Urban Growth Modeling with Artificial Intelligence Techniques Dr

Urban Growth Modeling with Artificial Intelligence Techniques Dr. Jie Shan and Sharaf Al-kheder Geomatics Engineering School of Civil Engineering Purdue University jshan@purdue. edu The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Outline (1) n n n n Introduction. Statement of the problem. Research objectives. Literature review. Problem solving approach. Crisp cellular automata modeling. Calibration with genetic algorithms. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Outline (2) n n n Fuzzy guided cellular automata modeling. Neural networks for boundary modeling. Discussion and analysis. Concluding remarks. Recommendations and future work. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Introduction: motivation n n City population excessive increase worldwide. infrastructure services demand. Athens urban growth Cairo 1965 18 million in this area! Cairo 1998 Los Angeles Urban modeling is a necessity! Mexico city!! The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Introduction: Urban growth facts n 1970 to 1990, more than 30, 000 sq. m. of U. S. rural land became urban (Statesman Journal, 1991). n 1969 to 1989, U. S. population increased by 22. 5%, and VMT (vehicles miles traveled) by 98. 4% (Federal Highway Administration, 1991). n 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). The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Statement of the problem n n Excessive unplanned urban growth. Absence of a standard urban growth model and a robust calibration module. Evaluation strategy. Satellite imagery availability with minimal cost. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Research objectives n n n 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. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Literature review: General n Two types of urban models: Ø 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) ]. Ø Model’s applicability: - Physical aspects [e. g. , Alonso, (1978)]. - Social aspects [e. g. , Jacobs, (1961)]. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Literature review: Cellular Automata n n n Fastest emerging urban dynamic models. Multi-dimensional discrete system. Uses simple yet accurate transition rules for urban modeling. Uses social and physical factors. Fits urban process spatially in imagery. Better in urban modelling than mathematical models (Batty and Xie, 1994 a). The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Literature review: Cellular Automata n n 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, 1992 a; 1992 b) CA used by Batty and Xie (1994 a) for modeling of Cardiff (UK) and Savannah (GA). The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Literature review: Cellular Automata n SLEUTH (Slope, Land use, Exclusion, Urban extent, Transportation, Hillshade), Clarke et al. (1997) ¡ ¡ n Four types of data: land cover, slope, transportation, and protected lands. Five factors for urban growth (e. g. , SLOPE and ROAD-GRAVITY. Complex transition rules. Visual and statistical tests for calibration. Clarke and Gydos (1998) applied “SLEUTH” for urban growth in San Francisco region & Washington D. C/Baltimore. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Literature review: Cellular Automata n n Yang and Lo (2003) used “SLEUTH” to test urban modeling scenarios in Atlanta, GA. Wu and Webster (1998) used Multi Criteria Evaluation analysis to identify CA parameter values. Neural networks used by Li and Yeh (2001) to calibrate CA rules. Wu (2002) development probability based CA model. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Literature review: Genetics Algorithms n n Recent direction in CA calibration. Colonna et al (1998) used GA to generate new rules for CA to simulate the land use changes of Rome, Italy. Wong et al (2001): GA for household and employment distributions’ parameters for Hong Kong. Goldstein (2003): SLEUTH calibration. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Literature review: Fuzzy Logic (FL) n n n Extend binary theory for continuous status. FL for geographic boundaries with high spatial variability (Wang and Hall, 1996). Gradual change in land use conditions over time (Dragicevic & Marceau, 2000). FL in Wu (1996; 1998) work to define CA transition rules for land conversion. Liu and Phinn (2003) identify pixel state change with a fuzzy membership function. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Literature review: Neural Networks (NN) n n n NN to mimic biological neural networks. NN simulate geo-spatial complex systems (Openshaw, 1998). Liu (2000) used NN to detect the change from non-urban to urban land use. Yeh and Li (2002): NN with CA for urban simulation to model land use change. NN with GIS to forecast land use change (Pijanowski et al. , 2002). The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Literature review: Unsolved issues n n n A standard model for defining & calibrating CA transition rules is absent in literature. Most models do not have an explicit transition rules [e. g. , Wu model, 2002)]. CA models do not use multispectral imagery for urban extent or other data directly. They use cadastral maps instead. Time consuming calibration (SLEUTH : 135 days). No effective search methods for calibration. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Literature review: Unsolved issues n n An effective evaluation scheme is needed to help select the best rules. Spatial calibration is not included in most CA calibration algorithms to date. A fuzzy guided cellular automata model is needed, where CA rules can be designed as a function of the FL output. Calibration in fuzzy CA urban modeling needs to be clearly identified. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Problem solving approach Multitemporal satellite imagery Other input data (Population, DEM, road networks) Crisp CA model Simulated CA images CRISP CA Fuzzy CA model Ground truth imagery Simulated Fuzzy CA images Calibration Urban growth modeling The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006) FUZZY CA

