the asa-cssa-sssa international annual meetings (november 12-16, 2006) urban growth modeling...

The ASA-CSSA-SSSA International Annual Meetings (November 12-16, 2006)

Urban Growth ModelingUrban Growth Modeling with Artificial Intelligence TechniquesArtificial Intelligence Techniques

Dr. Jie Shan and Sharaf Al-khederGeomatics Engineering School of Civil Engineering Purdue University [email protected]


Outline (1)

Introduction. Statement of the problem. Research objectives. Literature review. Problem solving approach. Crisp cellular automata modeling. Calibration with genetic algorithms.


Outline (2)

Fuzzy guided cellular automata modeling.

Neural networks for boundary modeling.

Discussion and analysis. Concluding remarks. Recommendations and future work.


Introduction: motivationmotivation

Athens urban growthAthens urban growth

18 million 18 million in this in this area!area!

Los AngelesLos Angeles

City population excessive increase worldwide. infrastructure services demand.

Cairo 1965Cairo 1965

Cairo 1998Cairo 1998

Urban modeling is Urban modeling is a necessity!a necessity!

Mexico city!!Mexico city!!


Introduction: Urban growth factsUrban growth facts

1970 to 1990, more than 30,000 sq.m. of U.S. rural land became urban (Statesman Journal, 1991).

1969 to 1989, U.S. population increased by 22.5%, and VMT (vehicles miles traveled) by 98.4% (Federal Highway Administration, 1991).

1983 to 1987, U.S. population increased by 9.2 million, and # of cars and trucks increased by 20.1 millions (Statistical Abstract of United States, 1989).


Statement of the problem

Excessive unplanned urban growth. Absence of a standard urban growth

model and a robust calibration module.

Evaluation strategy. Satellite imagery

availability with minimal cost.


Research objectives

Cellular automata, imagery, & other inputs for urban growth modeling.

Imagery based design to minimize input data and modeling uncertainty.

A spatiotemporal algorithm besides genetic algorithms to enhance calibration efficiency.

Fuzzy logic theory for continuous urban growth modeling.

Neural networks for boundary modeling.


Literature review: GeneralGeneral

Two types of urban models: Scale-based models: - Specific [e.g., BASS II (Bay Area Simulation

System) for San Francisco, Landis(1992)].

- General [e.g., HILT (Human Induced Land

Transformations), Kirtland, (1993) ]. Model’s applicability:

- Physical aspects [e.g., Alonso, (1978)].

- Social aspects [e.g., Jacobs, (1961)].


Literature review: Cellular AutomataCellular Automata

Fastest emerging urban dynamic models.Fastest emerging urban dynamic models. Multi-dimensional discrete system. Multi-dimensional discrete system. Uses simple yet accurate transition rules Uses simple yet accurate transition rules

for urban modeling.for urban modeling. Uses social and physical factors.Uses social and physical factors. Fits urban process spatially in imagery.Fits urban process spatially in imagery. Better in urban modelling than Better in urban modelling than

mathematical models mathematical models (Batty and Xie, 1994a)(Batty and Xie, 1994a)..



Earliest implementation of CA for geographic systems by Tobler (1979).

Couclelis (1985) provided theoretical framework for CA in complex geographic problems [e.g., structure]

CA first used for urban modeling by White et al. (White and Engelen, 1992a; 1992b)

CA used by Batty and Xie (1994a) for modeling of Cardiff (UK) and Savannah (GA).



SLEUTH (Slope, Land use, Exclusion, Urban SLEUTH (Slope, Land use, Exclusion, Urban extent, Transportation, Hillshade), extent, Transportation, Hillshade), Clarke et Clarke et al. (1997)al. (1997) Four types of data: land cover, slope, Four types of data: land cover, slope,

transportation, and protected lands.transportation, and protected lands. Five factors for urban growth (e.g., Five factors for urban growth (e.g., SLOPE and SLOPE and

ROAD-GRAVITY.ROAD-GRAVITY. Complex transition rules.Complex transition rules. Visual and statistical tests for calibration.Visual and statistical tests for calibration.

Clarke and Gydos (1998)Clarke and Gydos (1998) applied “SLEUTH” applied “SLEUTH” for urban growth in San Francisco region & for urban growth in San Francisco region & Washington D.C/Baltimore.Washington D.C/Baltimore.



