Geographical weighted principal component analysis-based urban ecological coupling analysis method and system

Abstract

The present application provides a kind of urban ecological coupling analysis method and system of geographical weighted principal component analysis.The present application divides research area according to administrative unit and selects ecological resilience and urban resilience index and carries out normalization processing;The geometric center of each administrative unit in the study area is calculated, the weight of ecological resilience and urban resilience index is calculated by geographical weighted principal component analysis method, and the ecological-urban resilience coupling coordination degree (CCD) is further calculated;The variation trend and spatial distribution characteristics of CCD are calculated by Theil-Sen estimation and standard deviation ellipse method;The length of the long axis and the short axis of the standard deviation ellipse of the CCD of the study area, the variation trend of the CCD, are combined to judge the ecological quality and urban development level of the study area.The present application has the advantages that multi-source heterogeneous data is fused to construct an index system, the heterogeneity in space of different indexes and their dependence inertia are fully considered, and the variation trend of ecological resilience, urban resilience and CCD is accurately calculated and analyzed from the time and space dimensions respectively.

Description

Technical Field

[0001] This invention belongs to the fields of remote sensing and geographic information, and ecology, and particularly relates to a method and system for urban ecological coupling analysis using geographic weighted principal component analysis. Background Technology

[0002] With the increasing severity of global climate change, resource scarcity, and ecological degradation, the United Nations General Assembly proposed the Sustainable Development Goals in 2015, aiming to eradicate poverty, protect the Earth's environment, and promote high-quality green development in regions. As a crucial carrier of modernization, cities need to scientifically and rationally plan their production, living, and ecological spaces, properly handling the relationship between urban production, living conditions, and ecological environmental protection. Improving the quality of economic development while ensuring the quality of people's lives is a goal of my country's regional sustainable and coordinated development. Therefore, there is an urgent need to construct an evaluation system that can quantify the state of the ecological environment and urban development.

[0003] Ecological resilience and urban resilience are receiving increasing attention and importance as evaluation standards that comprehensively reflect the quality of regional ecological environment and urban development. Ecological resilience and urban resilience refer to the ability of ecosystems and urban systems to maintain their basic functional structure and recover and rebuild after facing the impact and disturbance of external factors. Accurately quantifying ecological resilience and urban resilience can provide scientific and systematic data support for regional development decisions. Promoting the continuous growth of ecological resilience and urban resilience can not only promote resource recycling and ecological environment improvement, but also enhance the adaptability and resilience of cities. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention proposes a method and system for urban ecological coupling analysis using geographic weighted principal component analysis.

[0005] The technical solution of this invention is a geographically weighted principal component analysis method for urban ecological coupling analysis, comprising the following steps: Step 1: Divide the study area into multiple administrative units according to the district and county level, and obtain multiple ecological resilience indicators and multiple urban resilience indicators for each administrative unit; Step 2: Calculate the area of ​​each administrative unit, and further calculate the geometric center of each administrative unit; Step 3: Standardize the multiple ecological resilience indicators of each administrative unit using the range standardization method to obtain multiple normalized ecological resilience indicators for each administrative unit. Standardize the multiple urban resilience indicators of each administrative unit using the range standardization method to obtain multiple normalized urban resilience indicators for each administrative unit. Step 4: Calculate the weight of each normalized ecological resilience index and the weight of each normalized urban resilience index for each administrative unit using geographic weighted principal component analysis. Step 5: Based on the calculation results of ecological resilience and urban resilience, further calculate the ecological-urban resilience coupling coordination degree; Step 6: Repeat steps 3 to 5 to calculate the ecological-urban resilience coupling coordination degree for different years, and calculate the changing trend of the ecological-urban resilience coupling coordination degree using the Thiel-Sen estimation method. Step 7: Characterize the spatial distribution of the CCD by calculating the corresponding parameters of the standard deviation ellipse; Step 8: Combine the lengths of the major and minor axes of the standard deviation ellipse of the ecological-urban coupling coordination degree of the entire study area with the changing trend of the ecological-urban resilience coupling coordination degree to determine the ecological-urban resilience coupling coordination degree of the study area. As a preferred option, the area of ​​each administrative unit in step 2 is calculated as follows: Determine the coordinates of each vertex of the administrative unit, with the vertices arranged clockwise. For each side of the polygon, calculate the area of ​​the trapezoid formed by this side and the horizontal line passing through the first vertex of the polygon. Calculate the area of ​​the entire administrative unit. The area of ​​each administrative unit is calculated using the following formula:

[0006] in, Indicates the first The area of ​​each administrative unit, This indicates the number of vertices in the administrative unit. and They represent the first The first administrative unit The latitude and longitude coordinates of each vertex. and It is the first The first administrative unit The latitude and longitude coordinates of the next vertex arranged clockwise from the previous vertex. Step 2 involves calculating the geometric center of each administrative unit, specifically as follows:

[0007]

[0008] in, Indicates the first The longitude coordinates of the geometric center of each administrative unit. Indicates the first Latitude coordinates of each administrative unit; Preferably, the multiple ecological resilience indicators of each administrative unit in step 3 are standardized using the range standardization method, as follows:

[0009] i∈[1,M], j∈[1,N] In the formula, For the first The first administrative unit A normalized ecological resilience index For the first The first administrative unit One ecological resilience indicator and These are the maximum and minimum values ​​of multiple ecological resilience indicators, where M represents the number of administrative units and N represents the number of indicators.

