CN114937364A - Construction method of urban rail transit hierarchical network based on topological transformation - Google Patents

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

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CN114937364A
CN114937364A CN202210687695.XA CN202210687695A CN114937364A CN 114937364 A CN114937364 A CN 114937364A CN 202210687695 A CN202210687695 A CN 202210687695A CN 114937364 A CN114937364 A CN 114937364A
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CN114937364B (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 an urban rail transit hierarchical network based on topological transformation. The method comprises the following steps: acquiring an urban rail topological network, carrying out coordinate processing on each station in the urban rail topological network based on a continuous network theory, and constructing a three-dimensional European space object of the urban rail topological network; acquiring a three-dimensional European space object topological relation transformation rule according to a nine-intersection model, designing a first-layer topological transformation function, simplifying a station set of the urban rail transit network through the first-layer topological transformation function, and completing the first-layer construction of the rail topological network; and designing a link screening algorithm, and utilizing a second-layer topology conversion function to simplify a link set in the urban rail transit network so as to complete construction of the urban rail transit double-layer topology network. The method can efficiently extract the network elements in the urban rail transit network with a complex connection structure.

Description

Construction method of urban rail transit hierarchical network based on topological 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 topological transformation.
Background
Urban rail transit is one of basic traffic ways, and orderly operation of the society is effectively guaranteed. 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. Therefore, station line information of the urban rail transit network is increased suddenly, and the complexity of a network topological structure is increased. Although diversified choices are provided for passengers who choose to travel on the track, great challenges are brought to the operation management of urban rail transit at the technical level.
Basic research such as path search algorithms, network traffic analysis, and the like are developed based on network topology. Therefore, networks are urgently needed to simplify and retain essential key elements as a carrier of basic research. The hierarchy can provide a less complex topological network, and existing contracted hierarchies include many variants, such as highway hierarchies and vertex routing. Usually, after a local contraction rule is defined, the vertex is resolved or expanded, and the vertex direct link is reconstructed according to a self-defined weight.
At present, the building algorithm of the rail transit hierarchical network in the prior art is not uniform aiming at the standards of different network building hierarchical structures, and the cross-network popularization cannot be realized. For example, in a large-scale road network, a shrinkage hierarchy is used to solve the problem of deterministic routing, and a shortcut edge needs to be added to the original structure of the road network to deal with the change of the road network structure. However, the manner and standard of adding the shortcut edge may vary according to the importance of the edge. Too many variables make the uncertainty factor too large when dealing with network layering. Especially for the urban rail transit network with a complex transfer structure, the applicability of the similar method is not good, and the method cannot provide support for a theoretical method taking a network topological structure as a carrier.
Disclosure of Invention
The embodiment of the invention provides a construction method of an urban rail transit hierarchical network based on topological transformation, so as to realize efficient extraction of urban rail transit network elements.
In order to achieve the purpose, the 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 rail topological network, carrying out coordinate processing on each station in the urban rail topological network based on a continuous network theory, and constructing a three-dimensional European space object of the urban rail topological network;
designing a first layer of topology transformation function, acquiring a three-dimensional European space object topology relation transformation rule according to a nine-intersection model, and utilizing the first layer of topology transformation function and the three-dimensional European space object topology relation transformation rule to simplify the station set of the urban rail transit network and complete the first layer construction of the rail topology network;
and designing a second-layer topology conversion function, designing a link screening algorithm according to the Dail algorithm, and simplifying a link set in the urban rail transit 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.
Preferably, the acquiring the urban rail topology network coordinates each station in the urban rail topology network based on a continuous network theory, and constructs a three-dimensional european space object of the urban rail topology network, including:
let the urban rail transit topology network be denoted as G (V, E), where V and E denote a site set and a link set, respectively, and V ═ E 1 ∪V 2 In which V is 1 And V 2 Respectively representing a transfer station set and a non-transfer station set in a three-dimensional European space
Figure BDA0003700296140000021
A Cartesian coordinate system (X, Y, Z) is established, and the space coordinate of the transfer station is marked as (X) i ,y i 0), i ═ 1, 2.., n', spatial seating of non-transfer stations is marked as (x) j ,y j ,0)，j＝1,2,...,n”；
Constructing an open rectangle U by using the coordinate extreme values as follows:
Figure BDA0003700296140000031
the minimum value of the coordinates of the open rectangle U is
Figure BDA0003700296140000032
Is composed of the minimum value of the coordinates of all transfer stations and non-transfer stations. Maximum value of open rectangular coordinates of
Figure BDA0003700296140000033
The transfer station is composed of the maximum value of the coordinates of all transfer stations and non-transfer stations, namely:
Figure BDA0003700296140000034
wherein x is i ,x j ,y i ,y j The coordinate values of the transfer station and the non-transfer station, respectively.
Using TN asl Showing the urban rail transit network contained in the open rectangle U;
constructing an open rectangle A based on the open rectangle U according to the mapping f 1 Topology network TN (twisted nematic) with split rectangular U asl And (3) carrying out spatial mapping:
Figure BDA0003700296140000035
wherein eta represents TN asl A translation distance along the Z-axis;
open rectangle a represents the following:
Figure BDA0003700296140000036
wherein:
Figure BDA0003700296140000037
according to the space coordinates of non-transfer stations in the open rectangle A
Figure BDA0003700296140000038
Constructing an open rectangle B according to the mapping f 2 Bisecting non-transfer stations within rectangle AAnd (3) carrying out spatial mapping:
Figure BDA0003700296140000039
where ω ∈ (0,)1 denotes the ratio of contraction of A, and x' has a value between
Figure BDA0003700296140000041
Y' has a value between
Figure BDA0003700296140000042
In the meantime.
