In the first post () we have described how thermal potentials can be used to analyze territories in general. In the following publications, it was planned to describe how information about spatial objects is stored in databases, how models are built from the main components, and in general what tasks of territory analysis can be. But first things first.
The use of the method of thermal potentials, first of all, makes it possible to form a general idea of the territory of interest to us. For example, taking the initial information from OSM for Barcelona (Catalonia), and, having carried out an integral analysis without selecting parameters, we can obtain "thermal" images of the first principal components. We also talked about "heat" maps in the first article, but it would not be superfluous to recall that the term "heat map" arose due to the physical meaning of the potentials used for integral analysis. Those. in the problems of physics, the potential is temperature, and in the problems of territory analysis, the potential is the total effect of all factors of influence on a specific point of the territory.
Below is an example of a "heat" map of Barcelona, obtained as a result of an integral analysis.
"Heat" map of the first principal component, without selection of parameters, Barcelona
And by setting a specific parameter (in this case, we chose industry), you can get a "heat" map directly from it.
"Heat" map of the first principal component, industry, Barcelona
Of course, the analysis tasks are much broader and more diverse than obtaining a general assessment of the selected territory, therefore, as an example, in this article we will consider the problem of finding the best place when placing a new object and the technical implementation of the thermal potential method for its solution, and in the following publications we will look at others.
Solving the problem of finding the best place when placing a new object will help determine how much the territory is “ready to accept” this new object, how it will correlate with other objects already existing in the territory, how valuable this new object will be for the territory and what value it will add.
Stages of technical implementation
The technical implementation can be represented by the sequence of performing the procedures listed below:
- Preparation of the information environment.
- Search, collection and processing of initial information.
- Construction of a grid of nodes in the analyzed territory.
- Splitting the factors of the territory into fragments.
- Calculation of potentials from factors.
- Selection of factors to create thematic integral characteristics of the territory.
- Application of the method of principal components to obtain integral indicators of the territory.
- Creation of models for choosing a place for the construction of a new facility.
Stage 1. Information environment preparation
At this stage, it is necessary to choose a database management system (DBMS), determine the sources of information, methods of collecting information, the amount of information collected.
For work, we used the PostgeSql database (DB), but it is worth noting that any other database that works with SQL queries will do.
The database will store the initial information - spatial data about objects: data types (points, lines, polygons), their coordinates and other characteristics (length, area, number), as well as all the calculated values \uXNUMXb\uXNUMXbobtained as a result of the work carried out and the results of the work themselves .
Statistical information is also presented as spatial data (for example, districts of an oblast with statistical data assigned to these districts).
As a result of the transformation and processing of the collected initial information, tables are formed containing information about linear, point and area factors, their identifiers and coordinates.
Stage 2. Search, collection and processing of initial information
As initial information for solving this problem, we use information from open cartographic sources containing information about the territory. The leader, in our opinion, is OSM information, which is updated daily around the world. However, if you manage to collect information from other sources, it will not be worse.
Information processing consists in bringing it to uniformity, eliminating false information and preparing it for loading into the database.
Stage 3. Building a grid of nodes in the analyzed territory
To ensure the continuity of the analyzed territory, it is necessary to build a grid on it, the nodes of which have coordinates in a given coordinate system. In each node of the grid, the value of the potential will subsequently be determined. This will allow you to visualize homogeneous areas, clusters and final results of the analysis.
Depending on the tasks to be solved, there are two options for constructing a grid:
- Grid with regular step (S1) - is an overview throughout the territory. It is used to calculate potentials from factors, determine the integral characteristics of the territory (principal components and clusters), and display simulation results.
When choosing this grid, you must specify:
- grid step - the interval through which the grid nodes will be located;
- the border of the analyzed territory, which may correspond to the administrative-territorial division, or it may be an area on the map that limits the territory of the calculation in the form of a polygon.
