空间格局引力加权Voronoi图模型研究与应用

发布时间：2018-05-15 11:35

本文选题：乘法加权Voronoi图 + 引力模型　；参考：《中国矿业大学(北京)》2016年博士论文

【摘要】：乘法加权Voronoi图是一种顾及生成元权重的空间分割方法,引力模型及衍生模型是一类测度地理实体空间关联的空间相互作用模型。两者均体现了地理实体吸引力差异,顾及了地理实体吸引力随距离衰减的特征,是较为常用、直接的地理实体空间吸引范围界定方法,多用于解决城市空间格局演变、城市等级体系构建、农村居民点布局优化、设施可达性分析、设施选址优化等问题,可以有效指导城市规划、区域资源分配、设施合理布局等。引力模型及衍生模型以作用量形式表达地理实体相互作用,乘法加权Voronoi图以图形形式反映地理实体有形边界,两理论、方法之间存在紧密联系,可以有效结合。扩展断裂点模型即其中典型,自提出后,受到广泛应用,成为城市、区域“一体化”、“公共服务设施均等化”等政策背景下的研究热点。受限于乘法加权Voronoi图实现、扩展困难等问题,两方法结合形式多为利用引力模型确定地理实体权重形式,借助乘法加权Voronoi图实现地理实体吸引范围划分,缺少深层次研究及功能扩展。两方法结合理论有待深入挖掘,应用有待拓展延伸。以此为出发点,确立本文研究主题“乘法加权Voronoi图和引力模型结合应用及扩展”。借助GIS工具实现乘法加权Voronoi图构建,结合相关引力模型,提出一套适合表达、分析地理实体空间格局的模型和方法,包括空间相互作用模型、空间等级体系构建方法和空间可达性方法。针对人口老龄化加剧问题,应国家政策号召,选取北京市养老机构为研究对象,从空间相互作用、空间等级体系和空间可达性视角探求北京市养老机构空间格局,为北京市养老设施布局规划提供依据与支持。主要研究内容与成果如下:(1)推导得出引力模型、Reilly模型、断裂点模型和Huff模型经转换符合乘法加权Voronoi图定义,确立了引力模型及衍生模型的图形表达形式。(2)引力加权Voronoi图模型研究①证明了引力模型一般形式变形后符合乘法加权Voronoi图空间分割原理,给出引力模型、Reilly模型、断裂点模型和Huff模型图形形式的统一表达方式,即引力加权Voronoi图模型,总结其性质、推论与空间格局评价指标。②对比了四种地理实体吸引范围划分方法,包括:缓冲区法、常规Voronoi图法、服务区分析法和引力加权Voronoi图模型法。指出引力加权Voronoi图模型适用条件。③回顾了常用乘法加权Voronoi图矢栅生成方法,指出两类方法优缺点,基于拓扑求并法,利用C#和ArcGIS Engine,实现乘法加权Voronoi图矢量生成,用于构建引力加权Voronoi图模型。给出算法基本思想,详述算法功能实现思路。通过实验验证表明:本文方法生成的乘法加权voronoi图包含非连通区域和空洞,符合乘法加权voronoi图性质。借助斑块形状指数验证空洞与等面积圆周长之比,证明空洞均为标准圆形,表明本文方法生成圆弧为标准圆弧,精度为100%。生成200个点状生成元(范围:100m×100m)的乘法加权voronoi图用时24.95s,在数据量不大、生成元所处范围不大的情况下,算法效率较高。④确定了养老机构吸引力评判指标,给出养老机构吸引力指标构建方法。⑤利用引力加权voronoi图模型划分北京市养老机构服务范围,借助模型空间格局评价指标,分析了北京市养老机构服务范围、覆盖老年人口数量、供需比等,指出北京市养老机构发展现状:城六区养老机构服务范围小,服务老年人口数高,远郊区县养老机构服务范围大,服务老年人口数低;顺义区养老机构吸引力差距较小,昌平区、门头沟区和延庆县养老机构吸引力差距较大;城六区养老机构床位供不应求,远郊区县养老机构床位供大于求;养老机构间空间相互作用量相对均衡。(3)基于引力加权voronoi图模型的地理实体空间等级体系构建①提出了基于引力加权voronoi图模型的地理实体空间层次确立方法,给出具体实现步骤。②结合voronoi树图与引力加权voronoi图模型,给出引力加权voronoi树图概念,归纳相关推论,阐述算法具体实现。确立了基于引力加权voronoi树图的空间等级体系划分方法。总结引力加权voronoi树图与voronoi树图差异。③对比voronoi图法与引力加权voronoi图模型法异同,指出在不考虑摩擦系数情况下,两方法构造局部中心可能不同,点集归属可能不同。调整某生成元与邻域生成元集合权重,voronoi图法局部中心数量不会变化,各级点集归属不会发生变化;引力加权voronoi图模型法的局部中心数量可能发生变化,各级点集归属可能发生变化。在考虑距离摩擦系数情况下,利用引力加权voronoi图模型构建空间等级体系,b趋近于0时,生成元局部中心只有一个,即为权重最大生成元,层次为两层;b趋近于￥时,结果与voronoi图法一致,即顾及距离摩擦系数时,voronoi图法是引力加权voronoi图模型法在b越趋近于￥时的特例。④利用引力加权voronoi图模型生成乘法加权voronoi图,确认养老机构层次与等级,构建引力加权voronoi树图,确立了北京市养老机构四级体系。得出结论:权重大的养老机构未必为局部中心、北京市养老机构局部中心多位于远郊、城六区养老机构高等级局部中心包含低一级局部中心数量远大于其他城区、养老机构局部中心布局与老年人口密度分布基本一致。(4)基于引力加权voronoi图模型的空间可达性分析①提出了基于引力加权voronoi图模型的空间可达性方法。给出方法基本思想,详述方法实现思路。②利用两步移动搜索法(空间阻隔阈值s0设为3300m、5000m、7000m、10000m等)和引力加权Voronoi图模型法(邻域值k设为0和1)计算北京市养老机构可达性。统计分析两方法可达性最小值、最大值、均值和标准差,计算不同搜索参数下两方法所求可达性值的史皮尔曼等级相关系数,运用“最小-最大规范化”方法将两方法可达性线性变换,映射到区间[1,10],对应生成散点图,可知:随搜索范围扩大,两方法统计参数变化趋势相同,且均值接近。引力加权Voronoi图模型法k取0、1时,分别与两步移动搜索法s0取7000m、16000m所求结果相关程度最高。s0取值较小时,引力加权Voronoi图模型法计算可达性值多高于两步移动搜索法。s0值取值较大时,引力加权Voronoi图模型法计算可达性值多低于两步移动搜索法。总结引力加权Voronoi模型法优点:克服了两步移动搜索法未使用空间阻隔系数、未体现供给点差异和空间相互作用等问题,避免了区域可达性值为0的情况。③将两步移动搜索法和引力加权Voronoi图模型法计算可达性值录入北京市街道数据,利用ArcGIS进行分级渲染,对比地图效果可知:引力加权Voronoi图模型法k取0时,可达性空间格局与两步移动搜索法s0取值较小时相似。k取1时,与两步移动搜索法s0取值较大时相似。从地理学角度出发,总结引力加权Voronoi图模型法优点:构建可达性空间格局过渡效果更为明显。④基于引力加权Voronoi图模型法描绘了北京市养老机构街道尺度、区域尺度空间可达性格局。街道尺度空间格局可区分北京市高值、低值可达性区域。区域尺度可达性总体呈现“北高南低”的规律,且中间区域可达性较高,中心城区和远郊边缘区域可达性较低,由城中心向远郊呈现“低-高-低”的层次结构。结合北京市老年人口密度分布图,可以体现北京市养老机构床位供需可达性的空间错位。
[Abstract]:The multiplicative weighted Voronoi graph is a spatial segmentation method considering the weight of the generating element. The gravitational model and the derived model are a class of spatial interaction models for measuring the spatial correlation of geographical entities. Both of them reflect the differences in the attraction of geographical entities and take into account the characteristics of the attractiveness of geographical entities, which are more common and direct. The method of defining the scope of space attraction is more used to solve the urban spatial pattern evolution, the construction of urban hierarchy, the optimization of