The open rectangle B is represented as follows:
Figure BDA0003700296140000043
wherein:
Figure BDA0003700296140000044
the open rectangle B contains only non-transfer sites, the set of which is denoted omega B Wherein the spatial coordinates of the non-transfer station are recorded as
Figure BDA0003700296140000045
Preferably, the designing a first-layer topology transformation function, obtaining a three-dimensional european space object topology relationship transformation rule according to a nine-intersection model, and implementing station set simplification of the urban rail transit network by using the first-layer topology transformation function and the three-dimensional european space object topology relationship transformation rule to complete the first-layer construction of the rail topology network, includes:
extracting a set omega of non-transfer sites B The non-transfer station in (1) is set according to the X-axis coordinate value
Figure BDA0003700296140000046
Arranging in descending order to make m be the sequence value corresponding to the non-transfer station j, i.e.
Figure BDA0003700296140000047
Establishing a first-level topology transfer function based on m
Figure BDA0003700296140000048
According to a first layer topology transfer function
Figure BDA0003700296140000049
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, along with the separation of the non-transfer stations in the open rectangle B from the open rectangle A one by one, taking the non-transfer stations in the open rectangle A as the original images of the non-transfer stations in the open rectangle B, and mapping f 2 The station sets V in G (V, E) are simplified, and the first layer construction of the orbit topology network is completed.
Preferably, the set omega of non-transfer sites is extracted B The processing procedure of the non-transfer station in (1) comprises the following steps:
step 1, initializing, namely, firstly, initializing the topological relation between the open rectangle A and the open rectangle B, recording the times of moving the open rectangle B as gamma, and taking:
Figure BDA0003700296140000051
the step size of the first movement B, namely the abscissa of each non-transfer station in B needs to be added
Figure BDA0003700296140000052
In moving
Figure BDA0003700296140000053
Then, the boundary intersection of the open rectangle A and the open rectangle B is no longer an empty set, and the boundary extreme values of the open rectangle A and the open rectangle B are compared:
Figure BDA0003700296140000054
calculating a nine-intersection model of the open rectangle A and the open rectangle B:
Figure BDA0003700296140000055
wherein: a. the o /B o Is the interior of the set of spatial objects;
Figure BDA0003700296140000056
is the boundary of the set of spatial objects; a. the - /B - Is relative to the European space
Figure BDA0003700296140000057
Outside of the set of objects of (1);
and 2, extracting a non-transfer station with the abscissa label of m belonging to [1, m-2], specifically, when gamma belongs to [2, m-1], generalizing the adopted moving step formula as follows:
Figure BDA0003700296140000058
wherein ε is 10 -6 When gamma is equal to [2, m-1]]And comparing the boundary extreme values of A and B to obtain:
Figure BDA0003700296140000059
calculating a nine-way model:
Figure BDA0003700296140000061
the topological relation between A and B is changed from 'Covers' to 'Overlap' when the gamma is 2 times of moving B, and the topological relation is continued until the gamma is m-1 times of moving B;
when B is moved each time, the abscissa of the non-transfer station in B needs to be added
Figure BDA0003700296140000067
According to the nine-intersection model evolution rule, the area of the station A is shrunk in the process of extracting non-transfer stations one by one, and the position coordinates of the stations in the station A are updated through a formula (9) to shrink the area of the station A;
Figure BDA0003700296140000063
wherein:
Figure BDA0003700296140000064
Figure BDA0003700296140000065
if the station ordinate in A is on the baseline xi before the second move B, the station position remains stationary; if the station ordinate in A is below baseline ξ before the second move B, the station position up-shift shortens the elevation Δ y γ Half of (1); otherwise, the station moves up to shorten the longitudinal height Δ y γ Half of (1);
non-transfer station
Figure BDA0003700296140000066
Are extracted by adopting the moving step length of the formula (8), along with the extraction of non-transfer stations, in order to keep the original topological structure, the gamma belongs to the [2, m-1]]At this time, after each shift B, transfer station information in a adjacent to the extracted non-transfer station is stored and the link between transfer stations needs to be reconnected, and the transfer stations adjacent to S2 are S1 and S3, which are written as:
list { (L2, S2, Up) - (L2, S1, Up), (L2, S3, Up) }, and link reconnection between S1 and S3; transfer sites adjacent to S4 are S3 and S5, so it is written as List { (L2, S4, Up) - (L2, S3, Up), (L2, S5, Up) }, and the link between S3 and S5 is reconnected;
and 3, extracting the non-transfer station with the abscissa label of m-1, and taking the moving step length as follows:
Figure BDA0003700296140000071
the abscissa of each non-transfer station in B needs to be added
Figure BDA0003700296140000072
Non-transfer station
Figure BDA0003700296140000073
Is extracted, the boundary extreme values of A and B are compared,
Figure BDA0003700296140000074
Figure BDA0003700296140000075
if yes, when the rectangle B is moved to the mth time, the nine-intersection model is calculated to know that:
Figure BDA0003700296140000076
the opening rectangle B is moved to the right
Figure BDA0003700296140000077
Then, the topological relation between A and B is changed from 'Overlap' to 'Meet', and meanwhile, the area of A is reduced to the minimum and the last link reconnection is needed according to the fact that the coordinate of A is updated according to the step (9);
step 4, extracting the non-transfer stations with the abscissa label m, wherein after the m-th movement of the rectangle B, the topological relation between A and B is Meet, namely the same non-transfer stations exist on the boundary of A and B, and taking
Figure BDA00037002961400000710
And (5) continuing moving the right B to complete the complete separation of the A and the B, and updating the nine-intersection model as follows:
Figure BDA0003700296140000079
so far, the topological relation between a and B is changed from "Meet" to "disajoint" when moving the rectangle B for the m +1 th time, and the non-transfer stations with the abscissa label m are extracted, so that all the non-transfer stations are extracted.