[0010] In the formula, For the first The first administrative unit A normalized urban resilience index For the first The first administrative unit Urban resilience indicators and These are the maximum and minimum values ​​of multiple city resilience indicators; Preferably, step 4 involves calculating the weight of each normalized ecological resilience index for each administrative unit, as detailed below:

[0011]

[0012]

[0013] In the formula, Indicates the first The variance-covariance matrix is ​​obtained by geographically weighting multiple normalized ecological resilience indicators of an administrative unit. Ecological resilience indicators matrix, Indicates the number of administrative units. Indicates the number of indicators. Indicates the first A diagonal matrix of spatial weights constructed from the Euclidean distances between the geometric center latitude and longitude coordinates of each administrative unit and the center latitude and longitude coordinates of each administrative unit. The weights of each normalized urban resilience index for each administrative unit are calculated as follows:

[0014]

[0015]

[0016] In the formula, Indicates the first The variance-covariance matrix is ​​obtained by geographically weighting the normalized indicators of urban resilience from multiple city resilience data within each administrative unit. Urban resilience indicators matrix, Indicates the number of administrative units. Indicates the number of indicators. Indicates the first A diagonal matrix of spatial weights constructed from the Euclidean distances between the geometric center latitude and longitude coordinates of each administrative unit and the center latitude and longitude coordinates of each administrative unit. The geographically weighted eigenvectors and eigenvalues ​​of the ecological resilience index are calculated by decomposing the local variance-covariance matrix, as shown in the following formula:

[0017]

[0018]

[0019] In the formula, and They are the first The diagonal matrix of the geographically weighted eigenvectors and geographically weighted eigenvalues ​​of the ecological resilience indicators of each administrative unit; For the first The first administrative unit The geographically weighted characteristic value of the first ecological resilience indicator, i.e., the first... The first administrative unit Normalized ecological resilience index Distance from each administrative unit The sum of the products of .

[0020] For the Each ecological resilience indicator for each administrative unit Weights in geographically weighted principal component analysis calculations The calculation method is as follows:

[0021]

[0022] In the formula, It is in the The first administrative unit The first ecological resilience indicator Local loads of geographically weighted principal components; Indicates the first The first administrative unit was generated by geographically weighted principal component analysis. Local variance contribution of each ecological resilience indicator; The formula for calculating the ecological resilience process using geographically weighted principal component analysis is as follows:

[0023] In the formula, ER represents ecological resilience. For the first The first administrative unit The normalized values ​​of each ecological indicator For the first The first administrative unit The weights of each ecological resilience indicator; The geographically weighted eigenvector and eigenvalues ​​of the urban resilience index are calculated by decomposing the local variance-covariance matrix, as shown in the following formula:

[0024]

[0025]

[0026] In the formula, and They are the first The diagonal matrix of geographically weighted eigenvectors and geographically weighted eigenvalues ​​of urban resilience indicators for each administrative unit; For the first The first administrative unit The geographically weighted characteristic value of the city resilience index, i.e., the first... The first administrative unit Normalized urban resilience index Distance from each administrative unit The sum of the products of .

[0027] For the The first administrative unit The weights of each city resilience index in the geographically weighted principal component analysis calculation The calculation method is as follows:

[0028]

[0029] In the formula, It is in the The first administrative unit The first of the city resilience indicators Local loads of geographically weighted principal components; Indicates the first The first administrative unit was generated by geographically weighted principal component analysis. Local variance contribution of individual city resilience indicators; The formula for calculating urban resilience processes using geographically weighted principal component analysis is as follows:

[0030] In the formula, UR represents urban resilience. For the first The first administrative unit The normalized values ​​of the city resilience index For the first The first administrative unit Weighting of city resilience indicators; As a preferred embodiment, the calculation of the ecological-urban resilience coupling coordination degree in step 5 is as follows: ,

[0031]

[0032] In the formula, The degree of coupling between urban resilience and ecological resilience. and These represent urban resilience and ecological resilience, respectively. This is an index for the coordination of ecological environment and urban development resilience. To ensure the coordination degree of ecological-urban resilience coupling; and These respectively represent the contributions of ecological resilience and urban resilience to regional development; Preferably, step 6 involves calculating the slope of the straight line using robust nonparametric statistics to assess the coordination degree of the ecological-urban resilience coupling through Thiel-Sen estimation, as detailed below:

[0033] In the formula, Indicates the starting year of the phase. Indicates the year the phase ends. and This indicates the CCD for the corresponding year. This indicates that the CCD is showing an upward trend during this period. This indicates that the CCD is showing a downward trend during this stage. Indicates taking the median value; The significance of the CCD time series trend calculation results estimated by Thiel-Sen was tested using the MK test. The formula is as follows:

[0034]

[0035]

[0036]

[0037]

[0038]

[0039] In the formula, This indicates the number of years in which the Eco-Urban Resilience Coupling Coordination (CCD) was included in the calculation. It is a symbolic function.

[0040] Preferably, the formulas for calculating the length of the major axis, the length of the minor axis, and the direction angle of the major axis of the standard deviation ellipse in step 7 are as follows:

[0041]

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] In the formula, This refers to the number of administrative units within the region. For the first Eco-urban coupling coordination degree of each administrative unit and The first number calculated in step 2 is respectively The geometric coordinates of latitude and longitude of each administrative unit; and The first The x-coordinate and y-coordinate of the center point of the standard deviation ellipse of each administrative unit; and The first The coordinate deviation of the spatial coordinates of each administrative unit from the average center; , These represent the lengths of the major and minor axes of the ellipse representing the standard deviation of the ecological-urban coupling coordination degree across the entire study area; The direction angle of the major axis of the standard deviation ellipse is the angle between due north and the major axis of the ellipse in a clockwise direction; Indicates the first The CCD of each administrative unit is used as the weight; the major axis of the standard deviation ellipse represents the distribution direction of the CCD, and the minor axis represents the distribution range of the CCD. The larger the ratio of the major axis to the minor axis of the standard deviation ellipse, the more obvious the directionality of the CCD distribution, and vice versa. Using the CCD of each administrative unit as a weight, the movement process of the center of gravity is calculated and analyzed based on the coordinate position of the corresponding administrative unit, as shown in the following formula:

[0048] In the formula, and The first The longitude and latitude coordinates of the weighted average center of each administrative unit. and The first The longitude and latitude coordinates of the geographical center of each administrative unit. For the first CCD value of each administrative unit.

