CN114937364B - Construction method of urban rail transit hierarchical network based on topology transformation - Google Patents

Construction method of urban rail transit hierarchical network based on topology transformation Download PDF

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CN114937364B
CN114937364B CN202210687695.XA CN202210687695A CN114937364B CN 114937364 B CN114937364 B CN 114937364B CN 202210687695 A CN202210687695 A CN 202210687695A CN 114937364 B CN114937364 B CN 114937364B
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CN114937364A (en
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四兵锋
郝媛媛
赵春亮
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Beijing Jiaotong University
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Abstract

The invention provides a construction method of a hierarchical network of urban rail transit based on topology transformation. The method comprises the following steps: acquiring an urban orbit topological network, and carrying out coordinated processing on each station in the urban orbit topological network based on a continuous network theory to construct a three-dimensional European space object of the urban orbit topological network; acquiring a three-dimensional European space object topological relation transformation rule according to a nine-intersection model, designing a first layer topological conversion function, simplifying a site set of an urban rail transit network through the first layer topological conversion function, and completing first layer construction of the rail topological network; and designing a link screening algorithm, and simplifying a link set in the urban rail network by using a second-layer topology conversion function to complete the construction of the urban rail transit double-layer topology network. The method can efficiently extract network elements in the urban rail transit network with complex connection structure.

Description

Construction method of urban rail transit hierarchical network based on topology transformation
Technical Field
The invention relates to the technical field of urban rail transit network system analysis, in particular to a construction method of an urban rail transit hierarchical network based on topology transformation.
Background
Urban rail transit is taken as one of basic traffic modes, and the orderly operation of society is effectively ensured. In order to better exert the advantages of convenience, reliability, comfort and the like, the scale of the urban rail transit network is continuously enlarged, and the coverage area is continuously expanded. This has led to a sudden increase in the line of stops information for urban rail transit networks, and an increase in the complexity of the network topology. While providing diversified choices for passengers selecting the track for traveling, the method also brings great challenges to the operation management of urban rail transit at the technical level.
Basic research such as path search algorithms, network traffic analysis, etc. is developed based on network topology. Therefore, the network is used as a carrier of basic research, and the key elements necessary for the network are required to be simplified and kept. The hierarchy may provide a topology network of lower complexity, and existing shrink hierarchies contain many variations, such as highway hierarchies and vertex routing. Usually, the vertex is resolved or expanded after the local contraction rule is defined, and the vertex direct link is reconstructed according to the self-defined weight.
At present, the construction algorithm of the track traffic layered network in the prior art is not uniform for different standards of the hierarchical structure construction of the network, and can not realize cross-network popularization. For example, in large-scale road networks, where deterministic routing problems are solved using a level of contraction, it is necessary to add quick edges to the original structure of the road network to handle changes in the road network structure. However, the manner and criteria of adding shortcut edges may also vary according to the importance of the edges. Too many variables make the uncertainty factor too large in handling network layering. Especially for urban rail transit networks with complex transfer structures, the similar methods are not good in applicability and cannot provide support for theoretical methods taking network topology structures as carriers.
Disclosure of Invention
The embodiment of the invention provides a construction method of an urban rail transit hierarchical network based on topology transformation, which is used for realizing efficient extraction of urban rail transit network elements.
In order to achieve the above purpose, the present invention adopts the following technical scheme.
A construction method of an urban rail transit hierarchical network based on topology transformation comprises the following steps:
acquiring an urban orbit topological network, and carrying out coordinated processing on each station in the urban orbit topological network based on a continuous network theory to construct a three-dimensional European space object of the urban orbit topological network;
designing a first layer topology conversion function, acquiring a three-dimensional European space object topology relation transformation rule according to a nine-way model, and utilizing the first layer topology conversion function and the three-dimensional European space object topology relation transformation rule to realize site set simplification of an urban rail transit network, so as to complete first layer construction of the rail topology network;
and designing a second-layer topology conversion function, designing a link screening algorithm according to a Dail algorithm, and simplifying a link set in the urban rail network by using the second-layer topology conversion function and the link screening algorithm to complete the construction of the urban rail transit double-layer topology network.
Preferably, the obtaining the urban rail topology network coordinates each station in the urban rail topology network based on the continuous network theory, and constructs a three-dimensional European space object of the urban rail topology network, including:
let urban rail transit topology network be denoted G (V, E), where V and E represent site and link sets, v= { V 1 ∪V 2 }, wherein V 1 And V 2 Respectively representing a transfer station set and a non-transfer station set in a three-dimensional European spaceA Cartesian coordinate system (X, Y, Z) is established, and the space sitting of the transfer station is marked as (X) i ,y i 0), i=1, 2,..n', the spatial sitting of the non-transfer station is marked (x j ,y j ,0)，j＝1,2,...,n”；
The following open rectangle U is constructed using the coordinate extremum:
minimum value of coordinates of open rectangle UIs composed of the minimum value of the coordinates of all transfer stations and non-transfer stations. Maximum value of open rectangular coordinates +.>Is composed of the maximum value of the coordinates of all transfer stations and non-transfer stations, namely:
wherein x is i ,x j ,y i ,y j Respectively a transfer station and a non-transfer stationCoordinate values.