Preferably, the completing the first layer construction of the track topology network includes:
the extraction of all non-transfer sites in the open rectangle A is completed through the first layer of topological conversion function. Meanwhile, the area of the open rectangle A continuously shrinks in the process of extracting the station until the area is minimum, and then the folded open rectangle A needs to be restored to obtain the topological network TN only containing the transfer station and the reconnection link information tsl Within open rectangle A, except for t 0 All transfer stations except the transfer station positioned on the baseline xi at the moment need to move along the opposite direction during contraction, and the height of longitudinal shortening is as follows:
Figure BDA0003700296140000081
and (5) opening all transfer stations in the rectangle A to be restored to the original positions, and completing the construction of the first layer of the track topology network.
Preferably, the designing a second-layer topology conversion function, designing a link screening algorithm according to a data algorithm, and simplifying a link set in the urban rail transit 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 includes:
on the basis of the urban rail transit hierarchical topological network, the topological network TN aiming at transfer stations and reconnection link information contained in the open rectangular set A tsl Establishing effective link screening conditions for the determined transfer sitesIn combination, TN tsl And judging the effectiveness of all links in the urban rail transit network, and finishing the construction of the urban rail transit double-layer topology network after eliminating invalid links.
Preferably, the topological network TN for the transfer stations and the reconnection link information contained in the open rectangle set a is based on the urban rail transit hierarchical topological network tsl And constructing effective link screening conditions, including:
on the basis of an urban rail transit layered topology network, at TN tsl For transfer site combinations (T) α ,T β ) The condition for judging the validity of the link is given based on the Dial algorithm as follows:
Figure BDA0003700296140000091
wherein: t is μ ,T η ,T α ,T β Is TN tsl Transfer station in, T μ ,T η Is a transfer station combination (T) α ,T β ) Transfer stations connected directly at will;
Figure BDA0003700296140000092
is T μ And T α Minimum travel cost in between;
Figure BDA0003700296140000093
is T η And T β Minimum travel cost in between;
Figure BDA0003700296140000094
is (T) μ ,T η ) Travel cost of direct links between them;
Figure BDA0003700296140000095
is T α ,T β Travel cost of the shortest path between the two stations; h: expanding the coefficient, and determining the range of searching the effective path;
for transfer station combinations (T) α ,T β ) Any direct link (T) of μ ,T η ) If it is
Figure BDA0003700296140000096
Figure BDA0003700296140000097
And
Figure BDA0003700296140000098
the sum of the three is less than or equal to
Figure BDA0003700296140000099
1+ H times of, then the link (T) μ ,T η ) Is effective.
Preferably, said combination of determined transfer stations combines TN tsl Judging the effectiveness of all links in the urban rail transit network, and finishing the construction of the urban rail transit double-layer topology network after eliminating invalid links, wherein the construction comprises the following steps:
introducing a second layer topology conversion function based on link validity conditions
Figure BDA00037002961400000910
Simplified TN tsl For each pair of transfer station combinations (T) α ,T β ) To turn TN tsl Further simplify and obtain
Figure BDA00037002961400000911
Figure BDA00037002961400000912
Comprising only transfer stations and α ,T β ) In conjunction with TN, of active links between asl And TN nts And finishing the construction of the urban rail transit double-layer topology network.
According to the technical scheme provided by the embodiment of the invention, the method realizes the purpose of efficiently extracting the network elements in the urban rail transit network with large 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.
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In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a processing flow chart of a method for constructing an urban rail transit hierarchical network based on topology transformation according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a nine-intersection model evolution rule and a spatial object topological relation provided in an embodiment of the present invention;
fig. 3 is a diagram illustrating link reconnection and List generation during a non-transfer site 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 a schematic diagram of an open rectangle U 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 the 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 view of a partial beijing urban rail transit network according to an embodiment of the present invention.
Fig. 10 is a schematic diagram of an orbital hierarchical topology network obtained after a first-layer topology is transformed according to an embodiment of the present invention;
fig. 11 is a schematic diagram of a two-layer simplified track topology network obtained after the topology transformation of the second layer according to the embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of 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 the context clearly indicates otherwise. 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. As used herein, the term "and/or" 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 convenience of understanding the embodiments of the present invention, the following description will be further explained by taking several specific embodiments as examples in conjunction with the drawings, and the embodiments are not to be construed as limiting the embodiments of the present invention.
The embodiment of the invention provides a method for constructing an urban rail transit hierarchical network based on topology transformation, wherein a double-layer topological network of urban rail transit aiming at different transfer station combinations is obtained by station extraction and effective link screening, and the aim of efficiently extracting urban rail transit network elements is fulfilled.
The method of the embodiment of the invention is characterized in that firstly, based on an original topological structure of an urban rail, a homomorphic open rectangle containing different station line information networks is constructed by establishing a mapping operator. And then constructing a first-layer topological conversion function of the simplified site set by relying on a nine-intersection model idea. And continuously changing the topological relation of the space objects by moving the open rectangle set to finish the extraction of the non-transfer sites. This process can be used in a generalized manner. Therefore, the urban rail transit hierarchical topology network is obtained. Next, a second layer topology transformation function that reduces the set of links is designed based on the improved Dial algorithm. And by constructing an effective link condition, removing ineffective links from the topological network only comprising the links of the transfer stations to form a double-layer simplified track topological network.