rural residential point layout, the accessibility analysis of facilities, and the optimization of facility location, which can effectively guide the urban planning, the distribution of regional resources, the rational layout of facilities and so on. The formula expresses the interaction of geographical entities, multiplicative weighted Voronoi maps reflect the tangible boundary of physical entities in graphic form. Two theory, there is a close connection between the methods, and it can be effectively combined. The extension of the fracture point model is typical. Since it is proposed, it is widely applied to become City, regional "integration" and "equalization of public service facilities". The research hotspot under the background of policy is limited to the realization of multiplicative weighted Voronoi graph and expansion difficulty. The two method combines the gravitational model to determine the geographical entity weight form by using the gravitational model, and uses the multiplicative weighted Voronoi graph to realize the division of geographical entity attraction range, lack of deep study and function expansion. The two method is to be combined with the theory. In depth, the application needs to be extended. As a starting point, the topic "multiplicative weighted Voronoi graph and gravity model combined application and expansion" is established. With the help of GIS tools, the multiplicative weighted Voronoi graph is constructed and a set of models and methods suitable for expression and analysis of the spatial pattern of geographic entities are proposed in combination with the relevant gravitational model. This paper includes spatial interaction model, spatial hierarchy system construction method and spatial accessibility method. According to the problem of population aging, Beijing city pension institutions are selected as the research object, and the spatial pattern of Beijing pension institutions is explored from spatial interaction, spatial hierarchy system and spatial accessibility angle, for Beijing City The main research contents and results are as follows: (1) the gravitational model, the Reilly model, the fracture point model and the Huff model are defined by the multiplicative weighted Voronoi diagram, and the graphical representation of the gravitational model and the derived model is established. (2) the study of the gravitational weighted Voronoi diagram model is proved by 1 After the gravitational model is generally deformed, it conforms to the principle of space division of the multiplicative weighted Voronoi graph, and gives the unified expression of the gravitational model, the Reilly model, the fracture point model and the graphical form of the Huff model, that is, the gravitational weighted Voronoi graph model, and sums up its properties, the inference and the spatial lattice evaluation index. Secondly, it compares four kinds of geographical entity attraction. The method of peri division, including buffer zone method, conventional Voronoi graph method, service area analysis method and gravitational weighted Voronoi graph model, points out the application conditions of gravitational weighted Voronoi graph model. Thirdly, it reviews the common multiplicative weighted Voronoi graph vector grid generation method, points out the advantages and disadvantages of the two kinds of methods, and uses C# and ArcGIS Engine to realize multiplication based on topology. The method weighted Voronoi graph vector is generated and used to construct the gravitational weighted Voronoi graph model. The basic idea of the algorithm is given and the realization of the algorithm is detailed. It is proved by experimental verification that the multiplicative weighted Voronoi graph generated by this method contains the non connected regions and holes, which