CN110211378B - Urban traffic health index system evaluation method based on complex network theory - Google Patents
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Abstract
The invention provides an urban traffic health index system evaluation method based on a complex network theory, which mainly comprises the following steps: a: establishing a reliability index R of the urban traffic network; b: establishing a brittleness index B of the urban traffic network; c: establishing an elasticity index S of the urban traffic network; based on the obtained actual urban traffic operation data, introducing seepage analysis to calculate the size of a functional subgroup of the urban traffic network under a given threshold value, and establishing a traffic network reliability index R; key roads in the traffic network are excavated, a road set which enables functional subgroups of the traffic network to be crashed to a certain proportion is analyzed, and a brittleness index B of the urban traffic network is established; and finally, establishing an elasticity index S of the urban traffic network through the whole process of generation-evolution-dissipation. The establishment of the urban traffic health index system can provide support for the evaluation of the actual running state of urban traffic, the formulation of targeted traffic management measures and the improvement of the urban traffic health level.
Description
Technical Field
The invention provides an urban traffic health index system evaluation method based on a complex network theory, relates to an urban traffic health index system evaluation method based on a complex network theory and a big data technology, and belongs to the technical field of complex network science and urban traffic big data.
Background
Urban traffic generally refers to the public traffic and the transportation of passengers and goods between the road systems in urban and suburban areas of a city. With the aid of the method and concept of a complex network, urban traffic is generally abstracted into a network consisting of a plurality of interconnected nodes (intersections) and connecting edges (roads) between them. On the basis of a statically connected road network, all roads and all local areas in the traffic network are organically connected through a dynamic traffic flow network which runs continuously on the urban traffic network. Due to the connection of the static structure and the organic connection of the dynamic structure, the traffic jam occurring in the local area may affect the normal operation of the peripheral area and even the overall traffic network, and thus the urban traffic jam of various scales is caused. Meanwhile, severely insufficient traffic capacity, ever-increasing travel demands, and frequent external operational disturbances due to extreme weather and environmental influences all bring stress and challenges to the normal operation of urban traffic networks at all times. For city managers, the great resource waste and huge economic loss caused by urban traffic congestion bring obstacles to the further development of cities. Therefore, understanding the operation mode of the urban traffic network, exploring the three processes of generation, evolution and dissipation of urban traffic congestion and utilizing the existing resources to treat and control the urban traffic congestion are important subjects of urban managers and urban traffic industry practitioners at present. All these problems are based on the fact that effective physical quantities and indexes are introduced to quantitatively calculate and evaluate the health status of the urban traffic network.
For the measurement of the health state of the urban traffic network, the recently widely used sensor hardware technology provides a sufficient data source for research, and the traffic big data technology which is mature increasingly in the urban traffic field provides help for the processing of data. They are one of the main contents of the "smart city" project that is currently advocated. For the emerging concept of city morphology, smart city, the existing concepts and explanations are: the smart city utilizes various information technologies or innovative concepts to communicate and integrate the system and service of the city, so as to improve the efficiency of resource application, optimize city management and service, and improve the quality of life of citizens. The smart city fully applies a new generation of information technology to the urban informatization advanced form based on the innovation of the next generation of knowledge society in various industries of the city, realizes the deep integration of informatization, industrialization and urbanization, is beneficial to relieving the large urban diseases, improves the urbanization quality, realizes the fine and dynamic management, improves the urban management effect and improves the quality of life of citizens. Based on the knowledge of the connotation and the target of the smart city, urban traffic is used as a key system for supporting various traffic travel activities of urban citizens in life, entertainment, work and the like, and plays an irreplaceable role in constructing the smart city. For the above-mentioned urban development and the challenges faced by urban traffic, it is first necessary to find the indexes for effective measurement of the health status of the urban traffic network, and finally combine these indexes or physical quantities organically to construct the health index system of urban traffic, so as to make good pulse and good medicine for the "big urban disease" of urban traffic congestion, and ensure the healthy and stable operation of urban traffic.
The invention constructs a health index system of urban traffic from three angles of urban traffic network reliability, traffic network fragility and traffic network elasticity based on a seepage theory, a traffic reliability theory and an elasticity theory. The main contents are as follows:
from the urban traffic network reliability perspective. And constructing a dynamic urban traffic flow network based on the acquired urban traffic operation data and the urban road network static structure. Calculating functional subgroup size parameters of the urban traffic network under given seepage thresholds at different moments by carrying out seepage analysis on the dynamic urban traffic network, and establishing a reliability index R of the traffic network;
from the point of view of fragility of urban traffic networks. For a single road in a given urban traffic network, sorting the roads of different levels in the road network according to the calculated relationship between the functional subgroups and the roads at each moment, and finding out the key road with the largest influence on the network. Finally, calculating the size of a key road set required by the functional subgroups of the network to reach the specified scale, and establishing a brittleness index B of the traffic network;
from the perspective of urban traffic network resiliency. Whether the running states of roads have continuity or not is analyzed by counting the running states of the roads with different levels in the traffic network, namely whether the roads are congested at a specific time or not. By introducing a time dimension, the functional sub-group of the urban traffic network of the two-dimensional plane is expanded into a congestion communication sub-group of a three-dimensional space. Therefore, the system analyzes the development track of the whole process of occurrence, evolution and dissipation of the traffic jam and establishes the elasticity index S of the traffic network.
By combining the three aspects, the invention provides an urban traffic health index system evaluation method based on a complex network theory, which has the following advantages: 1. the theoretical basis of the method is a complex network theory, a seepage theory, an elasticity theory and the like, is solid, and provides theoretical support for understanding the urban traffic operation rule; 2. the urban traffic health index system is comprehensively considered from three aspects of reliability, brittleness and elasticity, is beneficial to comprehensively grasping the urban traffic health state, and provides support for further prediction and regulation of the urban traffic health condition; 3. the health index system is based on actual traffic operation data, so that the health condition of actual traffic is disclosed, and the urban traffic health index system provided by the invention is close to the actual condition; 4. the urban traffic health index system provided by the invention has clear calculation process thought and clear process, can be used for real-time calculation and evaluation of urban traffic health states, and is beneficial to formulating targeted measures for improving the urban traffic running states.