By TN asl Representing an urban rail transit network contained in the open rectangle U;
open rectangle A is constructed based on open rectangle U, according to mapping f 1 Topology network TN contained in split rectangle U asl And (3) performing space mapping:
Wherein eta represents TN asl A translation distance along the Z axis;
open rectangle a is represented as follows:
wherein:
according to the space coordinates of non-transfer sites in the open rectangle AConstructing an open rectangle B according to the mapping f 2 Space mapping is carried out on non-transfer sites in the open rectangle A:
wherein ω is E (0,) 1 represents the ratio of shrinking A, and x' has a value betweenThe value of y' is between +.>Between them.
Open rectangle B is represented as follows:
wherein:
open rectangle B contains only non-transfer sites, and the set of these non-transfer sites is denoted as Ω B Wherein the non-transfer station space is marked as
Preferably, the step of designing a first layer topology conversion function, obtaining a three-dimensional euclidean space object topology relation transformation rule according to a nine-intersection model, and using the first layer topology conversion function and the three-dimensional euclidean space object topology relation transformation rule to achieve site set simplification of an urban rail transit network, and completing first layer construction of the rail topology network comprises the following steps:
extracting a set Ω of non-transfer sites B The non-transfer station of (2) is used for transmitting the non-transfer station according to the X-axis coordinate valueThe descending order is carried out, so that m is the sequence value corresponding to the non-transfer station j, namely +.>Establishing a first layer topology conversion function based on m >According to the first layer topology transfer function->Moving the open rectangle B to the right along the X axis until the open rectangle B is completely separated from the open rectangle A, wherein the open rectangle A is separated from the open rectangle B one by one along with non-transfer stations in the open rectangle BA is separated, the non-transfer site in the open rectangle A is used as the original image of the non-transfer site in the open rectangle B, and the image f is mapped 2 Is extracted one by one under the relation of G (V, E), the simplification of the station set V in G (V, E) is completed, and the first layer construction of the track topology network is completed.
Preferably, the extracting the collection Ω of non-transfer sites B The processing procedure of the non-transfer station in the (a) comprises the following steps:
step 1, initializing, namely initializing the topological relation between the open rectangle A and the open rectangle B, marking the secondary number of the moving open rectangle B as gamma, and taking:
as the step size of the first movement B, i.e. the abscissa of each non-transfer station in B needs to be added
In motionThen, the boundary intersection of the open rectangle A and the open rectangle B is not empty any more, and the boundary extreme values of the open rectangle A and the open rectangle B are compared:
and calculating a nine-intersection model of the open rectangle A and the open rectangle B:
wherein: a is that o /B o Is the interior of a collection of spatial objects;is the boundary of a set of spatial objects; a is that - /B - Is->Is outside of the object set;
Step 2, extracting non-transfer sites with the abscissa marks of m epsilon [1, m-2], and specifically, generalizing the adopted moving step formula when gamma epsilon [2, m-1 ]:
where ε=10 -6 When gamma is E [2, m-1]Comparing boundary extremum of A and B to obtain:
and (3) calculating a nine-crossing model:
the topological relation of A and B is changed from 'Covers' to 'overlay' at the gamma=2nd time of moving B, and the topological relation is continued until the gamma=m-1 th time of moving B;
every time B is moved, the abscissa of non-transfer stations in B is addedUpdating the position of the station B, and according to the evolution rule of the nine-cross model, shrinking the area of the station A in the process of extracting the non-transfer stations one by one, and updating the position coordinates of the station in the station A through a formula (9);
wherein:
if the station ordinate in A is on the baseline ζ before moving B for the second time, the station position remains motionless; if the station ordinate in A is below baseline ζ before moving B a second time, the station position moves up by a reduced longitudinal height Δy γ Half of (2); otherwise, the station moves up to shorten the longitudinal height deltay γ Half of (2);
non-transfer stationAre extracted by adopting the moving step length of the formula (8), and along with the extraction of the non-transfer station, in order to maintain the original topological structure, the method is characterized in that gamma is E [2, m-1 ]In this case, after each movement B, transfer station information adjacent to the extracted non-transfer station in a is stored and links between transfer stations need to be reconnected, and transfer stations adjacent to S2 are S1 and S3, which are recorded as:
list { (L2, S2, up) - (L2, S1, up), (L2, S3, up) }, and the link between S1 and S3 is reconnected; the transfer sites adjacent to S4 are S3 and S5, so are denoted List { (L2, S4, up) - (L2, S3, up), (L2, S5, up) }, and the link between S3 and S5 is reconnected;
step 3, extracting a non-transfer station with an abscissa mark of m-1, and taking the moving step length as follows:
the abscissa of each non-transfer station in B is added withNon-transfer site->Is extracted, compares the boundary extremum of A and B,
when the rectangle B is moved on the mth time, the nine-intersection model is calculated as follows:
open rectangle B is shifted rightThen, the topological relation between A and B is changed from 'Overlap' to 'Meet', and meanwhile, the coordinate of A is updated according to the step (9), so that the area of A is reduced to the minimum, and the last link reconnection is required;
step 4, extracting non-transfer sites with the abscissa number of m, wherein after moving open the rectangle B for the mth time, the topological relation between A and B is 'Meet', namely, the same non-transfer sites exist on the boundary between A and B, and the non-transfer sites are fetched And continuously moving the B to the right to complete the complete separation of the A and the B, and updating the nine-intersection model to be:
the topological relation between A and B is converted into 'dispatch' from 'Meet' when moving open rectangle B for m+1st time, and the non-transfer sites with the abscissa number of m are extracted, so that the extraction of all non-transfer sites is completed.