[0049] Preferably, step 8 is as follows: when and At that time, the ecological-urban resilience coupling coordination degree of the study area showed a low clustering growth trend, reflecting that the ecological quality and urban economic level of the multiple administrative units with relatively dispersed spatial distribution in the study area are in a development mode of continuous improvement. when and At that time, the ecological-urban resilience coupling coordination degree in the study area showed a high clustering growth trend, reflecting that the ecological quality and urban economic level of multiple administrative units with relatively concentrated spatial distribution in the study area are in a development mode of continuous improvement. when and At that time, the ecological-urban resilience coupling coordination degree in the study area showed a high clustering growth trend, reflecting that the ecological quality and urban economic level of multiple administrative units with relatively dispersed spatial distribution in the study area were in a development pattern of continuous decline. when and At that time, the ecological-urban resilience coupling coordination degree in the study area showed a high clustering growth trend, reflecting that the ecological quality and urban economic level of multiple administrative units with relatively concentrated spatial distribution in the study area were in a development pattern of continuous decline.

[0050] The technical solution of this invention is a geographically weighted principal component analysis urban ecological coupling analysis system, comprising the following steps: The module for obtaining resilience indicators of administrative units is used to divide the study area into multiple administrative units according to the district and county level, and to obtain multiple ecological resilience indicators and multiple urban resilience indicators for each administrative unit. The administrative unit geometric center calculation module is used to calculate the area of ​​each administrative unit and further calculate the geometric center of each administrative unit. The Administrative Unit Resilience Index Normalization Module is used to standardize multiple ecological resilience indicators of each administrative unit using the range standardization method to obtain multiple normalized ecological resilience indicators for each administrative unit. It also uses the range standardization method to standardize multiple urban resilience indicators of each administrative unit to obtain multiple normalized urban resilience indicators for each administrative unit. The weight calculation module for the resilience index of administrative units is used to calculate the weight of each normalized ecological resilience index and the weight of each normalized urban resilience index of each administrative unit using the geographically weighted principal component analysis method. The Eco-Urban Resilience Coupling Coordination Degree Calculation Module is used to further calculate the Eco-Urban Resilience Coupling Coordination Degree based on the calculation results of Ecological Resilience and Urban Resilience. The Eco-Urban Resilience Coupling Change Trend Calculation Module is used to repeatedly call the Administrative Unit Resilience Index Normalization Module, the Administrative Unit Resilience Index Weight Calculation Module, and the Eco-Urban Resilience Coupling Coordination Degree Calculation Module in sequence to calculate the Eco-Urban Resilience Coupling Coordination Degree in different years and calculate the change trend of Eco-Urban Resilience Coupling Coordination Degree through the Thiel-Sen estimation method. The spatial distribution feature characterization module is used to characterize the spatial distribution features of the CCD by calculating the corresponding parameters of the standard deviation ellipse. The module for judging the coordination degree of ecological and urban resilience coupling is used to judge the coordination degree of ecological and urban resilience coupling in the study area by combining the length of the major axis and the length of the minor axis of the standard deviation ellipse of the ecological-urban coupling coordination degree of the entire study area and the changing trend of the ecological-urban resilience coupling coordination degree. Compared to existing methods, the advantages and positive effects of this invention are as follows: Most existing methods only analyze single ecosystems that focus on ecological environment or urban economic development. In contrast, this method first integrates multi-source heterogeneous data and scientifically selects a large number of evaluation indicators based on the overall situation of the region to analyze ecological resilience and urban resilience and their coupling and coordination relationship.

[0051] This invention calculates indicator weights using geographic weighted principal component analysis. Compared to the more subjective analytic hierarchy process (AHP) and the entropy weight method, which is easily affected by fluctuations in indicator size, geographic weighted principal component analysis not only calculates weights based on the contribution of different indicators, but also fully considers the spatial heterogeneity and dependency inertia of different indicators, making the CCD calculation results more accurate.

[0052] By conducting multi-scale analysis of CCD calculation results from the temporal and spatial dimensions, it is possible not only to reflect the CCD value change process of different levels of administrative units, but also to divide, for example, the upper reaches of the Yangtze River, the middle reaches of the Yangtze River, and the lower reaches of the Yangtze River, and to compare and evaluate the spatiotemporal change process of CCD between different regions. Attached Figure Description

[0053] Figure 1 : Flowchart of the method according to an embodiment of the present invention.

[0054] Figure 2 : Spatial distribution map of the ecological-urban resilience coupling coordination degree of the Yangtze River Economic Belt in this embodiment of the invention. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] In specific implementation, the method proposed in the technical solution of this invention can be automatically executed by those skilled in the art using computer software technology. System devices for implementing the method, such as computer-readable storage media storing the corresponding computer program of the technical solution of this invention and computer equipment including the computer program running the corresponding computer program, should also be within the protection scope of this invention.

[0057] This study selects the Yangtze River Economic Belt as the research object and conducts analysis. As an important economic development corridor in China, the Yangtze River Economic Belt covers more than 20% of the country's total area, and its population and economy both account for over 40%. As of 2020, the GDP of the Yangtze River Economic Belt accounted for 44.28% of the national total, and after years of development, it has become a vital hinterland for China's economy. The Yangtze River Basin is rich in ecological resources and biodiversity, with diverse and abundant mineral resources, and it also contains enormous water and hydropower resources, providing crucial guarantees and support for the resource needs of regional industrial development. This embodiment uses various districts and counties within the Yangtze River Economic Belt as research data units, with a research timeframe from 2000 to 2020.