Disclosure of Invention
The invention mainly provides a method for evaluating an urban traffic health index system, namely an urban traffic health index system evaluation method based on a complex network theory; the urban traffic network is a life line system for urban economic development and urban resident travel, and has extremely important significance in normal and stable operation. Therefore, based on a complex network theory, a seepage theory, an elasticity theory and the like, the urban traffic health index system is evaluated and established from three aspects of urban traffic network reliability, urban traffic network fragility and urban traffic network elasticity, and support is provided for the diagnosis of the health state of urban traffic, the formulation of targeted management measures and the improvement of the urban traffic operation level.
In view of the above technical problems and the object of the present invention, the present invention provides a method for evaluating an urban traffic health index system based on a complex network theory, wherein the scheme comprises the following parts:
objects of the invention
Aiming at the current situation of urban traffic development and the background of wide application of various emerging technologies, the invention aims to provide an urban traffic health index system evaluation method based on a complex network theory. Based on the obtained actual urban traffic operation data, an urban traffic health index system is established by means of three main indexes of urban traffic network reliability, urban traffic network fragility and urban traffic network elasticity. Specifically, the method comprises the following steps: introducing seepage analysis to calculate the size of a functional subgroup of the urban traffic network under a given threshold value, and establishing a traffic network reliability index R; key roads in the traffic network are excavated, a road set which enables functional subgroups of the traffic network to be crashed to a certain proportion is analyzed, and a brittleness index B of the urban traffic network is established; and finally, establishing an elastic index S of the urban traffic network by introducing the whole process of generation, evolution and dissipation of traffic jam subgroups on three-dimensional space-time by describing the time dimension. The establishment of the urban traffic health index system can provide support for the evaluation of the actual running state of urban traffic, the formulation of targeted traffic management measures and the improvement of the urban traffic health level.
(II) technical scheme
In order to achieve the purpose, the method adopts the technical scheme that: an urban traffic health index system evaluation method based on a complex network theory.
The invention relates to an urban traffic health index system evaluation method based on a complex network theory, which comprises the following steps:
step A: establishing a reliability index R of the urban traffic network;
and B: establishing a brittleness index B of the urban traffic network;
and C: establishing an elasticity index S of the urban traffic network;
wherein, the reliability index R for establishing the urban traffic network in the step A has the following specific meanings: processing the acquired actual running data of the urban traffic, and combining a static urban traffic road network to obtain a dynamic traffic flow network; introducing seepage analysis, and establishing a reliability index R of the urban traffic network by calculating the network functional subgroup size at each moment under a given seepage threshold; comprises the following steps:
step A1: establishing a static road network G (N, L);
step A2: establishing an initial velocity matrix M0；
Step A3: completing speed compensation and normalization to obtain a complete speed matrix M1；
Step A4: calculating a traffic network reliability index R, namely a maximum connected sub-group G;
in step a1, the "static road network G (N, L) is established" specifically as follows: according to the actually acquired urban map data, firstly extracting the connection relation between roads; secondly, selecting a suitable geographic coverage range of urban traffic according to research needs, such as selecting a five-ring traffic network in Beijing; then, according to a complex network method, abstracting a road intersection into nodes in the network, abstracting a road in the road network into connecting edges among the nodes in the network, and thus establishing a traffic network; meanwhile, most roads of the urban traffic network run in two directions, and a directed connected graph is adopted for calculation; for the convenience of subsequent calculation, after selecting a proper range, ensuring that the selected traffic network is a strong connection graph; a strongly connected clique as referred to herein means that in the directed graph G (N, L) (where N is the set of nodes in the directed graph and L is the set of connected edges), if for each pair of nodes vi、vj，vi≠vjFrom viTo vjAnd from vjTo viIf paths exist, G (N, L) is called a strong communication graph; the obtained strong communication graph in the selected geographic range is the established static road network;
therein, step A2 describes "establishing an initial velocity matrix M0", it is as follows: corresponding to the static road network obtained in A1, at any time tiGenerating a transverse vector V according to the sequence relation of the roads by using the corresponding speeds of all K roadsi＝(v1,v2…vK) (ii) a Further, the process is repeated for all TI moments, and finally all transverse vectors are integrated to generate an initial speed matrix M0＝(V1,V2…VTI) Storing in a computer in a linked list form; the traffic operation data is vehicle speed data on the road collected by a specific data collector and is used for reflecting the operation state of the road at the moment; each track at each momentThe roads all have unique speed values;
the "speed compensation is completed" in step a3, which is specifically performed as follows: the data acquisition device in the collection process can generate accidental faults and other unpredictable events, so that the speed of a part of roads is not recorded at a part of time; that is, the original velocity matrix M0There is a partial missing value (actually recorded as 0); in consideration of the need of the calculation process, compensation is made here for the missing values of these velocity records; first, find the velocity matrix M0And compensating for the speed deficiency value; for time tiCompensation of the missing value of speed for the lower road L, a set of adjacent edges (L) of the road L in the road network G (N, L) is foundn1,ln2…lnm) (ii) a Searching whether the continuous edges in the set have speed records at the moment; finally, taking the average value of the speeds of the adjacent sides with the speed records; comprises the following steps:
if all the speeds of the adjacent sides of the road l are not recorded, skipping the compensation of the loop, and keeping the speed of the road l at the moment to be 0; the obtained speed matrix M 'is compensated for'0Updating M0Continuing to compensate until all 0 values in the speed matrix are compensated to obtain a speed matrix M1；
Wherein, the normalization in step A3 is performed to obtain a complete velocity matrix M2", it is as follows: for any road i, the slave velocity matrix M1Extracting speed value sequence V of all the time of the roadiExtracting the maximum speed limit v of the road sectioni_maxDividing each speed of the sequence of speed values by the maximum speed limit vi_maxTo obtain a normalized velocity vi_ratioAs follows:
vi_ratio＝vi/vi_max
finally, the normalization operation is carried out on all roads to obtain a normalized speed matrix M2＝((V1_ratio,V2_ratio…VTI_ratio))；
Wherein, the step A4 of calculating the reliability index R of the traffic network, namely the maximum connected sub-cluster G, comprises the following specific steps: based on the normalized speed matrix M obtained in A32Introducing seepage analysis to calculate a reliability index, namely a maximum connected sub-group G, for the traffic network; wherein, the general process of the seepage analysis is as follows: setting a speed threshold value q at any time, and setting a speed value v at the timeiDeleting roads i smaller than the speed threshold q; then gradually increasing the speed threshold q according to the actual scale of the network and the calculation precision requirement, initializing the network G (N, L) and repeatedly carrying out the previous step of edge deletion operation; in the seepage analysis process, the maximum connected group G has a representation effect on the whole network functionality; while taking into account that the velocity matrix that has been normalized is obtained, a given threshold q is setcCalculating the maximum connected sub-clusters at each moment; firstly, deleting the corresponding time t in the networkiThe lower velocity value being less than the velocity threshold qcThen finding the maximum function connected sub-group G' by using a breadth first method (BFS); wherein, the maximum function connected sub-group G' refers to the first big connected sub-group in the whole network; storing all the connection edges, nodes and connection relations; then, for all time instants (t)1,t2…tTI) Performing the operation to finally obtain a maximum function connected sub-cluster set at all the moments; comprises the following steps:
wherein: n is the number of connected edges of the initial network, and size (G) is the number of connected edges of the sub-cluster G.
