基于误差反馈控制的变系数城市扩张模型构建及应用

doi:10.13249/j.cnki.sgs.2014.05.594

摘要/Abstract

摘要：

通过模拟结果与实际情况的误差分析,将研究区划分为4种像元类型,包括漏算误差像元（Omission Error, OE）、超算误差像元（Commission Error, CE）、正确模拟的城市像元（Urban Correct, UC）及正确模拟的非城市像元（Non-urban Correct, NUC）。利用线性规划方法,将误差反馈到城市扩张模型中,动态修正模型系数,构建基于误差反馈控制的变系数城市扩张空间布局模型反映城市扩张的内在特征,最后以北京市为例,模拟了其1997~2009年的城市扩张过程,通过与传统Logistic-CA模型的模拟结果对比,验证变系数模型的有效性与实用性。研究结果表明：传统Logistic-CA模型在2001年、2005年和2009年的模拟精度分别为73.842%、64.704 %和63.953%,而基于误差反馈控制的变系数城市扩张模型的模拟精度分别为75.624%、66.537%和69.142%,较Logistic-CA回归模型提高了1.782、1.833和5.189个百分点,取得了更好的模拟效果。

关键词: 城市扩张模拟, Logistic-CA模型, 误差反馈控制, 变系数, 北京

Abstract:

Urban growth model was the simplification of the urban area, which was expected to present and simulate the dynamic processes of urbanization through the mathematical methods, and provide a very useful analysis tool to understand and capture the characteristics of urban growth. The Logistic-CA model was widely used in the existing researches of the urban growth simulation, while it was difficulty to reflect the nonlinear and dynamic characteristics of the urban growth for its static coefficients. To deal with this deficiency, a variable-coefficient urban growth model was developed through the error feedback control in this artcle. Firstly, four pixel types were generated according to the comparison between the simulation result and real situation, which includes the Omission Error (OE) pixels, Commission Error (CE) pixels, Urban Correct (UC) pixels and Non-urban Correct (NUC) pixels, then the simulation error was mapped into the urban growth model to modify the coefficients through the linear programming method. Finally, the variable-coefficient urban growth model was built based on the error feedback control. To validate the effect of the variable-coefficient model, both the Logistic-CA and variable-coefficient model were used to simulate the urban growth process of Beijing City from the year of 1997 to 2009. The results showed that the accuracies of Logistic-CA model in 2001, 2005 and 2009 were 73.842%, 64.704% and 63.953%, respectively, while these values of the variable-coefficient urban growth model were 75.624%, 66.537% and 69.142%, which were 1.782%, 1.833% and 5.189% greater than the former. It can be demonstrated that the variable-coefficient model could present the real situation of urban growth and obtain a better simulate results. The results of this article had a high theoretical and practical significance, for it could provide a new method and view to guide the research of urban growth simulation, but also provide an ancillary evidence for the urban planning and decision.

Key words: urban growth simulation, Logistic-CA model, Error Feedback Control, variable-coefficient, Beijing

中图分类号:

F291.1

冯徽徽, 刘慧平. 基于误差反馈控制的变系数城市扩张模型构建及应用[J]. 地理科学, 2014, 34(5): 594-600.

Hui-hui FENG, Hui-ping LIU. The Variable-coefficient Urban Growth Model Based on the Error Feedback Control[J]. SCIENTIA GEOGRAPHICA SINICA, 2014, 34(5): 594-600.