Yang and Lo (2003)Yang and Lo (2003) used “SLEUTH” to test used “SLEUTH” to test urban modeling scenarios in Atlanta, GA.urban modeling scenarios in Atlanta, GA.

Wu and Webster (1998)Wu and Webster (1998) used Multi Criteria used Multi Criteria Evaluation analysis to identify CA Evaluation analysis to identify CA parameter values.parameter values.

Neural networks used by Neural networks used by Li and Yeh (2001)Li and Yeh (2001) to calibrate CA rules.to calibrate CA rules.

Wu (2002)Wu (2002) development probability based development probability based CA model.CA model.


Literature review: GeneticsGenetics AlgorithmsAlgorithms

Recent direction in CA calibration.Recent direction in CA calibration. Colonna et al (1998)Colonna et al (1998) used GA to used GA to

generate new rules for CA to simulate generate new rules for CA to simulate the land use changes of Rome, Italy.the land use changes of Rome, Italy.

Wong et al (2001)Wong et al (2001): GA for household : GA for household and employment distributions’ and employment distributions’ parameters for Hong Kong. parameters for Hong Kong.

Goldstein (2003):Goldstein (2003): SLEUTH calibration.SLEUTH calibration.


Literature review: Fuzzy Logic (FL)Fuzzy Logic (FL)

Extend binary theory for continuous status.Extend binary theory for continuous status. FL for geographic boundaries with high FL for geographic boundaries with high

spatial variability spatial variability (Wang and Hall, 1996)(Wang and Hall, 1996).. Gradual change in land use conditions over Gradual change in land use conditions over

time time (Dragicevic & Marceau, 2000)(Dragicevic & Marceau, 2000).. FL in FL in Wu (1996; 1998)Wu (1996; 1998) work to define CA work to define CA

transition rules for land conversion.transition rules for land conversion. Liu and Phinn (2003)Liu and Phinn (2003) identify pixel state identify pixel state

change with a fuzzy membership function. change with a fuzzy membership function.


Literature review: Neural NetworksNeural Networks (NN)(NN)

NN to mimic biological neural networks.NN to mimic biological neural networks. NN simulate geo-spatial complex systems NN simulate geo-spatial complex systems

(Openshaw, 1998)(Openshaw, 1998).. Liu (2000)Liu (2000) used NN to detect the change used NN to detect the change

from non-urban to urban land use.from non-urban to urban land use. Yeh and Li (2002)Yeh and Li (2002): NN with CA for urban : NN with CA for urban

simulation to model land use change.simulation to model land use change. NN with GIS to forecast land use change NN with GIS to forecast land use change

(Pijanowski et al., 2002)(Pijanowski et al., 2002)..


Literature review: Unsolved issuesUnsolved issues

A standard model for defining & calibrating A standard model for defining & calibrating CA transition rules is absent in literature.CA transition rules is absent in literature.

Most models do not have an explicit transition Most models do not have an explicit transition rules rules [e.g., Wu model, 2002)][e.g., Wu model, 2002)]..

CA models do not use multispectral imagery CA models do not use multispectral imagery for urban extent or other data directly. They for urban extent or other data directly. They use cadastral maps instead. use cadastral maps instead.

Time consuming calibration Time consuming calibration (SLEUTH :135 days)(SLEUTH :135 days)..

No effective search methods for calibration. No effective search methods for calibration.


Literature review: Unsolved issuesUnsolved issues

An effective evaluation scheme is needed to An effective evaluation scheme is needed to help select the best rules.help select the best rules.

Spatial calibration is not included in most CA Spatial calibration is not included in most CA calibration algorithms to date.calibration algorithms to date.

A fuzzy guided cellular automata model is A fuzzy guided cellular automata model is needed, where CA rules can be designed as needed, where CA rules can be designed as a function of the FL output. a function of the FL output.

Calibration in fuzzy CA urban modeling Calibration in fuzzy CA urban modeling needs to be clearly identified.needs to be clearly identified.