Preferably, the first layer construction of the track topology network is completed, including:
and (3) extracting all non-transfer sites in the open rectangle A through a first layer topology conversion function. The area of the open rectangle A is continuously contracted until the area is minimum in the process of extracting the station, and then the open rectangle A which is folded needs to be restored to obtain a topology network TN only comprising the transfer station and reconnection link information tsl In open rectangle A, except t 0 All transfer stations except the transfer station on the base line xi at the moment need to move along the opposite direction when contracting, and the longitudinal shortening height is as follows:
and all transfer stations in the open rectangle A are restored to the original positions, and the first layer construction of the track topology network is completed.
Preferably, the designing a second layer topology conversion function, designing a link screening algorithm according to a Dail algorithm, and using the second layer topology conversion function and the link screening algorithm to simplify a link set in the urban rail network, and completing construction of the urban rail traffic double-layer topology network includes:
Based on urban rail transit hierarchical topology network, topology network TN aiming at transfer sites and reconnection link information contained in open rectangular set A tsl Constructing effective link screening conditions, combining determined transfer sites, and combining TN tsl And judging the effectiveness of all links in the network, and completing the construction of the urban rail transit double-layer topology network after invalid links are removed.
Preferably, the topology network TN aims at the transfer sites and reconnection link information contained in the open rectangular set A on the basis of the urban rail transit hierarchical topology network tsl Constructing effective link screening conditions, including:
on the basis of a hierarchical topology network of urban rail transit, on the basis of TN (total network technology) tsl For transfer station combination (T α ,T β ) The conditions for judging the link effectiveness based on the Dial algorithm are as follows:
wherein: t (T) μ ,T η ,T α ,T β Is TN (TN) tsl Transfer station in, T μ ,T η Is a transfer station combination (T) α ,T β ) A transfer station which is arbitrarily and directly connected with the transfer station;is T μ And T is α Minimum travel cost between; />Is T η And T is β Minimum travel cost between; />Is (T) μ ,T η ) Travel cost of the direct link between the two links; />Is T α ,T β The travel cost of the shortest path between the two; h: the expansion coefficient is used for determining the range of searching the effective path;
For transfer station combination (T α ,T β ) Is a direct link (T) μ ,T η ) If provided And +.>The sum of the three is less than or equal to%>Is 1+H times of the number of the link (T) μ ,T η ) Is effective.
Preferably, the pair-determined transfer station combines TN tsl The validity of all links in the network is judged, and the construction of the urban rail transit double-layer topology network is completed after invalid links are removed, including:
introducing a layer two topology transfer function based on link availability conditionsSimplifying TN tsl For each pair of transfer station combinations (T α ,T β ) TN is TN tsl Further simplify, get-> Comprising only transfer stations (T) α ,T β ) Effective link between them, combined with TN asl And TN (TN) nts And (5) constructing the double-layer topology network of the urban rail transit.
The technical scheme provided by the embodiment of the invention can be seen that the method of the invention achieves the aim of efficiently extracting network elements in the urban rail transit network with huge scale and complex connection structure.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a process flow diagram of a method for constructing a hierarchical network of urban rail transit based on topology transformation provided by an embodiment of the invention;
fig. 2 is a schematic diagram of evolution rules of a nine-intersection model and a topological relation of a space object according to an embodiment of the present invention;
fig. 3 is a link reconnection and List generation in a non-transfer station extraction process according to an embodiment of the present invention;
fig. 4 is a flowchart for constructing a first layer topology network of urban rail transit according to an embodiment of the present invention;
fig. 5 is a flowchart for constructing a second-layer topology network of urban rail transit according to an embodiment of the present invention;
fig. 6 is an open rectangular U schematic diagram of a topology network according to an embodiment of the present invention;
fig. 7 is a schematic diagram of open rectangles a and B based on an open rectangle U structure according to an embodiment of the present invention;
FIG. 8 is a schematic diagram of a hierarchical topology network for (N ', K') according to an embodiment of the present invention;
fig. 9 is a schematic diagram of a part of a Beijing urban rail transit network according to an embodiment of the present invention.
Fig. 10 is a schematic diagram of a hierarchical topology network of a track obtained after a first layer topology transformation according to an embodiment of the present invention;
fig. 11 is a schematic diagram of a topology network of a simplified track with a double layer obtained after a second layer topology transformation according to an embodiment of the present invention.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below by referring to the drawings are exemplary only for explaining the present invention and are not to be construed as limiting the present invention.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless expressly stated otherwise, as understood by those skilled in the art. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. The term "and/or" as used herein includes any and all combinations of one or more of the associated listed items.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
For the purpose of facilitating an understanding of the embodiments of the invention, reference will now be made to the drawings of several specific embodiments illustrated in the drawings and in no way should be taken to limit the embodiments of the invention.
The embodiment of the invention provides a construction method of an urban rail transit hierarchical network based on topology transformation, wherein a site extraction and effective link screening are adopted to obtain an urban rail transit double-layer topology network aiming at different transfer site combinations, so that the aim of efficiently extracting urban rail transit network elements is fulfilled.
