CN109559510B - Multi-MFD sub-area boundary coordination control method based on random distribution control algorithm - Google Patents

Multi-MFD sub-area boundary coordination control method based on random distribution control algorithm Download PDF

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CN109559510B
CN109559510B CN201811395511.2A CN201811395511A CN109559510B CN 109559510 B CN109559510 B CN 109559510B CN 201811395511 A CN201811395511 A CN 201811395511A CN 109559510 B CN109559510 B CN 109559510B
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闫飞
杜宇浩
程兰
丁洁
阎高伟
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Taiyuan University of Technology
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Abstract

The invention belongs to the technical field of traffic control, and provides a method for coordinately controlling boundaries of multiple MFD sub-areas based on a random distribution control algorithm. To adjustThe traffic resource distribution in the peak period of the morning and evening is uneven. The traffic control method comprises the following steps: s1: collecting modeling data; s2: estimating the probability distribution of the number of vehicles; s3: establishing a basic function representation model of a vehicle number probability distribution density function; s4: establishing input variables and leadsn-a non-linear prediction model between 1 weight vector; s5: and solving the control quantity output. The output control is a green ratio matrix of each zone boundary signal lamp, and the number of vehicles in each zone is adjusted by changing the time length of the zone boundary signal lamp. The invention can furthest relieve the problem of unreasonable distribution of vehicles in the urban road network and improve the utilization efficiency of the urban road network.

Description

Multi-MFD sub-area boundary coordination control method based on random distribution control algorithm
Technical Field
The invention belongs to the technical field of traffic control, and particularly relates to a method for coordinately controlling boundaries of multiple MFD sub-areas based on a random distribution control algorithm.
Background
Since the emergence of the telecommunication signals, the development of the control mode of the telecommunication signals is from timing control, induction control to self-adaptive control; the control range is from single intersection to trunk line coordination control to regional signal coordination control. The traditional point or line signal control method can only improve local traffic conditions, but cannot deal with regional and large-scale traffic jam. The traditional area coordination control system mainly utilizes the theory of main road coordination control to divide the congested area into a plurality of sub-areas for optimization control, thereby realizing the coordination control of the whole area.
In recent years, the relationship between three parameters, namely the macro road network flow, density and speed, described by mfd (macroscopic functional map) provides a better method for solving traffic congestion. Therefore, many scholars such as Hajiahmadi, Haddad and the like establish a prediction model for the accumulated number of vehicles in the MFD subarea (subarea for short) to further perform traffic control; these methods do not take into account the problem of the non-uniformity of the spatial distribution of the cumulative number of vehicles.
Disclosure of Invention
In order to solve the problem that the number of vehicles in each subarea is unreasonable in distribution and the road network area traffic can not be kept in a good running state, the invention provides a method for coordinately controlling the boundaries of a plurality of MFD subareas based on a random distribution control algorithm, so that the area can be subjected to traffic control according to the optimal number of vehicles obtained by the MFD, and the whole road network can achieve optimal traffic.
In order to solve the technical problems, the invention adopts the technical scheme that: 1. a method for coordinating and controlling boundaries of a plurality of MFD subareas based on a random distribution control algorithm comprises the following steps:
s1, modeling collected data: reasonably dividing the road network into N MFD subregions, adding a counting device at the intersection of the boundary of each MFD subregion, and collecting the number N of vehicles in each MFD subregioniForming a data set N { N }1,N2...NnAnd the queue length L of vehicles at the boundary entrance of each subarea of the MFD at the corresponding time pointiBoundary exit vehicle queuing length LoForming a data set;
s2, estimating the probability distribution of the number of vehicles: processing the vehicle number data of each MFD subarea to obtain a probability density function of vehicle number distribution;
s3, establishing a basic function representation model of the vehicle number probability distribution density function;
s4, queuing length L of vehicles at boundary entrance of each MFD sub-areaiBoundary exit vehicle queuing length LoThe first n-1 weight vectors and the split matrix of the number of vehicles at the corresponding moment are used as input variables of the model, a nonlinear prediction model between the input variables and the first n-1 weight vectors is established, the model is trained through collected historical data, the relation between the basis function weight of the probability distribution density function of the vehicles and the input variables is obtained, and the probability distribution density function of the number of vehicles at the next moment is predicted;
and S5, constructing and solving a performance index function related to the expected and predicted vehicle number probability distribution and the controlled variable to obtain the output of the controlled variable.
