CN103632212A - System and method for predicating time-varying user dynamic equilibrium network-evolved passenger flow - Google Patents
System and method for predicating time-varying user dynamic equilibrium network-evolved passenger flow Download PDFInfo
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Abstract
The invention discloses a system and method for predicating time-varying user dynamic equilibrium network-evolved passenger flow and belongs to the technical field of urban rail traffic safety. The system comprises an AFC (auto fare collection) system, and a video terminal and the like. A network database is sequentially connected with a passenger flow distribution module, a passenger flow correction module and a passenger flow analysis module. The passenger flow video analysis module is connected with the network database module and the passenger flow correction module respectively. The video terminal and the AFC system transmit passenger information data and store the same in a network database. The passenger flow video analysis module analyzes real-time video data, and the passenger flow correction module adopts an AUKF (adaptive unscented Kalman filter) for preprocessing. The passenger flow data are matched and predicated by means of a passenger flow prediction algorithm, and services like an inquiry are provided by a human-computer interaction terminal. The requirements of multiple users for road network short-term prediction under emergency conditions are met, real-time distribution and dynamic prediction for the bounded rationality of the passenger flow are realized, and real-time inquiring, sharing and decision making of enterprises for passenger flow information are met.
Description
Technical Field
The invention relates to a time-varying user equilibrium dynamic network evolution passenger flow prediction system and method, and belongs to the technical field of urban rail transit safety.
Background
Along with the increase of urban rail transit construction in China, the importance of safe operation and emergency scheduling is increasingly highlighted. Particularly, when an unconventional emergency is faced, a method for quickly and effectively simulating and predicting the passenger flow distribution condition of urban rail transit under the emergency in real time is not available, so that an operation decision-making department can make a correct decision.
The travel Origin-Destination (OD) distribution of the existing rail transit network mainly performs normal network estimation on offline data, and in an emergency, OD estimation needs to perform online estimation under the support of real-time data, and meanwhile, the OD estimation can adapt to the influence of network structure change on an estimation system, so that the obvious change of passenger flow demand is dynamically tracked.
In an emergency, due to changes of network connectivity and congestion characteristics, a passenger may even have to change a daily balanced path decision of the passenger, so that unbalanced time-varying state occurs in the passenger flow of the rail transit network, and the existing system and method are difficult to accurately estimate the dynamic network state in the emergency.
Research on a passenger flow balanced distribution method and application based on an Adaptive Unscented Kalman Filter (AUFK) and a foreground accumulation theory is mature. The existing rail transit network video platform provides a large amount of available passenger flow video resources, and the historical OD passenger flow can also provide basis for short-time passenger flow prediction under the condition of an emergency. How to combine the prior art with resources to realize the short-time prediction of road network passenger flow in an emergency is a technical problem to be solved.
The self-adaptive unscented Kalman filtering is a method which takes linear Kalman filtering as a framework and adopts a deterministic sampling strategy to approximate nonlinear distribution on the basis of lossless transformation. The state space of a linear random system consisting of a state equation and an observation equation is adopted to describe the filter, and the state variable of the filter is optimally estimated by a recursion algorithm according to the estimation criterion of the linear unbiased minimum mean square error by utilizing the recursion of the state equation, so that the optimal estimation of the useful signal with noise being filtered is obtained.
An Automatic Fare Collection (AFC) center is an automatic Fare Collection and Fare Collection system which integrates computer technology, information Collection and processing technology and mechanical manufacturing, has strong intelligent functions, can accurately count, store and transmit ticket data of a rail transit road network every day, and provides convenient conditions for obtaining historical traffic data of the road network;
the video terminal is a camera device with a video analyzing and counting function, is distributed at the positions of an escalator, a platform, a channel and the like of a station, is used for detecting rail transit real-time passenger flow data and transmitting the passenger flow data, and provides possibility for obtaining road network real-time passenger flow conditions.
The Cumulative Prospect Theory (CPT) was first proposed by Tverseky and Kahneman in 1992. The CPT considers the prospect of uncertain factors and risks at the same time, and considers loss and gain respectively, so that the structural effect (the same amount of different expression forms cannot determine the same preference sequence) reflected by people in a selection experiment, the non-linearity of preference (the influence of the same probability variation on the preference is inconsistent), resource dependence (in uncertainty decision, the selection will of people is influenced not only by the uncertain degree but also by the self-ability), risk pursuit (when people face small probability to win large reward or face determined loss and large loss of fixed probability, the risk pursuit is shown) and avoidance loss (the perception of loss by people is much stronger than that of equal amount of gain) are well explained. The model of the accumulated foreground theory is expressed as follows:
appearance result P of a foreground PiThen, it is represented as (x)1,p1;x2,p2;...;xn,pn). The result xiArranged in descending order as x1≥x2≥...≥xn(at this point, the reference point or present situation is 0), the sequence isRelative to the change in status quo. A positive result is obtained and a negative result is a loss. Thus, a model of accumulated foreground theory can be expressed as:
wherein: x is the number of1≥...≥xk≥0≥xk+1≥...≥xn. Here, U (x) is a cost function, giving each result a real value, which is strictly increasing; w (p) is a probability weight function, w-For the probability weight of loss, w+Probability weight for revenue; the decision weight pi (p) is defined by a probability weight function w-And w+Generated in the interval [0,1 ]]Inner stringency increments, and values at 0 and 1 are 0 and 1.
Then, CPT can be converted to the following equation:
the core idea of the Deletion path search Algorithm based on the depth-first Deletion Algorithm is to delete a certain arc on the existing shortest path in the directed graph and find a replacement arc to find the next optional shortest path. The deletion algorithm is actually implemented by adding additional nodes and corresponding arcs in the directed graph.
