CN110843870A - Method for maintaining fixed capacity of high-speed railway network graph under abnormal event - Google Patents

Method for maintaining fixed capacity of high-speed railway network graph under abnormal event Download PDF

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CN110843870A
CN110843870A CN201911149049.2A CN201911149049A CN110843870A CN 110843870 A CN110843870 A CN 110843870A CN 201911149049 A CN201911149049 A CN 201911149049A CN 110843870 A CN110843870 A CN 110843870A
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train
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CN110843870B (en
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许心越
李建民
王铭铭
石睿
张可
李燕秋
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Beijing Jiaotong University
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Abstract

The embodiment of the invention provides a method for maintaining the fixed capacity of a high-speed rail network graph in an abnormal event, which predicts the delay of a train by using a GBRT model, constructs a train delay operation alternative graph optimization model based on operation adjustment, generates a feasible train operation graph and calculates the capacity of the high-speed rail network in the abnormal event; calculating the capacity of the road sections according to the generated adjusted train running diagram, constructing a high-speed rail network capacity weight network under an abnormal event, and identifying the bottleneck road sections of the high-speed rail network capacity; the method comprises the steps of simulating the running of the high-speed train under different delay conditions by using OPENTRACK simulation software, analyzing the capacities of a high-speed rail section and a station under an abnormal event, feeding back a calculation result serving as capacity constraint to a substitute graph optimization model based on running adjustment, iteratively calculating the capacity of the high-speed rail network under the abnormal event, realizing accurate estimation of the capacity of the high-speed rail network, making a capacity maintenance strategy, and providing a macroscopic reference for high-speed rail scheduling and running graph adjustment.

Description

Method for maintaining fixed capacity of high-speed railway network graph under abnormal event
Technical Field
The invention relates to the technical field of rail transit capacity analysis, in particular to a method for maintaining the fixed capacity of a high-speed rail network graph in an abnormal event.
Background
The occurrence of abnormal events always restricts the improvement of the capacity of a high-speed railway network, different types of abnormal events can cause train delays of different degrees, serious abnormal events are often long in duration, the capacity loss is serious, the transportation capacity and the transportation capacity are unbalanced, and troubles are caused to the running organization and the operation plan of a high-speed train. The abnormal events are mainly divided into natural disasters, accident disasters, public health and social safety. In particular to driving accidents, fire disasters, explosions, geological disasters, meteorological disasters, facility equipment accidents and other events.
In recent years, the construction of high-speed railways in China is rapidly developed and gradually becomes a main channel for passenger transportation in China, and once abnormal events occur, capacity loss or line interruption is caused, so that the whole transportation system is seriously influenced. Therefore, the method for maintaining the fixed capacity of the high-speed railway network graph in the abnormal event is constructed, the change of the capacity of the high-speed railway network in the abnormal event and the bottleneck identification of the capacity of the high-speed railway network are researched, a decision basis is provided for dispatching and commanding from a macroscopic level, the method is beneficial to improving the railway traffic organization efficiency under the high-speed railway network forming condition, and the traffic safety is guaranteed.
Disclosure of Invention
The embodiment of the invention provides a method for maintaining the capacity of a high-speed rail network map under an abnormal event, which is characterized in that a train delay operation alternative map optimization model based on operation adjustment is constructed based on a high-speed rail train late delay prediction and adjustment strategy, the capacity of a section and a station is taken as dynamic constraint of the model, the accurate estimation of the capacity of the high-speed rail network is realized, a capacity maintenance strategy is established, and a macroscopic reference is provided for high-speed rail scheduling and operation map adjustment.
In order to achieve the purpose, the invention adopts the following technical scheme.
A method for maintaining the fixed capacity of a high-speed railway network graph under an abnormal event comprises the following steps:
s1: predicting delay time of a high-speed rail train based on a GBRT model;
s2: station constructed by applying OPENTACT simulation software and method for constructing stationThe topological graph of the high-speed rail network of the interval simulates the running of the high-speed train under different delay times, and the capacity N of the high-speed rail section under abnormal events is calculated according to the simulation resultqAnd station capacity Nw;
s3: using the delay time as model input data, and taking the section capacity NqAnd building a high-speed rail network substitution graph optimization model based on operation adjustment by taking station capacity Nw as model constraint, generating a high-speed rail train operation graph under an abnormal event and calculating network capacity Nz；
S4: constructing a high-speed rail network capacity weight network under an abnormal event based on a high-speed rail train running diagram and the network capacity under the abnormal event, and identifying a high-speed rail network capacity bottleneck road section;
s5: dividing the road network into sections and stations by the bottleneck road section, and calculating to obtain the section capacity of the high-speed rail under the new abnormal event by turning to S2And station capability
Figure BDA0002283029640000022
S6: it is determined whether the following statement is true,
Figure BDA0002283029640000023
epsilon is a sufficiently small positive number
If the statement is true, stopping iteration and entering S7; otherwise, turning to S3 for loop iteration;
s7: ability to export high-speed rail sections in abnormal events
Figure BDA0002283029640000024
Station capacity
Figure BDA0002283029640000025
Road network capability Nz。
Preferably, the S1 includes:
the method adopts a method of gradient regression tree GBRT ensemble learning to predict the arrival delay of the high-speed rail, takes 7 variables of train number, drawing arrival time, total travel length, station stations, train travel time, travel percentage and late time as independent variables of a prediction model, takes the delay time of each train number arriving at a subsequent station as an output variable, and comprises the following steps based on the GBRT high-speed rail delay prediction:
s11: data input, known training data set
Figure BDA0002283029640000031
Wherein xiIs an input variable, yiIs the corresponding output variable, the loss function L (y, f (x)) is a squared error loss function,
Figure BDA0002283029640000032
the iteration number M;
s12: the goal of the model is to find an approximation F towards the function F (x)0(x) And minimizes the expectation of a given loss function on the data set, gamma being a constant term, being the initial value of the model,
Figure BDA0002283029640000033
s13: the value of the negative gradient of the loss function at the current model is calculated and used as an estimate of the residual, then the negative gradient is defined as,
Figure BDA0002283029640000034
s14: for residual errors, the model fits it to a regression tree hm(x) Then the step size of the model gradient descent method is calculated as follows,
s15: the model is updated in such a way that,
fm(x)＝fm-1(x)+γmhm(x)
s16: finishing M times of iteration to obtain a regression tree,
Figure BDA0002283029640000036
s17: and outputting the arrival delay time of the train.