Problem solving approach

Multitemporal Multitemporal satellitesatellite

imagery imagery

Other input data Other input data (Population, DEM, road networks)(Population, DEM, road networks)

Fuzzy CA model

Simulated CA images

Simulated Fuzzy CA images

Ground truth

imagery

Calibration

Urban growth modeling

CRISP CACRISP CA FUZZY CAFUZZY CA

Crisp CA model


Problem solving approach

Multitemporal Multitemporal satellitesatellite

imagery imagery

Other input data Other input data (Population, DEM, road networks)(Population, DEM, road networks)

Crisp CA model

Simulated CA images

Ground truth

imagery

Calibration

Urban growth modelingCA-GACA-GA

GA automated calibration

NN model

NN NN modelingmodeling

Boundary modeling


Crisp CA modeling: outline CA theory.CA theory. Artificial city modeling.Artificial city modeling. CA based urban growth model design.CA based urban growth model design. A spatiotemporal calibration algorithm.A spatiotemporal calibration algorithm. Design an evaluation scheme. Design an evaluation scheme. Indianapolis growth modeling.Indianapolis growth modeling. Integrate with GIS, such as ArcGIS (VBA).Integrate with GIS, such as ArcGIS (VBA). Analysis and discussion.Analysis and discussion.


Crisp CA modeling: theory By Ulam and von Neumann in 1940s to study By Ulam and von Neumann in 1940s to study

complex systems complex systems (von Neumann, 1966)(von Neumann, 1966).. 2-dimensional CA for our work.2-dimensional CA for our work. Four CA components: Four CA components:

pixels;pixels; States (e.g., Water);States (e.g., Water); Neighborhood:Neighborhood:

33

)(

1,1

)(

,1

)(

1,1

)(

1,

)(

,

)(

1,

)(

1,1

)(

,1

)(

1,1

)(

,

x

t

ji

t

ji

t

ji

t

ji

t

ji

t

ji

t

ji

t

ji

t

ji

t

ji

aaa

aaa

aaa

A

yyxx ),(

ShapeShape

States functionStates function


Four CA components (cont’d)Four CA components (cont’d) Transition rules such as IF-THEN rulesTransition rules such as IF-THEN rules Future state of a pixel: Future state of a pixel:

Example: Example: (Game of Life)(Game of Life)

Crisp CA modeling: theory

)( )(

,

t

jiA

1. IF 1 inactive pixel surrounded by 3 active pixels, activate.

2. IF surrounded by 2 or 3 pixels, remains active.

3. Else, become or stay inactive.


Crisp CA modeling: Artificial city

Effect of land use. Effect of land use. E.g.,E.g., roads drive urban growth. roads drive urban growth. 200x200 pixels input image. 200x200 pixels input image. CA rulesCA rules (3x3 (3x3 neighborhood):neighborhood): IF test pixel is urban, river, road, IF test pixel is urban, river, road,

lake or has pollution source in the lake or has pollution source in the

neighborhood THEN no change.neighborhood THEN no change. IF test pixel is non-urban, it IF test pixel is non-urban, it

changes to urban if in neighborhoodchanges to urban if in neighborhood Three of more urban pixels. Three of more urban pixels. At least one road AND one urban pixels. At least one road AND one urban pixels. At least one lake pixel AND one urban pixel.At least one lake pixel AND one urban pixel.


Crisp CA modeling: Artificial city

CA CA simulates urban simulates urban

growth at 0, 25, 50 growth at 0, 25, 50

and 60 iterations.and 60 iterations. Effect of road &Effect of road &

lakes in driving lakes in driving

growth.growth. Pollution source Pollution source

buffer zones.buffer zones. Conservation of water.Conservation of water.


Crisp CA model design: Data Indianapolis growth modelingIndianapolis growth modeling Excessive growth from 1973 to 2003.Excessive growth from 1973 to 2003. MSS/TM MSS/TM imagesimages (1973, 1982, 1987, 1992 and (1973, 1982, 1987, 1992 and

2003) 2003) and and population densitypopulation density input data input data.. Images projected to UTM NAD1983 zone 16N.Images projected to UTM NAD1983 zone 16N. Ground reference data to classify images.Ground reference data to classify images. 7 classes : water, road, commercial, forest, 7 classes : water, road, commercial, forest,

residential, pasture and row crops.residential, pasture and row crops. Commercial and residential as urban class.Commercial and residential as urban class.