[0058] Selection of Ecological and Urban Resilience Indicators. Based on the geographical location, ecological environment, and urban development of the Yangtze River Economic Belt, representative, systematic, and data-accessible indicators were selected. The indicators for evaluating ecological resilience were constructed from multiple dimensions, including vegetation, soil, water, and air. These indicators mainly include 11 items: temperature, precipitation, urban heat island risk index, precipitation erosivity, total solar radiation, vegetation cover, leaf area index, net primary productivity of vegetation, soil moisture, standardized precipitation evapotranspiration index, and PM2.5. These indicators comprehensively reflect the ecological resilience of the Yangtze River Economic Belt by focusing on the causal relationship between human activities and the ecological environment. Detailed county-level districts were selected as research units, and indicators were constructed from the perspectives of population, economy, urban development, and carbon emissions to quantify the Yangtze River Economic Belt's ability to maintain urban functions and promote urban development during rapid urban growth. The evaluation indicators for assessing urban resilience are constructed from multiple perspectives, including "city-population-economy". They mainly include 10 indicators: population density, population growth rate, urban area ratio, urban population size, urban population proportion, per capita arable land area, per capita GDP, fossil fuel CO2 emissions, nighttime light intensity, and nighttime light concentration index.

[0059] Data preprocessing is performed based on the acquired data types: ① Raster data: Since the acquired raster data comes from various types and methods such as product datasets, remote sensing inversion calculations, and Google Earth Engine, according to the research method of this embodiment, the raster data needs to be unified to a 1km spatial resolution through data resampling; ② Point vector data: The selected indicators include meteorological station data such as temperature, precipitation, and radiation, which need to be interpolated to 1km spatial resolution raster data through methods such as inverse distance weighting or Kriging interpolation; ③ Statistical form data: Based on the corresponding district / county location, the data is converted into point vector data, and then the data is interpolated to convert it into 1km spatial resolution raster data.

[0060] Based on the data category and nature, raster data of uniform resolution is used to calculate the indicator values ​​for each district and county through methods such as mean synthesis, maximum value synthesis, and cluster calculation.

[0061] The names and data sources of the data are shown in Table 1: Table 1: Ecological and Environmental Data and Urban Development Data of the Yangtze River Economic Belt

[0062] The following is in conjunction with the appendix Figure 1-2 The specific implementation of this invention is a motion planning method and system based on a risk potential field map, as detailed below: Figure 1 This is a flowchart of a method according to an embodiment of the present invention.

[0063] Step 1: Divide the Yangtze River Economic Belt into multiple administrative units at the county and district levels, and obtain multiple ecological resilience indicators and multiple urban resilience indicators for each administrative unit. The ecological resilience indicators include 11 indicators: temperature, precipitation, urban heat island risk index, precipitation erosivity, total solar radiation, vegetation coverage, leaf area index, net primary productivity of vegetation, soil moisture, standardized precipitation evapotranspiration index, and PM2.5. The urban resilience indicators include 10 indicators: population density, population growth rate, urban area ratio, urban population size, urban population proportion, per capita arable land area, per capita GDP, fossil fuel CO2 emissions, nighttime light intensity, and nighttime light concentration index.

[0064] Step 2: Calculate the area of ​​each administrative unit in the Yangtze River Economic Belt, and further calculate the geometric center of each administrative unit; The area of ​​each administrative unit mentioned in step 2 is calculated in the following specific process: Determine the coordinates of each vertex of each administrative unit in the Yangtze River Economic Belt. The vertices are arranged in a clockwise direction. For each side of the polygon, calculate the area of ​​the trapezoid formed by this side and the horizontal line passing through the first vertex of the polygon. Calculate the area of ​​the entire administrative unit. The area of ​​each administrative unit is calculated using the following formula:

[0065] in, Indicating the first in the Yangtze River Economic Belt The area of ​​each administrative unit, This indicates the number of vertices in the administrative unit. and They represent the first The first administrative unit The latitude and longitude coordinates of each vertex. and It is the first The first administrative unit The latitude and longitude coordinates of the next vertex arranged clockwise from the previous vertex. Step 3 involves calculating the geometric center of each administrative unit within the Yangtze River Economic Belt. The specific calculation is as follows:

[0066]

[0067] in, Indicates the first The longitude coordinates of the geometric center of each administrative unit. Indicates the first Latitude coordinates of each administrative unit; Step 3: Standardize multiple ecological resilience indicators of each administrative unit in the Yangtze River Economic Belt using the range standardization method to obtain multiple normalized ecological resilience indicators for each administrative unit. Standardize multiple urban resilience indicators of each administrative unit using the range standardization method to obtain multiple normalized urban resilience indicators for each administrative unit. Step 3 describes the standardization of multiple ecological resilience indicators for each administrative unit within the Yangtze River Economic Belt using the range standardization method, as follows:

[0068] i∈[1,M], j∈[1,N] In the formula, For the Yangtze River Economic Belt The first administrative unit A normalized ecological resilience index For the first The first administrative unit One ecological resilience indicator and These are the maximum and minimum values ​​of multiple ecological resilience indicators, where M represents the number of administrative units and N represents the number of indicators.