In step S2, the vehicle number data of each MFD subregion is processed to obtain a formula of a probability density function of the vehicle number distribution, where the formula is:
Figure BDA0001875055940000021
wherein, κ∑(. cndot.) represents a multidimensional kernel function, u (k) represents a split matrix, and γ (N, u (k)) represents a probability density distribution where γ represents the number of vehicles N when the current split is u (k).
The step S3 specifically includes the following steps:
s301, selecting a Gaussian radial basis function as a basis function of the vehicle number probability distribution density function, namely:
Figure BDA0001875055940000022
s302, determining a weighted expression of the basis functions, wherein the probability density function of the number of vehicles is expressed by the weighted sum of the basis functions as follows:
γ(N,u(k))＝C(N)V(k)+Bn(N)wn(k)+e0(N,k)；
wherein, C (N) ═ B1(N),B2(N),…,Bn-1(N)]，V(k)＝[w1(k),w2(k),…,wn-1(k)]T，wn(k) Is the weight corresponding to the nth basis function, e0(N, k) is the error of the approximation of the regional vehicle number probability distribution density function;
s303, solving the weight V (k) of each basis function of the vehicle number probability distribution density function, and determining the weight corresponding to each basis function, wherein the calculation formula is as follows:
Figure BDA0001875055940000023
wherein the content of the first and second substances,
Figure BDA0001875055940000024
the step S4 specifically includes the following steps:
s401: selecting input variables and queuing the vehicles at the entrance of each zone boundary by the length LiExit queue length L of vehicles at boundary of each zoneoCurrent control output u (k) ═ u1(k),u2(k),…,um(k)]And the first n-1 weight vectors V (k) of the vehicle number probability distribution at the corresponding moment are merged into an input variable which is recorded as: x ═ Li,Lo,u(k),V(k)]L×(2+n+m)。
S402: selecting a prediction model, selecting a random weight neural network, and expressing the network model as follows:
Figure BDA0001875055940000031
where s represents the activation function in a random weight neural network, ωj＝[ωj1,ωj2,…,ωjm]TConnecting the input weights, β, of the jth hidden unit for m input nodesj＝[βj1,βj2,…,βj(n-1)]TConnecting the output weights of the output nodes for the jth hidden layer, bjIs the bias of the jth implicit cell.
S403: training the model, randomly giving a group of input layer weights and biases, and training the model by using L groups of collected historical data, wherein an objective function is as follows:
Figure BDA0001875055940000032
s404: obtaining optimal output weight value by solving generalized inverse of H matrix
Figure BDA0001875055940000033
The formula is as follows:
Figure BDA0001875055940000034
wherein the content of the first and second substances,
Figure BDA0001875055940000035
Figure BDA0001875055940000036
s405: establishing a relation between the basis function weight and the input variable, wherein the expression is as follows:
Figure BDA0001875055940000037
s406: predicting the vehicle number probability distribution density function at the next moment, wherein the expression is as follows:
γm(N,u(k+1))＝C(N)Vm(k+1)+Bn(T)wn(k+1)；
in step S5, the expression of the performance index function relating to the expected, predicted vehicle number probability distribution and the control amount is constructed as follows:
J(u(k))＝∫(γm(N,u(k))-g(N,u(k))2dN+u(k)TRu(k)；
wherein g (N, u (k)) represents a desired vehicle number probability distribution, γm(N, u (k)) represents a predicted vehicle number probability distribution;
the calculation formula of the control quantity output is as follows: u (k) ═ argminJ.