Problem solving approach Multitemporal satellite imagery Other input data (Population, DEM, road networks) Crisp CA model Simulated CA images Ground truth imagery Calibration CA-GA NN model GA automated calibration Urban growth modeling The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006) Boundary modeling NN modeling

Crisp CA modeling: outline n n n n CA theory. Artificial city modeling. CA based urban growth model design. A spatiotemporal calibration algorithm. Design an evaluation scheme. Indianapolis growth modeling. Integrate with GIS, such as Arc. GIS (VBA). Analysis and discussion. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Crisp CA modeling: theory n n n By Ulam and von Neumann in 1940 s to study complex systems (von Neumann, 1966). 2 -dimensional CA for our work. Four CA components: Ø Ø Ø pixels; States (e. g. , Water); Neighborhood: States function Shape The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Crisp CA modeling: theory n Four CA components (cont’d) Ø Ø Transition rules such as IF-THEN rules Future state of a pixel: n Example: (Game of Life) 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. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Crisp CA modeling: Artificial city n n n Ø Ø Effect of land use. E. g. , roads drive urban growth. 200 x 200 pixels input image. CA rules (3 x 3 neighborhood): IF test pixel is urban, river, road, lake or has pollution source in the neighborhood THEN no change. IF test pixel is non-urban, it changes to urban if in neighborhood ¡ Three of more urban pixels. ¡ At least one road AND one urban pixels. ¡ At least one lake pixel AND one urban pixel. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Crisp CA modeling: Artificial city n n CA simulates urban growth at 0, 25, 50 and 60 iterations. Effect of road & lakes in driving growth. Pollution source buffer zones. Conservation of water. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Crisp CA model design: Data n n n n Indianapolis growth modeling Excessive growth from 1973 to 2003. MSS/TM images (1973, 1982, 1987, 1992 and 2003) and population density input data. Images projected to UTM NAD 1983 zone 16 N. Ground reference data to classify images. 7 classes : water, road, commercial, forest, residential, pasture and row crops. Commercial and residential as urban class. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Crisp CA model design: Data n n n 1990 & 2000 population census tract maps. Population density is computed per tract. Exponential model between density and distance from city center for 1990 and 2000. Parameters (A & B) are updated yearly according to rate of change (1990 & 2000). population density grids as input. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006) 1990

Crisp CA model design: Rules n n Ø Ø CA rules represent land use & constrains effect. CA rules (3 x 3 neighborhood): IF test pixel is water, road OR urban (residential or commercial) THEN no change. IF test pixel is nonurban (forest, pasture OR row crops) THEN It becomes urban if its: ¡ ¡ Population density ≥ threshold (Pi) AND has neighboring residential pixels # ≥ threshold (Ri). Population density ≥ threshold (Pi) AND has neighboring commercial pixels # ≥ threshold (Ci). Pi continuous [0: 0. 1: 3], Ri & Ci [0: 1: 8] The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Crisp CA model design: Evaluation n 3 evaluation measures for each rule combination (P, R, C)i : 1. Fitness: 2. Type I error: Pixels that urban in real but nonurban in simulated. 3. Type II error: Pixels that nonurban in real but urban in simulated. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Crisp CA model design: Calibration Spatial & temporal calibration modules. n Spatial calibration: - Site specific features. - Evaluation based on township. - Same rules, variable values. n Temporal calibration: - Rule change over time. - Variable urban growth pattern. n The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Crisp CA model design: Modeling n n CA Modeling in Arc. GIS through VBA. Two multitemporal imagery sets: - Training images: calibration. - Testing images: prediction & validation. n n n CA runs for all combinations (P, R, C)i from 1973 till 1982, first calibration year, and evaluated. Evaluation results arranged in descending order (ratio of Type I & II sum to total pixel count ). Rule with min. avg. error & fitness closest to 100% (± 10%) is selected for each township. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Crisp CA model design: Modeling n n n Recalibration at 1987. Best rules at 1987 to predict 1992 (5 years). Calibration at 1992 to predict 2003 (11 years). Final calibration at 2003 for future prediction (2010 and 2020). Close urban pattern match. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006) Simulation