[0069] In the formula, For the first The first administrative unit A normalized urban resilience index For the first The first administrative unit Urban resilience indicators and These are the maximum and minimum values ​​of multiple city resilience indicators; Step 4: Calculate the weight of each normalized ecological resilience index and the weight of each normalized urban resilience index for each administrative unit in the Yangtze River Economic Belt using geographically weighted principal component analysis. Step 4 involves calculating the weight of each normalized ecological resilience index for each administrative unit, as detailed below:

[0070]

[0071]

[0072] In the formula, This indicates the first in the Yangtze River Economic Belt The variance-covariance matrix is ​​obtained by geographically weighting multiple normalized ecological resilience indicators of an administrative unit. Ecological resilience indicators matrix, This indicates the number of administrative units within the Yangtze River Economic Belt. Indicates the number of indicators. This indicates the first in the Yangtze River Economic Belt A diagonal matrix of spatial weights constructed from the Euclidean distances between the geometric center latitude and longitude coordinates of each administrative unit and the center latitude and longitude coordinates of each administrative unit. The weights of each normalized urban resilience index for each administrative unit in the Yangtze River Economic Belt are calculated as follows:

[0073]

[0074]

[0075] In the formula, This indicates the first in the Yangtze River Economic Belt The variance-covariance matrix is ​​obtained by geographically weighting the normalized indicators of urban resilience from multiple city resilience data within each administrative unit. Urban resilience indicators matrix, This indicates the number of administrative units within the Yangtze River Economic Belt. Indicates the number of indicators. This indicates the first in the Yangtze River Economic Belt A diagonal matrix of spatial weights constructed from the Euclidean distances between the geometric center latitude and longitude coordinates of each administrative unit and the center latitude and longitude coordinates of each administrative unit. The geographically weighted eigenvectors and eigenvalues ​​of the ecological resilience index are calculated by decomposing the local variance-covariance matrix, as shown in the following formula:

[0076]

[0077]

[0078] In the formula, and They are the first in the Yangtze River Economic Belt The diagonal matrix of the geographically weighted eigenvectors and geographically weighted eigenvalues ​​of the ecological resilience indicators of each administrative unit; The first in the Yangtze River Economic Belt The first administrative unit The geographically weighted characteristic value of the first ecological resilience indicator, i.e., the first... The first administrative unit Normalized ecological resilience index Distance from each administrative unit The sum of the products of .

[0079] For the first in the Yangtze River Economic Belt Each ecological resilience indicator for each administrative unit Weights in geographically weighted principal component analysis calculations The calculation method is as follows:

[0080]

[0081] In the formula, It is the first in the Yangtze River Economic Belt The first administrative unit The first ecological resilience indicator Local loads of geographically weighted principal components; This indicates the first in the Yangtze River Economic Belt The first administrative unit was generated by geographically weighted principal component analysis. Local variance contribution of each ecological resilience indicator; The formula for calculating the ecological resilience process using geographically weighted principal component analysis is as follows:

[0082] In the formula, ER represents ecological resilience. The first in the Yangtze River Economic Belt The first administrative unit The normalized values ​​of each ecological indicator The first in the Yangtze River Economic Belt The first administrative unit The weights of each ecological resilience indicator; The geographically weighted eigenvector and eigenvalues ​​of the urban resilience index are calculated by decomposing the local variance-covariance matrix, as shown in the following formula:

[0083]

[0084]

[0085] In the formula, and They are the first in the Yangtze River Economic Belt The diagonal matrix of geographically weighted eigenvectors and geographically weighted eigenvalues ​​of urban resilience indicators for each administrative unit; The first in the Yangtze River Economic Belt The first administrative unit The geographically weighted characteristic value of the city resilience index, i.e., the first... The first administrative unit Normalized urban resilience index Distance from each administrative unit The sum of the products of .

[0086] For the first in the Yangtze River Economic Belt The first administrative unit The weights of each city resilience index in the geographically weighted principal component analysis calculation The calculation method is as follows:

[0087]

[0088] In the formula, It is the first in the Yangtze River Economic Belt The first administrative unit The first of the city resilience indicators Local loads of geographically weighted principal components; This indicates the first in the Yangtze River Economic Belt The first administrative unit was generated by geographically weighted principal component analysis. Local variance contribution of individual city resilience indicators; The formula for calculating urban resilience processes using geographically weighted principal component analysis is as follows:

[0089] In the formula, UR represents urban resilience. The first in the Yangtze River Economic Belt The first administrative unit The normalized values ​​of the city resilience index The first in the Yangtze River Economic Belt The first administrative unit Weighting of city resilience indicators; Step 5: Based on the calculation results of ecological resilience and urban resilience, further calculate the ecological-urban resilience coupling coordination degree; Step 5, which calculates the ecological-urban resilience coupling coordination degree, is as follows: ,

[0090]

[0091] In the formula, The degree of coupling between urban resilience and ecological resilience. and These represent urban resilience and ecological resilience, respectively. This is an index for the coordination of ecological environment and urban development resilience. To ensure the coordination degree of ecological-urban resilience coupling; and These respectively represent the contributions of ecological resilience and urban resilience to regional development; Ecological resilience and urban resilience play equally important roles in regional ecological priority and intensive development, therefore they are usually set as... The calculated CCD results for the Yangtze River Economic Belt are as follows: Figure 2 As shown.

[0092] Step 6: CCD time-varying trend analysis. Robust nonparametric statistical trend calculation is performed using Thiel-Sen estimation, which has the advantages of being independent of data distribution and having strong robustness. By selecting the median of the slope of a straight line constructed from paired points, a straight line is fitted to the sampled points in the plane. The formula for calculating the changing trend of CCDs in various districts and counties of the Yangtze River Economic Belt from 2000 to 2020 is as follows:

[0093] In the formula, Indicates the starting year of the phase. Indicates the year the phase ends. and This indicates the CCD for the corresponding year. This indicates that the CCD (Carbon Diode) of the Yangtze River Economic Belt showed an upward trend during this period. This indicates that the CCD of the Yangtze River Economic Belt showed a downward trend during this period. This represents the median. The significance of the CCD time series trend calculation results estimated by Thiel-Sen is tested using the MK test. The formula is as follows:

[0094]

[0095]

[0096]

[0097]

[0098]

[0099] In the formula, This indicates the number of years in which the Eco-Urban Resilience Coupling Coordination (CCD) was included in the calculation. It is a symbolic function.