The processing flow chart of the construction method of 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 processing procedures:
constructing an urban rail transit network space object: let the urban rail transit topology network be denoted as G (V, E), where V and E denote a site set and a link set, respectively, and V ═ E 1 ∪V 2 In which V is 1 And V 2 Representing a transfer station set and a non-transfer station set, respectively. In three-dimensional European space
Figure BDA0003700296140000121
In the method, a Cartesian coordinate system (X, Y, Z) is established, and the spatial coordinates of the transfer station are marked as (X) i ,y i 0), i ═ 1, 2.., n', spatial seating of non-transfer stations is marked as (x) j ,y j ,0)，j＝1,2,...,n”。
The open rectangle U is constructed using the coordinate extrema as follows:
Figure BDA0003700296140000122
the minimum value of the coordinates of the open rectangle U is
Figure BDA0003700296140000123
Is composed of the minimum value of the coordinates of all transfer stations and non-transfer stations. Maximum value of open rectangular coordinates of
Figure BDA0003700296140000124
Is formed by the maximum value of the coordinates of all transfer stations and non-transfer stations, i.e.
Figure BDA0003700296140000125
Wherein x is i ,x j ,y i ,y j The coordinate values of the transfer station and the non-transfer station, respectively.
Using TN asl And showing the urban rail transit network contained in the open rectangle U.
Based on the open rectangle U, an open rectangle a is constructed. First, according to f 1 Topology network TN (twisted nematic) with split rectangular U asl And (3) carrying out spatial mapping:
Figure BDA0003700296140000131
wherein eta represents TN asl Translation distance along the Z-axis.
The open rectangle a can be represented as follows:
Figure BDA0003700296140000132
wherein:
Figure BDA0003700296140000133
according to the space coordinates of non-transfer stations in the open rectangle A
Figure BDA0003700296140000134
Rectangular B is constructed. First, according to f 2 And (3) carrying out space mapping on non-transfer stations in the open rectangle A:
Figure BDA0003700296140000135
where ω ∈ (0,)1 denotes the ratio of contraction of A, and x' has a value between
Figure BDA0003700296140000136
Y' has a value between
Figure BDA0003700296140000137
In the meantime.
The open rectangle B can be represented as follows:
Figure BDA0003700296140000138
wherein:
Figure BDA0003700296140000139
at this time, the open rectangle B includes only the non-transfer sites, and the set of these non-transfer sites is represented as Ω B Wherein the spatial coordinates of the non-transfer station are recorded as
Figure BDA0003700296140000141
Constructing a first-layer topological network of the urban rail:
extracting a set omega of non-transfer sites B The non-transfer station is set according to the X-axis coordinate value
Figure BDA0003700296140000142
Arranging in descending order to make m be the sequence value corresponding to the non-transfer station j, i.e.
Figure BDA0003700296140000143
Establishing a first-level topology transfer function based thereon
Figure BDA0003700296140000144
I.e., B moves to the right along the X-axis until it is completely separated from a. In this process, as the non-transfer stations in B separate from A one by one, the non-transfer stations in A are the original images of the non-transfer stations in B at f 2 The inverse mapping relation is extracted one by one. Further, 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 omega of non-transfer sites B The processing procedure of the non-transfer station in (2) comprises the following steps:
step 1, initialization. First, the topological relation between a and B is initialized. We note the number of times the rectangle B is moved open as gamma. Taking:
Figure BDA0003700296140000145
the step size of the first shift B, i.e. the abscissa of each non-transfer station in B, needs to be added
Figure BDA0003700296140000146
In moving
Figure BDA0003700296140000147
Thereafter, the boundary intersection of a and B is no longer an empty set. At this time, the boundary extremum of a and B are compared:
Figure BDA0003700296140000148
calculating a nine-way intersection model of A and B:
Figure BDA0003700296140000149
wherein: a. the o /B o Is the interior of the set of spatial objects;
Figure BDA00037002961400001410
is the boundary of the set of spatial objects; a. the - /B - Is relative to the European space
Figure BDA0003700296140000151
Is outside of the set of objects.
According to the nine-intersection model evolution rule and the spatial object topological relation shown in fig. 2, after B is moved for the first time, the topological relation between a and B is "Covers", that is, the station in B is not moved out of a. Therefore, the site coordinates within a do not need to be updated.
And 2, extracting a non-transfer station with the abscissa label of m belonging to [1, m-2 ]. Specifically, when γ ∈ [2, m-1], the employed move step formula can be generalized as:
Figure BDA0003700296140000152
wherein ε is 10 -6 . The extraction process at this stage can be generalized because when γ ∈ [2, m-]Comparing the boundary extreme values of A and B can obtain:
Figure BDA0003700296140000153
therefore, calculating the nine-intersection model can know that:
Figure BDA0003700296140000154
the topological relation between a and B changes from "Covers" to "Overlap" at the γ ═ 2 th movement B, and continues until after γ ═ m-1 th movement B.
When B is moved each time, the abscissa of the non-transfer station in B needs to be added
Figure BDA0003700296140000155
To update the location of the B-site. In addition, according to the nine-intersection model evolution rule, the area of A is shrunk in the process of extracting the non-transfer stations one by one. Therefore, we shrink the area of a by updating the position coordinates of the station within a by equation (9).
Figure BDA0003700296140000161
Wherein:
Figure BDA0003700296140000162
Figure BDA0003700296140000163
specifically, if the station ordinate within a is on the baseline ξ before the second move B, then the station position remains stationary; if the station ordinate in A is below baseline ξ before the second move B, the station position up-shift shortens the elevation Δ y γ Half of (1); otherwise, the station moves up to shorten the longitudinal height Δ y γ Half of that.
Thus, the non-transfer station
Figure BDA0003700296140000164
Can be extracted by using the moving step of equation (8). In addition, along with the extraction of non-transfer sites, in order to keep the original topological structure, the method belongs to gamma epsilon [2, m-1]]Then, after each shift B, transfer station information in a adjacent to the extracted non-transfer station will be saved and the links between transfer stations need to be reconnected. In the method, the travel time is adopted as the link weight instead of the link distance. Fig. 3 is a schematic diagram illustrating link reconnection and List generation in a non-transfer site 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. Adjacent to S2The transfer stations of (1) are S1 and S3, so they are written as:
list { (L2, S2, Up) - (L2, S1, Up), (L2, S3, Up) }, and link reconnection between S1 and S3; transfer sites adjacent to S4 are S3 and S5, so it is written as List { (L2, S4, Up) - (L2, S3, Up), (L2, S5, Up) }, and the link between S3 and S5 is reconnected.