The method of the embodiment of the invention firstly constructs the same embryo open rectangle containing different station line information networks by establishing a mapping operator based on the original topological structure of the urban rail. And then constructing a first layer topology conversion function of the simplified site set by relying on the thought of the nine-intersection model. And continuously changing the topological relation of the space object by moving the rectangular set to finish the extraction of the non-transfer site. This process can be used generalizing. Thus, the urban rail transit hierarchical topology network is obtained. Next, a layer two topology conversion function is designed that simplifies the link set based on the modified Dial algorithm. By constructing effective link conditions, invalid links are removed from a topological network only comprising transfer station links, and a double-layer simplified track topological network is formed.
The process flow chart of the method for constructing the urban rail transit hierarchical network based on topology transformation provided by the embodiment of the invention is shown in fig. 1, and comprises the following process steps:
constructing an urban rail transit network space object: let urban rail transit topology network be denoted G (V, E), where V and E represent site and link sets, v= { V 1 ∪V 2 }, wherein V 1 And V 2 Representing a transfer station set and a non-transfer station set, respectively. In three-dimensional European spaceA Cartesian coordinate system (X, Y, Z) is established, and the space sitting of the transfer station is marked as (X) i ,y i 0), i=1, 2,..n', the spatial sitting of the non-transfer station is marked (x j ,y j ,0)，j＝1,2,...,n”。
The following open rectangle U is constructed using the coordinate extremum:
minimum value of coordinates of open rectangle UIs composed of the minimum value of the coordinates of all transfer stations and non-transfer stations. Maximum value of open rectangular coordinates +.>Is composed of the maximum value of the coordinates of all transfer stations and non-transfer stations, i.e
Wherein x is i ,x j ,y i ,y j Coordinate values of the transfer station and the non-transfer station are respectively.
By TN asl Representing an urban rail transit network comprised by an open rectangle U.
Based on the open rectangle U, an open rectangle a is constructed. First, according to f 1 Topology network TN contained in split rectangle U asl And (3) performing space mapping:
Wherein eta represents TN asl Translation distance along the Z axis.
Open rectangle a can be represented as follows:
wherein:
according to the space coordinates of non-transfer sites in the open rectangle AAn open rectangle B is constructed. First, according to f 2 Space mapping is carried out on non-transfer sites in the open rectangle A:
wherein ω is E (0,) 1 represents the ratio of shrinking A, and x' has a value betweenBetween which are locatedThe value of y' is between +.>Between them.
Open rectangle B may be expressed as follows:
wherein:
in this case, the open rectangle B includes only non-transfer sites, and the set of these non-transfer sites is denoted as Ω B Wherein the non-transfer station space is marked as
Constructing a first-layer topological network of the urban rail:
extracting a set Ω of non-transfer sites B The non-transfer station of (2) is used for transmitting the non-transfer station according to the X-axis coordinate valueThe descending order is carried out, so that m is the sequence value corresponding to the non-transfer station j, namely +.>Based on this, a first layer topology conversion function is created>I.e. B moves right along the X-axis until it is completely separated from a. In the process, as the non-transfer stations in B are separated from A one by one, the non-transfer stations in A are used as the primary images of the non-transfer stations in B, at f 2 The inverse mapping relationship is extracted one by one. Furthermore, simplification of the station set V in G (V, E) can be completed, and the first layer construction of the track topology network can be completed.
Extracting a set Ω of non-transfer sites B The processing procedure of the non-transfer station in the (a) comprises the following steps:
and step 1, initializing. First, the topological relation between A and B is initialized. We will note the number of times moved by rectangle B as γ. Taking:
as the step size of the first movement B, i.e. the abscissa of each non-transfer station in B needs to be added
In motionThereafter, the intersection of the boundaries of A and B is no longer an empty set. At this time, the boundary extremum of a and B is compared:
and calculating a nine-intersection model of A and B:
wherein: a is that o /B o Is the interior of a collection of spatial objects;is the boundary of a set of spatial objects; a is that - /B - Is->Is outside of the object set.
According to the evolution rule of the nine-cross model and the topological relation of the space object shown in fig. 2, after the first movement B, the topological relation of a and B is "coverage", i.e. the station in B is not moved out of a. Thus, the site coordinates within A do not need to be updated.
And 2, extracting a non-transfer site with the abscissa mark of m epsilon [1, m-2 ]. Specifically, when γε [2, m-1], the motion step formula used can be generalized to:
where ε=10 -6 . The extraction process at this stage can be generalized because when gamma.epsilon.2, m-]1, comparing boundary extremum of A and B can obtain:
Thus, the calculation of the nine-cross model can be seen as:
the topology of a and B is changed from "Covers" to "overlay" at the γ=2nd shift B and continues until after the γ=m-1 th shift B.
Every time B is moved, the abscissa of non-transfer stations in B is addedTo update the location of the B site. In addition, according to the evolution rule of the nine-cross model, the area of A is contracted in the process of extracting non-transfer sites one by one. Thus, we update the position coordinates of the stations within A by equation (9) to shrink the area of A.
Wherein:
specifically, if the station ordinate in a is on baseline ζ before moving B a second time, the station position remains motionless; if the station ordinate in A is below baseline ζ before moving B a second time, the station position moves up by a reduced longitudinal height Δy γ Half of (2); otherwise, the station moves up to shorten the longitudinal height deltay γ Half of (a) is provided.