Crisp CA model design: Data

1990 & 2000 population census tract maps.1990 & 2000 population census tract maps. Population density is computed per tract. Population density is computed per tract. Exponential model between density and distance Exponential model between density and distance

from city center for 1990 and 2000.from city center for 1990 and 2000.

Parameters (A & B) are updated Parameters (A & B) are updated

yearly according to rate of change yearly according to rate of change

(1990 & 2000).(1990 & 2000). population density grids as input.population density grids as input.

B DISTANCEPOPULATION DENSITY A e

19901990


Crisp CA model design: Rules CA rules represent land use & constrains effect.CA rules represent land use & constrains effect. CA rulesCA rules (3x3 neighborhood): (3x3 neighborhood): IF test pixel is water, road OR urban (residential IF test pixel is water, road OR urban (residential

or commercial) THEN no change. or commercial) THEN no change. IF test pixel is nonurban (forest, pasture OR row IF test pixel is nonurban (forest, pasture OR row

crops) THEN It becomes urban if its: crops) THEN It becomes urban if its: Population density Population density ≥ ≥ threshold (threshold (PPii) AND has ) AND has

neighboring residential pixels # neighboring residential pixels # ≥≥ threshold ( threshold (RRii). ).

Population density Population density ≥≥ threshold ( threshold (PPii) AND has ) AND has

neighboring commercial pixels # neighboring commercial pixels # ≥≥ threshold ( threshold (CCii).). PPii continuous [0:0.1:3], R continuous [0:0.1:3], Ri i & C& Ci i [0:1:8][0:1:8]


Crisp CA model design: EvaluationEvaluation

3 evaluation measures for each rule 3 evaluation measures for each rule combination combination (P,R,C)(P,R,C)ii ::

1. Fitness:1. Fitness:

2. Type I error:2. Type I error:

Pixels that urban in real but Pixels that urban in real but

nonurban in simulated. nonurban in simulated.

3. Type II error:3. Type II error:

Pixels that nonurban in real Pixels that nonurban in real

but urban in simulated. but urban in simulated.

%100___

__

counturbantruthGround

counturbanSimulatedFitness


Crisp CA model design: CalibrationCalibration

Spatial & temporalSpatial & temporal

calibration modules.calibration modules. Spatial calibration:Spatial calibration:

- Site specific features.- Site specific features.

- Evaluation based on township.- Evaluation based on township.

- Same rules, variable values.- Same rules, variable values. Temporal calibration:Temporal calibration:

- Rule change over time.- Rule change over time.

- Variable urban growth pattern. - Variable urban growth pattern.


Crisp CA model design: ModelingModeling

CA Modeling in ArcGIS through VBA.CA Modeling in ArcGIS through VBA. Two multitemporal imagery sets:Two multitemporal imagery sets: - Training images:- Training images: calibration. calibration.

- Testing images:- Testing images: prediction & validation. prediction & validation.

CA runs for all combinations CA runs for all combinations (P,R,C)(P,R,C)ii from 1973 till from 1973 till

19821982, first calibration year, and evaluated., first calibration year, and evaluated. Evaluation results arranged in descending order Evaluation results arranged in descending order

(ratio of Type I & II sum to total pixel count ). (ratio of Type I & II sum to total pixel count ). Rule with Rule with min. avg. error & fitness closest to 100% min. avg. error & fitness closest to 100%

(±10%) is selected(±10%) is selected for each township.for each township.


Crisp CA model design: ModelingModeling

Recalibration at 1987.Recalibration at 1987. Best rules at 1987 to Best rules at 1987 to

predict 1992 (5 years).predict 1992 (5 years). Calibration at 1992 Calibration at 1992

to predict 2003 (11 years).to predict 2003 (11 years). Final calibration at 2003 Final calibration at 2003

for future prediction for future prediction

(2010 and 2020).(2010 and 2020). Close urban pattern match.Close urban pattern match.

Simulation


Crisp CA model design: ModelingModeling Spatial calibration effect.Spatial calibration effect. Close Close

fitness fitness

to 100%.to 100%. Small Small

average average

errors errors

24-25%.24-25%.