[0100] Step 7: Characterize the spatial distribution of the CCD by calculating the corresponding parameters of the standard deviation ellipse; Step 7: The formulas for calculating the length of the major axis, the length of the minor axis, and the direction angle of the major axis of the standard deviation ellipse are as follows:

[0101]

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] In the formula, The number of administrative units in the Yangtze River Economic Belt. The first in the Yangtze River Economic Belt Eco-urban coupling coordination degree of each administrative unit and These are the first two numbers in the Yangtze River Economic Belt calculated in step 2. The geometric coordinates of latitude and longitude of each administrative unit; and They are the first in the Yangtze River Economic Belt The x-coordinate and y-coordinate of the center point of the standard deviation ellipse of each administrative unit; and The first The coordinate deviation of the spatial coordinates of each administrative unit from the average center; , These represent the lengths of the major and minor axes of the ellipse representing the standard deviation of the ecological-urban coupling coordination degree in the Yangtze River Economic Belt. The direction angle of the major axis of the standard deviation ellipse is the angle between due north and the major axis of the ellipse in a clockwise direction; This indicates that the first [part of] the Yangtze River Economic Belt The CCD of each administrative unit is used as the weight; the major axis of the standard deviation ellipse represents the distribution direction of the standard deviation ellipse of the CCD in the Yangtze River Economic Belt, and the minor axis represents the distribution range of the standard deviation ellipse of the CCD. The larger the ratio of the major axis to the minor axis of the standard deviation ellipse, the more obvious the directionality of the CCD distribution, and vice versa. Using the CCD of each administrative unit as a weight, the movement process of the center of gravity is calculated and analyzed based on the coordinate position of the corresponding administrative unit, as shown in the following formula:

[0108] In the formula, and They are the first in the Yangtze River Economic Belt The longitude and latitude coordinates of the weighted average center of each administrative unit. and They are the first in the Yangtze River Economic Belt The longitude and latitude coordinates of the geographical center of each administrative unit. For the first CCD value of each administrative unit.

[0109] Step 8: Combine the lengths of the major and minor axes of the standard deviation ellipse of the ecological-urban coupling coordination degree in the Yangtze River Economic Belt with the changing trend of the ecological-urban resilience coupling coordination degree to determine the ecological-urban resilience coupling coordination degree in the study area. Step 8 is described in detail below: when and At that time, the ecological-urban resilience coupling coordination degree of the Yangtze River Economic Belt showed a low-cluster growth trend, reflecting that the ecological quality and urban economic level of multiple administrative units with relatively dispersed spatial distribution in the Yangtze River Economic Belt are in a development mode of continuous improvement. when and At that time, the ecological-urban resilience coupling coordination degree of the Yangtze River Economic Belt showed a high clustering growth trend, reflecting that the ecological quality and urban economic level of multiple administrative units with relatively concentrated spatial distribution in the Yangtze River Economic Belt are in a development mode of continuous improvement. when and At that time, the ecological-urban resilience coupling coordination degree of the Yangtze River Economic Belt showed a high clustering growth trend, reflecting that the ecological quality and urban economic level of multiple administrative units with relatively dispersed spatial distribution in the Yangtze River Economic Belt were in a development mode of continuous decline. when and At that time, the ecological-urban resilience coupling coordination degree of the Yangtze River Economic Belt showed a high clustering growth trend, reflecting that the ecological quality and urban economic level of multiple administrative units with relatively concentrated spatial distribution in the Yangtze River Economic Belt were in a development pattern of continuous decline.

[0110] This invention provides a geographically weighted principal component analysis system for urban ecological coupling analysis, comprising: The module for obtaining resilient indicators of administrative units is used to divide the Yangtze River Economic Belt into multiple administrative units according to the district and county level, and to obtain multiple ecological resilience indicators and multiple urban resilience indicators for each administrative unit. The administrative unit geometric center calculation module is used to calculate the area of ​​each administrative unit and further calculate the geometric center of each administrative unit. The Administrative Unit Resilience Index Normalization Module is used to standardize multiple ecological resilience indicators of each administrative unit using the range standardization method to obtain multiple normalized ecological resilience indicators for each administrative unit. It also uses the range standardization method to standardize multiple urban resilience indicators of each administrative unit to obtain multiple normalized urban resilience indicators for each administrative unit. The weight calculation module for the resilience index of administrative units is used to calculate the weight of each normalized ecological resilience index and the weight of each normalized urban resilience index of each administrative unit using the geographically weighted principal component analysis method. The Eco-Urban Resilience Coupling Coordination Degree Calculation Module is used to further calculate the Eco-Urban Resilience Coupling Coordination Degree based on the calculation results of Ecological Resilience and Urban Resilience. The Eco-Urban Resilience Coupling Change Trend Calculation Module is used to repeatedly call the Administrative Unit Resilience Index Normalization Module, the Administrative Unit Resilience Index Weight Calculation Module, and the Eco-Urban Resilience Coupling Coordination Degree Calculation Module in sequence to calculate the Eco-Urban Resilience Coupling Coordination Degree in different years and calculate the change trend of Eco-Urban Resilience Coupling Coordination Degree through the Thiel-Sen estimation method. The spatial distribution feature characterization module is used to characterize the spatial distribution features of the CCD by calculating the corresponding parameters of the standard deviation ellipse. The Ecological-Urban Resilience Coupling Coordination Degree Assessment Module is used to assess the ecological-urban resilience coupling coordination degree of the study area by combining the lengths of the major and minor axes of the standard deviation ellipse of the ecological-urban coupling coordination degree across the entire study area and the changing trend of the ecological-urban resilience coupling coordination degree.