Preferably, the S3 includes:
s31: constructing a macro substitution graph model;
s32: and constructing a replacement graph optimization model based on operation adjustment.
Preferably, the S31 includes:
according to train operation basic information and infrastructure data, a substitution graph node set is constructed by taking a block partition as a unit, stations are abstracted into a block partition from a macroscopic level, and the construction process of a concrete substitution graph is as follows, wherein the stations only serve as one node:
s311: acquiring basic information of train operation and infrastructure data;
s312: generating a node set N by the block partition, and generating a substitute arc set F by the connecting arcs of adjacent nodes;
s313: pair
Figure BDA0002283029640000041
If it is notGenerating a substitute pair set A from ((i, j), (h, k));
s314: generating a substitution graph G ═ (N, F, a);
in the formula: n is a node set; f is an alternative arc set; a is a set of alternate pairs;
Figure BDA0002283029640000043
the starting time of the train entering the interval, namely the starting moment of the node k, j;
Figure BDA0002283029640000044
the end time of the train leaving interval, namely the end time of the nodes i and h; (k, i), (j, h) are substitutedAn arc, which is a directed edge of adjacent nodes k and i or j and h, and the direction indicates the sequence relation between the train operation; ((i, j), (h, k)) is an alternate pair.
Preferably, the train operation basic information includes: train starting and ending and arrival and departure and passing time information of a station, a train running route and a train;
the infrastructure data includes: interval distance and line allowable speed.
Preferably, said 32 comprises:
the method comprises the following steps of constructing a substitution graph optimization model based on operation adjustment by taking the minimum number of stopped trains and the total delay time of the trains as targets and taking capacity constraint, train departure time windows, train operation time, train forward and backward relation, train interval tracking time and station interval time as constraint conditions, wherein the specific model construction process is as follows:
(1) objective function
The capability of the high-speed railway under the abnormal event is kept with the minimum number of the trains to be stopped and the total time of the trains at the later point as the optimization target,
Figure BDA0002283029640000045
in the formula: q. q.sc，qdRespectively calculating the outage penalty number and the late penalty number; tau iskPlanning a starting moment for the train at the k node; x is the number ofkFor train shutdown, if the train is shutdown at node k, xk1, otherwise 0;
(2) constraint conditions
① capability constraint
The train runs in a road network and meets the maximum train number which can pass each block subarea in a given time range, namely the train is dynamically limited by the capacity of a section and a station;
Figure BDA0002283029640000051
Figure BDA0002283029640000052
Figure BDA0002283029640000053
Figure BDA0002283029640000054
in the formula: s represents a set of the block partitions in the interval; v represents a set of which the block subareas are located in a station; τ represents a train set;
Figure BDA0002283029640000055
representing whether the train runs in a block zone S or not, wherein S belongs to S;
Figure BDA0002283029640000056
indicating whether the train runs in a block zone V or not, wherein V belongs to V; n is a radical ofq,sRepresenting the capacity of the q section, and the occlusion partition s is located in the q section; nw, v represents the capacity of w stations, and the block subarea v is positioned at the w stations;
② train departure time window constraint
The occurrence time of the train at the node k is not earlier than the planning time, when the occurrence time is later than the point, the occurrence time of the train at the node k is not later than the planning time of the train plus the maximum time later,
Figure BDA0002283029640000057
Figure BDA0002283029640000058
in the formula (I), the compound is shown in the specification,the starting time of the train entering the interval, namely the starting time of the k node; tau iskThe planned starting time of the behavior represented by node k; x is the number ofkFor train shutdown, if the train is shutdown at node k, xk1, otherwise 0; t isDThe maximum late time of the train;
③ train operation time constraints
The starting time of the running behavior of the train at the node i meets the starting time of the direct preceding node k of the node i
Figure BDA0002283029640000061
And the running time t of the k nodekThe sum of (a) and (b),
Figure BDA0002283029640000062
in the formula (I), the compound is shown in the specification,
Figure BDA0002283029640000063
the starting time of the train entering the interval, namely the starting time at the node i;
Figure BDA0002283029640000064
the starting time of the train entering the interval, namely the starting time of the k node; t is tkThe running time of the train on the section, namely the running time of 1 block subarea; f, replacing an arc set;
④ train front-rear relationship constraint
In order to avoid conflict, two trains cannot occupy the same block subarea at the same time,
Figure BDA0002283029640000065
Figure BDA0002283029640000066
in the formula (I), the compound is shown in the specification,
Figure BDA0002283029640000067
and
Figure BDA0002283029640000068