1992 Prediction sample

Prediction


Crisp CA modeling: AnalysisAnalysis

Better connectivity for modeling

0

1

2

3

4

5

6

7

8

9

10

0 2 4 6 8 10 12 14 16 18 20 22 24

Township#

Re

sid

en

tia

l ru

le v

alu

e

1982 1987 1992Rule vary spatially

0

1

2

3

4

5

6

7

8

9

10

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Township#

Resid

en

tial

rule

valu

e

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

Resid

en

tial

co

un

t

Rule value

Count

Rule vs. class count 1992 calibration


Crisp CA modeling: AnalysisAnalysis

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

11000

12000

13000

14000

0 100 200 300 400 500 600 700Iteration#

Err

or

TypI

TypeII

Average error

Rule redesign 1987

calibration

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Township#

Err

or(

%)

0

5000

10000

15000

20000

25000

Urb

an c

ou

nt

TypeI

Urban

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Township#

Err

or(

%)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000

No

nu

rban

co

un

t

TypeII

Nonurban

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Township#

Err

or(

%)

0

5000

10000

15000

20000

25000

30000

To

tal c

ou

nt

Weighted error

Count

Type I vs. urban

Type II vs. nonurbanAvg. vs. total count


Genetic algorithms calibration: MotivationMotivation

Introduced by Introduced by Holland (1975)Holland (1975) to mimic to mimic evolutionary processes in nature.evolutionary processes in nature.

Manipulates a set of feasible solutions to find Manipulates a set of feasible solutions to find an optimal solution.an optimal solution.

Effective for complex search spaces.Effective for complex search spaces. Why GA?Why GA? CA is computationally extensive CA is computationally extensive

(lager # of combinations, need days). (lager # of combinations, need days). Increase calibration time with parameter #s. Increase calibration time with parameter #s. Assign higher weights for good solutions.Assign higher weights for good solutions.


Genetic algorithms calibration: designdesign

GA extends CA modelGA extends CA model

to automate calibration to automate calibration

while searching for while searching for

optimal rule values. optimal rule values. GA operations:GA operations:

- - initial population design; initial population design;

- selection; - selection;

- crossover and mutation.- crossover and mutation.


Genetic algorithms calibration: initial populationinitial population designdesign

CA transition rules design is used.CA transition rules design is used. Each combination of Each combination of (R,C,P)(R,C,P)ii presents a presents a

string in the initial population pool.string in the initial population pool. 30 strings for each township.30 strings for each township. Binary encoding.Binary encoding.

String exampleString example


Genetic algorithms calibration: initial populationinitial population designdesign

CA run for all 30 strings for evaluation CA run for all 30 strings for evaluation (fitness, Type I and II errors).(fitness, Type I and II errors).

Objective function (based on modeling errors) Objective function (based on modeling errors) to guide GA to optimal solution:to guide GA to optimal solution:

Total modeling error (urban count and Total modeling error (urban count and structure) per township to be minimized.structure) per township to be minimized.

ErrorIIGAErrorIGAfunctionobjectiveGA ____

countTotal

TypeIITypeIErrorIIGA

__

%)100(_ fitnessAbsErrorIGA deviation from 100%, urban count

Modeling errors, urban pattern


Genetic algorithms calibration: Elitism and Rank SelectionElitism and Rank Selection

Strings ordered based on GA objective function Strings ordered based on GA objective function in ascending order (min. to max.).in ascending order (min. to max.).

String with lowest objective function has a rank String with lowest objective function has a rank of 30, the second one 29,etc.of 30, the second one 29,etc.

Selection probabilitySelection probability

Expected count:Expected count:

Final countFinal count

f

fpselect i

i

ipselect30

Sample calculation


Genetic algorithms calibration: Elitism and Rank SelectionElitism and Rank Selection

The best 6 strings in terms of objective The best 6 strings in terms of objective function are copied directly to next function are copied directly to next generation (elitism).generation (elitism).

The rest 24 strings are selected using rank The rest 24 strings are selected using rank selection (string count).selection (string count).

This will end the selection process with a This will end the selection process with a total of 30 strings. total of 30 strings.

Bad strings are not selected (search is Bad strings are not selected (search is directed to good strings).directed to good strings).


Genetic algorithms calibration: Crossover and mutation Crossover and mutation

Crossover:Crossover: a pair of strings meet to produce a pair of strings meet to produce offspring (same or better quality). offspring (same or better quality).