[0111] The aforementioned modules for calculating the geometric center of administrative units, normalizing the resilience index of administrative units, calculating the weight of the resilience index of administrative units, calculating the coordination degree of ecological-urban resilience coupling, calculating the changing trend of ecological-urban resilience coupling, characterizing the spatial distribution, and judging the coordination degree of ecological-urban resilience coupling are all deployed on the server.

[0112] It should be understood that any parts not described in detail in this specification belong to the prior art.

[0113] It should be understood that the above description of the embodiments is quite detailed, but it should not be considered as a limitation on the scope of protection of this invention. Those skilled in the art can make substitutions or modifications under the guidance of this invention without departing from the scope of protection of the claims of this invention, and all such substitutions or modifications fall within the scope of protection of this invention. The scope of protection of this invention should be determined by the appended claims.

Claims

1. A method of urban ecological coupling analysis by geographic weighted principal component analysis, characterized in that, Includes the following steps: Step 1: Divide the study area into multiple administrative units according to the district and county level, and obtain multiple ecological resilience indicators and multiple urban resilience indicators for each administrative unit; Step 2: Calculate the area of ​​each administrative unit, and further calculate the geometric center of each administrative unit; Step 3: Standardize the multiple ecological resilience indicators of each administrative unit using the range standardization method to obtain multiple normalized ecological resilience indicators for each administrative unit. Standardize the multiple urban resilience indicators of each administrative unit using the range standardization method to obtain multiple normalized urban resilience indicators for each administrative unit. Step 4: Calculate the weight of each normalized ecological resilience index and the weight of each normalized urban resilience index for each administrative unit using geographic weighted principal component analysis. Step 5: Based on the calculation results of ecological resilience and urban resilience, further calculate the ecological-urban resilience coupling coordination degree; Step 6: Repeat steps 3 to 5 to calculate the ecological-urban resilience coupling coordination degree for different years, and calculate the changing trend of the ecological-urban resilience coupling coordination degree using the Thiel-Sen estimation method. Step 7: Characterize the spatial distribution of the CCD by calculating the corresponding parameters of the standard deviation ellipse; Step 8: Combine the lengths of the major and minor axes of the standard deviation ellipse of the ecological-urban coupling coordination degree of the entire study area with the changing trend of the ecological-urban resilience coupling coordination degree to determine the ecological-urban resilience coupling coordination degree of the study area.

2. The urban ecological coupling analysis method based on geographic weighted principal component analysis according to claim 1, characterized in that: The area of ​​each administrative unit mentioned in step 2 is calculated in the following specific process: Determine the coordinates of each vertex of the administrative unit, with the vertices arranged clockwise. For each side of the polygon, calculate the area of ​​the trapezoid formed by this side and the horizontal line passing through the first vertex of the polygon. Calculate the area of ​​the entire administrative unit. The area of ​​each administrative unit is calculated using the following formula: in, Indicates the first The area of ​​each administrative unit, This indicates the number of vertices in the administrative unit. and They represent the first The first administrative unit The latitude and longitude coordinates of each vertex. and It is the first The first administrative unit The latitude and longitude coordinates of the next vertex arranged clockwise from the previous vertex.

3. The urban ecological coupling analysis method based on geographic weighted principal component analysis according to claim 2, characterized in that: Step 2 involves calculating the geometric center of each administrative unit, specifically as follows: in, Indicates the first The longitude coordinates of the geometric center of each administrative unit. Indicates the first Latitude coordinates of each administrative unit.

4. The urban ecological coupling analysis method based on geographic weighted principal component analysis according to claim 3, characterized in that: Step 3 describes the standardization of multiple ecological resilience indicators for each administrative unit using the range standardization method, as follows: i∈[1,M], j∈[1,N] In the formula, For the first The first administrative unit A normalized ecological resilience index For the first The first administrative unit One ecological resilience indicator and These are the maximum and minimum values ​​of multiple ecological resilience indicators, where M represents the number of administrative units and N represents the number of indicators. In the formula, For the first The first administrative unit A normalized urban resilience index For the first The first administrative unit Urban resilience indicators and These are the maximum and minimum values ​​of multiple city resilience indicators.

5. The urban ecological coupling analysis method based on geographic weighted principal component analysis according to claim 4, characterized in that: Step 4 involves calculating the weight of each normalized ecological resilience index for each administrative unit, as detailed below: In the formula, Indicates the first The variance-covariance matrix is ​​obtained by geographically weighting multiple normalized ecological resilience indicators of an administrative unit. Ecological resilience indicators matrix, Indicates the number of administrative units. Indicates the number of indicators. Indicates the first A diagonal matrix of spatial weights constructed from the Euclidean distances between the geometric center latitude and longitude coordinates of each administrative unit and the center latitude and longitude coordinates of each administrative unit. The weights of each normalized urban resilience index for each administrative unit are calculated as follows: In the formula, Indicates the first The variance-covariance matrix is ​​obtained by geographically weighting the normalized indicators of urban resilience from multiple city resilience data within each administrative unit. Urban resilience indicators matrix; The geographically weighted eigenvectors and eigenvalues ​​of the ecological resilience index are calculated by decomposing the local variance-covariance matrix, as shown in the following formula: In the formula, and They are the first The diagonal matrix of the geographically weighted eigenvectors and geographically weighted eigenvalues ​​of the ecological resilience indicators of each administrative unit; For the first The first administrative unit The geographically weighted characteristic value of the first ecological resilience indicator, i.e., the first... The first administrative unit Normalized ecological resilience index Distance from each administrative unit The sum of the products of; For the Each ecological resilience indicator for each administrative unit Weights in geographically weighted principal component analysis calculations The calculation method is as follows: In the formula, It is in the The first administrative unit The first ecological resilience indicator Local loads of geographically weighted principal components; Indicates the first The first administrative unit was generated by geographically weighted principal component analysis. Local variance contribution of each ecological resilience indicator; The formula for calculating the ecological resilience process using geographically weighted principal component analysis is as follows: In the formula, ER represents ecological resilience. For the first The first administrative unit The normalized values ​​of each ecological indicator For the first The first administrative unit The weights of each ecological resilience indicator; The geographically weighted eigenvector and eigenvalues ​​of the urban resilience index are calculated by decomposing the local variance-covariance matrix, as shown in the following formula: In the formula, and They are the first The diagonal matrix of geographically weighted eigenvectors and geographically weighted eigenvalues ​​of urban resilience indicators for each administrative unit; For the first The first administrative unit The geographically weighted characteristic value of the city resilience index, i.e., the first... The first administrative unit Normalized urban resilience index Distance from each administrative unit The sum of the products of; For the The first administrative unit The weights of each city resilience index in the geographically weighted principal component analysis calculation The calculation method is as follows: In the formula, It is in the The first administrative unit The first of the city resilience indicators Local loads of geographically weighted principal components; Indicates the first The first administrative unit's geographic weighted principal component analysis generated the... Local variance contribution of individual city resilience indicators; The formula for calculating urban resilience processes using geographically weighted principal component analysis is as follows: In the formula, UR represents urban resilience. For the first The first administrative unit The normalized values ​​of the city resilience index For the first The first administrative unit The weights of each city's resilience indicators.