Thus, the non-transfer stationCan be extracted by using the movement step size of equation (8). In addition, along with the extraction of non-transfer sites, in order to maintain the original topological structure, the non-transfer sites are extracted in gamma E [2, m-1]At this time, after each movement B, transfer station information adjacent to the extracted non-transfer station in a will be saved and links between transfer stations need to be reconnected. In this method, link weights are travel times rather than link distances. Fig. 3 is a schematic diagram of link reconnection and List generation in a non-transfer station extraction process according to an embodiment of the present invention. Fig. 3 gives an example of link reconnection when non-transfer stations S2 and S4 are extracted. Transfer stations adjacent to S2 are S1 and S3, and so are denoted as:
List { (L2, S2, up) - (L2, S1, up), (L2, S3, up) }, and the link between S1 and S3 is reconnected; the transfer sites adjacent to S4 are S3 and S5, and are therefore denoted as List { (L2, S4, up) - (L2, S3, up), (L2, S5, up) }, and the link between S3 and S5 is reconnected.
And 3, extracting a non-transfer station with the abscissa number of m-1. The moving step length is taken as follows:
the abscissa of each non-transfer station in B is added withNon-transfer site->Is extracted. At this time, the boundary extremum of A and B is compared,
in particular the number of the elements to be processed,this is true. Therefore, we find that at the mth shift open rectangle B, the calculation of the nine-intersection model can be found:
open rectangle B is shifted rightThe topological relationship of A and B is then converted from "overlay" to "Meet". At the same time, as shown in (9), updating the coordinates of a shows that the area of a is reduced to a minimum and the last link reconnection is required.
And 4, extracting a non-transfer station with the abscissa number of m. Note that after the mth move open rectangle B, the topological relationship of a and B is "Meet", i.e., the same non-transfer site exists on the boundary of a and B. Thus, the process of extracting the site has not been completed. Therefore we getAnd continuing to move B rightward to complete the complete separation of A and B. Meanwhile, the nine-intersection model is updated as follows:
To this end, the topological relation of A and B is changed from "Meet" to "dispatch" when moving open rectangle B for the m+1st time. The non-transfer stations with the abscissa number m are extracted, so far we have completed the extraction of all non-transfer stations.
After the preliminary work of constructing the space object of the nine-interchange model, on the premise of keeping the original network topology structure, all non-transfer stations in the urban rail transit network are extracted according to the evolution rule of the nine-interchange model. Then, constructing a hierarchical topology network of urban rails, wherein a first-layer urban rail transit network construction flow provided by the embodiment of the invention is shown in fig. 4, and comprises the following processing procedures:
and through the first layer topology conversion function, the extraction of all non-transfer sites in the open rectangle A is completed. While the area of open rectangle a continues to shrink during the extraction of the station until it is minimal. Next, it is necessary to restore the "folded" open rectangle a, and further obtain a topology network TN containing only transfer site and reconnection link information tsl . Within the open rectangle A, except t 0 All transfer stations other than the transfer station at the moment on the baseline ζ need to move in the opposite direction when contracting. Note that the area of the reduction of a is just the area of B, so the height of the longitudinal reduction is Thus, all transfer sites in the open rectangle A are restored to the original positions, and the first layer construction of the track topology network is completed.
Fig. 5 is a flowchart for constructing a second-layer topology network of urban rail transit, according to an embodiment of the present invention, including the following processing procedures:
link validity condition: the TN is given below tsl For transfer station combination (T α ,T β ) In order to reduce the repetition of the calculation of invalid links.
First, a condition for judging the validity of a link is given based on a Dial algorithm:
wherein: t (T) μ ,T η ,T α ,T β Is TN (TN) tsl Transfer station in, T μ ,T η Is a transfer station combination (T) α ,T β ) A transfer station which is arbitrarily and directly connected with the transfer station;is T μ And T is α Minimum travel cost between; />Is T η And T is β Minimum travel cost between; />Is (T) μ ,T η ) Travel cost of the direct link between the two links; />Is T α ,T β The travel cost of the shortest path between the two; h: the expansion coefficient determines the range of the search effective path.
Equation (12) shows that for transfer station combinations (T α ,T β ) Is a direct link (T) μ ,T η ) If provided C T The sum of the three is less than or equal to%>Is 1+H times of the number of the link (T) μ ,T η ) Is effective. Further, TN tsl The link channel in (a)After the screening, the number of invalid links will be effectively reduced.
And (3) link screening: introducing a layer two topology transfer function based on link availability conditionsSimplifying TN tsl . Thus, for each pair of transfer station combinations (T α ,T β ) TN is TN tsl Further simplify, get->So that the number of the parts to be processed,comprising only transfer stations (T) α ,T β ) An active link between them. Combining TN asl TN and TN nts The dual layer simplifies the track topology network generation.
Embodiment two:
simple example of a track topology network: urban rail transit topology network G (V, E), in V K, M, …, etc. represent stations, the position coordinates of each station are denoted (x, y, 0), and a, b, … represent a direct link between two stations. Obtaining an open rectangle by screening the coordinate extremumTopology network TN containing all site link information asl . FIG. 6 is a schematic diagram of an open rectangle U of a topology network according to an embodiment of the present invention, for the open rectangle U and TN contained therein asl Taking a continuous mapping f 1 An open rectangle a is obtained. Marking non-transfer site coordinates within A asTaking a bijective function f for all non-transfer sites in A 2 Further, the non-transfer site in the example is mapped to an open rectangle + ->In, and the coordinates will beMarked as->Wherein G ", F", Q ", H" are located on the boundary of B, E ", D", S "belong to the interior of B. Open rectangle B contains non-transfer site topology network TN nts 。
Fig. 7 is a schematic diagram of open rectangles a and B based on an open rectangle U structure according to an embodiment of the present invention. The open rectangle B contains 7 non-transfer stations, arranged in descending order of the station abscissa as follows:
at the same time m max ＝5＜j max =7 holds.