And 3, extracting the non-transfer station with the abscissa label of m-1. The moving step is taken as follows:
Figure BDA0003700296140000171
the abscissa of each non-transfer station in B needs to be added with
Figure BDA0003700296140000172
Non-transfer station
Figure BDA0003700296140000173
Is extracted. At this time, the boundary extreme values of A and B are compared,
Figure BDA0003700296140000174
in particular, it is possible to use, for example,
Figure BDA0003700296140000175
this is true. Therefore, we conclude that when moving rectangle B the mth time, we calculate the nine-intersection model to know:
Figure BDA0003700296140000176
the opening rectangle B is moved to the right
Figure BDA0003700296140000177
Thereafter, the topological relationship between A and B is changed from "Overlap" to "Meet". Meanwhile, updating the coordinates of A according to (9) shows that the area of A is reduced to the minimum and the last link reconnection is needed.
And 4, extracting the non-transfer stations with the abscissa labels of m. Note that after the mth move away from rectangle B, the topological relationship of a to B is "Meet", i.e., there are identical non-transfer sites on the boundary of a and B. Thus, the process of extracting the site has not been completed. Therefore, we get
Figure BDA0003700296140000178
And B is moved to the right continuously, and the complete separation of A and B is completed. Meanwhile, the nine-intersection model is updated as follows:
Figure BDA0003700296140000179
to this end, the topological relationship between A and B is changed from "Meet" to "Disjoin" when moving rectangle B on the m +1 th time. The non-transfer sites with the abscissa label m are extracted, and so far, the extraction of all the non-transfer sites is completed.
After the preparatory work of constructing the nine-intersection model space object, all non-transfer stations in the urban rail transit network are extracted according to the evolution rule of the nine-intersection model on the premise of keeping the original network topology structure. Then, an urban rail transit network hierarchical topology is constructed, and a first-layer urban rail transit network construction process provided by the embodiment of the present invention is shown in fig. 4, and includes the following processing procedures:
and completing the extraction of all the non-transfer sites in the open rectangle A through the first layer of topology conversion function. While the area of the open rectangle a continues to shrink during the extraction of the station until it is minimum. Next, the "folded" open rectangle a needs to be restored, and a topological network TN is obtained that only includes transfer site and reconnection link information tsl . Within open rectangle A, except t 0 All transfer stations except the one at the time on the baseline xi need to move in the opposite direction during contraction. Note that the area of the decrease in A is exactly the area of B, so the height of the longitudinal decrease is
Figure BDA0003700296140000181
Thus, 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.
Fig. 5 is a flowchart for constructing an urban rail transit second-layer topology network according to an embodiment of the present invention, which includes the following processing procedures:
and link validity conditions are as follows: at TN is given below tsl For transfer station combinations (T) α ,T β ) To reduce duplicate computations for invalid links.
Firstly, conditions for judging the effectiveness of the link are given based on Dial algorithm:
Figure BDA0003700296140000182
wherein: t is μ ,T η ,T α ,T β Is TN tsl Transfer station in, T μ ,T η Is a transfer station combination (T) α ,T β ) Transfer stations connected directly to each other;
Figure BDA0003700296140000183
is T μ And T α Minimum travel cost therebetween;
Figure BDA0003700296140000184
is T η And T β Minimum travel cost in between;
Figure BDA0003700296140000185
is (T) μ ,T η ) Travel cost of direct links between them;
Figure BDA0003700296140000186
is T α ,T β Travel cost of the shortest path between the two; h: the expansion coefficient determines the range of searching for the valid path.
Equation (12) shows that for the transfer station combination (T) α ,T β ) Any direct link (T) of μ ,T η ) If, say, provided that
Figure BDA0003700296140000191
Figure BDA0003700296140000192
And C T The sum of the three is less than or equal to
Figure BDA0003700296140000193
1+ H times of, then the link (T) μ ,T η ) Is effective. Further, TN tsl The number of invalid links is effectively reduced after the links in (1) are screened.
And (3) link screening: introducing a second layer topology conversion function based on link validity conditions
Figure BDA0003700296140000194
Simplified TN tsl . Thus, for each pair of transfer station combinations (T) α ,T β ) Mixing TN tsl Further simplify and obtain
Figure BDA0003700296140000195
Therefore, the temperature of the molten steel is controlled,
Figure BDA0003700296140000196
comprising only transfer stations and α ,T β ) The active link between. Incorporating TN asl And TN nts The two-tier simplified orbit topology network generation.
Example two:
simple example of a track topology network: the urban rail transit topological network G (V, E), in V K, M, … and the like represent stations, the position coordinates of each station are marked as (x, y,0), and a, b and … represent direct links between two stations. Obtaining an open rectangle by screening the coordinate extreme value
Figure BDA0003700296140000197
And a topological network TN containing all site link information asl . Fig. 6 is a schematic diagram of a topology network according to an embodiment of the present inventionOpen rectangle U schematic diagram, for open rectangle U and TN that it contains asl Taking successive mappings f 1 To obtain an open rectangle a. Labeling non-transfer site coordinates within A as
Figure BDA0003700296140000198
Taking bijective function f for all non-transfer sites in A 2 Further, the non-transfer sites in the example are mapped to open rectangles
Figure BDA0003700296140000199
Within, and the coordinates will be marked as
Figure BDA00037002961400001910
Wherein G ', F ', Q ', H ' are located on the boundary of B, and E ', D ', S ' belong to the interior of B. The open rectangle B comprises a 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:
Figure BDA00037002961400001911
while m is max ＝5＜j max The same holds true for 7.