The calculation method of the control quantity output comprises the following steps:
constructing a discrete control model;
optimizing the quadratic form to obtain a complete global minimization solution u (k);
the value of u (k) is adjusted to an appropriate range according to the combination of the limiting conditions.
Compared with the prior art, the invention has the following beneficial effects: according to the invention, the probability distribution information of the number of vehicles in the control area is used as a feedback quantity, the macroscopic road network is divided into subareas according to the difference of traffic density, the number distribution of the vehicles in each MFD subarea is predicted by using a random distribution control algorithm, the comparison with the expected optimal number distribution of the vehicles is carried out, and the output of a control variable is calculated, so that the optimal number of the vehicles obtained by the area according to the MFD is controlled, the whole road network achieves the optimal traffic, the unreasonable distribution problem of the vehicles in the urban road network is relieved to the greatest extent, and the utilization efficiency of the urban road network is improved.
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FIG. 1 is a system flow diagram of the present invention;
FIG. 2 is a flow chart of distribution estimation;
FIG. 3 is a flow chart of a prediction model established using a random weight neural network;
FIG. 4 is a flow chart for solving a control quantity split matrix;
fig. 5 is a system control block diagram of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments; all other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a coordination control method for a plurality of MFD sub-area boundaries based on a random distribution control algorithm, which can be divided into two parts to operate on the specific implementation: off-line modeling and real-time prediction and control.
The specific implementation steps of the off-line modeling are as follows:
n traffic sub-areas are reasonably divided in an urban road network, the vehicle distribution in each sub-area is assumed to be relatively uniform, a macroscopic basic graph (MFD) in each traffic sub-area is drawn, namely, the corresponding vehicle number range Y is obtained when the flow of each sub-area is optimal, and then relatively sharp Gaussian distribution with the expected vehicle number distribution of each sub-area as the expected value Y is obtained, and according to the Gaussian distribution, a combined probability density function can be obtained.
As shown in fig. 1, the method for coordinating and controlling the boundaries of a plurality of MFD sub-regions based on a random distribution control algorithm provided by the present invention comprises the following steps:
and S1, collecting modeling data.
The modeling data acquisition can be realized by adopting the following modes: the historical data needed for modeling are: the number of lanes at the intersection of each sub-area boundary, the queuing length Li of vehicles at the entrance of each area boundary in different time periods, the queuing length Lo of vehicles at the exit of each area boundary, an intersection green signal ratio matrix and the total number of vehicles in different time periods on the roads in each sub-area. A counting device and a video acquisition device are additionally arranged at each intersection to record continuous data for a plurality of times (2-3 months), so that a historical data set is formed.
And S2, estimating the probability distribution of the number of vehicles.
The vehicle number data of a plurality of sub-areas are mathematically processed and converted into a probability density function gamma (N, u (k)) of the vehicle number distribution:
Figure BDA0001875055940000051
where N { N }1,N2...NnDenotes the number of vehicles in each sub-area, n is the number of sub-areas, κ∑(. cndot.) is a multidimensional kernel function, and u (k) represents a split matrix. And converting the road network region into a probability distribution form of the number of vehicles through the formula.
S3, establishing a basis function representation model γ (N, u (k)) f of the vehicle number probability distribution density functionTPDF(C(N),V(k))。
Specifically, as shown in fig. 2, the building of the basis function model is mainly divided into the following steps.
S301, selecting a basis function, wherein the embodiment selects a Gaussian radial basis function as the basis function of the probability distribution density function of the number of vehicles
Figure BDA0001875055940000052
Wherein N is ∈ [ a, b ]]The number information of the collected vehicles; mu.si,σiThe center value and width of the function for the ith network node.
S302: a weighted representation of the basis functions is determined.