- Irregular grid (S2) describes separate points of the territory (for example, centroids). It also calculates potentials from factors, determines the integral characteristics of the territory (main components and clusters). Modeling with the calculated principal components is carried out on a grid with an irregular step, and to visualize the simulation results, the numbers of clusters from grid nodes with an irregular step are transferred to grid nodes with a regular step according to the principle of coordinate proximity.
In the database, information about the coordinates of grid nodes is stored in the form of a table containing the following information for each node:
- node identifier;
- node coordinates (x, y).
Examples of grids with a regular step to different territories with different steps are shown in the figures below.
Coverage grid of the city of Nizhny Novgorod (red dots). Coverage grid of the Nizhny Novgorod region (blue dots).
Stage 4. Splitting territory factors into fragments
For further analysis, the extended factors of the territory must be converted into an array of discrete factors so that each grid node contains information about each factor present in it. Linear factors are divided into segments, areal - into fragments.
The partitioning step is selected based on the area of the territory and the specifics of the factor, for large areas (region) the partitioning step can be 100-150 m, for smaller areas (city) the partitioning step can be 25-50 m.
In the database, information about the results of splitting is stored in the form of a table containing the following information for each fragment:
- factor identifier;
- coordinates of the centroids of the obtained fragments of the partition (x, y);
- length/area of partition fragments.
Stage 5. Calculation of potentials from factors
One of the possible and understandable approaches to the analysis of initial information is the consideration of factors as potentials from objects of influence.
We use the fundamental solution of the Laplace equation for the two-dimensional case - the logarithm of the distance from the point.
Taking into account the requirement of a finite value of the potential at zero and the limitation of the value of the potential at large distances, the potential is defined as follows:
at r (1)
for r2>r>=r1
for r>=r2
Type of influence potential from a point object
The logarithmic function must be bounded at zero and reasonably bounded at some distance from the factors. If you do not limit the potential at large distances from the factor, then you would have to take into account a huge amount of information far from the analyzed point, which practically does not affect the analysis. Therefore, we introduce the value of the radius of action of the factor, beyond which the contribution to the potential from the factor is equal to zero.
For the city, the value of the radius of the factor is taken equal to half an hour pedestrian accessibility - 2 meters. For the area should talk about half an hour transport accessibility - 20 meters.
Thus, as a result of calculating the potential values, we have the total potential from each factor at each node of the regular grid.
Stage 6. Selection of factors to create thematic integral characteristics of the territory
At this stage, the most significant and informative factors are selected to create thematic integral characteristics of the territory.
The selection of factors can be carried out automatically by setting certain boundaries for the parameters (correlation, percentage of influence, etc.), or by expert means, knowing the subject of the problem and having some idea of the territory.
After the most significant and informative factors are selected, you can proceed to the next stage - the interpretation of the main components.
Stage 7. Application of the method of principal components to obtain integral indicators of the territory. Clustering
The initial information about the factors of the territory, converted at the previous stage into the potentials calculated for each grid node, is combined into new integral indicators - the main components.
The principal component method analyzes the variability of factors in the study area and, based on the results of this analysis, finds their most variable linear combination, which makes it possible to calculate the measure of their change - dispersion over the territory.
Let's take a general task for compiling a model for approximating the function of a linear model to given values
(2)
Where i is the component number,
n is the number of components involved in the calculation
j – node index of the territory point, j=1..k
k - the number of all grid nodes of the territory, which were used to calculate the main components
— coefficient at the i-th main component of the model
– value of the i-th principal component at the j-th point
B is the free term of the model
is the potential at the j-th point of the factor for which we are building a model
Define the unknowns in the equation (2) by the least squares method, using the properties of the principal components:
(3)
Where i and i2 are component numbers, i<>i2
j is the index of the territory node
k is the number of all territory nodes
(4)
(3) means no correlation between the components
(4) – the total value of any component is equal to zero.