the starting time of the train entering the interval, namely the starting time of the nodes i, k, h and j; t is tkiAnd tjhTo replace the values of the arcs, the nodes are respectively representedThe preparation time from k to node i and the preparation time from node j to node h; f. of(k,i|j,h)The train operation sequence is (k, i | j, h) belongs to A, if the arc (i, j) is selected, f (k, i | j, h) is 1, otherwise, 0 is obtained; m is an arbitrarily large positive number; a replaces the pair set;
⑤ train stopping restriction
If the train stops at the k node, the train stops at all the subsequent nodes of the k node,
xi＝xk，k,i∈V,(k,i)∈F
in the formula, xkFor train shutdown, if the train is shutdown at node k, xk1, otherwise 0; x is the number ofiTo stop operation at node i
⑥ tracking train interval time and station interval time constraints
The train tracking interval time of the adjacent 2 trains is more than or equal to the minimum safe interval time t between the 2 trainszminValues of substitute arcs corresponding to substitute maps
Figure BDA0002283029640000069
Should be greater than or equal to t determined by train speed, interlock and block equipment typezminThe actual departure interval time of 2 trains adjacent in the same direction of the station is more than or equal to the minimum safe interval time tfmin，
Figure BDA00022830296400000610
Figure BDA0002283029640000071
In the formula, tzminMinimum safe interval time for train operation; t is tfminThe minimum departure interval time of adjacent trains at the same station;
Figure BDA0002283029640000072
the starting time of the train entering the interval, namely the starting time of the k node;
Figure BDA0002283029640000073
the starting time of the train leaving interval, namely the ending time at the node i; a set of N nodes; p (k) the occurrence position, interval or track of the behavior corresponding to node k; p (i) the occurrence position, interval or track of the behavior corresponding to the node i; hqAn interval set; hgA set of tracks;
(3) model solution
Adopting MATLAB R2018b to program, calling IBM ILOG CPLEX 12.6.0 to realize the proposed method, setting the relevant parameters of CPLEX as default values, solving the mixed integer linear programming model by a built-in branch cutting algorithm combining a branch-and-bound method and a secant plane method, and generating a train running sequence in the solving process according to the following steps:
s321: randomly generating a high-speed train operation sequence by a Fisher-Yates shuffle algorithm;
s322: dynamically sampling to generate all possible train running sequences;
s323: it is determined whether the following statement is true,
Figure BDA0002283029640000074
if the statement is true, stopping sampling and outputting a generated sequence; otherwise, continuing sampling;
s324: for any line in the road network, excluding trains which do not run on the line in the sequence,
Figure BDA0002283029640000075
s325: for any station in the road network, all trains passing through the station are included in the sequence according to the front and back running relation,
Figure BDA0002283029640000076
s326: generating a feasible sequence Sseq，
Figure BDA0002283029640000077
In the formula:and
Figure BDA0002283029640000079
are respectively N and (N-N)Δ) Sample standard deviation of individual samples;
Figure BDA00022830296400000710
and
Figure BDA00022830296400000711
are respectively N and (N-N)Δ) A sample mean of individual samples; n is the number of sequences generated; n is a radical ofΔIs the number of sequences generated between measurements;
Figure BDA0002283029640000081
is the convergence tolerance of the standard deviation of the samples,
Figure BDA0002283029640000082
is the convergence tolerance of the sample mean; c is a constraint type; c. C-To exclude sequence constraints, c+To contain sequence constraints c+；ecA line corresponding to constraint c; sseqA train sequence generated for a set of trains;
Figure BDA0002283029640000083
is the position of the train in the sequence; erIs a set of lines in path r;
Figure BDA0002283029640000084
is composed of
Figure BDA0002283029640000085
The path the train travels.
Preferably, the constructing a high-speed rail network capacity weight network under the abnormal event comprises:
on the basis of a high-speed rail train running diagram under an abnormal event, a road network is decomposed into a combination of sections by combining a locomotive road-crossing system and a riding system, the running direction of the train is not considered, the road network is finally abstracted into a non-directional capacity weight network, and the capacity weight of each section is obtained according to the following formula:
in the formula: n is the number of passing trains in the section; t is the occupied time of the train for m times on the plan operation diagram; t is1And (5) counting the occupied time of the train for the adjusted running chart.
Preferably, the dividing of the road network into sections and stations by the bottleneck road section includes:
s51: calculating the section capacity by the generated adjusted train operation diagram, constructing a non-directional weight traffic network G, and generating an adjacent matrix A of the traffic network GG；
S52: computing a diagonal matrix D of a traffic network GGAnd generates a laplacian matrix LG；
S53: normalized Laplace matrix LG；
S54: calculating the second small eigenvalue λ of the normalized Laplace matrix2And feature vectors
S55: according to the feature vector
Figure BDA0002283029640000088
And a threshold value tau, dividing the traffic network, wherein the cut edge is a traffic bottleneck section.