The non-transfer sites within the extraction example are performed in order of increasing m and the extraction process is shown in table 1.
TABLE 1 example network extraction procedure for non-transfer sites
Recovering the area of the open rectangle A which is folded to obtain a topology network TN only containing transfer site and link information tsl And with TN asl ，Ω B Fig. 8 is a schematic diagram of a hierarchical topology network for (N ', K') according to an embodiment of the present invention. Given the transfer site combination (N ', K'), a link screening algorithm is invoked. For (N ', K'), TN is judged according to the requirement of the formula (12) tsl The validity of each link. Through TN calculation tsl Will be further simplified intoWith TN asl ，TN nts Together forming a two-layer topology network.
Taking Beijing city track network as an example, an implementation procedure description is given. The network comprises 17 transfer stations, 22 non-transfer stations and 7 lines, and fig. 9 is a schematic diagram of a part of Beijing urban rail transit network provided by the embodiment of the invention. And acquiring the position coordinates of each station, and establishing a topological structure G (V, E) of the track network. And the first layer of simplification of the network is realized through site extraction, so that a hierarchical topology network is obtained. Fig. 10 is a schematic diagram of a hierarchical topology network of a track obtained after a first layer of topology transformation according to an embodiment of the present invention. And (3) giving a transfer station combination List (L2, siemens, up) - (L1, national trade, up) in the existing track network, and obtaining a double-layer simplified track topology network schematic diagram after obtaining a second-layer topology transformation shown in FIG. 11 through a second-layer effective link screening.
Site storage based on GIS data: typically, when building a track topology network, stations are often kept on the network map in the form of points or serial numbers. In the present invention, the site is not only saved as a node to construct a network topology, but also the latitude and longitude based on the GIS site are captured and stored in the data. In this way, the abstract symbols representing the sites are materialized, and the specific positions of the sites in the track network can be accurately acquired.
Network construction considering travel cost: in a topology network, line segments are used to represent links between two sites. The connection relation between sites is embodied in the storage of the link data. The cost of travel of the train schedule is stored in the data as a link weight. Thus, the connection relationship between the stations is preserved. The connection relation is used for reconstructing the topological structure of the urban rail transit network, so that the obtained network structure is closer to actual operation. Therefore, the two points are combined, and the topological network construction can be realized by utilizing the position coordinate data and the link data of the station.
Maintaining the stability of the urban rail transit network topology: there are two conventional ways to simplify site aggregation: the first is to delete stations of a particular type directly. And secondly, setting a constraint and deleting the sites violating the constraint. However, both methods may destroy the original topology of the network. The goal of simplification is to maintain topology while reducing sites. It is clear that conventional methods present challenges in achieving this goal. For this purpose, the invention proposes an urban rail transit hierarchical network algorithm based on topology transformation to accomplish this goal.
Sites within the open rectangle are divided into two types, transfer stations and non-transfer stations. The proposed method is to extract sites rather than delete a class of sites directly. As non-transfer stations are extracted, adjacent transfer stations are recorded in a List and the link in which the extracted non-transfer station is located is reconnected. And updating the link set after extracting the non-transfer station.
Site extraction is the core of link screening, namely after recovering a rectangular area, if the topology network is stable, a transfer site link topology network TN can be obtained tsl . This is the basis for screening valid links. The algorithm based on the topology transformation layering simplified urban rail transit network can accurately construct the topological network of the urban rail transit, the link weight is adjusted by calling the running time of the train schedule, and the extracted layering network topology does not destroy the original topological relation, which is a precondition for link screening.
In summary, the embodiment of the invention provides a topology transformation-based urban rail transit hierarchical network construction method, which achieves the purpose of efficiently extracting network elements in an urban rail transit network with huge scale and complex connection structure. The complexity of the connection structure of the rail transit network directly determines the calculation efficiency as a basis for searching the shortest (K-short) path and realizing upper tasks such as passenger flow distribution. On the premise of limited calculation cost, the premise of effectively improving the calculation efficiency is to extract complete network elements, and greatly reduce the calculation redundancy of traversing the network elements under the constraint of not influencing the calculation result. The invention provides a specific method for constructing a simplified layered track topology network, which can greatly improve the efficiency of urban track traffic network analysis and passenger flow calculation and has important engineering practice significance.
Those of ordinary skill in the art will appreciate that: the drawing is a schematic diagram of one embodiment and the modules or flows in the drawing are not necessarily required to practice the invention.
From the above description of embodiments, it will be apparent to those skilled in the art that the present invention may be implemented in software plus a necessary general hardware platform. Based on such understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a storage medium, such as a ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the embodiments or some parts of the embodiments of the present invention.
In this specification, each embodiment is described in a progressive manner, and identical and similar parts of each embodiment are all referred to each other, and each embodiment mainly describes differences from other embodiments. In particular, for apparatus or system embodiments, since they are substantially similar to method embodiments, the description is relatively simple, with reference to the description of method embodiments in part. The apparatus and system embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
The present invention is not limited to the above-mentioned embodiments, and any changes or substitutions that can be easily understood by those skilled in the art within the technical scope of the present invention are intended to be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.

