagram;
Fig. 5 is consuming time-neighbours' radius size fitted figure of embodiment.
Embodiment
Figure 3 shows that the simcity synoptic diagram in certain city, will be example with simcity synoptic diagram shown in Figure 3 below, adopt the inventive method respectively and come the simcity expansion based on the method for traditional cellular automaton.Comprise in the simcity that industrial land, merchant take ground, residential land, water body, road and unused land several types, mark off the planning key area according to city planning simultaneously; Choose the land used cellular apart from road distance and planning factors as the cellular attribute; Road changes the bigger and road influence degrees at different levels of the influence of construction land into to unused land and varies in size, and is transformed to the basis with map algebraically distance of obstacle, calculates each cellular respectively apart from the one-level road
Figure 886364DEST_PATH_IMAGE013
And the distance of secondary road
Figure 768869DEST_PATH_IMAGE014
, as shown in Figure 4; Definition land used cellular is apart from the road distance attribute
Figure 59036DEST_PATH_IMAGE015
, represent the combined influence of roads at different levels to the land used cellular, right simultaneously Carry out normalization, obtain
Figure 626469DEST_PATH_IMAGE012
The attribute layer, wherein,
Figure 47086DEST_PATH_IMAGE016
Be sign of operation, can be any computing in addition subtraction multiplication and division or other complex calculation, can determine according to different cities Characteristics of Development and condition.The artificial interference is one of factor of influence very important in the urban development, the limitation attribute of definition planning here layer
Figure 457339DEST_PATH_IMAGE018
As follows:
Figure 8273DEST_PATH_IMAGE019
In the method simcity expansion of employing based on traditional cellular automaton, consider planning factors and apart from the influence of road distance, judge that simultaneously neighbours' cellular is the construction land number, and adopt random number to judge whether the center cellular is converted into construction land, so that the result meets the randomness of real world development.Specific algorithm is that to last row of last column, each iteration judges that all whether the center cellular is unused land, if then carry out next step judgement, otherwise jumps into another circulation from first row, the first row iteration; If for unused land calculate its neighbours' cellular and other factor factor pairs its be converted to the effect degree of urban land S I, j T+1 'If this probability is greater than a certain random number, then the center element dysuria with lower abdominal colic turns to urban land.
The inventive method is an example with mole type (Moore type) neighbours and adiabatic border, at first defines neighbours' matrix and is
Figure 2011102274233100002DEST_PATH_IMAGE050
, then the definable transformation rule is:
Figure 871187DEST_PATH_IMAGE051
Wherein
Figure 95495DEST_PATH_IMAGE043
, ,
Figure 893873DEST_PATH_IMAGE045
Be sign of operation, can be any computing in addition subtraction multiplication and division or other complex calculation, can determine according to different cities Characteristics of Development and condition.Try to achieve according to following formula
Figure 244083DEST_PATH_IMAGE039
Be concrete numeric type, need corresponding with cellular state.Here adopt stochastic matrix to determine cellular state:
Figure 2011102274233100002DEST_PATH_IMAGE052
When the matrix operation result more than or equal to
Figure 694918DEST_PATH_IMAGE049
The time, unused land is converted into construction land, otherwise does not change.Wherein, Decide by urban development speed.Table 1 is depicted as the comparison consuming time of adopting the inventive method and the expansion of traditional cellular automaton simcity.
The comparison consuming time of table 1 the inventive method and traditional cellular automation method
Figure 269436DEST_PATH_IMAGE053
Adopt least square method to obtain the inventive method and traditional cellular automation method quadratic fit function consuming time, as follows:
Figure 2011102274233100002DEST_PATH_IMAGE054
Figure 2011102274233100002DEST_PATH_IMAGE055
Wherein, Be the consuming time of traditional cellular automation method;
Figure 293892DEST_PATH_IMAGE057
Be the consuming time of the inventive method; It is neighbours' radius.