Disclosure of Invention
The invention provides a time-varying user equilibrium dynamic network evolution passenger flow prediction system and method aiming at the defect that the existing system and method are difficult to accurately estimate the dynamic network state under the emergency.
A time-varying user equilibrium dynamic network evolution passenger flow prediction system comprises an AFC system, a video terminal, a passenger flow analysis service center system and a man-machine interaction terminal; wherein,
the AFC system is used for providing passenger card swiping detail data;
the video terminal acquires real-time video data and extracts real-time passenger flow data from the real-time video data;
the passenger flow analysis service center system is used for analyzing historical passenger flow data and real-time video data to obtain a passenger flow distribution prediction result and sending the prediction result to the man-machine interaction terminal;
the man-machine interaction terminal consists of a set number of computers and is used for inputting emergency information and predicting and inquiring passenger flow distribution at specific positions;
the passenger flow analysis service center system comprises a network database, a passenger flow sorting module, a passenger flow correction module and a passenger flow analysis module,
the network database is connected with the passenger flow clearing module, the passenger flow correction module and the passenger flow analysis module in sequence;
and the network database is respectively connected with the AFC system and the video terminal.
The invention also provides a time-varying user equilibrium dynamic network evolution passenger flow prediction method, which comprises the following steps:
step 1: the video terminal transmits and stores the acquired real-time data in a network database, and the AFC system transmits and stores the passenger card swiping detailed data in the network database;
step 2: the passenger flow sorting module is used for sorting passenger card swiping detail data acquired from the network database, transmitting data such as station entrance and exit amount of a station, transfer amount of a transfer station, section passenger flow of a line and the like acquired by sorting to the passenger flow correction module, and meanwhile, the passenger flow correction module is used for acquiring real-time passenger flow data from the network database; (when people swipe cards on a subway, the time and place of arrival and the time and place of departure are recorded, so-called clearing is to distribute the passenger flow by using a passenger flow distribution algorithm according to the information, and the obtained result is a basic passenger flow data table of the station's station arrival and departure amount, the transfer amount of the transfer station and the section passenger flow of the line, see the passenger card swiping detailed table, the section flow table and the like.)
Passenger card reading detail list
| Field(s) | Name (R) | Type (B) | Whether or not it is empty | Description of the invention |
| CardDate | Date of data | Char(8) | Whether or not | YYYYMMDD |
| ProductCode | Product numbering | Char(6) | Whether or not | |
| CardID | Ticket card number | Varchar(30) | Whether or not | |
| CardType | Kind of ticket and card | Varchar(10) | Whether or not | |
| InStaCode | Station code | Char(4) | Whether or not | |
| InStaTime | Inbound time stamping | Char(19) | Whether or not | Example (c): 2012-10-3115:09:00 |
| InLineCode | Inbound line numbering | Char(2) | Whether or not | |
| OutStaCode | Outbound station code | Char(4) | Whether or not | |
| OutStaTime | Outbound time stamping | Char(19) | Whether or not | Example (c): 2012-10-3115:09:00 |
| OutLineCode | Outbound line numbering | Char(2) | Whether or not |
Cross-section flow meter
Inbound and outbound passenger flow data sheet
Data table for passenger flow of station
The passenger flow sorting module is used for sorting passenger card swiping detail data acquired from a network database as follows:
(1) according to the actual situation of the urban rail transit network, when the generalized travel time is taken as the travel impedance, the road impedance AijThe following formula:
Aij＝tij；
in the formula tijThe train running time between adjacent stations i, j is obtained;
passing through a station:
Bk＝tk；
wherein the node impedance BkIndicating presence of passenger in vehicleThe time spent by the station;
transfer station
Comprises the following steps:
wherein, tkThe station stopping time of the train at the k station is obtained;
transfer time for transferring from the line p to the line q at the station k comprises transfer running time and waiting time, wherein the transfer running time is equal to the transfer distanceDivided by the average pace V of the passengerbrAnd the waiting time can be changed into the departure interval H of the riding routeqHalf of that.
(3) Total trip impedance on mth path to w
The expression of (A) is as follows:
the impedance of each path can be calculated according to the formula
Therefore, an impedance matrix of a road network is obtained, K gradually-shortened paths are obtained according to a deleted path search algorithm based on depth priority by combining an adjacent matrix of the road network, effective paths are screened out, and the passenger flow distribution proportion of the paths is calculated: when the active path set element is unique, the active path takes 100% of the traffic; when the elements of the effective path set are not unique, the total-existence method is used for passenger flow distribution, and the basic passenger flow data tables of the station entrance and exit volume, the number of detained people, the transfer volume of the transfer station and the section passenger flow volume of the line are finally obtained.
And step 3: the passenger flow correction module calls an AUKF algorithm to preprocess the distribution matrix and the real-time passenger flow data output by the unbalanced model, updates and corrects the model on line, accurately tracks the real-time change of the system state so as to adapt to the change of the passenger flow distribution after the change of the road network structure, and takes the corrected passenger flow data as the input data of the subsequent passenger flow distribution prediction.
And calling an AUKF algorithm to preprocess the algorithm to analyze as follows, and introducing an analysis process by taking station entering amount as an example:
Q1(t + k) is the arrival passenger flow at the station L in k time periods after the time t; let V (t) be station arrival passenger flow at time t, and V (t-1) be station arrival passenger flow at a time period before time t. The influence of the station passenger flow volume at the m time periods on the station passenger flow volume at the station L is considered.