Wherein, the brittleness index B for establishing the urban traffic network in the step B has the following specific meanings: brittleness is generally used to measure the resistance of a material to external forces, deformation and fracture; for the urban traffic network, brittleness is a network attribute and is used for finding weak nodes and links which easily damage, degrade performance and even crash the system in operation of the traffic system and measuring the influence of the weak nodes on the system; for a traffic system, even if a weak link is attacked or disturbed by low intensity, serious consequences are likely to be generated, so that how to find the weak node and measure the influence of the weak node is particularly important; measuring the network breakdown resisting capacity of the traffic network from a road level, and establishing a brittleness index B of the traffic network; due to geographical factors, road design conditions and functional differences of different areas, the traffic network is an anisotropic system, namely different roads play different roles in the overall operation of the network; in reality, roads are generally divided into different classes: intercity high speed, city fast, city arterial road, etc.; however, in the process of guaranteeing the operation of the traffic network, the actual functions of roads with different grades are not necessarily completely matched with the grades; for example, a road with a very low grade in a traffic network may be a bottleneck edge between two areas, and plays an important role in area intercommunication and congestion dissipation; therefore, the actual action grades of different roads need to be explored; secondly, establishing brittleness indexes of the urban traffic network by means of the roads; comprises the following steps:
b1, calculating and sequencing the importance levels of all roads;
step B2: establishing a brittleness index B, and analyzing the brittleness level of the traffic network;
in step B1, "calculate and rank the importance levels of all roads", the specific procedure is as follows: according to the maximum function connected sub-cluster set at each moment determined in the step a4, for any road i, firstly, it is determined whether it belongs to the road side set of the maximum function connected sub-cluster:
wherein e (t) is used for indicating whether the road i belongs to the maximum function connected subgroup G' with the critical threshold value of q at the moment of t; wherein, 1 represents that the road i is in G ', and 0 represents that the road i is not in G';
counting the times of the road appearing in the continuous edges of the maximum function connected sub-clusters
Finally, dividing the total time number TI into the importance level O (i) of the road:
performing the above operation on each road, and finally obtaining the importance level values O ═ (O (1), O (2) … O (l)) of all roads; further, the roads are sorted according to the descending order of the importance levels;
wherein, in step B2, the brittleness index is established and the traffic network brittleness level is analyzed, which comprises the following steps: assume that the initial size of the network is L0Setting a certain ratio pcThe network size at this time is L0*pc(ii) a Defining the size of the network to be broken to L by referring to the measure of the brittleness of the network and the process of breaking down the network0*pcMinimum set of roads l to be removedG＝(l1i,l2i…lni) To measure the traffic network G (N, L) at any time t within a statistical time periodiA brittleness index of (d); it should be noted that, here, all roads in the traffic network G (N, L) are ranked in advance, so the number of elements in the minimum road set can be equivalent to the index B for measuring the brittleness of the traffic network; comprises the following steps:
B(t)＝size(lG(L0,pc))
wherein size (l)G) Is represented byGNumber of roads in the sequence.
