發(fā)布時(shí)間：2018-05-15 11:35

  本文選題：乘法加權(quán)Voronoi圖 + 引力模型��； 參考：《中國(guó)礦業(yè)大學(xué)(北京)》2016年博士論文

【摘要】：乘法加權(quán)Voronoi圖是一種顧及生成元權(quán)重的空間分割方法,引力模型及衍生模型是一類(lèi)測(cè)度地理實(shí)體空間關(guān)聯(lián)的空間相互作用模型。兩者均體現(xiàn)了地理實(shí)體吸引力差異,顧及了地理實(shí)體吸引力隨距離衰減的特征,是較為常用、直接的地理實(shí)體空間吸引范圍界定方法,多用于解決城市空間格局演變、城市等級(jí)體系構(gòu)建、農(nóng)村居民點(diǎn)布局優(yōu)化、設(shè)施可達(dá)性分析、設(shè)施選址優(yōu)化等問(wèn)題,可以有效指導(dǎo)城市規(guī)劃、區(qū)域資源分配、設(shè)施合理布局等。引力模型及衍生模型以作用量形式表達(dá)地理實(shí)體相互作用,乘法加權(quán)Voronoi圖以圖形形式反映地理實(shí)體有形邊界,兩理論、方法之間存在緊密聯(lián)系,可以有效結(jié)合。擴(kuò)展斷裂點(diǎn)模型即其中典型,自提出后,受到廣泛應(yīng)用,成為城市、區(qū)域“一體化”、“公共服務(wù)設(shè)施均等化”等政策背景下的研究熱點(diǎn)。受限于乘法加權(quán)Voronoi圖實(shí)現(xiàn)、擴(kuò)展困難等問(wèn)題,兩方法結(jié)合形式多為利用引力模型確定地理實(shí)體權(quán)重形式,借助乘法加權(quán)Voronoi圖實(shí)現(xiàn)地理實(shí)體吸引范圍劃分,缺少深層次研究及功能擴(kuò)展。兩方法結(jié)合理論有待深入挖掘,應(yīng)用有待拓展延伸。以此為出發(fā)點(diǎn),確立本文研究主題“乘法加權(quán)Voronoi圖和引力模型結(jié)合應(yīng)用及擴(kuò)展”。借助GIS工具實(shí)現(xiàn)乘法加權(quán)Voronoi圖構(gòu)建,結(jié)合相關(guān)引力模型,提出一套適合表達(dá)、分析地理實(shí)體空間格局的模型和方法,包括空間相互作用模型、空間等級(jí)體系構(gòu)建方法和空間可達(dá)性方法。針對(duì)人口老齡化加劇問(wèn)題,應(yīng)國(guó)家政策號(hào)召,選取北京市養(yǎng)老機(jī)構(gòu)為研究對(duì)象,從空間相互作用、空間等級(jí)體系和空間可達(dá)性視角探求北京市養(yǎng)老機(jī)構(gòu)空間格局,為北京市養(yǎng)老設(shè)施布局規(guī)劃提供依據(jù)與支持。主要研究?jī)?nèi)容與成果如下:(1)推導(dǎo)得出引力模型、Reilly模型、斷裂點(diǎn)模型和Huff模型經(jīng)轉(zhuǎn)換符合乘法加權(quán)Voronoi圖定義,確立了引力模型及衍生模型的圖形表達(dá)形式。(2)引力加權(quán)Voronoi圖模型研究①證明了引力模型一般形式變形后符合乘法加權(quán)Voronoi圖空間分割原理,給出引力模型、Reilly模型、斷裂點(diǎn)模型和Huff模型圖形形式的統(tǒng)一表達(dá)方式,即引力加權(quán)Voronoi圖模型,總結(jié)其性質(zhì)、推論與空間格局評(píng)價(jià)指標(biāo)。②對(duì)比了四種地理實(shí)體吸引范圍劃分方法,包括:緩沖區(qū)法、常規(guī)Voronoi圖法、服務(wù)區(qū)分析法和引力加權(quán)Voronoi圖模型法。指出引力加權(quán)Voronoi圖模型適用條件。③回顧了常用乘法加權(quán)Voronoi圖矢柵生成方法,指出兩類(lèi)方法優(yōu)缺點(diǎn),基于拓?fù)淝蟛⒎?利用C#和ArcGIS Engine,實(shí)現(xiàn)乘法加權(quán)Voronoi圖矢量生成,用于構(gòu)建引力加權(quán)Voronoi圖模型。給出算法基本思想,詳述算法功能實(shí)現(xiàn)思路。