The correction model of the station passenger flow is as follows:
in the formula H0,H1,H2,...,Hm-1Is a parameter matrix; hi＝[c′1(t),c′2(t),...,c′n(t)](ii) a c is a state variable; v (t) ═ v1(t),v2(t),...,vn(t)]TIs a passenger flow volume vector;
is a predicted inbound passenger volume; w (t) is observation noise, namely an error absolute value of the inbound passenger flow recorded by the video and the inbound passenger flow output by the model, and the covariance matrix of w (t) is R (t).
The following transformations are made:
the following results were obtained:
where y (t) is an observation vector; x (t) is a state vector; a (t) is an observation matrix; b (t) is a state transition matrix; b (t) is model noise, u (t-1) is zero-mean white noise, and its covariance matrix is Q (t-1).
Using kalman filtering theory, the following system of equations can be obtained:
in the formula
For updated state estimation, K (t) optimal Kalman gain, P (t | t-1) is the prediction estimation covariance matrix, P (t) is the updated covariance estimation, and P (0|0) is the covariance estimation of the initial state, which is the diagonal matrix.
When in use
After the determination, the corrected value of the station arrival passenger flow is
The above process can effectively correct the deviation of the actual passenger flow brought by the passenger flow distribution algorithm, thereby obtaining the corrected data correction process of the basic passenger flow data table of the station entering amount, the rest of the station exiting amount, the transfer amount of the transfer station and the section passenger flow of the line, which is the same as the above process.
And 4, step 4: when the human-computer interaction terminal does not input the emergency to the passenger flow analysis module, executing the step 5, otherwise, executing the step 6;
and 5: the passenger flow analysis module utilizes a passenger flow prediction algorithm to fit and predict passenger flow data to obtain predicted passenger flow data under daily conditions, and the predicted passenger flow data is sent to the man-machine interaction terminal for inquiry;
the passenger flow prediction algorithm is a method for fitting and predicting passenger flow data, and is a support vector machine based on a mixed kernel function. And adopting a clustering analysis method to divide the passenger flow into the passenger flow of the working days of Monday to Friday and the passenger flow of the holiday of Saturday to respectively predict. As shown in fig. 5, the flow of the prediction method is as follows:
(1) firstly, constructing a kernel function:
wherein, the polynomial kernel function Kpoly＝[(x·xi)+1]dRadial basis kernel function Krbf＝exp[-||x-xi||2/2σ2]。xiFor the width of the kernel function, x is the input variable and λ is a constant.
And selecting parameters in the model. The parameters in the model comprise a penalty factor C and an insensitive factor epsilon, and the polynomial order d is 2. Obtaining the parameters in the model according to the trial value and the empirical value: c is 100, epsilon is 0.01 and d is 2.
Selecting an error function, presetting an error, and analyzing the error by adopting a Mean Square Error (MSE):
wherein y isiIs the expected output of the test sample,
is a predicted value, l represents the number of sample points. Remove the default error to 10-3。
(2) Constructing parameter pairs: and respectively taking the hidden layer node numbers of different mixed odd functions and radial basis functions to obtain N pairs of different parameters. And selecting a pair of parameter pairs, inputting a training sample for training, and obtaining a prediction function.
(3) Testing the model: inputting a test sample, and obtaining actual output data of the test sample through a prediction function;
(5) and calculating errors and recording the errors and the prediction functions corresponding to the group of parameters. Calculating to obtain a corresponding mean square error through an error function by utilizing the expected output of the test sample and the actual output data of the test sample;
(6) recording errors, judging whether the number of the parameter pairs reaches N, if so, performing the next step, and otherwise, returning to the step (3);
(7) selecting a set of parameters to train the model: selecting a parameter pair generating the minimum error, judging whether the error is smaller than a preset error, if so, performing the next step, otherwise, returning to the step (2), and constructing a new two-dimensional network plane by taking the parameter corresponding to the minimum error as a center;
(8) outputting a prediction model: obtaining an optimal parameter pair-level prediction model meeting a preset error;
(9) obtaining a prediction result: and inputting passenger flow data by using the prediction model, predicting and obtaining a prediction result.
Step 6: the passenger flow analysis module adjusts a road network topological structure according to the accident information, utilizes a random user balanced traffic distribution model to deduce and predict passenger flow distribution, and sends predicted passenger flow data obtained by prediction to the man-machine interaction terminal for inquiry;
in the case of an emergency, the transit time of a path is a random variable. Under such conditions, the travel time of the route and the probability distribution thereof become the selection basis of travelers. Each feasible path corresponds to an actual travel utility variable x and a probability function p thereof. According to the principle of a foreground theory, a traveler is limited under the condition that the road network transit time is uncertain, the basis for selecting behaviors is the perception utility of a trip path, and the perception utility is obtained by depending on a subjective utility function and a subjective probability function:
(a) and the subjective utility function v (x) is subjective utility formed by the traveler according to the actual utility of each path, and represents the influence of the actual utility level on the psychology of the traveler.
(b) The subjective probability function w (p) is the subjective occurrence probability formed by the traveler according to the actual occurrence probability of the path utility, and represents the influence of the actual utility probability function p on the perception utility.
The method essentially utilizes the travel utility of the path to replace the generalized time used in traditional passenger distribution as the impedance in path selection.
When a traveler makes a decision, the traveler has a requirement on the probability of arriving at a destination on time, and the required probability can be regarded as the requirement of the traveler on the reliability of the path traveling time.