According to the RBF network approximation principle, the probability density function of the vehicle number distribution at the time k is expressed by the weighted sum form of the basis functions, namely the expression of gamma (N, u (k)) is as follows:
γ(N,u(k))＝C(N)V(k)+Bn(N)wn(k)+e0(N,k)； (3)
wherein, C (N) ═ B1(N),B2(N),…,Bn-1(N)]，V(k)＝[w1(k),w2(k),…,wn-1(k)]T，wn(k) Is the weight corresponding to the nth basis function, e0(N, k) is the error of the approximation to the regional vehicle number probability distribution density function.
S303: a weight value for each basis function is determined.
Order to
Figure BDA0001875055940000053
Figure BDA0001875055940000054
The nth weight ωn(k) The nonlinear function h (v (k)) of the weight vector v (k) can be expressed as:
Figure BDA0001875055940000055
according to the two formulas (3) and (4):
Figure BDA0001875055940000061
left-multiplying both sides of formula (5) by [ C ]T(N)Rn(N)]TAnd in the interval [ Nmin Nmax]Is integrated, when the matrix is
Figure BDA0001875055940000062
When not singularity, can be transformed to obtain:
Figure BDA0001875055940000063
therefore, the weight v (k) of each basis function can be obtained by the formula (6).
S4, establishing a nonlinear prediction model f between the input variable and the first n-1 weight vectorsVPDF(X)。
As shown in fig. 3, the establishment of the non-linear prediction model is mainly divided into the following steps:
s401: selecting an input variable, and setting the vehicle number data N for each area obtained in step S1 to N1,N2,…NS]And the length L of vehicle queue at entrance of each zone boundary at corresponding time pointiExit queue length L of vehicles at boundary of each zoneoCurrent control output u (k) ═ u1(k),u2(k),…,um(k)]And merging the first n-1 weight vectors V (k) of the vehicle number probability distribution at the current moment into input, and recording as: x ═ Li,Lo,u(k),V(k)]L×(2+n+m)。
S402: selecting a prediction model, selecting a random weight neural network, and expressing the network model as follows:
Figure BDA0001875055940000064
where s represents the activation function in a random weight neural network, ωj＝[ωj1,ωj2,…,ωjm]TConnecting the input weights, β, of the jth hidden unit for m input nodesj＝[βj1,βj2,…,βj(n-1)]TConnecting the output weights of the output nodes for the jth hidden layer, bjIs the bias of the jth implicit cell.
S403: training the model, randomly giving a group of input layer weights and biases, and training the model by using L groups of collected historical data, wherein an objective function is as follows:
Figure BDA0001875055940000065
s404: obtaining optimal output weight value by solving generalized inverse of H matrix
Figure BDA0001875055940000066
The formula is as follows:
Figure BDA0001875055940000067
wherein the content of the first and second substances,
Figure BDA0001875055940000071
Figure BDA0001875055940000072
s405: establishing a relation between the basis function weight and the input variable:
Figure BDA0001875055940000073
s406: and predicting the vehicle number probability distribution density function at the next moment:
γm(N,u(k+1))＝C(N)Vm(k+1)+Bn(N)wn(k+1)； (11)
and S5, constructing and solving a performance index function related to the expected and predicted vehicle number probability distribution and the controlled variable to obtain the output of the controlled variable.
The control quantity optimization module calculates expected regional vehicle number distribution information and vehicle number probability distribution feedback information, determines a sub-regional boundary intersection split ratio matrix U (k) to carry out boundary control on the traffic flow flowing into and out of the sub-regions, and further enables an output probability density function gamma (N, u (k)) to track an expected vehicle probability density function g (N, u (k)), namely the number of accumulated vehicles in each sub-region is close to the optimal Y. As shown in fig. 4, solving the control quantity output mainly includes the following steps:
s501, constructing a performance index function J related to expectation, predicted vehicle number probability distribution and control quantity:
J(u(k))＝∫...∫(γm(N1,...,Nnu(k))-g(N1,...,Nn,u(k))2dN1...dNn+u(k)TRu(k)； (12)
wherein R is a predetermined weighting matrix for limiting u (k).