The extraction of the non-transfer sites within the example was done in order of increasing m and the extraction process is presented in table 1.
TABLE 1. procedure for example network abstraction of non-transfer sites
Figure BDA0003700296140000201
The area of the rectangle A which is folded is restored to obtain the topological network TN only containing the information of the transfer site and the link tsl And is combined with TN asl ，Ω B Collectively forming a hierarchical topology network, fig. 8 is a hierarchical topology for (N ', K') according to an embodiment of the present inventionAnd (4) a network schematic diagram. Given a combination of transfer sites (N ', K'), a link screening algorithm is invoked. For (N ', K'), TN is judged according to the requirement of formula (12) tsl The availability of each link within. Calculated TN tsl Will be further simplified into
Figure BDA0003700296140000202
And TN asl ，TN nts Together forming a two-layer topology network.
Taking the Beijing city orbit network as an example, the implementation process is explained. 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 realizing the first-layer simplification of the network through site extraction to obtain a hierarchical topology network. Fig. 10 is a schematic diagram of an orbital hierarchical topology network obtained after the first-layer topology is transformed according to an embodiment of the present invention. Giving a transfer site combination List { (L2, Xizhu, Up) - (L1, national trade, Up) } in the existing track network, and obtaining a second-layer topology transformation shown in FIG. 11 through second-layer effective link screening to obtain a schematic diagram of a two-layer simplified track topology network.
Site storage based on GIS data: generally, when a track topology network is constructed, stations are often stored on a network map in the form of points or sequence numbers. In the present invention, sites are not only saved as nodes to build a network topology, but are also captured and stored in data based on latitude and longitude of GIS sites. By materializing the abstract symbols representing the stations in this way, the concrete positions of the stations in the orbital network can be accurately obtained.
And (3) constructing a network considering travel cost: in a topological network, a line segment is used to represent a link between two stations. The connection relation between the sites is embodied in the storage of the link data. The travel costs of the train schedule are stored in the data as link weights. Thus, the connection relationship between the sites is preserved. The connection relation is used for reconstructing a topological structure of the urban rail transit network, so that the obtained network structure is closer to actual operation. Therefore, by combining the above two points, the topological network can be constructed by using the position coordinate data of the station and the link data.
The stability of the urban rail transit network topology is maintained: there are two traditional ways to simplify site aggregation: the first is to directly delete a specific type of station. And secondly, setting constraints and deleting sites violating the constraints. 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 the conventional method presents challenges in achieving this goal. Therefore, the invention provides an urban rail transit hierarchical network algorithm based on topology transformation to achieve the aim.
The stations in the open rectangle are divided into a transfer station and a non-transfer station. The proposed method is to extract sites rather than delete a class of sites directly. As the non-transfer stations are extracted, the adjacent transfer stations are recorded in the List, and the links where the extracted non-transfer stations are located are reconnected. And extracting the non-transfer stations and then updating the link set.
The site extraction is the core of link screening, and after a rectangular area is recovered, if a topological network is stable, a TN (transport network) of a transfer site link topological network can be obtained tsl . This is the basis for screening for valid links. The algorithm for simplifying the urban rail transit network based on the topology transformation hierarchy can accurately construct the topological network of the urban rail transit, the running time of a train schedule is called to adjust the weight of the link, and the extracted hierarchical network topology does not damage the original topological relation, which is a precondition for carrying out 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 large scale and complex connection structure. The track traffic network is used as a support for searching the shortest (K-short) path and realizing the upper-layer tasks such as passenger flow distribution, and the complexity of the connection structure directly determines the calculation efficiency. On the premise of limited calculation cost, the premise of effectively improving the calculation efficiency is to extract complete network elements, and the calculation redundancy of traversing the network elements is greatly reduced under the constraint of not influencing the calculation result. The invention provides a specific method for constructing a simplified and layered track topology network, 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 understand that: the figures are schematic representations of one embodiment, and the blocks or processes shown in the figures are not necessarily required to practice the present invention.
From the above description of the embodiments, it is clear to those skilled in the art that the present invention can be implemented by software plus necessary general hardware platform. Based on such understanding, the technical solutions of the present invention may be embodied in the form of software products, which may be stored in a storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and include instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method according to the embodiments or some parts of the embodiments.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for apparatus or system embodiments, since they are substantially similar to method embodiments, they are described in relative terms, as long as they are described in partial descriptions of method embodiments. The above-described embodiments of the apparatus and system are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one position, or may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. One of ordinary skill in the art can understand and implement without inventive effort.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (8)

1. A construction method of an urban rail transit hierarchical network based on topology transformation is characterized by comprising the following steps:
acquiring an urban rail topological network, carrying out coordinate processing on each station in the urban rail topological network based on a continuous network theory, and constructing a three-dimensional European space object of the urban rail topological network;
designing a first layer of topology conversion function, acquiring a three-dimensional European space object topology relationship transformation rule according to a nine-intersection model, and utilizing the first layer of topology conversion function and the three-dimensional European space object topology relationship transformation rule to simplify the station set of the urban rail transit network and complete the first layer construction of the rail topology network;
designing a second layer topology conversion function, designing a link screening algorithm according to the Dail algorithm, and utilizing the second layer topology conversion function and the link screening algorithm to simplify the link set in the urban rail transit network so as to complete the construction of the urban rail transit double-layer topology network.