Reliability of travel time:
the psychological expectation of time for a traveler to wish to reach a destination can be expressed as:
since the path travel time is continuously and randomly distributed, the above formula can be converted into:
wherein
Is the inverse of the path travel time distribution function, and therefore,
the travel time is a function of the traffic flow of the road section, namely the travel time of the rho percentile of the route k is the expected value of the travel time of the psychological route of the travelers. As shown in fig. 3, the cumulative distribution function from the normal distribution can be:
the traveler determines a reference point for sensing travel time by a path between OD pairs according to the existing travel experience so as to ensure that the traveler can arrive at the destination in time. In the case of departure time determination, the reference point may divide the path travel time into an early arrival and a late arrival. Since there are many different travel paths between OD pairs. The expected travel time of each path is taken as the reference time
OD versus inter-r trip reference time is its minimum expected travel time for the path, i.e. <math>
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According to different requirements of travelers on the probability of arriving at the destination on time, the travelers are divided into M types and expressed as <math>
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The numerical values of these probabilities can be assigned by investigation in practical applications, and then:
the above equation is a linear programming equation, and there is a unique optimal solution, expressed as:
in the formula,
lagrange multiplier as constraint condition
When the traveler selects the route to travel, the traveler can obtain the balanced distribution result of the traffic flow by taking the maximum travel utility as the target. The traveler evaluates the traveling utility of each path before deciding the traveling path, and the prospect utility curve of the path is steeper in the loss area than in the benefit area, and the present loss is characterized to have a larger influence on the traveler than the potential income, and the traveler is shown as risk avoidance in the benefit area, and the traveler is shown as risk seeking in the loss area.
According to the Theory of Cumulative Prospect (CPT), the subjective probability w in earnings+The calculation formula of (p) is:
at loss, subjective probability w-The calculation formula of (p) is:
setting the reference point of the travel time of the path between OD and r as xrAnd then, the perceived path travel time of the path k is:
wherein:
in the formula, x is the actual path travel time,
is the perceived travel time, x, of the OD to the inter-r path kmAnd xrRespectively, an upper limit and a lower limit of travel time on the path k, and alpha and beta are constants.
And seeking the balance state of the final user of the traffic network by utilizing a balance passenger flow analysis module in combination with the established utility function.
In determining whether to be in traffic network [ N, A]In (d), the set v ═ of all link flows (v ═ v1,…,va,…v|A|)TAnd the relationship between the path flow and the road section flow
Wherein N and A are respectively a node and a road section in a rail transit road network, vaIs the traffic flow on the road segment a, where | represents the cardinality of the set,
to the roadThe path K belongs to KrF is the set of traffic flows on all paths, KrFor the set of all paths, r represents the starting point,
the correlation matrix is the incidence matrix of the path flow and the road section flow; r and S represent a set of OD pairs in the network, QrsDenotes the random traffic volume, p, starting from the origin R ∈ R to S ∈ SrsAll paths from r to s are represented, and since the travel requirements are random, the path p ∈ p from r to srsAnd the traffic volume q on the road section a ∈ ApAnd q isa。
After the travel utility of the traveler is known, user balanced passenger flow distribution can be carried out. The utility of various travelers in sensing the travel k on the path between r and OD is
The traffic network user equilibrium state based on the accumulated foreground theory can be expressed as:
in the formula,
for traffic flow for class j users on path k,
the conditions for user equalization are as follows:
the reference points for travel utility are selected as follows:
the calculation formula of the utility of the path perception travel is as follows:
in the above formula, the first and second carbon atoms are,
for the travel demands of OD on j-th class passengers among r, the nonlinear equation can be solved by using variational inequality transformation to obtain an optimal solution, namely, the balanced passenger flow distribution of users is achieved, so that a final road network passenger flow prediction result is obtained and is output through a human-computer interaction terminal;
when calculation is carried out, a convergence check error is given, the traffic flow and travel time distribution of the paths are calculated by using the corrected passenger flow data, corresponding reference points are calculated by using formulas (6) - (9), the perceived travel utility of each path is calculated by using formulas (10) and (11), the steepest descent direction and the step length are calculated by using the current passenger flow distribution and the perceived travel utility, then the passenger flow of the paths is updated, and the process is circulated until the error is within the convergence check error, and the model achieves the optimal result. And finally, carrying out statistical calculation on the data of the station entrance and exit amount, the number of detained people, the transfer amount, the cross section passenger flow and the like of each station to obtain and output a final result.
And 7: the man-machine interaction terminal provides service for the digital transmission of the emergency information and the query of the passenger flow analysis result.
The invention has the beneficial effects that: the method meets the demand of multiple users on short-time traffic prediction of the road network under the condition of emergency, realizes real-time distribution and dynamic prediction on the limited traffic, and meets the requirements of enterprise users on real-time viewing, sharing and decision of traffic information.
Drawings
FIG. 1 is a block diagram of the system architecture of the present invention.
FIG. 2 is a flow chart of the method of the present invention.
FIG. 3 is a comparison diagram of the trip reliability and the trip time probability distribution in the foreground theory of the present invention.
Fig. 4 is a road network structure diagram according to an embodiment of the present invention.
Fig. 5 is a flow chart of passenger flow prediction in a normal case in the present invention.
Fig. 6 is a passenger flow prediction data diagram in a normal situation in the embodiment of the present invention.
Detailed description of the invention
The embodiments of the present invention will now be described more fully hereinafter with reference to the accompanying drawings.
Fig. 1 is a block diagram showing an example of application of the passenger flow prediction system of the present invention. As shown in fig. 1, the system includes an AFC system, a video terminal, a passenger flow analysis service center system, and a human-computer interaction terminal; the passenger flow analysis service center system comprises a network database, a passenger flow clearing module, a passenger flow correction module and a passenger flow analysis module, wherein the network database is sequentially connected with the passenger flow clearing module, the passenger flow correction module and the passenger flow analysis module; the passenger flow video analysis module is respectively connected with the network database and the passenger flow correction module; the network database is respectively connected with the AFC system and the video terminal; the passenger flow analysis module is connected with the human-computer interaction terminal.