Crossover probability is selected as 80% where Crossover probability is selected as 80% where 24 strings are crossed over:24 strings are crossed over:

6 elitism strings crossedover to produce new 6 elitism strings crossedover to produce new

6 strings to be added with a total of 12 strings.6 strings to be added with a total of 12 strings. First 18 strings First 18 strings

in the selectionin the selection

are crossedover.are crossedover.

Crossover point


Genetic algorithms calibration: Crossover and mutation Crossover and mutation

After crossover: new 30 strings produced. After crossover: new 30 strings produced. Mutation: inversion of string bits for diverse Mutation: inversion of string bits for diverse

structure and not stuck with bad solutions. structure and not stuck with bad solutions. Last stage in finalizing new population.Last stage in finalizing new population. Mutation for best 6 strings for Mutation for best 6 strings for (R,C)(R,C)ii by by

random addition of +1 or -1.random addition of +1 or -1.


Genetic algorithms calibration: Modeling and Evaluation Modeling and Evaluation

CA run for new population CA run for new population

for objective values. for objective values. Repeat GA process for Repeat GA process for

20 iterations. 20 iterations. Rules with minimum GA Rules with minimum GA

objective function values objective function values

are selected per township.are selected per township. Close match with reality & Close match with reality &

crisp CA.crisp CA.



Minimum GA objectiveMinimum GA objective

value at early stagevalue at early stageTownship#9

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Generation#

GA

ob

jec

tiv

e f

un

cti

on

198719922003



Short running time for GA (6 hrs. avg.) compared to Short running time for GA (6 hrs. avg.) compared to crisp CA (4 days).crisp CA (4 days).

Close modeling results to CA.Close modeling results to CA.

60

80

100

120

140

160

180

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Township#

Fit

nes

s (%

)

Fitness-GAFitness-crisp CA

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Township#

Typ

eI e

rro

r (%

)

TypeI-GATypeI-crisp CA

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Township#

Ty

pe

II e

rro

r (%

)

TypeII-GA

TypeII-crisp CA

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Township#

Ave

rag

e er

ror

(%)

Average error-GA

Average error-crisp CA

1987 calibration1992 prediction


Fuzzy guided CA modeling: MotivationMotivation

Crisp CA is binary (develop/undeveloped), urban Crisp CA is binary (develop/undeveloped), urban growth is continuous in space. growth is continuous in space.

A pixel might be partially developed.A pixel might be partially developed. Fuzzy logic identify pixel development potential.Fuzzy logic identify pixel development potential. Level of development identifies Level of development identifies # of urban pixels# of urban pixels

in neighborhood for test pixel to develop.in neighborhood for test pixel to develop. Fuzzy logic to provide initial values for CA rule Fuzzy logic to provide initial values for CA rule

calibration.calibration. Crisp CA is extended with fuzzy logic to achieve Crisp CA is extended with fuzzy logic to achieve

the continuous condition in space.the continuous condition in space.


Fuzzy guided CA modeling: TheoryTheory

Fuzzy logic first introduced by Zadeh from Fuzzy logic first introduced by Zadeh from University of California, Berkeley in 1965.University of California, Berkeley in 1965.

Fuzzy set is a continuous interval bounded by 0 Fuzzy set is a continuous interval bounded by 0 and 1 values:and 1 values:

The notation of a singleton: The notation of a singleton:

x: element in the fuzzy set, x: element in the fuzzy set,

: membership degree.: membership degree. Fuzzy set for all x is:Fuzzy set for all x is:

1, 0.0 0.3

( ) 5 2.5, 0.3 0.5

0, 0.5 x 1.0

x

x x x

( ) [0,1]x

( )( , ( )) , XxA x x or xx

)(x

iX

( )_ = ( )i

i

x

xFuzzy set x


Fuzzy guided CA modeling: designdesign

To design Fuzzy CA with artificial city.To design Fuzzy CA with artificial city. 3 Inputs:3 Inputs:

Membership function

Input image

Distance Distance to city to city centercenter

DEM

OUTPUT:OUTPUT: urban urban neighborhood pixels neighborhood pixels ##

for development.for development.