2. The method according to claim 1, wherein the obtaining of the urban rail topology network, the coordinate processing of each station in the urban rail topology network based on the continuous network theory, and the constructing of the three-dimensional european space object of the urban rail topology network comprises:
let the urban rail transit topology network be denoted as G (V, E), where V and E denote a site set and a link set, respectively, and V ═ E 1 ∪V 2 In which V is 1 And V 2 Respectively representing a transfer station set and a non-transfer station set in a three-dimensional European space
Figure FDA0003700296130000011
A Cartesian coordinate system (X, Y, Z) is established, and the space coordinate of the transfer station is marked as (X) i ,y i 0), i ═ 1, 2.., n', spatial seating of non-transfer stations is marked as (x) j ,y j ,，j＝1,2,...,n”；
The open rectangle U is constructed using the coordinate extrema as follows:
Figure FDA0003700296130000012
the minimum value of the coordinates of the open rectangle U is
Figure FDA0003700296130000013
Is composed of the minimum value of the coordinates of all transfer stations and non-transfer stations. Maximum value of the open rectangular coordinate is
Figure FDA0003700296130000021
The transfer station is composed of the maximum value of the coordinates of all transfer stations and non-transfer stations, namely:
Figure FDA0003700296130000022
wherein x is i ,x j ,y i ,y j The coordinate values of the transfer station and the non-transfer station, respectively.
Using TN asl Showing the urban rail transit network contained in the open rectangle U;
constructing an open rectangle A based on the open rectangle U according to the mapping f 1 Topology network TN (twisted nematic) with split rectangular U asl And (3) carrying out spatial mapping:
Figure FDA0003700296130000023
wherein eta represents TN asl Along the Z-axisA translation distance;
open rectangle a represents the following:
Figure FDA0003700296130000024
wherein:
Figure FDA0003700296130000025
according to the space coordinates of non-transfer stations in the open rectangle A
Figure FDA0003700296130000026
Constructing an open rectangle B according to the mapping f 2 And (3) carrying out space mapping on the non-transfer stations in the open rectangle A:
Figure FDA0003700296130000027
where ω ∈ (0,)1 denotes the ratio of contraction of A, and x' has a value between
Figure FDA0003700296130000028
Y' has a value between
Figure FDA0003700296130000029
In the meantime.
The open rectangle B is represented as follows:
Figure FDA0003700296130000031
wherein:
Figure FDA0003700296130000032
the open rectangle B contains only non-transfer sites, the set of which is denoted Ω B Wherein the spatial coordinates of the non-transfer station are recorded as
Figure FDA0003700296130000033
3. The method according to claim 2, wherein the designing a first layer topology transformation function, obtaining a three-dimensional Euclidean space object topology relationship transformation rule according to a nine-intersection model, and utilizing the first layer topology transformation function and the three-dimensional Euclidean space object topology relationship transformation rule to simplify the station set of the urban rail transit network and complete the first layer construction of the rail topology network comprises:
extracting a set omega of non-transfer sites B The non-transfer station is set according to the X-axis coordinate value
Figure FDA0003700296130000034
Arranging in descending order to make m be the sequence value corresponding to the non-transfer station j, i.e.
Figure FDA0003700296130000035
Establishing a first-level topology transfer function based on m
Figure FDA0003700296130000036
According to a first layer topology transfer function
Figure FDA0003700296130000037
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, along with the separation of the non-transfer stations in the open rectangle B from the open rectangle A one by one, taking the non-transfer stations in the open rectangle A as the original images of the non-transfer stations in the open rectangle B, and mapping f 2 The station sets V in G (V, E) are simplified, and the first layer construction of the orbit topology network is completed.
4. The method of claim 3, wherein the extracting of the set Ω of non-transfer sites is performed B The processing procedure of the non-transfer station in (2) comprises the following steps:
step 1, initializing, namely, firstly, initializing the topological relation between an open rectangle A and an open rectangle B, recording the times of moving the open rectangle B as gamma, and taking:
Figure FDA0003700296130000038
the step size of the first shift B, i.e. the abscissa of each non-transfer station in B, needs to be added
Figure FDA0003700296130000041
In moving
Figure FDA0003700296130000042
Then, the boundary intersection of the open rectangle A and the open rectangle B is no longer an empty set, and the boundary extreme values of the open rectangle A and the open rectangle B are compared:
Figure FDA0003700296130000043
calculating a nine-intersection model of the open rectangle A and the open rectangle B:
Figure FDA0003700296130000044
wherein: a. the o /B o Is the interior of the set of spatial objects;
Figure FDA0003700296130000045
is the boundary of the set of spatial objects; a. the - /B - Relative to the European space
Figure FDA0003700296130000046
Outside of the set of objects of (1);
and 2, extracting a non-transfer station with the abscissa label of m belonging to [1, m-2], specifically, when gamma belongs to [2, m-1], generalizing the adopted moving step formula as follows:
Figure FDA0003700296130000047
wherein ε is 10 -6 When gamma is equal to [2, m-1]]Comparing the boundary extreme values of A and B to obtain:
Figure FDA0003700296130000048
calculating a nine-way model:
Figure FDA0003700296130000049
the topological relation between A and B is changed from 'Covers' to 'Overlap' when the gamma is 2 times of moving B, and the topological relation is continued until the gamma is m-1 times of moving B;
when B is moved each time, the abscissa of the non-transfer station in B needs to be added
Figure FDA0003700296130000051
According to the nine-intersection model evolution rule, the area of the station A is shrunk in the process of extracting non-transfer stations one by one, and the position coordinates of the stations in the station A are updated through a formula (9) to shrink the area of the station A;
Figure FDA0003700296130000052
wherein:
Figure FDA0003700296130000053
Figure FDA0003700296130000054
if the station ordinate in A is on the baseline ξ before the second move B, then the station position remains motionless; if the station ordinate in A is below baseline ξ before the second move B, the station position is shifted up by the shortened vertical height Δ y γ Half of (1); otherwise, the station moves up to shorten the longitudinal height Δ y γ Half of (1);