conforms to the property of the multiplicative weighted Voronoi graph. Compared with the circle circumference of the equal area, it is proved that the cavity is all standard circle. It shows that this method generates the arc as the standard circular arc, and the precision is 100%. generation 200 point forming element (range: 100M * 100m) multiplicative Voronoi diagram for 24.95s. The algorithm has high efficiency when the amount of data is not large and the range of the generating element is not large. The evaluation index of institutional attractiveness and the method of constructing the attractiveness index of pension institutions. (5) to divide the service scope of Beijing pension institution by gravitational weighted Voronoi map model, and to analyze the service scope of Beijing pension institutions with the aid of model space pattern evaluation index, covering the number of elderly people and the ratio of supply and demand, and pointing out that the pension institutions in Beijing are issued. Present situation: the service scope of the city six district pension institutions is small, the elderly population is high, the service scope of the elderly pension institutions in the far suburbs is large, the number of elderly people is low, the attractiveness gap of Shunyi District pension institutions is small, Changping District, Mentougou district and Yanqing County have a large gap in attractiveness; the beds in the six district pension institutions are in short supply and the outskirts of the suburb are in short supply. The bed supply of the county pension institutions is larger than the demand; the spatial interaction between the pension institutions is relatively balanced. (3) the construction of the geographic entity spatial hierarchy based on the gravitational weighted Voronoi map model (1) puts forward the method for the establishment of the geographic entity spatial hierarchy based on the gravitational weighted Voronoi map model, and gives the concrete implementation steps. The force weighted Voronoi graph model gives the concept of gravitational weighted Voronoi tree graph, sums up the correlation inference and expounds the concrete realization of the algorithm. The method of dividing the spatial hierarchy system based on the gravitational weighted Voronoi tree graph is established. The difference between the gravitational weighted Voronoi tree and the Voronoi tree diagram is summarized. (3) the similarities and differences between the Voronoi diagram method and the gravitational weighted Voronoi map model are compared. It is pointed out that in the case of the coefficient of friction, the two method can be different in the local center, and the attribution of the point set may be different. The weight of the set of a generating element and the neighborhood generating element is adjusted. The number of local centers of the Voronoi graph method will not change, the location of the point set at all levels will not change, and the local center number of the gravitational weighted Voronoi graph model may occur. In the case of distance friction coefficient, in the case of distance friction coefficient, the space hierarchy system is constructed by gravitational weighted Voronoi graph model. When B approaches 0, only one local center of generating element is the maximum weight generating element and the level is two layers; the result is consistent with the Voronoi diagram method, that is to consider the distance friction, that is to consider the distance friction. When rubbing coefficient, the Voronoi graph method is the special example of the gravitational weighted Voronoi graph model in the closer to the B. (4) using the gravitational weighted Voronoi map to generate the multiplicative weighted Voronoi map, confirm the hierarchy and grade of the pension