Wherein, the "elasticity index S for establishing an urban traffic network" in step C has the specific meaning: the elasticity of the traffic network can reduce the degradation of the operation efficiency of the traffic system caused by random disturbance and natural disasters to the maximum extent and keep the smooth traffic of traffic flow; in combination with different stage division of a classical elastic triangle theory (as shown in fig. 2) in the elastic theory and a congestion propagation process in an actual traffic network, a disturbance event can cause initial damage to a certain position in the traffic network under a general condition, and then the initial damage can propagate along with a static structure of the traffic network to affect other areas; finally, due to the implementation of a proper recovery strategy, the running state of the system is recovered; the time dimension is introduced, and the change conditions of three processes of generation, evolution and dissipation of the three-dimensional urban traffic jam sub-group on the space and the time are analyzed; comprises the following steps:
step C1: finding out congested road sections at all times according to congestion judging standards of roads at different levels;
step C2: calculating a congestion sub-cluster set at all times;
step C3: finding out space-time development tracks of all the congested subgroups and calculating a traffic elasticity parameter S;
in step C1, "find the congested road segments at all times according to the different levels of road congestion criteria," specifically, the method is as follows: according to traffic experience data, congestion thresholds of roads of different levels in a general city are given: intercity high speed-40 km/h; city speed is-20 km/h; national road/urban arterial road-12 km/h; the provincial road/urban secondary road is-12 km/h; county road/city branch-10 km/h; rural/other-10 km/h; by definition, a road with real-time speed below a speed threshold is considered to be in a congested state at that moment; by defining congestion threshold vcThe road state function F (l) in the road network can be divided into a smooth state 1 and a congestion state 0; the following were used:
in step C2, "calculate the congestion sub-cluster set at all times," specifically, the method is as follows: removing unblocked roads at each moment, and finding all connected sub-cluster sets at the moment t according to the previously mentioned breadth first method (BFS) for the remaining congested roads at each moment(G1t,G2t…Gnt) (ii) a Then calculating a congestion connected sub-cluster set at all the moments within the statistical time; it should be noted here that the sub-clusters are undirected graphs, and thus the sub-clusters are weakly connected sub-clusters;
in step C3, "find out the spatio-temporal development trajectories of all congestion subgroups, and calculate the traffic elasticity parameter S", the specific method is as follows: according to the three-stage development process of generation-evolution-dissipation of the congestion subgroups, finding the development track of each original congestion subgroup by taking the roads in the congestion subgroups as clues; for a time range of [ t ]s,te]At any time t in the process ofiFor the linker group GiSearching all roads in the system, searching the connected sub-clusters to which the roads belong at the last moment, and expressing the development track of the empty sub-clusters during congestion by means of the continuity of the road congestion state; e.g. tiCommunicating sub-cluster G at timeiRoad l in1And l2In other words, find them at ti-1All the time belong to connected clusters
And
thus, Gi、
And
belonging to a part of the evolution process of the same space-time congestion subgroup; the space-time congestion subgroup development tracks of all the connected subgroups at each moment can be found, namely the cross-sectional area value M of the space-time congestion subgroup at the moment t is calculatedS(t); for a traffic network, the more serious the traffic jam occurs, the larger the coverage area is, and the larger the size of the jam connected sub-cluster at each moment is; conversely, if the network is very elastic against disturbances and congestion is occurring to a lesser extent, the size of the congested connected sub-cluster andthe duration will also be shorter; as shown in fig. 3: the integral value of the congestion connected sub-groups in continuous time periods can be used for measuring the elasticity S of the traffic network for resisting disturbance; then there are:
wherein t is0And t1Respectively, when the spatiotemporal congestion sub-cluster is generated and dissipated, and t1-t0Indicating the duration of the congestion clique.
Through the steps, the urban traffic health index system evaluation method based on the complex network theory provides a method combining practical traffic data with theories and methods such as a complex network, a seepage theory, an elasticity theory and the like, and provides an urban traffic health index system evaluation method aiming at practical running characteristics of urban roads; from three aspects of urban traffic network reliability, urban traffic network fragility and urban traffic network elasticity, an urban traffic health index system is evaluated and established, and support is provided for the diagnosis of the health state of urban traffic, the formulation of targeted management measures and the improvement of the urban traffic operation level.
(III) advantage innovation
The invention has the following innovation points:
1. the theoretical basis of the method is a complex network theory, a seepage theory, an elasticity theory and the like, is solid, and provides theoretical support for understanding the urban traffic operation rule;
2. the urban traffic health index system is comprehensively considered from three aspects of reliability, brittleness and elasticity, is beneficial to comprehensively grasping the urban traffic health state, and provides support for further prediction and regulation of the urban traffic health condition;
3. the health index system is based on actual traffic operation data, so that the health condition of actual traffic is disclosed, and the urban traffic health index system provided by the invention is close to the actual condition;
4. the urban traffic health index system provided by the invention has clear calculation process thought and clear process, and can be used for real-time calculation and evaluation of urban traffic health states.
In conclusion, the urban traffic health index system evaluation method based on the complex network theory helps us to establish an effective urban traffic health index system; meanwhile, the method can also provide support for understanding urban traffic operation rules, optimizing urban traffic management measures and improving the health state of a traffic network, and is favorable for formulating targeted measures for improving the urban traffic operation state.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a process diagram of elastic trigonometry theory.
FIG. 3 is a schematic diagram of the computation of spatiotemporal congestion subgroups.
The numbers, symbols and codes in the figures are explained as follows:
FIG. 2: pT(t) is the initial steady state value of the system, PT(t) is the actual state value of the system, which varies with time;
t0is the time at which the system state falls, t1Is the time at which the system state begins to stabilize, tEIs the time at which the system state reverts to the initial steady state.
FIG. 3: -MS(t) is the negative of the cross-sectional area of the congestion sub-cluster at time t;
t0is the time at which the formation of the congestion cluster begins, t1Is the moment when the congestion sub-cluster has completely dissipated.
Detailed Description
In order to make the technical problems and technical solutions to be solved by the present invention clearer, the following detailed description is made with reference to the accompanying drawings and specific embodiments. It is to be understood that the embodiments described herein are for purposes of illustration and explanation only and are not intended to limit the invention.
The invention aims to provide an evaluation method of an urban traffic health index system based on a plurality of challenges faced by the urban traffic operation and the background of mature development of related technologies, and comprehensively considering a traffic network reliability index, a traffic network brittleness index and a traffic network elasticity index. Based on the obtained actual urban traffic operation data, introducing seepage analysis to calculate the size of a functional subgroup of the urban traffic network under a given threshold value, and establishing a traffic network reliability index R; key roads in the traffic network are excavated, a road set which enables functional subgroups of the traffic network to be crashed to a certain proportion is analyzed, and a brittleness index B of the urban traffic network is established; and finally, establishing an elastic index S of the urban traffic network by introducing the whole process of generation, evolution and dissipation of traffic jam subgroups on three-dimensional space-time by describing the time dimension. The establishment of the urban traffic health index system can provide support for the evaluation of the actual running state of urban traffic, the formulation of targeted traffic management measures and the improvement of the urban traffic health level.
The invention is further described with reference to the following description and embodiments in conjunction with the accompanying drawings.
The invention takes the traffic network in Beijing city as an example: the initial traffic network size G (27878,52198) is a strongly connected sub-cluster containing 27878 nodes, 52198 connecting edges. For research and analysis, the nodes and edges are distributed in the five-ring line of Beijing. The correspondingly collected actual traffic operation data is road speed data in one day of Beijing City, and is obtained by vehicle speed weighted average processing at the corresponding time of the operation of the actual traffic operation data, so as to represent the actual operation state of the road at the time. The statistical time period is 00:00 am-23: 59pm, the data interval is 1min, and 1440 data monitoring points are shared in one day.