FUZZY RULES FUZZY RULES FUZZIFICATION FUZZIFICATION

Min-max (Mamdani method)Min-max (Mamdani method)

DEFUZZIFICATION (COA)DEFUZZIFICATION (COA)

For every pixel:For every pixel:

1.1. DEM value.DEM value.

2.2. Distance to Distance to city centercity center

OUTPUTOUTPUT

N

iiout

N

iiouti

y

yyy

1

1

*

*

)(

)(

*y

min

max

DEMDEMDistanceDistance OutputOutput

y yy

:Fuzzy output:Fuzzy output*y



Fuzzy output to design Fuzzy output to design CA rulesCA rules:: IF a pixel is urban, river, road, lake or has pollution IF a pixel is urban, river, road, lake or has pollution

source in neighborhood, THEN no change in its state. source in neighborhood, THEN no change in its state. IF a non-urban pixel has IF a non-urban pixel has ≥ ≥ urban pixels in its urban pixels in its

neighborhood, THEN change it to urban. neighborhood, THEN change it to urban. IF a non-urban pixel has road or lake in its IF a non-urban pixel has road or lake in its

neighborhood AND has neighborhood AND has ≥≥ ( -2) urban pixels in ( -2) urban pixels in neighborhood, THEN change it to urban.neighborhood, THEN change it to urban.

*y

*y


Fuzzy guided CA modeling: modelingmodeling

Step#Step#00

Step#Step#2525

Step#Step#5050

Step#Step#6060

Elevation effect

Road effect


Fuzzy guided CA modeling: IndianapolisIndianapolis

3 inputs beside the imagery are used.3 inputs beside the imagery are used. Fuzzy rules:Fuzzy rules:

MembershipMembership

functionsfunctions for inputs. for inputs. Fuzzy Fuzzy outputoutput represents neighborhood urban represents neighborhood urban

pixels for a test pixel to develop. pixels for a test pixel to develop.

DEM Roads

PopulationPopulation



CA rulesCA rules (function of fuzzy output): (function of fuzzy output): IF a pixel is road, water, commercial or residential, THEN no IF a pixel is road, water, commercial or residential, THEN no

change. change. IF nonurban (forest, pasture or row crops) pixel has IF nonurban (forest, pasture or row crops) pixel has ≥ ≥

residential pixels in neighborhood, THEN change to residential pixels in neighborhood, THEN change to residential.residential.

IF non-urban has IF non-urban has ≥ ≥ commercial pixels in neighborhood, commercial pixels in neighborhood, THEN change to commercial.THEN change to commercial.

IF commercial and residential pixels sum of non-urban pixel in IF commercial and residential pixels sum of non-urban pixel in neighborhood is neighborhood is ≥ ≥ pixels, pixels,

THEN change to whichever is greater.THEN change to whichever is greater. Fuzzy output approximate rule values.Fuzzy output approximate rule values.

RY

CY

SY

SS

CC

RR

yY

yY

yY

*

*

*



A small search range A small search range

based on fuzzy output. based on fuzzy output.

Spatial calibration Spatial calibration (township).(township).

Rule set with min. average Rule set with min. average

error & close fitness to error & close fitness to

100% is selected.100% is selected. CA run for calibration

and prediction

3,3 CR 30 S


Fuzzy guided CA modeling: AnalysisAnalysis

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

0 2 4 6 8 10 12 14 16 18 20 22 24

Township

Ave

rage

Err

or(%

)

calib1982 calib1987calib1992 calib2003

-3

-2

-1

0

1

2

3

4

5

6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Township#

Res

iden

tial

ru

le c

alib

rati

on

co

effi

cien

ts Res-60m-1987

Res-30m-1987

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Township#

Ty

pe

II

Err

or

(%)

TypeII-60-1992

TypeII-30-1992

Conclusions in crisp CA still valid.Conclusions in crisp CA still valid. Avg. error smaller at city townships.Avg. error smaller at city townships. Testing with 30m vs. 60m. More restrict rules for 30m. Smaller errors for 30m.

Rules, 30 vs. 60mTypeII 30 vs. 60m

Avg. error, 60m


Neural networks for boundary modeling

City boundary expansion indicates gross change of City boundary expansion indicates gross change of phenomena (e.g., political boundary).phenomena (e.g., political boundary).