institution, construct the gravitational weighted Voronoi tree, and establish the four level system of the old institution in Beijing. The local center of the pension institution in Beijing is mostly located in the far suburb. The high grade local center of the pension institution in the six District of the city is far larger than the other urban areas. The distribution of the local center of the pension institution is basically consistent with the distribution of the aged population density. (4) the spatial accessibility based on the gravitational weighted Voronoi map model. The method of spatial accessibility based on gravitational weighted Voronoi graph model is proposed. The basic idea of the method is given, and the method is described in detail. Secondly, the two step mobile search method (space barrier threshold S0 is set as 3300m, 5000m, 7000m, 10000m, etc.) and gravitational weighted Voronoi graph model (neighborhood value k is set to 0 and 1) can be used to calculate Beijing pension institutions The two methods of reachability minimum, maximum, mean, and standard difference, calculate the Spear Man rank correlation coefficient of the reachability value of the two methods under different search parameters, use the "minimum maximum normalization" method to transform the two method reachability linear transformation, map to the interval [1,10], corresponding to the scatter plot, we know: follow the search The variation trend of the two method is the same, and the mean value is close. When the gravitational weighted Voronoi graph model K takes 0,1, it takes 7000m with the two step moving search method S0, and the highest correlation degree of the result of the result is higher than that of the 16000m. The gravitational weighted Voronoi graph model method is much higher than the two step moving search method. When the gravitational weighted Voronoi graph model is used to calculate the reachability value, the reachability value is much lower than the two step moving search method. The advantages of the gravitational weighted Voronoi model method are summed up: the two step movement search method has not used the space barrier coefficient, does not reflect the supply point difference and space interaction, and avoids the area accessibility value of 0. Thirdly, the two step will be avoided. The mobile search method and gravitational weighted Voronoi graph model method are used to calculate the accessibility values into Beijing Street data, and use ArcGIS to make the hierarchical rendering. Compared to the map effect, it is known that when the gravitational weighted Voronoi graph model method is 0, the accessibility spatial pattern and the two step moving search method S0 value are similar to.K 1, and the two step mobile search method S0 is taken. From the geographical point of view, the advantages of gravitational weighted Voronoi graph model method are summarized from the geographical point of view: the transition effect of constructing the accessibility spatial pattern is more obvious. (4) based on the gravitational weighted Voronoi map model, the street scale of Beijing pension institution is described, and the regional scale space can reach the character Bureau. The street scale spatial pattern can distinguish the city of Beijing. The regional scale reachability generally presents the law of "North High South and low", with high accessibility in the middle area and low accessibility in the central and suburban fringe area, which presents a "low to high low" level structure from the city center to the outskirts. It can reflect the Beijing city's population density distribution map, which can reflect the Beijing city. The space dislocation of the accessibility of the old institutional beds.

【学位授予单位】：中国矿业大学(北京)
【学位级别】：博士
【学位授予年份】：2016
【分类号】：P208

【参考文献】