S502, solving the problem of control quantity output and converting into:
u(k)＝argminJ； (13)
wherein u (k) is a blocking matrix represented by the formula:
Figure BDA0001875055940000074
wherein
Figure BDA0001875055940000075
A boundary split matrix representing the i and j sub-regions, where uij1The first intersection representing the i and j sub-zone boundaries. And so on.
S503, constructing a discrete control model, and facilitating solution.
For discrete control systems, there are:
Vk+1＝AVk+Buk； (15)
the following relationship exists between the output probability density function and the control quantity:
γ(N,uk)＝a1γ(N,uk-1)+...+an-1γ(N,uk-n)+E(N)D0uk+...+E(N)Dmuk-m； (16)
where E (N) is a function vector for the number of vehicles N, whose dimensions correspond to the weight vector V, obtained by transformation of pre-selected basis functions. Wherein a isiAnd DjIs uniquely defined by A and B in the formula (15).
Recording:
Figure BDA0001875055940000081
the performance indicator function J is then given by equation (17):
Figure BDA0001875055940000082
s504, the quadratic form of the above formula is optimized, and a complete global minimization solution u (k) can be obtained:
Figure BDA0001875055940000083
s505, according to the limitation condition, u (k) is adjusted to a proper range.
If the two sub-regions are not adjacent, the split matrix is 0.
Meanwhile, attention is paid to the constraint:
umin≤ui≤umax；
Figure BDA0001875055940000084
as shown in FIG. 5, a system control block diagram of a method for coordinating and controlling boundaries of a plurality of MFD sub-zones based on a stochastic distribution control algorithm according to the present invention is shown, wherein an error feedback adjustment process according to a probability distribution of the number of vehicles in a predicted sub-zone and an expected probability distribution in a real-time process is reflected in the diagram. By comparing errors and calculating the control quantity u (k), the control quantity is fed back to the traffic light control in each sub-area, and the optimal coordination control of the vehicle distribution in each area of the traffic network can be realized. The invention predicts the vehicle number distribution of each MFD subarea by using a random distribution control algorithm, compares the vehicle number distribution with the expected optimal vehicle number distribution, calculates the output of a control variable, relieves the unreasonable vehicle distribution problem of an urban road network to the maximum extent, and improves the utilization efficiency of the urban road network.
Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.

Claims (5)

1. A method for coordinating and controlling boundaries of a plurality of MFD sub-areas based on a random distribution control algorithm is characterized by comprising the following steps:
s1, modeling collected data: reasonably dividing the road network into N MFD subregions, adding a counting device at the intersection of the boundary of each MFD subregion, and collecting the number N of vehicles in each MFD subregioniForming a data set N { N }1,N2...NnAnd the queue length L of vehicles at the boundary entrance of each subarea of the MFD at the corresponding time pointiBoundary exit vehicle queuing length LoForming a data set;
s2, estimating the probability distribution of the number of vehicles: processing the vehicle number data of each MFD subarea to obtain a probability density function of vehicle number distribution;
s3, establishing a basic function representation model of the vehicle number probability distribution density function; the step S3 specifically includes the following steps:
s301, selecting a Gaussian radial basis function as a basis function of the vehicle number probability distribution density function, namely:
Figure FDA0002842262880000011
μi,σithe center value and width of the function of the ith network node;
s302, determining a weighted expression of the basis functions, wherein the probability density function of the number of vehicles is expressed by the weighted sum of the basis functions as follows:
γ(N,u(k))＝C(N)V(k)+Bn(N)wn(k)+e0(N,k)；
wherein, C (N) ═ B1(N),B2(N),…,Bn-1(N)]，V(k)＝[w1(k),w2(k),…,wn-1(k)]T，wn(k) Is the weight corresponding to the nth basis function, e0(N, k) is the error of the approximation of the regional vehicle number probability distribution density function;
s303, solving the weight V (k) of each basis function of the vehicle number probability distribution density function, and determining the weight corresponding to each basis function, wherein the calculation formula is as follows:
Figure FDA0002842262880000012
wherein the content of the first and second substances,
Figure FDA0002842262880000013
Figure FDA0002842262880000021
s4, queuing length L of vehicles at boundary entrance of each MFD sub-areaiBoundary exit vehicle queuing length LoThe first n-1 weight vectors and the green signal ratio matrix of the probability distribution of the number of vehicles at the corresponding moment are used as input variables of the model, and the input variables and the first n-1 weight vectors are establishedTraining a nonlinear prediction model among vectors by using collected historical data to obtain the relation between a basis function weight of a vehicle probability distribution density function and an input variable, and predicting the vehicle number probability distribution density function at the next moment;
and S5, constructing and solving a performance index function related to the expected and predicted vehicle number probability distribution and the controlled variable to obtain the output of the controlled variable.