Table 2 is consuming time-neighbours' radius size match table
? Method based on traditional cellular automaton The inventive method
Constant term 2.267 -3.67×10 -2
Once 8.79×10 -2 7.32×10 -2
Quadratic term — 7.50×10 -2
Residual 0.0643 0.0022
From table 1 and fitting result shown in Figure 5, at radius
Figure 545489DEST_PATH_IMAGE059
The time, adopt the inventive method iteration once take time less than method based on traditional cellular automaton.But along with the increase of radius, the once required time of the inventive method iteration significantly increases.Main cause is, though need to adopt the method for traversal based on the method for traditional cellular automaton, causes its iteration time once longer, and the increase of radius is very little to the influence of traversal; And the inventive method needs to redefine each neighbours' matrix in each step-length, and along with the increase of radius, needs neighbours' matrix of definition to be quadratic power and increases, and is as shown in table 2, so trend along with the radius rising consuming time is obvious.From fitting result, based on being once linear relationship between the consuming time and radius size of the method for traditional cellular automaton, and be quadratic function relation between the consuming time and radius size of the inventive method.Because in actual applications, choose r=2 or 3 usually,
Figure 2011102274233100002DEST_PATH_IMAGE060
Situation very rare, so in the general applied research, if
Figure 519261DEST_PATH_IMAGE059
The time, the inventive method still is better than the method based on traditional cellular automaton.

Claims (2)

1. the city expansion analogy method based on cellular automaton is characterized in that, may further comprise the steps:
S1 is according to the city simulation drawing, urban land is divided into industrial land, merchant takes six types of ground, residential land, water body, road and unused lands, marks off according to city planning and plans the key area;
The definition of S2 land used cellular attribute layer:
S2-1 definition land used cellular is apart from road distance attribute layer
Figure 332134DEST_PATH_IMAGE001
:
Calculate the distance of each unused land cellular respectively apart from one-level road and secondary road ,
Figure 872444DEST_PATH_IMAGE003
, and definition land used cellular is apart from the road distance attribute , wherein,
Figure 652181DEST_PATH_IMAGE005
Be sign of operation, can determine according to different cities Characteristics of Development and condition;
Figure 2011102274233100001DEST_PATH_IMAGE006
Be cellular space size; Right simultaneously Carry out normalization and obtain the land used cellular apart from road distance attribute layer
Figure 986396DEST_PATH_IMAGE001
The planning limitation attribute layer of S2-2 definition unused land cellular
Figure 2011102274233100001DEST_PATH_IMAGE008
--:
Figure 497274DEST_PATH_IMAGE009
Wherein,
Figure 2011102274233100001DEST_PATH_IMAGE010
Expression is in the cellular space the iRow, the jThe cellular of row,
Figure 701991DEST_PATH_IMAGE011
S3 definition land used cellular exists
Figure 2011102274233100001DEST_PATH_IMAGE012
Neighbours' matrix constantly
Figure 87842DEST_PATH_IMAGE013
:
Figure 756720DEST_PATH_IMAGE015
Wherein,
rRadius for neighbours' scope;
Figure 2011102274233100001DEST_PATH_IMAGE016
,
Figure 687767DEST_PATH_IMAGE017
Represent the in neighbours' scope respectively
Figure 2011102274233100001DEST_PATH_IMAGE018
Row, the
Figure 2011102274233100001DEST_PATH_IMAGE019
The cellular of row, ,
Figure 2011102274233100001DEST_PATH_IMAGE022
Expression
Figure 6806DEST_PATH_IMAGE012
Constantly
Figure 530191DEST_PATH_IMAGE010
Place's cellular
Figure 897719DEST_PATH_IMAGE023
Figure 2011102274233100001DEST_PATH_IMAGE024
Individual neighbours' cellular,
Figure 827760DEST_PATH_IMAGE025
,
Figure 2011102274233100001DEST_PATH_IMAGE026