According to the technical scheme provided by the embodiment of the invention, the embodiment of the invention provides a method for maintaining the capacity of a high-speed railway network graph in an abnormal event, and the method uses the train delay predicted by a GBRT model to construct a train delay operation alternative graph optimization model based on operation adjustment, generate a feasible train operation graph and calculate the capacity of the high-speed railway network in the abnormal event; calculating the capacity of the road sections according to the generated adjusted train running diagram, constructing a high-speed rail network capacity weight network under an abnormal event, and identifying the bottleneck road sections of the high-speed rail network capacity; the method comprises the steps of simulating the running of high-speed trains with different delay times by using OPENTRACK simulation software, analyzing the capacities of high-speed rail sections and stations under abnormal events, feeding back a calculation result serving as capacity constraint to a substitute graph optimization model based on running adjustment, iteratively calculating the capacity of the high-speed rail network under the abnormal events, realizing accurate estimation of the capacity of the high-speed rail network, making a capacity maintenance strategy, and providing a macroscopic reference for high-speed rail scheduling and running graph adjustment.
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 schematic flow chart of a method for maintaining the fixed capacity of a graph of a highway network in an abnormal event;
FIG. 2 is a correlation of train delay to input variables;
FIG. 3 is a comparison of actual delays and predicted delays for three models (training set);
FIG. 4 is a comparison (test set) of actual delays and predicted delays for three models;
fig. 5 illustrates the recognition of the service network capacity bottleneck in the Yangtze delta area.
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 function 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 maintaining the fixed capacity of a high-speed railway network graph in an abnormal event, which comprises the following steps as shown in figure 1:
s1: and predicting delay time of the high-speed rail train based on the GBRT model.
And predicting the high-speed rail arrival delay by adopting a method of integrated learning of a progressive gradient regression tree (GBRT). GBRT generates strong learners in the form of weak learner sets, and performs learning and model prediction of training samples on the basis of the strong learners. Considering that 7 variables such as the arrival time, the travel percentage, the late time and the like of the high-speed rail map are taken as independent variables of a prediction model, the delay time of each train number arriving at a subsequent station is taken as an output variable, and the steps of the high-speed rail delay prediction based on the GBRT are as follows:
s11: data input, known training data set
Figure BDA0002283029640000111
Wherein xiIs an input variable, yiIs the corresponding output variable, the loss function L (y, f (x)) is a squared error loss function,
Figure BDA0002283029640000112
the iteration number M;
s12: the goal of the model is to find an approximation F towards the function F (x)0(x) And minimizes the expectation of a given loss function on the data set, gamma being a constant term, being the initial value of the model,
Figure BDA0002283029640000113
s13: the value of the negative gradient of the loss function at the current model is calculated and used as an estimate of the residual, then the negative gradient is defined as,
Figure BDA0002283029640000114
s14: for residual errors, the model fits it to a regression tree hm(x) Then the step size of the model gradient descent method is calculated as follows,
Figure BDA0002283029640000115
s15: the model is updated in such a way that,
fm(x)＝fm-1(x)+γmhm(x)
s16: finishing M times of iteration to obtain a regression tree,
Figure BDA0002283029640000116
s17: and outputting the arrival delay time of the train.
The embodiment of the invention verifies that the selected characteristic variables and the original data are shown in table 1, and before modeling, the modeling data needs to be preprocessed to obtain the correlation between train delay and the characteristic variables, which is shown in fig. 2. As can be seen from the graph, there is a complex relationship between the dependent variable arrival late and the respective variables, which is difficult to determine. Therefore, the machine learning model is considered to solve the complex relationship between the dependent variable and the independent variable to predict the delay of the high-speed train.
TABLE 1 original data Table for modeling
Since the delay time is directly absorbed by the buffer time when the delay time is too small, the delay of a high-speed train of 4min or less is not considered, and the modeling data sample amount is 1306 after data preprocessing such as noise reduction. 80% of the data in the data set was randomly selected as a training set for model training, and the remaining 20% of the data was selected as a test set. The model determines the optimal parameters through a grid search method.
The results of calculating the evaluation indexes of the different models using the training set are shown in table 2. As shown in Table 2, the coefficient of certainty of GBRT is as high as 0.9063, which is superior to that of the RF and SVR models, and MAE, MSE and RMSE are the lowest compared with the RF and SVR models, so the GBRT model has the best fitting effect compared with the RF and SVR models. To verify the validity of each model, test set data was entered into the trained model, and as a result, as shown in table 3, it can be seen that GBRT has slightly lower individual merit values in the test set relative to the training set, but still works best compared to both RF and SVR models. Therefore, the GBRT prediction model has a good effect on the delay prediction of the high-speed rail late.
TABLE 2 comparison of results for three models (training set)
Methods R2 MAE MSE RMSE
SVR 0.8730 0.6356 2.5791 1.6059
RF 0.8866 0.9957 2.1628 1.4706
GBRT 0.9063 0.4628 1.8845 1.3727
TABLE 3 comparison of results for three models (test set)
Figure BDA0002283029640000122
S2: constructing a high-speed rail network topological graph of stations and sections by using OPENTRACK simulation software, simulating the running of high-speed trains at different delay times, and calculating the capacity N of the high-speed rail section under abnormal events according to simulation resultsqAnd station capability Nw (initial value calculated separately).
S3: using delay time as model input data, and using section capacity NqAnd building a high-speed rail network substitution graph optimization model based on operation adjustment by taking station capacity Nw as model constraint, generating a high-speed rail train operation graph under an abnormal event and calculating network capacity Nz。
S31: and (5) constructing a macroscopic substitution graph model.