non-transfer station
Figure FDA0003700296130000055
Are extracted by adopting the moving step length of the formula (8), along with the extraction of non-transfer stations, in order to keep the original topological structure, the gamma belongs to the [2, m-1]]At this time, after each shift B, transfer station information in a adjacent to the extracted non-transfer station is stored and the link between transfer stations needs to be reconnected, and the transfer stations adjacent to S2 are S1 and S3, which are written as:
list { (L2, S2, Up) - (L2, S1, Up), (L2, S3, Up) }, and link reconnection between S1 and S3; transfer sites adjacent to S4 are S3 and S5, so it is written as List { (L2, S4, Up) - (L2, S3, Up), (L2, S5, Up) }, and the link between S3 and S5 is reconnected;
and 3, extracting the non-transfer stations with the abscissa labels of m-1, and taking the moving step length as follows:
Figure FDA0003700296130000061
the abscissa of each non-transfer station in B needs to be added
Figure FDA0003700296130000062
Non-transfer station
Figure FDA0003700296130000063
Is extracted, the boundary extreme values of A and B are compared,
Figure FDA0003700296130000064
Figure FDA0003700296130000065
if yes, when the rectangle B is moved to the mth time, the nine-intersection model is calculated to know that:
Figure FDA0003700296130000066
the opening rectangle B is moved to the right
Figure FDA0003700296130000067
Then, the topological relation between A and B is changed from 'Overlap' to 'Meet', and meanwhile, the area of A is reduced to the minimum and the last link reconnection is needed according to the fact that the coordinate of A is updated according to the step (9);
step 4, extracting the non-transfer stations with the abscissa label m, wherein after the m-th movement of the rectangle B, the topological relation between A and B is Meet, namely the same non-transfer stations exist on the boundary of A and B, and taking
Figure FDA0003700296130000068
And continuing moving the B to the right to complete the complete separation of the A and the B, and updating the nine-intersection model as follows:
Figure FDA0003700296130000069
so far, the topological relation between a and B is changed from "Meet" to "disajoint" when moving the rectangle B for the m +1 th time, and the non-transfer stations with the abscissa label m are extracted, so that all the non-transfer stations are extracted.
5. The method of claim 3, wherein the performing the first layer construction of the orbital topology network comprises:
the extraction of all non-transfer sites in the open rectangle A is completed through the first layer of topological conversion function. Meanwhile, the area of the open rectangle A continuously shrinks in the process of extracting the station until the area is minimum, and then the folded open rectangle A needs to be restored to obtain the topological network TN only containing the transfer station and the reconnection link information tsl Within open rectangle A, except for t 0 All transfer stations except the transfer station positioned on the baseline xi at the moment need to move along the opposite direction during contraction, and the height of longitudinal shortening is as follows:
Figure FDA0003700296130000071
and (5) recovering all transfer stations in the open rectangle A to the original positions, and finishing the construction of the first layer of the track topology network.
6. The method according to claim 5, wherein the designing a second layer topology conversion function, designing a link screening algorithm according to a Dail algorithm, and utilizing the second layer topology conversion function and the link screening algorithm to simplify a link set in the urban rail transit network to complete the construction of the urban rail transit double-layer topology network comprises:
on the basis of the urban rail transit hierarchical topological network, the topological network TN aiming at transfer stations and reconnection link information contained in the open rectangular set A tsl Establishing effective link screening conditions, combining the determined transfer sites and combining the TN tsl And judging the effectiveness of all links in the urban rail transit network, and finishing the construction of the urban rail transit double-layer topology network after eliminating invalid links.
7. The method of claim 6, wherein the urban rail transit hierarchical topologyOn the basis of the network, the topological network TN aiming at the transfer sites and reconnection link information contained in the open rectangle set A tsl And constructing effective link screening conditions, including:
on the basis of an urban rail transit layered topology network, at TN tsl For transfer site combinations (T) α ,T β ) Conditions for judging the effectiveness of the link are given based on Dial algorithm as follows:
Figure FDA0003700296130000072
wherein: t is μ ,T η ,T α ,T β Is TN tsl Transfer station in, T μ ,T η Is a transfer station combination (T) α ,T β ) Transfer stations connected directly to each other;
Figure FDA0003700296130000081
is T μ And T α Minimum travel cost therebetween;
Figure FDA0003700296130000082
is T η And T β Minimum travel cost in between;
Figure FDA0003700296130000083
is (T) μ ,T η ) Travel cost of the direct link between the two;
Figure FDA0003700296130000084
is T α ,T β Travel cost of the shortest path between the two stations; h: expanding the coefficient to determine the range of searching the effective path;
for transfer station combinations (T) α ,T β ) Any direct link (T) of μ ,T η ) If, say, provided that
Figure FDA0003700296130000085
Figure FDA0003700296130000086
And
Figure FDA0003700296130000087
the sum of the three is less than or equal to
Figure FDA0003700296130000088
1+ H times of, then the link (T) μ ,T η ) Is effective.
8. The method of claim 6 wherein combining the determined transfer sites combines TN tsl Judging the effectiveness of all links in the urban rail transit network, and finishing the construction of the urban rail transit double-layer topology network after eliminating invalid links, wherein the construction comprises the following steps:
introducing a second layer topology conversion function based on link validity conditions
Figure FDA0003700296130000089
Simplified TN tsl For each pair of transfer station combinations (T) α ,T β ) To turn TN tsl Further simplify and obtain
Figure FDA00037002961300000810
Figure FDA00037002961300000811
Only including transfer stations and (T) α ,T β ) Active link between, in conjunction with the TN asl And TN nts And finishing the construction of the urban rail transit double-layer topology network.
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