Expression
Figure 40566DEST_PATH_IMAGE012
Constantly Place's cellular
Figure 935076DEST_PATH_IMAGE024
Individual neighbours' cellular, from top to bottom
Figure 13891DEST_PATH_IMAGE016
Increase successively, from left to right
Figure 449551DEST_PATH_IMAGE017
Increase successively;
Figure 221198DEST_PATH_IMAGE027
For
Figure 2011102274233100001DEST_PATH_IMAGE028
Increase the extended matrix on border,
Figure 857322DEST_PATH_IMAGE028
For the unused land cellular exists State constantly;
S4 is right
Figure 29995DEST_PATH_IMAGE012
Moment neighbours' matrix
Figure 159494DEST_PATH_IMAGE013
Carry out the iteration of a step-length, obtain the unused land cellular and exist
Figure 597428DEST_PATH_IMAGE029
State constantly
Figure 2011102274233100001DEST_PATH_IMAGE030
, wherein,
Figure 955728DEST_PATH_IMAGE031
The representing matrix computing;
S5 is according to neighbours' matrix
Figure 116713DEST_PATH_IMAGE013
, calculate the transition probability that the unused land cellular is converted into urban land
Figure 2011102274233100001DEST_PATH_IMAGE032
:
Wherein,
Figure 2011102274233100001DEST_PATH_IMAGE034
Represent the distance of some neighbours' matrixes apart from the center cellular,
Figure 93077DEST_PATH_IMAGE035
Expression tThe set of all neighbours' matrixes constantly, lExpression the lIndividual neighbours' cellular,
Figure 2011102274233100001DEST_PATH_IMAGE036
,
Figure 504335DEST_PATH_IMAGE037
,
Figure 2011102274233100001DEST_PATH_IMAGE038
Be sign of operation, can determine according to different cities Characteristics of Development and condition;
S6 works as
Figure 503515DEST_PATH_IMAGE039
The time,
Figure 2011102274233100001DEST_PATH_IMAGE040
, unused land is converted into construction land; Otherwise,
Figure 479211DEST_PATH_IMAGE041
, unused land does not transform; Wherein,
Figure 2011102274233100001DEST_PATH_IMAGE042
Decide by urban development speed.
2. the city expansion analogy method based on cellular automaton according to claim 1 is characterized in that:
Adopt the conversion of map algebraically distance of obstacle among the described step S2-1, calculate the distance of each land used cellular respectively apart from one-level road and secondary road
Figure 829421DEST_PATH_IMAGE002
,
Figure 44371DEST_PATH_IMAGE003
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CN111797523A (en) * 2020-06-30 2020-10-20 南京图申图信息科技有限公司 Land use change-oriented multi-level vector cellular automaton modeling method

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CN104156537A (en) * 2014-08-19 2014-11-19 中山大学 Cellular automaton urban growth simulating method based on random forest
CN104992041A (en) * 2015-08-06 2015-10-21 武汉大学 City expansion boundary prediction method based on space syntax
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CN106251014A (en) * 2016-07-29 2016-12-21 西南交通大学 Development of urban space based on SVM GCA simulation and Forecasting Methodology
CN110009257A (en) * 2019-04-17 2019-07-12 青岛大学 Multiple dimensioned variable window cellular Automation Model based on urban traffic blocking sprawling analysis
CN110009257B (en) * 2019-04-17 2023-09-08 青岛大学 Multi-scale variable window cellular automaton model based on urban traffic congestion spreading analysis
CN110688726A (en) * 2019-08-19 2020-01-14 华南师范大学 Spatial orientation self-adaptive city expansion simulation method, system and storage medium
CN110688726B (en) * 2019-08-19 2023-01-10 华南师范大学 Spatial orientation self-adaptive city expansion simulation method, system and storage medium
CN111797523A (en) * 2020-06-30 2020-10-20 南京图申图信息科技有限公司 Land use change-oriented multi-level vector cellular automaton modeling method
CN111797523B (en) * 2020-06-30 2024-03-22 南京图申图信息科技有限公司 Land utilization change-oriented multi-level vector cellular automaton modeling method

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Application publication date: 20111123