通過(guò)實(shí)驗(yàn)驗(yàn)證表明:本文方法生成的乘法加權(quán)voronoi圖包含非連通區(qū)域和空洞,符合乘法加權(quán)voronoi圖性質(zhì)。借助斑塊形狀指數(shù)驗(yàn)證空洞與等面積圓周長(zhǎng)之比,證明空洞均為標(biāo)準(zhǔn)圓形,表明本文方法生成圓弧為標(biāo)準(zhǔn)圓弧,精度為100%。生成200個(gè)點(diǎn)狀生成元(范圍:100m×100m)的乘法加權(quán)voronoi圖用時(shí)24.95s,在數(shù)據(jù)量不大、生成元所處范圍不大的情況下,算法效率較高。④確定了養(yǎng)老機(jī)構(gòu)吸引力評(píng)判指標(biāo),給出養(yǎng)老機(jī)構(gòu)吸引力指標(biāo)構(gòu)建方法。⑤利用引力加權(quán)voronoi圖模型劃分北京市養(yǎng)老機(jī)構(gòu)服務(wù)范圍,借助模型空間格局評(píng)價(jià)指標(biāo),分析了北京市養(yǎng)老機(jī)構(gòu)服務(wù)范圍、覆蓋老年人口數(shù)量、供需比等,指出北京市養(yǎng)老機(jī)構(gòu)發(fā)展現(xiàn)狀:城六區(qū)養(yǎng)老機(jī)構(gòu)服務(wù)范圍小,服務(wù)老年人口數(shù)高,遠(yuǎn)郊區(qū)縣養(yǎng)老機(jī)構(gòu)服務(wù)范圍大,服務(wù)老年人口數(shù)低;順義區(qū)養(yǎng)老機(jī)構(gòu)吸引力差距較小,昌平區(qū)、門(mén)頭溝區(qū)和延慶縣養(yǎng)老機(jī)構(gòu)吸引力差距較大;城六區(qū)養(yǎng)老機(jī)構(gòu)床位供不應(yīng)求,遠(yuǎn)郊區(qū)縣養(yǎng)老機(jī)構(gòu)床位供大于求;養(yǎng)老機(jī)構(gòu)間空間相互作用量相對(duì)均衡。(3)基于引力加權(quán)voronoi圖模型的地理實(shí)體空間等級(jí)體系構(gòu)建①提出了基于引力加權(quán)voronoi圖模型的地理實(shí)體空間層次確立方法,給出具體實(shí)現(xiàn)步驟。②結(jié)合voronoi樹(shù)圖與引力加權(quán)voronoi圖模型,給出引力加權(quán)voronoi樹(shù)圖概念,歸納相關(guān)推論,闡述算法具體實(shí)現(xiàn)。確立了基于引力加權(quán)voronoi樹(shù)圖的空間等級(jí)體系劃分方法�？偨Y(jié)引力加權(quán)voronoi樹(shù)圖與voronoi樹(shù)圖差異。③對(duì)比voronoi圖法與引力加權(quán)voronoi圖模型法異同,指出在不考慮摩擦系數(shù)情況下,兩方法構(gòu)造局部中心可能不同,點(diǎn)集歸屬可能不同。調(diào)整某生成元與鄰域生成元集合權(quán)重,voronoi圖法局部中心數(shù)量不會(huì)變化,各級(jí)點(diǎn)集歸屬不會(huì)發(fā)生變化;引力加權(quán)voronoi圖模型法的局部中心數(shù)量可能發(fā)生變化,各級(jí)點(diǎn)集歸屬可能發(fā)生變化。在考慮距離摩擦系數(shù)情況下,利用引力加權(quán)voronoi圖模型構(gòu)建空間等級(jí)體系,b趨近于0時(shí),生成元局部中心只有一個(gè),即為權(quán)重最大生成元,層次為兩層;b趨近于￥時(shí),結(jié)果與voronoi圖法一致,即顧及距離摩擦系數(shù)時(shí),voronoi圖法是引力加權(quán)voronoi圖模型法在b越趨近于￥時(shí)的特例。④利用引力加權(quán)voronoi圖模型生成乘法加權(quán)voronoi圖,確認(rèn)養(yǎng)老機(jī)構(gòu)層次與等級(jí),構(gòu)建引力加權(quán)voronoi樹(shù)圖,確立了北京市養(yǎng)老機(jī)構(gòu)四級(jí)體系。