The invention relates to an urban traffic health index system evaluation method based on a complex network theory, which comprises the following steps as shown in figure 1:
step A: establishing a reliability index R of the urban traffic network;
and B: establishing a brittleness index B of the urban traffic network;
and C: establishing an elasticity index S of the urban traffic network;
wherein, the reliability index R for establishing the urban traffic network in the step A has the following specific meanings: and processing the acquired actual running data of the urban traffic, and combining a static urban traffic road network to obtain a dynamic traffic flow network. And (3) introducing seepage analysis, and establishing the reliability index of the urban traffic network by calculating the network functional subgroup size at each moment under a given seepage threshold. Comprises the following steps:
step A1: establishing a static road network G (N, L);
step A2: establishing an initial velocity matrix M0；
Step A3: completing speed compensation and normalization to obtain a complete speed matrix M1；
Step A4: and calculating a traffic network reliability index R, namely the maximum connected sub-cluster G.
In step a1, the "static road network G (N, L) is established" specifically as follows: according to the actually acquired city map data, the connection relation between roads is extracted first. Secondly, according to the research requirement, the suitable geographic coverage range of urban traffic is selected, and here, a five-ring traffic network in Beijing is selected. Then, according to the method of the complex network, the road intersection is abstracted into nodes in the network, and the road in the road network is abstracted into the connecting edges among the nodes in the network, so as to establish the traffic network. Meanwhile, most roads of the urban traffic network run in two directions, and the calculation adopts a directed connected graph. For the convenience of subsequent calculations, after selecting the appropriate range, we ensure that the selected traffic network is a strongly connected graph. A strongly connected clique as referred to herein means that in the directed graph G (N, L) (where N is the set of nodes in the directed graph and L is the set of connected edges), if for each pair of nodes vi、vj，vi≠vjFrom viTo vjAnd from vjTo viIf there are paths, G (N, L) is called a strong connection graph. The strong connection graph in the selected geographical range is the established static road network G (27878,52198);
therein, step A2 describes "establishing an initial velocity matrix M0", it is as follows: based on the acquired urban trafficActual operational data, corresponding to the static road network obtained in A1, at any one time tiGenerating a horizontal vector V according to the sequence relation of the roads by using the corresponding speeds of all 52198 roadsi＝(v1,v2…v52198). Further, the process is repeated for all 1440 moments, and finally all transverse vectors are integrated to generate an initial velocity matrix M0＝(V1,V2…V1440) And storing in the computer in a linked list form. The traffic operation data is vehicle speed data on the road collected by a specific data collector to reflect the operation state of the road at the moment. Each road has a unique speed value at each moment;
the "speed compensation is completed" in step a3, which is specifically performed as follows: occasional failures and other unpredictable events that may occur with the collection process data collection device may result in partial roads having no speed records at partial times. That is, the original velocity matrix M0There are partial missing values (actually recorded as 0). The missing values of these velocity records are compensated here, taking into account the requirements of the calculation process. First, find the velocity matrix M0And compensate for the missing velocity value. For time tiCompensation of the missing value of speed for the lower road L, a set of adjacent edges (L) of the road L in the road network G (N, L) is foundn1,ln2…lnm). And searching whether the speed record exists at the moment of the continuous edge in the set. And finally, taking the average value of the speeds of the adjacent sides with the speed records. Comprises the following steps:
if all the adjacent side speeds of the link l are not recorded, this loop of compensation is skipped, keeping the speed of the link l at that moment at 0. The obtained speed matrix M 'is compensated for'0Updating M0Continuing to compensate until all 0 values in the speed matrix are compensated to obtain a speed matrix M1；
Wherein, the normalization in step A3 is performed to obtain a complete velocity matrix M2", it is as follows: for any road i, the slave velocity matrix M1Extracting speed value sequence V of all the time of the roadiExtracting the maximum speed limit v of the road sectioni_maxDividing each speed of the sequence of speed values by the maximum speed limit vi_maxTo obtain a normalized velocity vi_ratioAs follows:
vi_ratio＝vi/vi_max
finally, the normalization operation is carried out on all roads to obtain a normalized speed matrix M2＝((V1_ratio,V2_ratio…V1440_ratio))；
Wherein, the step A4 of calculating the reliability index R of the traffic network, namely the maximum connected sub-cluster G, comprises the following specific steps: based on the normalized speed matrix M obtained in A32And introducing seepage analysis to calculate a reliability index, namely the maximum connected sub-group G, for the traffic network. Wherein, the general process of the seepage analysis is as follows: setting a speed threshold value q at any time, and setting a speed value v at the timeiDeleting roads i smaller than the speed threshold q; then, according to the actual scale of the network and the precision requirement of calculation, the speed threshold q is gradually increased, the network G is initialized (27878,52198) and the previous edge deletion operation is repeated. In the seepage analysis process, the maximum connected group G has a characterization effect on the whole network functionality. While taking into account that the velocity matrix that has been normalized is obtained, a given threshold q is setcThe maximum connected clique at each time instant was calculated as 0.5. Firstly, deleting the corresponding time t in the networkiThe lower velocity value being less than the velocity threshold qcThen finding the maximum function connected sub-group G' by using a breadth first method (BFS); wherein, the maximum function connected sub-group G' refers to the first big connected sub-group in the whole network; storing all the connection edges, nodes and connection relations; then, for all time instants (t)1,t2…t1440) This operation is carried out to finally obtain the maximum at all timesAnd functionally connecting the sub-cluster sets. Comprises the following steps:
wherein: n is the number of connected edges of the initial net 52198, and size (G) is the number of connected edges of the sub-cluster G.