According to train operation basic information and infrastructure data, a substitution graph node set is constructed by taking a block partition as a unit, stations are abstracted into a block partition from a macroscopic level, and the construction process of a concrete substitution graph is as follows, wherein the stations only serve as one node:
s311: obtaining train operation basic information and infrastructure data, wherein the train operation basic information comprises: information such as train starting and ending to a station, a train running route, train arrival, departure and passing time and the like; the infrastructure data includes section distance, line allowable speed, and the like.
S312: a set of nodes N is generated by the block partition, and a set of substitute arcs F is generated by the connecting arcs of the adjacent nodes.
S313: pair
Figure BDA0002283029640000132
If it is not
Figure BDA0002283029640000133
A set a of substitute pairs is generated from ((i, j), (h, k)).
S314: the alternative graph G ═ (N, F, a) is generated.
In the formula: n is a node set; f is an alternative arc set; a is substitutionA pair set;the starting time of the train entering the interval, namely the starting moment of the node k, j;the end time of the train leaving interval, namely the end time of the nodes i and h; (k, i), (j, h) are substitute arcs, and are directed edges of adjacent nodes k and i or j and h, and the directions indicate the precedence relationship between train operation; ((i, j), (h, k)) is an alternate pair.
S32: and constructing a replacement graph optimization model based on operation adjustment.
The method comprises the following steps of constructing a substitution graph optimization model based on operation adjustment by taking the minimum number of stopped trains and the total delay time of the trains as targets and taking capacity constraint, train departure time windows, train operation time, train forward and backward relation, train interval tracking time, station interval time and the like as constraint conditions, wherein the specific model construction process is as follows:
(1) model symbol
TABLE 4 model parameters
Figure BDA0002283029640000141
Figure BDA0002283029640000151
(2) Objective function
The capability of the high-speed railway under the abnormal event is kept with the minimum number of the trains to be stopped and the total time of the trains at the later point as the optimization target,
Figure BDA0002283029640000152
(3) constraint conditions
① capability constraint
The train running in the road network should satisfy the maximum train number that each block zone can pass in a given time range, namely, the train is limited by the dynamic of the capacity of the section and the station, the capacity of the section and the station is calculated according to the following claim 7,
Figure BDA0002283029640000154
Figure BDA0002283029640000155
Figure BDA0002283029640000161
② train departure time window constraint
The occurrence time of the train at the node k is not earlier than the planning time, when the occurrence time is later than the point, the occurrence time of the train at the node k is not later than the planning time of the train plus the maximum time later,
Figure BDA0002283029640000162
Figure BDA0002283029640000163
③ train operation time constraints
The starting time of the running behavior of the train at the node i meets the starting time of the direct preceding node k of the node i
Figure BDA0002283029640000164
And the running time t of the k nodekThe sum of (a) and (b),
Figure BDA0002283029640000165
④ train front-rear relationship constraint
In order to avoid conflict, two trains cannot occupy the same block subarea at the same time,
Figure BDA0002283029640000166
Figure BDA0002283029640000167
⑤ train stopping restriction
If the train stops at the k node, the train stops at all the subsequent nodes of the k node,
xi＝xk，k,i∈V,(k,i)∈F
⑥ tracking train interval time and station interval time constraints
The train tracking interval time of the adjacent 2 trains is more than or equal to the minimum safe interval time t between the 2 trainszmin. Corresponding to the values of the substitute arcs in the substitute graph
Figure BDA0002283029640000168
Should be greater than or equal to t determined by train running speed, interlock and block equipment type and the likezminThe value of (c). The actual departure interval time of the 2 trains adjacent in the same direction of the station is more than or equal to the minimum safe interval time tfmin，
Figure BDA0002283029640000169
Figure BDA00022830296400001610
(4) Model solution
The proposed method was implemented using MATLAB R2018b programming, calling IBM ILOG CPLEX 12.6.0. And setting relevant parameters of the CPLEX as default values, and solving the mixed integer linear programming model by a built-in branch cutting algorithm combining a branch-and-bound method and a cut plane method. Generating a train running sequence in the solving process according to the following steps:
s321, randomly generating a high-speed train operation sequence by a Fisher-Yates shuffle algorithm;
s322, dynamically sampling to generate all possible train operation sequences;
s323, judging whether the following sentence is true,
Figure BDA0002283029640000171
if the statement is true, stopping sampling and outputting a generated sequence; otherwise, continuing sampling;
s324: for any line in the road network, excluding trains which do not run on the line in the sequence,
Figure BDA0002283029640000172
s325: for any station in the road network, all trains passing through the station are included in the sequence according to the front and back running relation,
s326: generating a feasible sequence Sseq，
Figure BDA0002283029640000174
In the formula:
Figure BDA0002283029640000175
and
Figure BDA0002283029640000176
are respectively N and (N-N)Δ) Sample standard deviation of individual samples;
Figure BDA0002283029640000177
andare respectively N and (N-N)Δ) A sample of a sampleMean value; n is the number of sequences generated; n is a radical ofΔIs the number of sequences generated between measurements;
Figure BDA0002283029640000179
is the convergence tolerance of the standard deviation of the samples,
Figure BDA00022830296400001710
is the convergence tolerance of the sample mean; c is a constraint type; c. C-To exclude sequence constraints, c+To contain sequence constraints c+；ecA line corresponding to constraint c; sseqA train sequence generated for a set of trains;is the position of the train in the sequence; erIs a set of lines in path r;
Figure BDA00022830296400001712
is composed of
Figure BDA00022830296400001713
The path the train travels.