得出結(jié)論:權(quán)重大的養(yǎng)老機(jī)構(gòu)未必為局部中心、北京市養(yǎng)老機(jī)構(gòu)局部中心多位于遠(yuǎn)郊、城六區(qū)養(yǎng)老機(jī)構(gòu)高等級(jí)局部中心包含低一級(jí)局部中心數(shù)量遠(yuǎn)大于其他城區(qū)、養(yǎng)老機(jī)構(gòu)局部中心布局與老年人口密度分布基本一致。(4)基于引力加權(quán)voronoi圖模型的空間可達(dá)性分析①提出了基于引力加權(quán)voronoi圖模型的空間可達(dá)性方法。給出方法基本思想,詳述方法實(shí)現(xiàn)思路。②利用兩步移動(dòng)搜索法(空間阻隔閾值s0設(shè)為3300m、5000m、7000m、10000m等)和引力加權(quán)Voronoi圖模型法(鄰域值k設(shè)為0和1)計(jì)算北京市養(yǎng)老機(jī)構(gòu)可達(dá)性。統(tǒng)計(jì)分析兩方法可達(dá)性最小值、最大值、均值和標(biāo)準(zhǔn)差,計(jì)算不同搜索參數(shù)下兩方法所求可達(dá)性值的史皮爾曼等級(jí)相關(guān)系數(shù),運(yùn)用“最小-最大規(guī)范化”方法將兩方法可達(dá)性線(xiàn)性變換,映射到區(qū)間[1,10],對(duì)應(yīng)生成散點(diǎn)圖,可知:隨搜索范圍擴(kuò)大,兩方法統(tǒng)計(jì)參數(shù)變化趨勢(shì)相同,且均值接近。引力加權(quán)Voronoi圖模型法k取0、1時(shí),分別與兩步移動(dòng)搜索法s0取7000m、16000m所求結(jié)果相關(guān)程度最高。s0取值較小時(shí),引力加權(quán)Voronoi圖模型法計(jì)算可達(dá)性值多高于兩步移動(dòng)搜索法。s0值取值較大時(shí),引力加權(quán)Voronoi圖模型法計(jì)算可達(dá)性值多低于兩步移動(dòng)搜索法�？偨Y(jié)引力加權(quán)Voronoi模型法優(yōu)點(diǎn):克服了兩步移動(dòng)搜索法未使用空間阻隔系數(shù)、未體現(xiàn)供給點(diǎn)差異和空間相互作用等問(wèn)題,避免了區(qū)域可達(dá)性值為0的情況。③將兩步移動(dòng)搜索法和引力加權(quán)Voronoi圖模型法計(jì)算可達(dá)性值錄入北京市街道數(shù)據(jù),利用ArcGIS進(jìn)行分級(jí)渲染,對(duì)比地圖效果可知:引力加權(quán)Voronoi圖模型法k取0時(shí),可達(dá)性空間格局與兩步移動(dòng)搜索法s0取值較小時(shí)相似。k取1時(shí),與兩步移動(dòng)搜索法s0取值較大時(shí)相似。從地理學(xué)角度出發(fā),總結(jié)引力加權(quán)Voronoi圖模型法優(yōu)點(diǎn):構(gòu)建可達(dá)性空間格局過(guò)渡效果更為明顯。④基于引力加權(quán)Voronoi圖模型法描繪了北京市養(yǎng)老機(jī)構(gòu)街道尺度、區(qū)域尺度空間可達(dá)性格局。街道尺度空間格局可區(qū)分北京市高值、低值可達(dá)性區(qū)域。區(qū)域尺度可達(dá)性總體呈現(xiàn)“北高南低”的規(guī)律,且中間區(qū)域可達(dá)性較高,中心城區(qū)和遠(yuǎn)郊邊緣區(qū)域可達(dá)性較低,由城中心向遠(yuǎn)郊呈現(xiàn)“低-高-低”的層次結(jié)構(gòu)。結(jié)合北京市老年人口密度分布圖,可以體現(xiàn)北京市養(yǎng)老機(jī)構(gòu)床位供需可達(dá)性的空間錯(cuò)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.

【學(xué)位授予單位】：中國(guó)礦業(yè)大學(xué)(北京)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2016
【分類(lèi)號(hào)】：P208

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