Wherein, the brittleness index B for establishing the urban traffic network in the step B has the following specific meanings: brittleness is generally a measure of the ability of a material to withstand external forces, deform and fracture. For the urban traffic network, brittleness is a network attribute and is used for finding weak nodes and links which easily damage, degrade performance and even break down the system integrally in the operation of the traffic system and measuring the influence of the weak nodes on the system. For a traffic system, even if a weak link is attacked or disturbed by a low intensity, a serious result is likely to be generated, so that how to find the weak node and measure the influence of the weak node is particularly important. The capacity of the traffic network for resisting network breakdown is measured from the road level, and the brittleness index B of the traffic network is established. Due to geographical factors, road design conditions and functional differences of different areas, the traffic network is an anisotropic system, that is, different roads play different roles in the overall operation of the network. In reality, roads are generally divided into different classes: intercity high speed, city fast, city arterial road, etc. However, in the process of guaranteeing the operation of the traffic network, the actual functions of roads of different levels are not necessarily completely matched with the levels. For example, a road with a very low grade in a traffic network may be a bottleneck edge between two areas, and plays an important role in area intercommunication and congestion dissipation. Therefore, the actual action levels of different roads need to be explored. Secondly, the brittleness index of the urban traffic network is established by means of the roads. Comprises the following steps:
b1, calculating and sequencing the importance levels of all roads;
step B2: establishing a brittleness index B, and analyzing the brittleness level of the traffic network;
in step B1, "calculate and rank the importance levels of all roads", the specific procedure is as follows: according to the maximum function connected sub-cluster set at each moment determined in the step a4, for any road i, firstly, it is determined whether it belongs to the road side set of the maximum function connected sub-cluster:
wherein e (t) is used to indicate whether the road i belongs to the maximum function connected subgroup G' with the critical threshold q being 0.5 at time t; wherein, 1 represents that the road i is in G ', and 0 represents that the road i is not in G';
counting the times of the road appearing in the continuous edges of the maximum function connected sub-clusters
Finally, the total number of times 1440 is divided into the number of times, and the importance level o (i) of the road is obtained:
the above operation is performed for each road, and the importance level values O ═ O (1), O (2) … O (52198) for all roads are obtained finally. Further, the roads are sorted according to the descending order of the importance levels;
wherein, in the step B2, the brittleness index B is established and the traffic network brittleness level is analyzed, which comprises the following specific steps: the initial size of the network is L052198, a certain ratio p is setcWhen the network size is 0.5, the network size is L0*pc52198 × 0.5 ═ 26099. Defining the size of the network to be broken to L by referring to the measure of the brittleness of the network and the process of breaking down the network0*pc26099 minimum set of roads l that need to be removedG＝(l1i,l2i…lni) To measure any time t of the traffic network G (27878,52198) within a statistical time periodiThe index of brittleness of (2). It should be noted that all roads in the traffic network G (27878,52198) are ranked in advance, so the number of elements in the minimum set of roads can be equivalent to the index B that measures the fragility of the traffic network. Comprises the following steps:
B(t)＝size(lG(L0,pc))
wherein size (l)G) Is represented byGNumber of roads in the sequence.
Wherein, the "elasticity index S for establishing an urban traffic network" in step C has the specific meaning: the elasticity of the traffic network can reduce the degradation of the operation efficiency of the traffic system caused by random disturbance and natural disasters to the maximum extent and keep the smooth traffic of traffic flow. In combination with different stage divisions of a classical elastic trigonometric theory (as shown in fig. 2) in the elastic theory and a congestion propagation process in an actual traffic network, a disturbance event generally causes initial damage to a certain position in the traffic network, and then the initial damage propagates along with a static structure of the traffic network to affect other areas. Finally, the operating state of the system is restored due to the implementation of the appropriate restoration strategy. In the method, a time dimension is introduced, and the change conditions of three processes of generation, evolution and dissipation of a space-time three-dimensional urban traffic jam sub-group are analyzed. Comprises the following steps:
step C1: finding out congested road sections at all times according to congestion judging standards of roads at different levels;
step C2: calculating a congestion sub-cluster set at all times;
step C3: and finding out space-time development tracks of all the congested subgroups and calculating a traffic elasticity parameter S.
In step C1, "find the congested road segments at all times according to the different levels of road congestion criteria," specifically, the method is as follows: according to traffic experience data, congestion thresholds of roads of different levels in a general city are given: intercity high speed-40 km/h; city speed is-20 km/h; national road/urban arterial road-12 km/h; the provincial road/urban secondary road is-12 km/h; county road/city branch-10 km/h(ii) a Rural/other-10 km/h. By definition, a link whose real-time speed is below the speed threshold is considered to be congested at that time. By defining congestion threshold vcThe road state function f (l) in the road network can be divided into a smooth state 1 and a congestion state 0. The following were used:
in step C2, "calculate the congestion sub-cluster set at all times," specifically, the method is as follows: removing unblocked roads at each moment, and finding all connected sub-cluster sets (G) at the moment t according to the previously mentioned breadth first method (BFS) for the remaining congested roads at each moment1t,G2t…Gnt). And then calculating a congestion connected sub-cluster set for all the time points in the statistical time. It should be noted here that the sub-clusters are undirected graphs, and thus the sub-clusters are weakly connected sub-clusters.
In step C3, "find out the spatio-temporal development trajectories of all congestion subgroups, and calculate the traffic elasticity parameter S", the specific method is as follows: according to the three-stage development process of generation-evolution-dissipation of the congestion subgroups, the development tracks of the original congestion subgroups are found by taking the roads in the congestion subgroups as clues. For a time range of [ t ]s,te]At any time t in the process ofiFor the linker group GiAnd searching for the connected sub-clusters to which the links belong at the last moment, and expressing the development track of the empty sub-clusters in the congestion state by means of the continuity of the congestion state of the links. E.g. tiCommunicating sub-cluster G at timeiRoad l in1And l2In other words, find them at ti-1All the time belong to connected clusters
And
thus, Gi、
And
belonging to a part of the evolution process of the same space-time congestion subgroup. The space-time congestion subgroup development tracks of all the connected subgroups at each moment can be found, namely the cross-sectional area value M of the space-time congestion subgroup at the moment t is calculatedS(t) of (d). In the traffic network, the more serious the traffic congestion occurs, and the larger the coverage area is, the larger the size of the congestion connected sub-cluster at each time is. Conversely, if the network is very elastic against disturbances and congestion occurs to a lesser extent, the size and duration of the congested connected sub-cluster will also be shorter. As shown in fig. 3: the integral value of the congestion connected sub-groups in continuous time periods can be used for measuring the elasticity S of the traffic network for resisting disturbance. Then there are:
wherein t is0And t1Respectively, when the spatiotemporal congestion sub-cluster is generated and dissipated, and t1-t0Indicating the duration of the congestion clique.