FIG. 2 is a flow diagram of one embodiment of a passenger flow prediction method of the present invention. As shown in fig. 2, a time-varying user equilibrium dynamic network evolution passenger flow prediction method includes the following steps:
step 1: the video terminal transmits and stores the acquired real-time data in a network database, and the AFC system transmits and stores the passenger card swiping detailed data in the network database;
step 2: the passenger flow sorting module is used for sorting passenger card swiping detail data acquired from the network database, transmitting data such as station entrance and exit amount of a station, transfer amount of a transfer station, section passenger flow of a line and the like acquired by sorting to the passenger flow correction module, and meanwhile, the passenger flow correction module is used for acquiring real-time passenger flow data from the network database; (when people swipe cards on a subway, the arrival time and the departure time are recorded, so-called clearing is to distribute passenger flow by using a passenger flow distribution algorithm according to the information, and the obtained result is basic passenger flow data tables of the station's station arrival and departure amount, the number of detained people, the transfer amount of the transfer station, and the section passenger flow of the line, see the passenger card swiping detail table, the section flow table and the like in the following.)
Passenger card reading detail list
| Field(s) | Name (R) | Type (B) | Whether or not it is empty | Description of the invention |
| CardDate | Date of data | Char(8) | Whether or not | YYYYMMDD |
| ProductCode | Product numbering | Char(6) | Whether or not | |
| CardID | Ticket card number | Varchar(30) | Whether or not | |
| CardType | Kind of ticket and card | Varchar(10) | Whether or not | |
| InStaCode | Station code | Char(4) | Whether or not | |
| InStaTime | Inbound time stamping | Char(19) | Whether or not | Example (c): 2012-10-3115:09:00 |
| InLineCode | Inbound line numbering | Char(2) | Whether or not | |
| OutStaCode | Outbound station code | Char(4) | Whether or not | |
| OutStaTime | Outbound time stamping | Char(19) | Whether or not | Example (c): 2012-10-3115:09:00 |
| OutLineCode | Outbound line numbering | Char(2) | Whether or not |
Cross-section flow meter
Inbound and outbound passenger flow data sheet
Data table for passenger flow of station
The passenger flow sorting module is used for sorting passenger card swiping detail data acquired from a network database as follows:
(1) according to the actual situation of the urban rail transit network, when the generalized travel time is taken as the travel impedance, the road impedance AijThe following formula:
Aij＝tij；
in the formula tijThe train running time between adjacent stations i, j is obtained;
passing through a station:
Bk＝tk；
wherein the node impedance BkRepresents the time spent by passengers at the station;
transfer station
Comprises the following steps:
wherein, tkThe station stopping time of the train at the k station is obtained;
transfer time for transferring from the line p to the line q at the station k comprises transfer running time and waiting time, wherein the transfer running time is equal to the transfer distance
Divided by the average pace V of the passengerbrAnd the waiting time can be changed into the departure interval H of the riding routeqHalf of that.
(3) Total trip impedance on mth path to w
The expression of (A) is as follows:
the impedance of each path can be calculated according to the formula
Therefore, an impedance matrix of a road network is obtained, K gradually-shortened paths are obtained according to a deleted path search algorithm based on depth priority by combining an adjacent matrix of the road network, effective paths are screened out, and the passenger flow distribution proportion of the paths is calculated: when the active path set element is unique, the active path takes 100% of the traffic; when the elements of the effective path set are not unique, the total-existence method is used for passenger flow distribution, and the basic passenger flow data tables of the station entrance and exit volume, the number of detained people, the transfer volume of the transfer station and the section passenger flow volume of the line are finally obtained.
And step 3: the passenger flow correction module calls an AUKF algorithm to preprocess the distribution matrix and the real-time passenger flow data output by the unbalanced model, updates and corrects the model on line, accurately tracks the real-time change of the system state so as to adapt to the change of the passenger flow distribution after the change of the road network structure, and takes the corrected passenger flow data as the input data of the subsequent passenger flow distribution prediction.
And calling an AUKF algorithm to preprocess the algorithm to analyze as follows, and introducing an analysis process by taking station entering amount as an example:
Q1(t + k) is the arrival passenger flow at the station L in k time periods after the time t; let V (t) be station arrival passenger flow at time t, and V (t-1) be station arrival passenger flow at a time period before time t. The influence of the station passenger flow volume at the m time periods on the station passenger flow volume at the station L is considered.
The correction model of the station passenger flow is as follows:
in the formula H0,H1,H2,...,Hm-1Is a parameter matrix; hi＝[c′1(t),c′2(t),...,c′n(t)](ii) a c is a state variable; v (t) ═ v1(t),v2(t),...,vn(t)]TIs a passenger flow volume vector;
is a predicted inbound passenger volume; w (t) is observation noise, namely an error absolute value of the inbound passenger flow recorded by the video and the inbound passenger flow output by the model, and the covariance matrix of w (t) is R (t).
The following transformations are made:
the following results were obtained:
where y (t) is an observation vector; x (t) is a state vector; a (t) is an observation matrix; b (t) is a state transition matrix; b (t) is model noise, u (t-1) is zero-mean white noise, and its covariance matrix is Q (t-1).
Using kalman filtering theory, the following system of equations can be obtained:
in the formula
For updated state estimation, K (t) optimal Kalman gain, P (t | t-1) is the prediction estimation covariance matrix, P (t) is the updated covariance estimation, and P (0|0) is the covariance estimation of the initial state, which is the diagonal matrix.