图/表 6

图1

表1

图2

表2

图3

表3

参考文献 18

[19]	张亦汉,黎夏,刘小平,等.基于数据同化的元胞自动机[J].遥感学报,2011,15(3):475~491.
[20]	刘小平,黎夏,张啸虎,等.人工免疫系统与嵌入规划目标的城市模拟及应用[J].地理学报,2008,63(8):882~894.
[21]	White R,Engelen G,Uijee I.The use of constrained cellular automata for high-resolution modelling of urban land-use dynamics[J]. Environment and Planning B: Planning and Design,1997,24(4):323-343.
[22]	阮桂海,蔡建平,刘爱玉.数据统计与分析——SPSS应用教程[M].北京:北京大学出版社,2005.
[23]	王济川,郭志刚.Logistic回归模型:方法与应用[M].北京:高等教育出版社,2001.
[24]	韦玉春,陈锁忠.地理建模原理与方法[M].北京:科学出版社,2005
[25]	吕立新. 利用线性规划技术估计回归系数[J].预测,1993,1:65~66.
[26]	薛国强,宋建平,李貅,等.用线性规划法求解瞬变电磁场反射系数[J].西安工程学院学报,2002,24(3):72~75.
[27]	胡小荣,俞茂宏.用线性规划法求解克立格估值权系数的研究[J].地质与勘探,2001,37(3):53~57.
[28]	Pumain D,Julien T S,Sanders L.Urban dynamics of some French cities[J].European Journal of Operational Research,1986,25(1):3-10.
[29]	刘瑞,朱道林,朱战强,等.基于Logistic回归模型的德州市城市建设用地扩张驱动力分析[J].资源科学, 2009,31(11):1919~1926.
[30]	姜文亮. 基于GIS 和空间Logistic 模型的城市扩展预测——以深圳市龙岗区为例[J].经济地理,2007,27(5):800~804.
[31]	舒帮荣. 基于约束性模糊元胞自动机的城镇用地扩展模拟研究[D].南京:南京农业大学,2010.
[1]	唐华俊,吴文斌,杨鹏,等.土地利用/土地覆被变化(LUCC)模型研究进展[J].地理学报,2009,64(4):456~468.
[2]	Batty M,Xie Y,Sun Z.Modeling urban dynamics through GIS-based cellular automata[J].Computers, Environment and Urban Systems,1999,23(3):205-233.
[3]	Pumain D.Complex Artificial Environments[M].Berlin:Springer Berlin HeidelbergPublisher,2006.
[4]	Santé I,García A M, Miranda D, et al.Cellular automata models for the simulation of real-world urban processes: A review and analysis[J]. Landscape and Urban Planning, 2010, 96(2): 108-122.
[5]	Hu Z,Lo C P.Modeling urban growth in Atlanta using logistic regression[J].Computers, Environment and Urban Systems,2007,31(6):667-688.
[6]	Feng H,Liu H,Lv Y.Scenario prediction and analysis of urban growth using SLEUTH model[J]. Pedosphere,2012,22(2):206-216.
[7]	冯徽徽,夏斌,吴晓青,等.基于SLEUTH模型的东莞市区城市增长模拟研究[J].地理与地理信息科学,2008,24(6):76~80.
[8]	Ligtenberg A,Bregt A K,Lammeren R V.Multi-actor-based land use modeling: spatial planning using agents[J].Landscape and Urban Planning,2001,56(1-2):21-33.
[9]	黎夏,叶嘉安,刘小平,等.地理模拟系统:元胞自动机与多智能体[M].北京:科学出版社,2007.
[10]	高玉宏,张丽娟,李文亮,等.基于空间模型和CA的城市用地扩展模拟研究——以大庆市为例[J].地理科学, 2010,30(5):723~727.
[11]	何丹,金凤君,周璟,基于Logistic-CA-Markov的土地利用景观格局变化——以京津冀都市圈为例[J].地理科学,2011,31(8):903-910.
[12]	Fujita M,Mori T.Structural stability and evolution of urban systems[J].Regional Science and Urban Economics,1997,27(4-5):399-442.
[13]	Portugali J.Self-organizing cities[J]. Futures,1997,29(4/5):353-380.
[14]	Wilson A G.Complex spatial systems:challenges for modellers[J]. Mathematical and Computer Modelling,2002,36(3):379-387.
[15]	房艳刚,刘继生.城市系统演化的复杂性研究[J].人文地理,2008, 23(6): 37~41.
[16]	Clarke K C.Loose coupling a cellular automaton model and GIS: long term urban growth prediction for San Francisco and Washington/Baltimore[J].International Journal of Geographical Information Science,1998,12(7):699-714.
[17]	Clarke K C.Mapping and modelling land use change: an application of the SLEUTH Model, in landscape analysis and visualisation[C]//Pettit C et al. Spatial models for natural resource management and planning. Berlin:Springer,2008.
[18]	Clarke K C,Hoppen S.A self-modifying cellular automaton model of historical urbanization in the San Francisco Bay area[J]. Environment and Planning B: Planning and Design,1997,24(4):247-261.

年份	变量系数
年份	C	DEM	D₁	D₂	D₃	D₄	D₅
1997~2001年	-1.847	-14.581	-6.284	-2.109	-2.507	-0.656	3.175
2001~2005年	-1.847	-12.991	-5.599	-1.537	-2.234	-0.584	3.458
2005~2009年	-1.847	-10.523	-4.535	-1.860	-2.703	-0.473	4.184

年份	城市化像元总数	模拟正确的城市像元数	精度 (%)
2001	701244	517848	73.842
2005	910016	588775	64.704
2009	921627	589380	63.953

年份	城市化像元总数	模拟正确的城市像元数	精度 (%)
2001	701244	530280	75.624
2005	910016	605532	66.537
2009	921627	636586	69.142