The invention has not been described in detail and is within the skill of the art.
The above description is only a part of the embodiments 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.
Claims (1)
1. A method for evaluating an urban traffic health index system based on a complex network theory is characterized by comprising the following steps: the method comprises the following steps:
step A: establishing a reliability index R of the urban traffic network;
and B: establishing a brittleness index B of the urban traffic network;
and C: establishing an elasticity index S of the urban traffic network;
the reliability index R for establishing the urban traffic network in the step A has the following specific meanings: processing the acquired actual running data of the urban traffic, and combining a static urban traffic road network to obtain a dynamic traffic flow network; introducing seepage analysis, and establishing a reliability index R of the urban traffic network by calculating the network functional subgroup size at each moment under a given seepage threshold; comprises the following steps:
step A1: establishing a static road network G (N, L);
step A2: establishing an initial velocity matrix M0；
Step A3: completing speed compensation and normalization to obtain a complete speed matrix M1；
Step A4: calculating a traffic network reliability index R, namely a maximum connected sub-group G;
in step a1, the "static road network G (N, L) is established" specifically as follows: according to the actually acquired urban map data, firstly extracting the connection relation between roads; secondly, selecting a proper geographic coverage area of urban traffic according to research requirements, abstracting a road intersection into nodes in the network according to a complex network method, and abstracting a road in the road network into connecting edges among the nodes in the network so as to establish a traffic network; meanwhile, most roads of the urban traffic network run in two directions, and a directed connected graph is adopted for calculation; for the convenience of subsequent calculation, after selecting a proper range, ensuring that the selected traffic network is a strong communication graph; a strongly connected clique as referred to herein means in the directed graph G (N, L), where N is the set of nodes in the directed graph and L is the set of connected edges, if v is the set of nodes for each pairi、vj，vi≠vjFrom viTo vjAnd from vjTo viIf paths exist, G (N, L) is called a strong communication graph; the obtained strong communication graph in the selected geographic range is the established static road network;
therein, step A2 describes "establishing an initial velocity matrix M0", it is as follows: corresponding to the static road network obtained in A1, at any time tiGenerating a transverse vector V according to the sequence relation of the roads by using the corresponding speeds of all K roadsi＝(v1,v2…vK) (ii) a Further, the process is repeated for all TI moments, and finally all transverse vectors are integrated to generate an initial speed matrix M0＝(V1,V2…VTI) Storing in a computer in a linked list form; the traffic operation data is vehicle speed data on the road collected by a specific data collector and is used for reflecting the operation state of the road at the moment; each road has a unique speed value at each moment;
the "speed compensation is completed" in step a3, which is specifically performed as follows: the data acquisition device in the collection process can generate accidental faults and other unpredictable events, so that the speed of a part of roads is not recorded at a part of time; that is, the original velocity matrix M0There is a partial missing value-actually recorded as 0; in consideration of the need of the calculation process, compensation is made here for the missing values of these velocity records; first, find the velocity matrix M0And compensating for the speed deficiency value; for time tiCompensation of the missing value of speed for the lower road L, a set of adjacent edges (L) of the road L in the road network G (N, L) is foundn1,ln2…lnm) (ii) a Searching whether the continuous edges in the set have speed records at the moment; finally, taking the average value of the speeds of the adjacent sides with the speed records; comprises the following steps:
if all the speeds of the adjacent sides of the road l are not recorded, skipping the compensation of the loop, and keeping the speed of the road l at the moment to be 0; the obtained speed matrix M 'is compensated for'0Updating M0Continuing to compensate until all 0 values in the speed matrix are compensated to obtain a speed matrix M1；
Wherein, the normalization in step A3 is performed to obtain a complete velocity matrix M2", it is as follows: for any road i, the slave velocity matrix M1Extracting speed value sequence V of all the time of the roadiExtracting the maximum speed limit v of the road sectioni_maxDividing each speed of the sequence of speed values by the maximum speed limit vi_maxTo obtain a normalized velocity vi_ratioAs follows:
vi_ratio＝vi/vi_max
finally, the normalization operation is carried out on all roads to obtain a normalized speed matrix M2＝((V1_ratio,V2_ratio…VTI_ratio))；
Wherein, the step A4 of calculating the reliability index R of the traffic network, namely the maximum connected sub-cluster G, comprises the following specific steps: based on the normalized speed matrix M obtained in A32Introducing seepage analysis to calculate a reliability index, namely a maximum connected sub-group G, for the traffic network; wherein, the general process of the seepage analysis is as follows: setting a speed threshold value q at any time, and setting a speed value v at the timeiDeleting roads i smaller than the speed threshold q; then gradually increasing the speed threshold q according to the actual scale of the network and the calculation precision requirement, initializing the network G (N, L) and repeatedly carrying out the previous step of edge deletion operation; in the seepage analysis process, the maximum connected group G has a representation effect on the whole network functionality; while taking into account that the velocity matrix that has been normalized is obtained, a given threshold q is setcCalculating the maximum connected sub-clusters at each moment; firstly, deleting the corresponding time t in the networkiThe lower velocity value being less than the velocity threshold qcThe road is connected with the edge, and then the maximum function connected sub-group G' at the moment is found by using a breadth first method, namely BFS; wherein, the maximum function connected sub-group G' refers to the first big connected sub-group in the whole network; storing all the connection edges, nodes and connection relations;then, for all time instants (t)1,t2…tTI) Performing the operation to finally obtain a maximum function connected sub-cluster set at all the moments; comprises the following steps:
wherein: n is the number of connected edges of the initial network, and size (G) is the number of connected edges of the sub-cluster G;