Claims (5)

1. The method for constructing the urban rail transit hierarchical network based on topology transformation is characterized by comprising the following steps of:
acquiring an urban orbit topological network, and carrying out coordinated processing on each station in the urban orbit topological network based on a continuous network theory to construct a three-dimensional European space object of the urban orbit topological network;
designing a first layer topology conversion function, acquiring a three-dimensional European space object topology relation transformation rule according to a nine-way model, and utilizing the first layer topology conversion function and the three-dimensional European space object topology relation transformation rule to realize site set simplification of an urban rail transit network, so as to complete first layer construction of the rail topology network;
designing a second-layer topology conversion function, designing a link screening algorithm according to a Dail algorithm, and simplifying a link set in the urban rail network by using the second-layer topology conversion function and the link screening algorithm to complete construction of the urban rail transit double-layer topology network;
The obtaining of the urban rail topology network, the coordinated processing of each station in the urban rail topology network based on the continuous network theory, the construction of the three-dimensional European space object of the urban rail topology network comprises the following steps:
let urban rail transit topology network be denoted G (V, E), where V and E represent site and link sets, v= { V 1 ∪V 2 }, wherein V 1 And V 2 Respectively representing a transfer station set and a non-transfer station set in a three-dimensional European space R 3 A Cartesian coordinate system (X, Y, Z) is established, and the space sitting of the transfer station is marked as (X) i ,y i 0), i=1, 2,..n', the spatial sitting of the non-transfer station is marked (x j ,y j ,0)，j＝1,2,...,n”；
The following open rectangle U is constructed using the coordinate extremum:
minimum value of coordinates of open rectangle UIs made up of all transferThe minimum value of the coordinates of the station and the non-transfer station is formed, and the maximum value of the open rectangle coordinates is +.>Is composed of the maximum value of the coordinates of all transfer stations and non-transfer stations, namely:
wherein x is i ,y i Is the coordinate value of the transfer station, x j ,y j Coordinate values of non-transfer sites;
by TN asl Representing an urban rail transit network contained in the open rectangle U;
open rectangle A is constructed based on open rectangle U, according to mapping f 1 Topology network TN contained in split rectangle U asl And (3) performing space mapping:
Wherein eta represents TN asl A translation distance along the Z axis;
open rectangle a is represented as follows:
wherein:
according to the space coordinates of non-transfer sites in the open rectangle AConstructing an open rectangle B according to the mapping f 2 Space mapping is carried out on non-transfer sites in the open rectangle A:
wherein ω ε (0, 1) represents the ratio of the shrinkage of A, and x' has a value betweenThe value of y' is between +.>Between them;
open rectangle B is represented as follows:
wherein:
open rectangle B contains only non-transfer sites, and the set of these non-transfer sites is denoted as Ω B Wherein the non-transfer station space is marked as
The design of a first layer topology conversion function, the acquisition of a three-dimensional European space object topology relation transformation rule according to a nine-intersection model, the realization of site set simplification of an urban rail transit network by utilizing the first layer topology conversion function and the three-dimensional European space object topology relation transformation rule, and the completion of the first layer construction of the rail topology network comprise the following steps:
extracting a set Ω of non-transfer sites B The non-transfer station of (2) is used for transmitting the non-transfer station according to the X-axis coordinate valueThe descending order is carried out, so that m is the sequence value corresponding to the non-transfer station j, namely +.>Establishing a first layer topology conversion function F based on m 1 According to the first layer topology conversion function F 1 Moving the open rectangle B to the right along the X axis until the open rectangle B is completely separated from the open rectangle A, in the process, as the non-transfer stations in the open rectangle B are separated from the open rectangle A one by one, taking the non-transfer stations in the open rectangle A as the primary images of the non-transfer stations in the open rectangle B, mapping f 2 Is extracted one by one under the relation of G (V, E), the simplification of the station set V in G (V, E) is completed, and the first layer construction of the track topology network is completed;
the design of the second layer topology conversion function, the design of the link screening algorithm according to the Dail algorithm, the simplification of the link set in the urban rail network by using the second layer topology conversion function and the link screening algorithm, the construction of the urban rail transit double-layer topology network is completed, and the method comprises the following steps:
based on urban rail transit hierarchical topology network, topology network TN aiming at transfer sites and reconnection link information contained in open rectangular set A tsl Constructing effective link screening conditions, combining determined transfer sites, and combining TN tsl And judging the effectiveness of all links in the network, and completing the construction of the urban rail transit double-layer topology network after invalid links are removed.