When in use
After the determination, the corrected value of the station arrival passenger flow is
The above process can effectively correct the deviation of the actual passenger flow brought by the passenger flow distribution algorithm, thereby obtaining the corrected data correction process of the basic passenger flow data table of the station entering amount, the rest of the station exiting amount, the transfer amount of the transfer station and the section passenger flow of the line, which is the same as the above process.
And 4, step 4: when the human-computer interaction terminal does not input the emergency to the passenger flow analysis module, executing the step 5, otherwise, executing the step 6;
and 5: the passenger flow analysis module utilizes a passenger flow prediction algorithm to fit and predict passenger flow data to obtain predicted passenger flow data under daily conditions, and the predicted passenger flow data is sent to the man-machine interaction terminal for inquiry;
the passenger flow prediction algorithm is a method for fitting and predicting passenger flow data, and is a support vector machine based on a mixed kernel function. And adopting a clustering analysis method to divide the passenger flow into the passenger flow of the working days of Monday to Friday and the passenger flow of the holiday of Saturday to respectively predict. As shown in fig. 5, the flow of the prediction method is as follows:
(1) firstly, constructing a kernel function:
wherein, the polynomial kernel function Kpoly＝[(x·xi)+1]dRadial basis kernel function Krbf＝exp[-||x-xi||2/2σ2]。xiFor the width of the kernel function, x is the input variable and λ is a constant.
And selecting parameters in the model. The parameters in the model comprise a penalty factor C and an insensitive factor epsilon, and the polynomial order d is 2. Obtaining the parameters in the model according to the trial value and the empirical value: c is 100, epsilon is 0.01 and d is 2.
Selecting an error function, presetting an error, and analyzing the error by adopting a Mean Square Error (MSE):
wherein y isiIs the expected output of the test sample,
is a predicted value, l represents the number of sample points. Remove the default error to 10-3。
(2) Constructing parameter pairs: and respectively taking the hidden layer node numbers of different mixed odd functions and radial basis functions to obtain N pairs of different parameters. And selecting a pair of parameter pairs, inputting a training sample for training, and obtaining a prediction function.
(3) Testing the model: and inputting a test sample, and obtaining actual output data of the test sample through a prediction function.
(5) And calculating errors and recording the errors and the prediction functions corresponding to the group of parameters. And calculating to obtain a corresponding mean square error through an error function by utilizing the expected output of the test sample and the actual output data of the test sample.
(6) And recording errors, judging whether the number of the parameter pairs reaches N, if so, carrying out the next step, and otherwise, returning to 3.
(7) Selecting a set of parameters to train the model: selecting a parameter pair generating the minimum error, judging whether the error is smaller than a preset error, if so, performing the next step, otherwise, returning to the step (2), and constructing a new two-dimensional network plane by taking the parameter corresponding to the minimum error as a center;
(8) outputting a prediction model: obtaining the optimal parameter pair-level prediction model meeting the preset error
(9) Obtaining a prediction result: and inputting passenger flow data by using the prediction model, predicting and obtaining a prediction result.
Step 6: the passenger flow analysis module adjusts a road network topological structure according to the accident information, utilizes a random user balanced traffic distribution model to deduce and predict passenger flow distribution, and sends predicted passenger flow data obtained by prediction to the man-machine interaction terminal for inquiry;
in the case of an emergency, the transit time of a path is a random variable. Under such conditions, the travel time of the route and the probability distribution thereof become the selection basis of travelers. Each feasible path corresponds to an actual travel utility variable x and a probability function p thereof. According to the principle of a foreground theory, a traveler is limited under the condition that the road network transit time is uncertain, the basis for selecting behaviors is the perception utility of a trip path, and the perception utility is obtained by depending on a subjective utility function and a subjective probability function:
(a) and the subjective utility function v (x) is subjective utility formed by the traveler according to the actual utility of each path, and represents the influence of the actual utility level on the psychology of the traveler.
(b) The subjective probability function w (p) is the subjective occurrence probability formed by the traveler according to the actual occurrence probability of the path utility, and represents the influence of the actual utility probability function p on the perception utility.
The method essentially utilizes the travel utility of the path to replace the generalized time used in traditional passenger distribution as the impedance in path selection.
When a traveler makes a decision, the traveler has a requirement on the probability of arriving at a destination on time, and the required probability can be regarded as the requirement of the traveler on the reliability of the path traveling time.
Reliability of travel time:
the psychological expectation of time for a traveler to wish to reach a destination can be expressed as:
since the path travel time is continuously and randomly distributed, the above formula can be converted into:
wherein
Is the inverse of the path travel time distribution function, and therefore,
the travel time is a function of the traffic flow of the road section, namely the travel time of the rho percentile of the route k is the expected value of the travel time of the psychological route of the travelers. As shown in fig. 3, the cumulative distribution function from the normal distribution can be:
the traveler determines a reference point for sensing travel time by a path between OD pairs according to the existing travel experience so as to ensure that the traveler can arrive at the destination in time. In the case of departure time determination, the reference point may divide the path travel time into an early arrival and a late arrival. Since there are many different travel paths between OD pairs. The expected travel time of each path is taken as the reference timeOD versus inter-r trip reference time is its minimum expected travel time for the path, i.e. <math>
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The numerical values of these probabilities can be assigned by investigation in practical applications, and then:
the above equation is a linear programming equation, and there is a unique optimal solution, expressed as:
in the formula,
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When the traveler selects the route to travel, the traveler can obtain the balanced distribution result of the traffic flow by taking the maximum travel utility as the target. The traveler evaluates the traveling utility of each path before deciding the traveling path, and the prospect utility curve of the path is steeper in the loss area than in the benefit area, and the present loss is characterized to have a larger influence on the traveler than the potential income, and the traveler is shown as risk avoidance in the benefit area, and the traveler is shown as risk seeking in the loss area.
