基于误差反馈控制的变系数城市扩张模型构建及应用

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。

The Variable-coefficient Urban Growth Model Based on the Error Feedback Control

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.