Crisp CA model design: Modeling n n n Spatial calibration effect. 1992 Prediction sample Close fitness to 100%. Small average errors 24 -25%. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006) Prediction

Crisp CA modeling: Analysis Rule vary spatially Rule vs. class count 1992 calibration Better connectivity for modeling The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Crisp CA modeling: Analysis Rule redesign 1987 calibration Avg. vs. total count Type I vs. urban Type II vs. nonurban The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Genetic algorithms calibration: Motivation n n n Introduced by Holland (1975) to mimic evolutionary processes in nature. Manipulates a set of feasible solutions to find an optimal solution. Effective for complex search spaces. Why GA? CA is computationally extensive (lager # of combinations, need days). Increase calibration time with parameter #s. Assign higher weights for good solutions. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Genetic algorithms calibration: design GA extends CA model to automate calibration while searching for optimal rule values. n GA operations: - initial population design; - selection; - crossover and mutation. n The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Genetic algorithms calibration: initial population design n n CA transition rules design is used. Each combination of (R, C, P)i presents a string in the initial population pool. 30 strings for each township. Binary encoding. String example The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Genetic algorithms calibration: initial population design n n CA run for all 30 strings for evaluation (fitness, Type I and II errors). Objective function (based on modeling errors) to guide GA to optimal solution: deviation from 100%, urban count Modeling errors, urban pattern n Total modeling error (urban count and structure) per township to be minimized. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Genetic algorithms calibration: Elitism and Rank Selection n n Strings ordered based on GA objective function in ascending order (min. to max. ). String with lowest objective function has a rank of 30, the second one 29, etc. n Selection probability n Expected count: n Final count The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006) Sample calculation

Genetic algorithms calibration: Elitism and Rank Selection n n The best 6 strings in terms of objective function are copied directly to next generation (elitism). The rest 24 strings are selected using rank selection (string count). This will end the selection process with a total of 30 strings. Bad strings are not selected (search is directed to good strings). The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Genetic algorithms calibration: Crossover and mutation n n Ø Ø Crossover: a pair of strings meet to produce offspring (same or better quality). Crossover probability is selected as 80% where 24 strings are crossed over: 6 elitism strings crossedover to produce new 6 strings to be added with a total of 12 strings. First 18 strings in the selection are crossedover. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006) Crossover point

Genetic algorithms calibration: Crossover and mutation n n After crossover: new 30 strings produced. Mutation: inversion of string bits for diverse structure and not stuck with bad solutions. Last stage in finalizing new population. Mutation for best 6 strings for (R, C)i by random addition of +1 or -1. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Genetic algorithms calibration: Modeling and Evaluation n n CA run for new population for objective values. Repeat GA process for 20 iterations. Rules with minimum GA objective function values are selected per township. Close match with reality & crisp CA. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Genetic algorithms calibration: Modeling and Evaluation n Minimum GA objective value at early stage The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Genetic algorithms calibration: Modeling and Evaluation n Short running time for GA (6 hrs. avg. ) compared to crisp CA (4 days). n Close modeling results to CA. 1992 prediction 1987 calibration The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Fuzzy guided CA modeling: Motivation n n n Crisp CA is binary (develop/undeveloped), urban growth is continuous in space. A pixel might be partially developed. Fuzzy logic identify pixel development potential. Level of development identifies # of urban pixels in neighborhood for test pixel to develop. Fuzzy logic to provide initial values for CA rule calibration. Crisp CA is extended with fuzzy logic to achieve the continuous condition in space. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Fuzzy guided CA modeling: Theory n n n Fuzzy logic first introduced by Zadeh from University of California, Berkeley in 1965. Fuzzy set is a continuous interval bounded by 0 and 1 values: The notation of a singleton: x: element in the fuzzy set, : membership degree. n Fuzzy set for all x is: The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Fuzzy guided CA modeling: design n n To design Fuzzy CA with artificial city. 3 Inputs: DEM Input image n Membership function OUTPUT: urban neighborhood pixels # The ASA-CSSA-SSSA International Annual for development. Meetings (November 12 -16, 2006) Distance to city center

Fuzzy guided CA modeling: design n n FUZZY RULES FUZZIFICATION OUTPUT Min-max (Mamdani method) Distance For every pixel: DEM Output min 1. DEM value. 2. Distance to city center n DEFUZZIFICATION (COA) y The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006) y max : Fuzzy output y