2. The method for coordinated control of boundaries of multiple MFD subregions based on a stochastic distribution control algorithm as claimed in claim 1, wherein in step S2, the vehicle number data of each MFD subregion is processed to obtain the probability density function of the vehicle number distribution by the formula:
Figure FDA0002842262880000022
wherein, κ∑(. cndot.) represents a multidimensional kernel function, u (k) represents a split matrix, and γ (N, u (k)) represents a probability density distribution where γ represents the number of vehicles N when the current split is u (k).
3. The method for coordinated control of boundaries of a plurality of MFD subareas based on a stochastic distribution control algorithm as claimed in claim 1, wherein said step S4 specifically comprises the steps of:
s401: selecting input variables and queuing the vehicles at the entrance of each zone boundary by the length LiExit queue length L of vehicles at boundary of each zoneoCurrent control output u (k) ═ u1(k),u2(k),…,um(k)]And the first n-1 weight vectors V (k) of the vehicle number probability distribution at the corresponding moment are merged into an input variable which is recorded as: x ═ Li,Lo,u(k),V(k)]L×(2+n+m)；
S402: selecting a prediction model, selecting a random weight neural network, and expressing the network model as follows:
Figure FDA0002842262880000023
where s represents the activation function in a random weight neural network, ωj＝[ωj1,ωj2,…,ωjm]TConnecting the input weights, β, of the jth hidden unit for m input nodesj＝[βj1,βj2,…,βj(n-1)]TConnecting the output weights of the output nodes for the jth hidden layer, bjIs the bias of the jth hidden cell;
s403: training the model, randomly giving a group of input layer weights and biases, and training the model by using L groups of collected historical data, wherein an objective function is as follows:
Figure FDA0002842262880000031
s404: obtaining optimal output weight value by solving generalized inverse of H matrix
Figure FDA0002842262880000032
The formula is as follows:
Figure FDA0002842262880000033
wherein the content of the first and second substances,
Figure FDA0002842262880000034
Figure FDA0002842262880000035
s405: establishing a relation between the basis function weight and the input variable, wherein the expression is as follows:
Figure FDA0002842262880000036
s406: predicting the vehicle number probability distribution density function at the next moment, wherein the expression is as follows:
γm(N,u(k+1))＝C(N)Vm(k+1)+Bn(T)wn(k+1)。
4. the method for coordinated control of multiple MFD sub-zone boundaries based on a stochastic distribution control algorithm of claim 1, wherein in step S5, the expression of the performance indicator function related to the desired, predicted vehicle number probability distribution and the controlled variable is constructed as follows:
J(u(k))＝∫(γm(N,u(k))-g(N,u(k))2dN+u(k)TRu(k)；
wherein g (N, u (k)) represents a desired vehicle number probability distribution, γm(N, u (k)) represents a predicted vehicle number probability distribution;
the calculation formula of the control quantity output is as follows: u (k) ═ argminJ.
5. The method for coordinated control of the boundaries of the MFD sub-regions based on the stochastic distribution control algorithm as claimed in claim 4, wherein the output of the control variables is calculated by:
constructing a discrete control model;
optimizing the quadratic form to obtain a complete global minimization solution u (k);
the value of u (k) is adjusted to an appropriate range according to the combination of the limiting conditions.
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