Availability of historic imagery is problem.Availability of historic imagery is problem. City boundaries were digitized from classified City boundaries were digitized from classified

satellite images.satellite images. 3 datasets were used for NN training.3 datasets were used for NN training. Back Propagation (BPNN) algorithm for training.Back Propagation (BPNN) algorithm for training. Short (3 yr) and long-term (8 yr) predictions.Short (3 yr) and long-term (8 yr) predictions. Directional NN training.Directional NN training. Evaluation (root mean square).Evaluation (root mean square).



6 years boundaries of Indianapolis were digitized on 6 years boundaries of Indianapolis were digitized on classified satellite images. classified satellite images.

6 measurements6 measurements

at 3 degree radial interval.at 3 degree radial interval. A matrix of 120 A matrix of 120

by 6.by 6. 3 datasets 3 datasets

((RBFNRBFN):):

Real data, 1 & 5 Real data, 1 & 5

year interpolation. year interpolation.



Two-layer Back Propagation.Two-layer Back Propagation. 2003 from 2000 (short-term).2003 from 2000 (short-term). Same results for 3 datasets.Same results for 3 datasets. RMS= 3095.37 m.RMS= 3095.37 m.

Long term (8 yrs) prediction 2000 Long term (8 yrs) prediction 2000

from 1992 (long term).from 1992 (long term). Same performance for 3 datasets.Same performance for 3 datasets. RMS= 3713.28 m.RMS= 3713.28 m.

20032003

20002000



Growth in all directions Growth in all directions

is not the same is not the same

(directional growth).(directional growth). Higher weights for higher Higher weights for higher

growth directions.growth directions.

LakesLakes

RoadRoad

PopulationPopulation

Directional Directional factors:factors:


Directional boundary modeling

Closer match.Closer match. 2003 from 2000.2003 from 2000. RMS=1226.49m.RMS=1226.49m.

2000 from 1992.2000 from 1992. Weights effect.Weights effect. Better results.Better results. RMS=1650.01mRMS=1650.01m

20032003

20002000


Concluding remarks Artificial intelligence techniques fit the Artificial intelligence techniques fit the

complex nature of urban process.complex nature of urban process. Model design reduces the need for large Model design reduces the need for large

input data and modeling uncertainty.input data and modeling uncertainty. Simple, yet accurate transition rules easily Simple, yet accurate transition rules easily

interpreted by end users.interpreted by end users. Spatial calibration, township basis, took into Spatial calibration, township basis, took into

account site specific features.account site specific features. Temporal calibrationTemporal calibration importance.importance.


Concluding remarks Evaluation with 3 measures, fitness (urban count) Evaluation with 3 measures, fitness (urban count)

and 2 modeling errors (urban pattern), is helpful to and 2 modeling errors (urban pattern), is helpful to select the best rules.select the best rules.

GA reaches best solution in a timely manner.GA reaches best solution in a timely manner. GA modeling results close, quantitatively and GA modeling results close, quantitatively and

qualitatively, to crisp CA results.qualitatively, to crisp CA results. GA objective function optimal design.GA objective function optimal design. FL reflect linguistic knowledge of urban process. FL reflect linguistic knowledge of urban process. FL provides calibration initials. FL provides calibration initials. NN simulate boundary with close urban match. NN simulate boundary with close urban match.


Recommendations and future work

There is a need to study effect of image There is a need to study effect of image classification on modeling uncertainty.classification on modeling uncertainty.

Effect of fuzzy membership functions and rules Effect of fuzzy membership functions and rules for fuzzy guided CA on urban growth.for fuzzy guided CA on urban growth.

There is a need to tune spatial calibration There is a need to tune spatial calibration through using finer scale spatial units.through using finer scale spatial units.

Implementation of developed model to different Implementation of developed model to different case studies, representing cities with various case studies, representing cities with various size and urban growth behavior is needed. size and urban growth behavior is needed.


THANKS FOR THANKS FOR LISTENINGLISTENING

QUESTIONS??QUESTIONS??

the asa-cssa-sssa international annual meetings (november 12-16, 2006) urban growth modeling...

Documents

urban modeling

urban modelling

urban process

urban growth facts1970

boundary modeling

modeling uncertainty

standard urban growth

athens urban growth18