S4: and constructing a high-speed rail network capacity weight network under the abnormal event based on the high-speed rail train running diagram and the network capacity under the abnormal event, and further identifying the bottleneck road section of the high-speed rail network capacity.
The high-speed train operation diagram under the abnormal event obtained by the step S3 is combined with locomotive traffic and a riding system to decompose the road network into a combination of sections, and the road network is finally abstracted into a non-directional capability weight network without considering the train operation direction. The capacity weight for each segment is given by:
Figure BDA0002283029640000181
in the formula: n is the number of passing trains in the section; t is the occupied time of the train for m times on the plan operation diagram; t is1And (5) counting the occupied time of the train for the adjusted running chart.
S5: road network is drawn by bottleneck sectionDividing the high-speed rail into sections and stations, and converting S2 to obtain the capacity of the high-speed rail sections under a new abnormal event through calculation
Figure BDA0002283029640000182
And station capability
Figure BDA0002283029640000183
The method for identifying the bottleneck of the road network capacity based on spectral clustering comprises the following steps:
s51: calculating the section capacity by the generated adjusted train operation diagram, constructing a non-directional weight traffic network G, and generating an adjacent matrix A of the traffic network GG；
S52: computing a diagonal matrix D of a traffic network GGAnd generates a laplacian matrix LG；
S53: normalized Laplace matrix LG；
S54: calculating the second small eigenvalue λ of the normalized Laplace matrix2And feature vectors
S55: according to the feature vector
Figure BDA0002283029640000185
And a threshold value tau, dividing the traffic network, wherein the cut edge is a traffic bottleneck section.
Constructing a high-speed railway capacity weight network based on a high-speed railway network in a Yangtze river delta region and a train schedule; the spectral clustering method is adopted to identify the service capacity bottleneck of the high-speed railway, the result is shown in fig. 5(a) and (b), fig. 5(a) shows that the network is divided into two sub-regions, and the boundary of the sub-regions is the capacity bottleneck of the road network; fig. 5(b) shows that the network is divided into three sub-regions, and the boundaries of the sub-regions are the capacity bottlenecks of the road network.
S6: : it is determined whether the following statement is true,
Figure BDA0002283029640000186
epsilon is a sufficiently small positive number
If the statement is true, stopping iteration and entering S7; otherwise, turning to S3 for loop iteration;
s7: ability to export high-speed rail sections in abnormal events
Figure BDA0002283029640000191
Station capacity
Figure BDA0002283029640000192
Road network capability Nz。
In summary, the method for maintaining the mapping capability of the high-speed rail network in the abnormal event provided by the embodiment of the invention predicts the delay of the late point of the high-speed rail based on the GBRT prediction model, and the prediction effect is better than that of the RF model and the SVR model. The method comprises the steps of constructing a train delayed operation substitution graph optimization model based on operation adjustment to calculate the capacity of the high-speed rail network, utilizing OPENTRACK simulation software to simulate the operation of the high-speed train in real time, analyzing the capacity of a high-speed rail section and a station under an abnormal event, feeding back a calculation result serving as capacity constraint to the substitution graph optimization model based on the operation adjustment, iteratively calculating the capacity of the high-speed rail network under the abnormal event, realizing accurate estimation of the capacity of the high-speed rail network, formulating a capacity maintenance strategy and providing a macroscopic reference for high-speed rail scheduling and operation graph adjustment.
Those of ordinary skill in the art will understand that: the figures are merely schematic representations of one embodiment, and the blocks or flow diagrams 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 a software product, which may be stored in a storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and includes 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 the parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it 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 method for maintaining the fixed capacity of a high-speed railway network graph under an abnormal event is characterized by comprising the following steps:
s1: predicting delay time of a high-speed rail train based on a GBRT model;
s2: constructing a high-speed rail network topological graph of stations and sections by using OPENTRACK simulation software, simulating the running of high-speed trains at different delay times, and calculating the capacity N of the high-speed rail section under abnormal events according to simulation resultsqAnd station capacity Nw;
s3: using the delay time as model input data, and taking the section capacity NqStation energy Nw as modelConstructing a high-speed rail network alternative graph optimization model based on operation adjustment, generating a high-speed rail train operation graph under an abnormal event, and calculating the network capacity Nz；
S4: constructing a high-speed rail network capacity weight network under an abnormal event based on a high-speed rail train running diagram and the network capacity under the abnormal event, and identifying a high-speed rail network capacity bottleneck road section;
s5: dividing the road network into sections and stations by the bottleneck road section, and calculating to obtain the section capacity of the high-speed rail under the new abnormal event by turning to S2
Figure FDA0002283029630000011
And station capability
Figure FDA0002283029630000012
S6: it is determined whether the following statement is true,
Figure FDA0002283029630000013
epsilon is a sufficiently small positive number
If the statement is true, stopping iteration and entering S7; otherwise, turning to S3 for loop iteration;
s7: ability to export high-speed rail sections in abnormal events
Figure FDA0002283029630000014
Station capacity
Figure FDA0002283029630000015
Road network capability Nz。
2. The method according to claim 1, wherein the S1 includes:
the method adopts a method of gradient regression tree GBRT ensemble learning to predict the arrival delay of the high-speed rail, takes 7 variables of train number, drawing arrival time, total travel length, station stations, train travel time, travel percentage and late time as independent variables of a prediction model, takes the delay time of each train number arriving at a subsequent station as an output variable, and comprises the following steps based on the GBRT high-speed rail delay prediction:
s11: data input, known training data setWherein xiIs an input variable, yiIs the corresponding output variable, the loss function L (y, f (x)) is a squared error loss function,
Figure FDA0002283029630000022
the iteration number M;
s12: the goal of the model is to find an approximation F towards the function F (x)0(x) And minimizes the expectation of a given loss function on the data set, gamma being a constant term, being the initial value of the model,
Figure FDA0002283029630000023
s13: the value of the negative gradient of the loss function at the current model is calculated and used as an estimate of the residual, then the negative gradient is defined as,
Figure FDA0002283029630000024
s14: for residual errors, the model fits it to a regression tree hm(x) Then the step size of the model gradient descent method is calculated as follows,
Figure FDA0002283029630000025
s15: the model is updated in such a way that,
fm(x)＝fm-1(x)+γmhm(x)
s16: finishing M times of iteration to obtain a regression tree,
Figure FDA0002283029630000026
s17: and outputting the arrival delay time of the train.