the brittleness index B for establishing the urban traffic network in the step B has the specific meanings as follows: brittleness is generally used to measure the resistance of a material to external forces, deformation and fracture; for the urban traffic network, brittleness is a network attribute and is used for finding weak nodes and links which easily damage, degrade performance and even crash the system in operation of the traffic system and measuring the influence of the weak nodes on the system; for a traffic system, even if a weak link is attacked or disturbed by low intensity, serious consequences are likely to be generated, so that how to find the weak node and measure the influence of the weak node is particularly important; measuring the network breakdown resisting capacity of the traffic network from a road level, and establishing a brittleness index B of the traffic network; due to geographical factors, road design conditions and functional differences of different areas, the traffic network is an anisotropic system, namely different roads play different roles in the overall operation of the network; in reality, roads are generally divided into different classes: intercity high speed, city fast and city main road; however, in the process of guaranteeing the operation of the traffic network, the actual functions of roads with different grades are not necessarily completely matched with the grades; plays an important role in regional intercommunication and congestion dissipation; therefore, actual action levels of different roads need to be explored; secondly, establishing brittleness indexes of the urban traffic network by means of the roads; comprises the following steps:
b1, calculating and sequencing the importance levels of all roads;
step B2: establishing a brittleness index B, and analyzing the brittleness level of the traffic network;
in step B1, "calculate and rank the importance levels of all roads", the specific procedure is as follows: according to the maximum function connected sub-cluster set at each moment determined in the step a4, for any road i, firstly, it is determined whether it belongs to the road side set of the maximum function connected sub-cluster:
wherein e (t) is used for indicating whether the road i belongs to the maximum function connected subgroup G' with the critical threshold value of q at the moment of t; wherein, 1 represents that the road i is in G ', and 0 represents that the road i is not in G';
counting the times of the road appearing in the continuous edges of the maximum function connected sub-clusters
Finally, dividing the total time number TI into the importance level O (i) of the road:
performing the above operation on each road, and finally obtaining the importance level values O ═ (O (1), O (2) … O (l)) of all roads; further, the roads are sorted according to the descending order of the importance levels;
wherein, in step B2, the brittleness index is established and the traffic network brittleness level is analyzed, which comprises the following steps: assume that the initial size of the network is L0Setting a predetermined ratio pcThe network size at this time is L0*pc(ii) a Defining the size of the network to be broken to L by referring to the measure of the brittleness of the network and the process of breaking down the network0*pcMinimum set of roads l to be removedG＝(l1i,l2i…lni) To measure the traffic network G (N, L) at any time t within a statistical time periodiA brittleness index of (d); it should be noted that, here, all roads in the traffic network G (N, L) are ranked in advance, so the number of elements in the minimum road set can be equivalent to the index B for measuring the brittleness of the traffic network; comprises the following steps:
B(t)＝size(lG(L0,pc))
wherein size (l)G) Is represented byGThe number of roads in the sequence;
the step C of establishing the elasticity index S of the urban traffic network has the following specific meanings: the elasticity of the traffic network can reduce the degradation of the operation efficiency of the traffic system caused by random disturbance and natural disasters to the maximum extent and keep the smooth traffic of traffic flow; by combining different stages of a classical elastic triangle theory in an elastic theory and a congestion propagation process in an actual traffic network, a disturbance event can cause initial damage to one part in the traffic network under general conditions, and then the initial damage can propagate along with a static structure of the traffic network to affect other areas; finally, due to the implementation of a proper recovery strategy, the running state of the system is recovered; the time dimension is introduced, and the change conditions of three processes of generation, evolution and dissipation of the three-dimensional urban traffic jam sub-group on the space and the time are analyzed; comprises the following steps:
step C1: finding out congested road sections at all times according to congestion judging standards of roads at different levels;
step C2: calculating a congestion sub-cluster set at all times;
step C3: finding out space-time development tracks of all the congested subgroups and calculating a traffic elasticity parameter S;
in step C1, "find the congested road segments at all times according to the different levels of road congestion criteria," specifically, the method is as follows: according to traffic experience data, congestion thresholds of roads of different levels in a general city are given: intercity high speed-40 km/h; city speed is-20 km/h; national road/urban arterial road-12 km/h; the provincial road/urban secondary road is-12 km/h; county road/city branch-10 km/h; rural/other-10 km/h; by definition, the real-time speed is below the speed thresholdThe link l of (1) considers that it is in a congested state at that moment; by defining congestion threshold vcThe road state function F (l) in the road network can be divided into a smooth state 1 and a congestion state 0; the following were used:
in step C2, "calculate the congestion sub-cluster set at all times," specifically, the method is as follows: removing unblocked roads at each moment, and finding all connected sub-cluster sets (G) at the moment t according to the mentioned breadth first method, namely BFS, aiming at the rest blocked roads at each moment1t,G2t…Gnt) (ii) a Then calculating a congestion connected sub-cluster set at all the moments within the statistical time; it should be noted here that the sub-clusters are undirected graphs, and thus the sub-clusters are weakly connected sub-clusters;
in step C3, "find out the spatio-temporal development trajectories of all congestion subgroups, and calculate the traffic elasticity parameter S", the specific method is as follows: according to the three-stage development process of generation-evolution-dissipation of the congestion subgroups, finding the development track of each original congestion subgroup by taking the roads in the congestion subgroups as clues; for a time range of [ t ]s,te]At any time t in the process ofiFor the linker group GiSearching all roads in the system, searching the connected sub-clusters to which the roads belong at the last moment, and expressing the development track of the empty sub-clusters during congestion by means of the continuity of the road congestion state; at tiCommunicating sub-cluster G at timeiRoad l in1And l2Find them at ti-1All the time belong to connected clusters
And
thus, Gi、
And
belonging to a part of the evolution process of the same space-time congestion subgroup; the space-time congestion subgroup development tracks of all the connected subgroups at each moment can be found, namely the cross-sectional area value M of the space-time congestion subgroup at the moment t is calculatedS(t); for a traffic network, the more serious the traffic jam occurs, the larger the coverage area is, and the larger the size of the jam connected sub-cluster at each moment is; on the contrary, if the elasticity of the network for resisting disturbance is strong and the congestion degree is light, the size and duration of the congestion connected sub-cluster are also short; the integral value of the congestion connected sub-groups in continuous time periods can be used for measuring the elastic capacity S of the traffic network for resisting disturbance; then there are:
wherein t is0And t1Respectively, when the spatiotemporal congestion sub-cluster is generated and dissipated, and t1-t0Indicating the duration of the congestion clique.
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