Fuzzy guided CA modeling: design n Ø Ø Ø Fuzzy output to design CA rules: IF a pixel is urban, river, road, lake or has pollution source in neighborhood, THEN no change in its state. IF a non-urban pixel has ≥ urban pixels in its neighborhood, THEN change it to urban. IF a non-urban pixel has road or lake in its neighborhood AND has ≥ ( -2) urban pixels in neighborhood, THEN change it to urban. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Fuzzy guided CA modeling: modeling Step#0 Step#25 Road effect Step#50 Step#60 The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006) Elevation effect

Fuzzy guided CA modeling: Indianapolis n n 3 inputs beside the imagery are used. DEM Roads Fuzzy rules: Population n Membership functions for inputs. n Fuzzy output represents neighborhood urban pixels for a test pixel to develop. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Fuzzy guided CA modeling: Indianapolis n CA rules (function of fuzzy output): Ø IF a pixel is road, water, commercial or residential, THEN no change. IF nonurban (forest, pasture or row crops) pixel has ≥ residential pixels in neighborhood, THEN change to residential. IF non-urban has ≥ commercial pixels in neighborhood, THEN change to commercial. IF commercial and residential pixels sum of non-urban pixel in neighborhood is ≥ pixels, THEN change to whichever is greater. Ø Ø Ø n Fuzzy output approximate rule values. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Fuzzy guided CA modeling: Indianapolis n A small search range based on fuzzy output. n Spatial calibration (township). Rule set with min. average error & close fitness to 100% is selected. CA run for calibration and prediction n n The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Fuzzy guided CA modeling: Analysis n n n Conclusions in crisp CA still valid. Avg. error smaller at city townships. Avg. error, 60 m Testing with 30 m vs. 60 m. More restrict rules for 30 m. Smaller errors for 30 m. Rules, 30 vs. 60 m Type. II 30 vs. 60 m The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Neural networks for boundary modeling n n n n City boundary expansion indicates gross change of phenomena (e. g. , political boundary). Availability of historic imagery is problem. City boundaries were digitized from classified satellite images. 3 datasets were used for NN training. Back Propagation (BPNN) algorithm for training. Short (3 yr) and long-term (8 yr) predictions. Directional NN training. Evaluation (root mean square). The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Neural networks for boundary modeling 6 years boundaries of Indianapolis were digitized on classified satellite images. n 6 measurements at 3 degree radial interval. n A matrix of 120 by 6. n 3 datasets (RBFN): Real data, 1 & 5 year interpolation. n The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Neural networks for boundary modeling n n Two-layer Back Propagation. 2003 from 2000 (short-term). Same results for 3 datasets. RMS= 3095. 37 m. 2003 Long term (8 yrs) prediction 2000 from 1992 (long term). Ø Same performance for 3 datasets. 2000 The ASA-CSSA-SSSA International Annual Ø RMS= 3713. 28 m. Meetings (November 12 -16, 2006) Ø

Neural networks for boundary modeling n n Growth in all directions is not the same (directional growth). Higher weights for higher growth directions. Directional factors: Lakes Road The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006) Population

Directional boundary modeling n n n Closer match. 2003 from 2000. RMS=1226. 49 m. 2003 v 2000 from 1992. v Weights effect. 2000 v Better results. The ASA-CSSA-SSSA International Annual Meetings (November 2006) v 12 -16, RMS=1650. 01 m

Concluding remarks n n n Artificial intelligence techniques fit the complex nature of urban process. Model design reduces the need for large input data and modeling uncertainty. Simple, yet accurate transition rules easily interpreted by end users. Spatial calibration, township basis, took into account site specific features. Temporal calibration importance. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Concluding remarks n n n n Evaluation with 3 measures, fitness (urban count) and 2 modeling errors (urban pattern), is helpful to select the best rules. GA reaches best solution in a timely manner. GA modeling results close, quantitatively and qualitatively, to crisp CA results. GA objective function optimal design. FL reflect linguistic knowledge of urban process. FL provides calibration initials. NN simulate boundary with close urban match. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

Recommendations and future work n n There is a need to study effect of image classification on modeling uncertainty. Effect of fuzzy membership functions and rules for fuzzy guided CA on urban growth. There is a need to tune spatial calibration through using finer scale spatial units. Implementation of developed model to different case studies, representing cities with various size and urban growth behavior is needed. The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)

THANKS FOR LISTENING QUESTIONS? ? The ASA-CSSA-SSSA International Annual Meetings (November 12 -16, 2006)