3. The method according to claim 1, wherein the S3 includes:
s31: constructing a macro substitution graph model;
s32: and constructing a replacement graph optimization model based on operation adjustment.
4. The method according to claim 3, wherein the S31 includes:
according to train operation basic information and infrastructure data, a substitution graph node set is constructed by taking a block partition as a unit, stations are abstracted into a block partition from a macroscopic level, and the construction process of a concrete substitution graph is as follows, wherein the stations only serve as one node:
s311: acquiring basic information of train operation and infrastructure data;
s312: generating a node set N by the block partition, and generating a substitute arc set F by the connecting arcs of adjacent nodes;
s313: pair
Figure FDA0002283029630000031
If it is not
Figure FDA0002283029630000032
Generating a substitute pair set A from ((i, j), (h, k));
s314: generating a substitution graph G ═ (N, F, a);
in the formula: n is a node set; f is an alternative arc set; a is a set of alternate pairs;
Figure FDA0002283029630000033
the starting time of the train entering the interval, namely the starting moment of the node k, j;
Figure FDA0002283029630000034
for train departureThe end time of the open interval, namely the end time of the nodes i and h; (k, i), (j, h) are substitute arcs, and are directed edges of adjacent nodes k and i or j and h, and the directions indicate the precedence relationship between train operation; ((i, j), (h, k)) is an alternate pair.
5. The method of claim 4, wherein the train operation basic information comprises: train starting and ending and arrival and departure and passing time information of a station, a train running route and a train;
the infrastructure data includes: interval distance and line allowable speed.
6. The method of claim 4 or 5, wherein the 32 comprises:
the method comprises the following steps of constructing a substitution graph optimization model based on operation adjustment by taking the minimum number of stopped trains and the total delay time of the trains as targets and taking capacity constraint, train departure time windows, train operation time, train forward and backward relation, train interval tracking time and station interval time as constraint conditions, wherein the specific model construction process is as follows:
(1) objective function
The capability of the high-speed railway under the abnormal event is kept with the minimum number of the trains to be stopped and the total time of the trains at the later point as the optimization target,
Figure FDA0002283029630000035
in the formula: q. q.sc，qdRespectively calculating the outage penalty number and the late penalty number; tau iskPlanning a starting moment for the train at the k node; x is the number ofkFor train shutdown, if the train is shutdown at node k, xk1, otherwise 0;
(2) constraint conditions
① capability constraint
The train runs in a road network and meets the maximum train number which can pass each block subarea in a given time range, namely the train is dynamically limited by the capacity of a section and a station;
Figure FDA0002283029630000041
Figure FDA0002283029630000043
Figure FDA0002283029630000044
in the formula: s represents a set of the block partitions in the interval; v represents a set of which the block subareas are located in a station; τ represents a train set; thetat，sRepresenting whether the train runs in a block zone S or not, wherein S belongs to S; thetat，vIndicating whether the train runs in a block zone V or not, wherein V belongs to V; n is a radical ofq，sRepresenting the capacity of the q section, and the occlusion partition s is located in the q section; nw, v represents the capacity of w stations, and the block subarea v is positioned at the w stations;
② train departure time window constraint
The occurrence time of the train at the node k is not earlier than the planning time, when the occurrence time is later than the point, the occurrence time of the train at the node k is not later than the planning time of the train plus the maximum time later,
Figure FDA0002283029630000045
Figure FDA0002283029630000046
in the formula (I), the compound is shown in the specification,the starting time of the train entering the interval, namely the starting time of the k node; tau iskThe planned starting time of the behavior represented by node k; x is the number ofkFor train shutdown, if the train is shutdown at node k, xk1, otherwise 0; t isDThe maximum late time of the train;
③ train operation time constraints
The starting time of the running behavior of the train at the node i meets the starting time of the direct preceding node k of the node iAnd the running time t of the k nodekThe sum of (a) and (b),
Figure FDA0002283029630000052
in the formula (I), the compound is shown in the specification,
Figure FDA0002283029630000053
the starting time of the train entering the interval, namely the starting time at the node i;the starting time of the train entering the interval, namely the starting time of the k node; t is tkThe running time of the train on the section, namely the running time of 1 block subarea; f, replacing an arc set;
④ train front-rear relationship constraint
In order to avoid conflict, two trains cannot occupy the same block subarea at the same time,
Figure FDA0002283029630000055
Figure FDA0002283029630000056
in the formula (I), the compound is shown in the specification,
Figure FDA0002283029630000057
and
Figure FDA0002283029630000058