According to the Theory of Cumulative Prospect (CPT), the subjective probability w in earnings+The calculation formula of (p) is:
at loss, subjective probability w-The calculation formula of (p) is:
setting the reference point of the travel time of the path between OD and r as xrAnd then, the perceived path travel time of the path k is:
wherein:
in the formula, x is the actual path travel time,is the perceived travel time, x, of the OD to the inter-r path kmAnd xrRespectively, an upper limit and a lower limit of travel time on the path k, and alpha and beta are constants.
And seeking the balance state of the final user of the traffic network by utilizing a balance passenger flow analysis module in combination with the established utility function.
In determining whether to be in traffic network [ N, A]In (d), the set v ═ of all link flows (v ═ v1,…,va,…v|A|)TAnd the relationship between the path flow and the road section flow
Wherein N and A are respectively a node and a road section in a rail transit road network, vaIs the traffic flow on the road segment a, where | represents the cardinality of the set,belongs to K for path KrF is the set of traffic flows on all paths, KrFor the set of all paths, r represents the starting point,
the correlation matrix is the incidence matrix of the path flow and the road section flow; r and S represent a set of OD pairs in the network, QrsDenotes the random traffic volume, p, starting from the origin R ∈ R to S ∈ SrsAll paths from r to s are represented, and since the travel requirements are random, the path p ∈ p from r to srsAnd the traffic volume q on the road section a ∈ ApAnd q isa。
After the travel utility of the traveler is known, user balanced passenger flow distribution can be carried out. The utility of various travelers in sensing the travel k on the path between r and OD is
The traffic network user equilibrium state based on the accumulated foreground theory can be expressed as:
in the formula,
for traffic flow for class j users on path k,
the conditions for user equalization are as follows:
the reference points for travel utility are selected as follows:
the calculation formula of the utility of the path perception travel is as follows:
in the above formula, the first and second carbon atoms are,
for the travel demands of OD on j-th class passengers among r, the nonlinear equation can be solved by using variational inequality transformation to obtain an optimal solution, namely, the balanced passenger flow distribution of users is achieved, so that a final road network passenger flow prediction result is obtained and is output through a human-computer interaction terminal;
when calculation is carried out, a convergence check error is given, the traffic flow and travel time distribution of the paths are calculated by using the corrected passenger flow data, corresponding reference points are calculated by using formulas (6) - (9), the perceived travel utility of each path is calculated by using formulas (10) and (11), the steepest descent direction and the step length are calculated by using the current passenger flow distribution and the perceived travel utility, then the passenger flow of the paths is updated, and the process is circulated until the error is within the convergence check error, and the model achieves the optimal result. And finally, carrying out statistical calculation on the data of the station entrance and exit amount, the number of detained people, the transfer amount, the cross section passenger flow and the like of each station to obtain and output a final result.
And 7: the man-machine interaction terminal provides service for the digital transmission of the emergency information and the query of the passenger flow analysis result.
The following further explains the time-varying user equilibrium dynamic network evolution passenger flow prediction system and method by taking a certain urban rail transit network as an object and listing an embodiment.
As shown in FIG. 4, it is assumed that after a train arrives at station A after going down XXXX times on No. 1 line of subway in a city, people are cleared at station A due to faults. This failure caused a total of 20 minutes of interruption. The input quantity of the human-computer interaction terminal is as follows:
station a of line 1 predicts a 20 minute interruption time and a traffic route from a to E, G to F.
The passenger flow sorting module is used for sorting passenger card swiping detail data acquired from the network database, transmitting data such as station entrance and exit amount of a station, transfer amount of a transfer station, section passenger flow of a line and the like acquired by sorting to the passenger flow correction module, and meanwhile, the passenger flow correction module is used for acquiring real-time passenger flow data from the network database; the passenger flow correction module calls an AUKF algorithm to preprocess the distribution matrix and the real-time passenger flow data output by the unbalanced model, updates and corrects the model on line, accurately tracks the real-time change of the system state so as to adapt to the change of the passenger flow distribution after the change of the road network structure, and takes the corrected passenger flow data as the input data of the subsequent passenger flow distribution prediction.
When the system detects that the human-computer interaction terminal transmits the emergency information into the passenger flow analysis module, the passenger flow analysis module adjusts a road network topological structure according to the accident information, and estimates the influence station range of the emergency, as shown in fig. 4. Wherein the B, C, D station is a stop station, and other affected stations should take corresponding measures to deal with the potential large passenger flow risks.
Meanwhile, a random user balanced traffic distribution model is utilized to deduce and predict passenger flow distribution.
Calling historical synchronous passenger flow data and real-time passenger flow data to distribute traffic flow, and performing simulation to obtain the data of the station entrance and exit volume, the number of detained people and the section passenger flow volume of each affected station.
The results are as follows:
the station B has a total number of 604 persons, wherein the outbound passenger flow is 32 persons, and the detained passenger flow is 572 persons;
c, total number of 764 people at the station, wherein the outbound passenger flow is 78 people, and the detained passenger flow is 686 people;
d, the station has 724 people, wherein the outbound passenger flow is 27 people, and the detained passenger flow is 697 people;
the station entrance and exit amount prediction data of the affected stations within 10 minutes after the accident is shown in the following table:
| station name | Amount of arrival | Amount of outbound |
| G station | 620 | 395 |
| H station | 161 | 81 |
| I station | 127 | 40 |
| |
130 | 33 |
| K station | 41 | 32 |
| L station | 63 | 12 |
| M station | 29 | 5 |
| N station | 241 | 120 |
| O station | 243 | 93 |
| P station | 285 | 56 |
| Q station | 227 | 131 |
| R station | 8 | 3 |
| S station | 16 | 8 |
| T station | 11 | 2 |
And finally, outputting the calculation result to the user through a human-computer interaction module so as to realize the function of assisting decision-making for the user.