6. The urban ecological coupling analysis method based on geographic weighted principal component analysis according to claim 5, characterized in that: Step 6 describes the slope of the straight line obtained by robustly calculating the nonparametric statistical trend of the ecological-urban resilience coupling coordination degree using Thiel-Sen estimation, as detailed below: In the formula, Indicates the starting year of the phase. Indicates the year the phase ends. and This indicates the CCD for the corresponding year. This indicates that the CCD is showing an upward trend during this period. This indicates that the CCD is showing a downward trend during this stage. Indicates taking the median value; The significance of the results of the Theil-Sen estimate of the trend of the time series of the CCD was tested by means of the MK test The formula is as follows: wherein represents the number of years of the eco-city resilience coupling coordination degree (CCD) participating in the calculation, is a symbol function.

7. The urban ecological coupling analysis method based on geographic weighted principal component analysis according to claim 1, characterized in that: The formulas for calculating the length of the major axis, the length of the minor axis, and the direction angle of the major axis of the standard deviation ellipse described in step 7 are as follows: In the formula, This refers to the number of administrative units within the region. For the first Eco-urban coupling coordination degree of each administrative unit and The first number calculated in step 2 is respectively The geometric coordinates of latitude and longitude of each administrative unit; and The first The x-coordinate and y-coordinate of the center point of the standard deviation ellipse of each administrative unit; and The first The coordinate deviation of the spatial coordinates of each administrative unit from the average center; , These represent the lengths of the major and minor axes of the ellipse representing the standard deviation of the ecological-urban coupling coordination degree across the entire study area; The direction angle of the major axis of the standard deviation ellipse is the angle between due north and the major axis of the ellipse in a clockwise direction; Indicates the first The CCD of each administrative unit is used as the weight; the major axis of the standard deviation ellipse represents the distribution direction of the CCD, and the minor axis represents the distribution range of the CCD. The larger the ratio of the major axis to the minor axis of the standard deviation ellipse, the more obvious the directionality of the CCD distribution, and vice versa. Using the CCD of each administrative unit as a weight, the movement process of the center of gravity is calculated and analyzed based on the coordinate position of the corresponding administrative unit, as shown in the following formula: wherein and are the coordinates of the longitude and latitude of the weighted average center of the first administrative unit, respectively. 8.A system for urban eco-coupling analysis by geographical weighted principal component analysis, characterized in that, Includes the following steps: The module for obtaining resilience indicators of administrative units is used to divide the study area into multiple administrative units according to the district and county level, and to obtain multiple ecological resilience indicators and multiple urban resilience indicators for each administrative unit. The administrative unit geometric center calculation module is used to calculate the area of ​​each administrative unit and further calculate the geometric center of each administrative unit. The Administrative Unit Resilience Index Normalization Module is used to standardize multiple ecological resilience indicators of each administrative unit using the range standardization method to obtain multiple normalized ecological resilience indicators for each administrative unit. It also uses the range standardization method to standardize multiple urban resilience indicators of each administrative unit to obtain multiple normalized urban resilience indicators for each administrative unit. The weight calculation module for the resilience index of administrative units is used to calculate the weight of each normalized ecological resilience index and the weight of each normalized urban resilience index of each administrative unit using the geographically weighted principal component analysis method. The Eco-Urban Resilience Coupling Coordination Degree Calculation Module is used to further calculate the Eco-Urban Resilience Coupling Coordination Degree based on the calculation results of Ecological Resilience and Urban Resilience. The Eco-Urban Resilience Coupling Change Trend Calculation Module is used to repeatedly call the Administrative Unit Resilience Index Normalization Module, the Administrative Unit Resilience Index Weight Calculation Module, and the Eco-Urban Resilience Coupling Coordination Degree Calculation Module in sequence to calculate the Eco-Urban Resilience Coupling Coordination Degree in different years and calculate the change trend of Eco-Urban Resilience Coupling Coordination Degree through the Thiel-Sen estimation method. The spatial distribution feature characterization module is used to characterize the spatial distribution features of the CCD by calculating the corresponding parameters of the standard deviation ellipse. The Ecological-Urban Resilience Coupling Coordination Degree Assessment Module is used to assess the ecological-urban resilience coupling coordination degree of the study area by combining the lengths of the major and minor axes of the standard deviation ellipse of the ecological-urban coupling coordination degree across the entire study area and the changing trend of the ecological-urban resilience coupling coordination degree.

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