the starting time of the train entering the interval, namely the starting time of the nodes i, k, h and j; t is tkiAnd tjhRespectively representing the preparation time from the node k to the node i and the preparation time from the node j to the node h for replacing the value of the arc; f. of(k，i|j，h)The train operation sequence is (k, i | j, h) belongs to A, if the arc (i, j) is selected, f (k, i | j, h) is 1, otherwise, 0 is obtained; m is an arbitrarily large positive number; a replaces the pair set;
⑤ train stopping restriction
If the train stops at the k node, the train stops at all the subsequent nodes of the k node,
xi＝xk，k，i∈V，(k，i)∈F
in the formula, xkFor train shutdown, if the train is shutdown at node k, xk1, otherwise 0; x is the number ofiTo stop operation at node i
⑥ tracking train interval time and station interval time constraints
The train tracking interval time of the adjacent 2 trains is more than or equal to the minimum safe interval time t between the 2 trainszminValues of substitute arcs corresponding to substitute maps
Figure FDA0002283029630000059
Should be greater than or equal to t determined by train speed, interlock and block equipment typezminThe actual departure interval time of 2 trains adjacent in the same direction of the station is more than or equal to the minimum safe interval time tfmin，
Figure FDA00022830296300000510
Figure FDA0002283029630000061
In the formula, tzminMinimum safe interval time for train operation; t is tfminThe minimum departure interval time of adjacent trains at the same station;
Figure FDA0002283029630000062
the starting time of the train entering the interval, namely the starting time of the k node;
Figure FDA0002283029630000063
the starting time of the train leaving interval, namely the ending time at the node i; a set of N nodes; p (k) the occurrence position, interval or track of the behavior corresponding to node k; p (i) the occurrence position, interval or track of the behavior corresponding to the node i; hqAn interval set; hgA set of tracks;
(3) model solution
Adopting MATLAB R2018b to program, calling IBM ILOG CPLEX 12.6.0 to realize the proposed method, setting the relevant parameters of CPLEX as default values, solving the mixed integer linear programming model by a built-in branch cutting algorithm combining a branch-and-bound method and a secant plane method, and generating a train running sequence in the solving process according to the following steps:
s321: randomly generating a high-speed train operation sequence by a Fisher-Yates shuffle algorithm;
s322: dynamically sampling to generate all possible train running sequences;
s323: it is determined whether the following statement is true,
Figure FDA0002283029630000064
if the statement is true, stopping sampling and outputting a generated sequence; otherwise, continuing sampling;
s324: for any line in the road network, excluding trains which do not run on the line in the sequence,
Figure FDA0002283029630000065
s325: for any station in the road network, all trains passing through the station are included in the sequence according to the front and back running relation,
s326: generating a feasible sequence Sseq，
Figure FDA0002283029630000067
In the formula:
Figure FDA0002283029630000068
andare respectively N and (N-N)Δ) Sample standard deviation of individual samples;and
Figure FDA00022830296300000611
are respectively N and (N-N)Δ) A sample mean of individual samples; n is the number of sequences generated; n is a radical ofΔIs the number of sequences generated between measurements;
Figure FDA0002283029630000071
is the convergence tolerance of the standard deviation of the samples,
Figure FDA0002283029630000072
is the convergence tolerance of the sample mean; c is a constraint type; c. C-To exclude sequence constraints, c+To contain sequence constraints c+；ecA line corresponding to constraint c; sseqA train sequence generated for a set of trains;is the position of the train in the sequence; erIs a set of lines in path r;
Figure FDA0002283029630000074
is composed ofThe path the train travels.
7. The method of claim 6, wherein constructing a highroad network capacity weighting network in the event of an anomaly comprises:
on the basis of a high-speed rail train running diagram under an abnormal event, a road network is decomposed into a combination of sections by combining a locomotive road-crossing system and a riding system, the running direction of the train is not considered, the road network is finally abstracted into a non-directional capacity weight network, and the capacity weight of each section is obtained according to the following formula:
Figure FDA0002283029630000076
in the formula: n is the number of passing trains in the section; t is the occupied time of the train for m times on the plan operation diagram; t is1And (5) counting the occupied time of the train for the adjusted running chart.
8. The method of claim 7, wherein the dividing of the road network into sections and stations by bottleneck road segments comprises:
s51: calculating the section capacity by the generated adjusted train operation diagram, constructing a non-directional weight traffic network G, and generating an adjacent matrix A of the traffic network GG；
S52: computing a diagonal matrix D of a traffic network GGAnd generates a laplacian matrix LG；
S53: normalized Laplace matrix LG；
S54: calculating the second small eigenvalue λ of the normalized Laplace matrix2And feature vectors
Figure FDA0002283029630000077
S55: according to the feature vectorAnd a threshold value tau, dividing the traffic network, wherein the cut edge is a traffic bottleneck section.
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