Get:
(5)
Here the notation is the same as in the equation (2), means the average value of the potential
This result can be interpreted as follows:
The model is a simple expression consisting of the average value of the modeled value, and simple corrections to it by each of the components. At a minimum, the result must include the intercept B and the first principal component. Below are examples of heat maps of the first principal components for the Nizhny Novgorod region.
Based on the calculated principal components, it is possible to build homogeneous regions. this can be done both in terms of all parameters, and, for example, only in terms of pricing - i.e. perform clustering. For this, you can use . For each homogeneous region, the average value of the 1st main component, which characterizes the level of development of the territory, is calculated.
An example of clustering by pricing parameters for the Nizhny Novgorod region is given below.
Also, using the obtained principal components as parameters of the cost model, we can obtain the price surface of the territory.
Price surface of the city of Nizhny Novgorod
Stage 8. Creation of models for selecting a site for the construction of a new facility
To select the most attractive place for the location of a new object (hereinafter referred to as the “object”), it is necessary to compare the location of the “object” with the surrounding infrastructure. For the functioning of the "object" there must be enough resources to ensure its functioning, a large number of factors of both positive and negative impact on the "object" must be taken into account. The totality of these factors can be defined as a "nutrient" environment for the functioning of the "object". Correspondence of the number of objects to the amount of resources of the territory is the basis for the stable functioning of the "object".
The result of this comparison is the potential calculated for each point of the territory and allowing visually and analytically to analyze the choice of location for the placement of a new "object".
For trade, for example, among other things, a constant flow of buyers is important, which means that the list of factors that must be taken into account for trade objects should also include those that provide this flow (for example, social infrastructure facilities, places of work, places of residence, highways, etc. ).
On the other hand, if all the conditions for ensuring the functioning of trade objects are met, it is necessary to take into account the density of trade objects, since the “consumption” of the environment leads to a decrease in the possibility of purchases. The flow of people is not unlimited, the same applies to their financial resources and physical capabilities.
The algorithm for solving the problem of choosing the best location for an object is reduced to the fact that the potential obtained as a function of the principal components is as close as possible to the potential of a set of objects of the “object” type; then the difference between the potential of the model and the potential of objects of the “object” type is calculated; the value of the contribution potential of one "object" is subtracted from the obtained difference; the negative values obtained in this case are replaced by zero, i.e. those places where there are not enough resources for the functioning of the new “object” are eliminated.
As a result of the actions taken, we obtain points of the territory with a positive value of the potential, i.e. the places of the favorable location of our “object”.
In other words, we have the calculated potentials of all the factors at our disposal and the factor by which we want to build a model and make an analysis of the selected thematic area (trade, industry, culture, social sphere, etc.)
To do this, it is required to select factors for constructing environmental variables - the main components - and then calculate models based on them.
Factors are proposed to be selected by analyzing the correlations of all factors with the reference factor of the thematic area. For example, for culture, it can be theaters, for the education system, schools, etc.
We calculate the correlation of the standard potential with the potentials of all factors. We select those factors whose correlation coefficients in absolute value are greater than a certain value (often the value of the minimum correlation coefficient = 0 is taken).
(6)
where - the absolute value of the correlation coefficient of the i-th factor with the standard.
Correlation is calculated over all nodes of the grid covering the territory.
The difference between the potential of the model and the potential of objects of the same type as the new object in the equation (2) shows the potential of the territory, which can be used for the location of new facilities.
As a result, we obtain the value of the potential, which characterizes the degree of benefit of the location of the "object" in the study area.
An example of how you can graphically display the recommended areas for the location of a new "object" is given below.
Thus, the result of solving the problem of choosing the best location for a new object can be represented as an assessment of the territory in points at each point, giving an idea of the potential for locating an investment object, i.e. the higher the score, the more profitable it is to locate the object.
In conclusion, it should be said that in this article we have considered only one problem that can be solved using the analysis of territories, having data from open sources. In fact, there are a lot of tasks that can be solved with its help, their number is limited only by your imagination.
Source: habr.com