2. The method of claim 1, wherein the extracting the set Ω of non-transfer sites B The processing procedure of the non-transfer station in the (a) comprises the following steps:
step 1, initializing, namely initializing the topological relation between the open rectangle A and the open rectangle B, marking the secondary number of the moving open rectangle B as gamma, and taking:
as the step size of the first movement B, i.e. the abscissa of each non-transfer station in B needs to be added with L γ＝1 ；
In the movement L γ＝1 Then, the boundary intersection of the open rectangle A and the open rectangle B is not empty any more, and the boundary extreme values of the open rectangle A and the open rectangle B are compared:
and calculating a nine-intersection model of the open rectangle A and the open rectangle B:
wherein: a is that o And B o Is the interior of a collection of spatial objects;and->Is the boundary of a set of spatial objects; a is that - And B - Is relative to European space R 2 Is outside of the object set;
step 2, extracting non-transfer sites with the abscissa marks of m epsilon [1, m-2], and specifically, generalizing the adopted moving step formula when gamma epsilon [2, m-1 ]:
where ε=10 -6 When gamma is E [2, m-1]Comparing boundary extremum of A and B to obtain:
and (3) calculating a nine-crossing model:
the topological relation of A and B is changed from 'Covers' to 'overlay' at the gamma=2nd time of moving B, and the topological relation is continued until the gamma=m-1 th time of moving B;
every time B is moved, L is added to the abscissa of the non-transfer station in B γ ，γ∈[2,m-1]Updating the position of the station B, and according to the evolution rule of the nine-cross model, shrinking the area of the station A in the process of extracting the non-transfer stations one by one, and updating the position coordinates of the station in the station A through a formula (9);
wherein:
if the station ordinate in A is on the baseline ζ before moving B for the second time, the station position remains motionless; if the station ordinate in A is below baseline ζ before moving B a second time, the station position is moved up by a longitudinal height Δy γ Half of (2); otherwise, the station moves down by a longitudinal height Δy γ Half of (2);
non-transfer stationAre extracted by adopting the moving step length of the formula (8), and along with the extraction of the non-transfer station, in order to maintain the original topological structure, the method is characterized in that gamma is E [2, m-1]In this case, after each movement B, transfer station information adjacent to the extracted non-transfer station in a is stored and links between transfer stations need to be reconnected, and transfer stations adjacent to S2 are S1 and S3, which are recorded as:
list { (L2, S2, up) - (L2, S1, up), (L2, S3, up) }, and the link between S1 and S3 is reconnected; the transfer sites adjacent to S4 are S3 and S5, so are denoted List { (L2, S4, up) - (L2, S3, up), (L2, S5, up) }, and the link between S3 and S5 is reconnected;
Step 3, extracting a non-transfer station with an abscissa mark of m-1, and taking the moving step length as follows:
l is added to the abscissa of each non-transfer station in B γ＝m Non-transfer stationIs extracted, compares the boundary extremum of A and B,
when the rectangle B is moved on the mth time, the nine-intersection model is calculated as follows:
open rectangle B is shifted right by L γ＝m Then, the topological relation between A and B is changed from 'Overlap' to 'Meet', and meanwhile, the coordinate of A is updated according to the formula (9), so that the area of A is reduced to the minimum, and the last link reconnection is required;
step 4, extracting non-transfer sites with the abscissa number of m, and taking L after moving open the rectangle B for the mth time, wherein the topological relation between A and B is 'Meet', namely the same non-transfer sites exist on the boundary between A and B γ＝m+1 =λ, λ > 0 continues to move to the right B, complete a complete separation of a from B, nine-intersection model update as:
the topological relation between A and B is converted into 'dispatch' from 'Meet' when moving open rectangle B for m+1st time, and non-transfer sites with the abscissa number of m are extracted, so that the extraction of all non-transfer sites is completed.
3. The method of claim 1, wherein said performing a first layer of a track topology network comprises:
The extraction of all non-transfer sites in the open rectangle A is completed through a first layer topology conversion function, the area of the open rectangle A continuously contracts in the process of extracting sites until the area is minimum, and then the open rectangle A which is folded needs to be restored to obtain a topology network TN only comprising transfer sites and reconnection link information tsl In open rectangle A, except t 0 All transfer stations except the transfer station on the base line xi at the moment need to move along the opposite direction when contracting, and the longitudinal shortening height is as follows:
and all transfer stations in the open rectangle A are restored to the original positions, and the first layer construction of the track topology network is completed.
4. The method according to claim 1, wherein the topology network TN for transfer sites and reconnection link information contained in the open rectangular set a is based on a hierarchical topology network of urban rail transit tsl Constructing effective link screening conditions, including:
on the basis of a hierarchical topology network of urban rail transit, on the basis of TN (total network technology) tsl For transfer station combination (T α ,T β ) The conditions for judging the link effectiveness based on the Dial algorithm are as follows:
wherein: t (T) μ ,T η ,T α ,T β Is TN (TN) tsl Transfer station in, T μ ,T η Is a transfer station combination (T) α ,T β ) A transfer station which is arbitrarily and directly connected with the transfer station;is T μ And T is α Minimum travel cost between; />Is T η And T is β Minimum travel cost between; />Is T μ And T is η Travel cost of the direct link between the two links; />Is T α And T is β The travel cost of the shortest path between the two; h: the expansion coefficient is used for determining the range of searching the effective path;
for transfer station combination (T α ,T β ) Is a direct link (T) μ ,T η ) If providedAnd +.>The sum of the three is less than or equal to%>Is 1+H times of the number of the link (T) μ ,T η ) Is effective.
5. The method according to claim 1, characterized in thatThe method comprises combining the transfer sites determined by the pair to obtain TN tsl The validity of all links in the network is judged, and the construction of the urban rail transit double-layer topology network is completed after invalid links are removed, including:
based on the link availability condition, introducing a second layer topology conversion function F 2 Simplifying TN tsl For each pair of transfer station combinations (T α ,T β ) TN is TN tsl Further simplify and obtain Comprising only transfer stations (T) α ,T β ) Effective link between them, combined with TN asl And TN (TN) nts And (5) constructing the double-layer topology network of the urban rail transit. />
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