For normal traffic prediction, the user may select any period of time during the day. It is assumed here that the user chooses to view the profile traffic data situation every hour in a certain interval in the future day.
The system calls the same history data as the selected date type and makes the prediction by the support vector machine algorithm. The selected data is passenger flow data of 06:00-24:00 per day, when the user selects to view the section passenger flow data of each hour, the data volume per day is 18, and when historical data of 8 days is called for prediction, the output result is shown in fig. 6. The user can check the section passenger flow quantity value of the required prediction period, the comparison value with the historical synchronous section passenger flow quantity and the error condition from the graph.
The method meets the demand of multiple users on short-time traffic prediction of the road network under the condition of emergency, realizes real-time distribution and dynamic prediction on the limited traffic, and meets the requirements of enterprise users on real-time viewing, sharing and decision of traffic information.
Claims (8)
1. A time-varying user equilibrium dynamic network evolution passenger flow prediction system is characterized by comprising an AFC system, a video terminal, a passenger flow analysis service center system and a man-machine interaction terminal; wherein,
the AFC system is used for providing passenger card swiping detail data;
the video terminal acquires real-time video data and extracts real-time passenger flow data from the real-time video data;
the passenger flow analysis service center system is used for analyzing historical passenger flow data and real-time video data to obtain a passenger flow distribution prediction result and sending the prediction result to the man-machine interaction terminal;
the man-machine interaction terminal consists of a set number of computers and is used for inputting emergency information and predicting and inquiring passenger flow distribution at specific positions;
the passenger flow analysis service center system comprises a network database, a passenger flow sorting module, a passenger flow correction module and a passenger flow analysis module,
the network database is connected with the passenger flow clearing module, the passenger flow correction module and the passenger flow analysis module in sequence;
and the network database is respectively connected with the AFC system and the video terminal.
2. A time-varying user equilibrium dynamic network evolution passenger flow prediction method is characterized by comprising the following steps:
step 1: the video terminal transmits and stores the acquired real-time data in a network database, and the AFC system transmits and stores the passenger card swiping detailed data in the network database;
step 2: the passenger flow sorting module is used for sorting passenger card swiping detail data acquired from the network database, transmitting data such as station entrance and exit amount of a station, transfer amount of a transfer station, section passenger flow of a line and the like acquired by sorting to the passenger flow correction module, and meanwhile, the passenger flow correction module is used for acquiring real-time passenger flow data from the network database;
and step 3: the passenger flow correction module calls an AUKF algorithm to preprocess the distribution matrix and the real-time passenger flow data output by the unbalanced model, updates and corrects the model on line, accurately tracks the real-time change of the system state so as to adapt to the change of the passenger flow distribution after the change of the road network structure, and takes the corrected passenger flow data as the input data of the subsequent passenger flow distribution prediction;
and 4, step 4: when the human-computer interaction terminal does not input the emergency to the passenger flow analysis module, executing the step 5, otherwise, executing the step 6;
and 5: the passenger flow analysis module utilizes a passenger flow prediction algorithm to fit and predict passenger flow data to obtain predicted passenger flow data under daily conditions, and the predicted passenger flow data is sent to the man-machine interaction terminal;
step 6: the passenger flow analysis module adjusts a road network topological structure according to the accident information and utilizes a random user balanced traffic distribution model to deduce and predict passenger flow distribution;
and 7: the man-machine interaction terminal provides service for the digital transmission of the emergency information and the inquiry of the predicted passenger flow data.
3. The time-varying user balanced dynamic network evolving passenger flow prediction method according to claim 2, characterized in that the passenger flow sorting module sorts passenger swiping card detail data obtained from a network database, and the method is as follows:
(1) according to the actual situation of the urban rail transit network, when the generalized travel time is taken as the travel impedance, the road impedance AijThe following formula:
Aij＝tij；
in the formula, tijThe train running time between adjacent stations i, j is obtained;
passing through a station:
Bk＝tk；
wherein the node impedance BkRepresents the time spent by passengers at the station;
transfer station
Comprises the following steps:
wherein, tkThe station stopping time of the train at the k station is obtained;
transfer time for transferring from the line p to the line q at the station k comprises transfer running time and waiting time, wherein the transfer running time is equal to the transfer distance
Divided by the average pace V of the passengerbrDeparture interval H of the waiting time transfer routeqHalf of (1);
(3) total trip impedance on mth path to w
The expression of (A) is as follows:
respectively calculating the impedance of each path according to the formula
Therefore, an impedance matrix of a road network is obtained, K gradually-shortened paths are obtained according to a deleted path search algorithm based on depth priority by combining an adjacent matrix of the road network, effective paths are screened out, and the passenger flow distribution proportion of the paths is calculated: when the active path set element is unique, the active path takes 100% of the traffic; when the elements of the effective path set are not unique, the total-existence method is used for passenger flow distribution, and the basic passenger flow data tables of the station entrance and exit volume, the number of detained people, the transfer volume of the transfer station and the section passenger flow volume of the line are finally obtained.
4. The time-varying user equilibrium dynamic network evolution passenger flow prediction method according to claim 2, characterized in that the method for invoking the AUKF algorithm to preprocess the algorithm comprises:
let Q1(t + k) is the arrival passenger flow at the station L in k time periods after the time t; v (t) is station arrival passenger flow at the time t, and V (t-1) is station arrival passenger flow at a time period before the time t; considering the influence of station arrival passenger flow in m time periods on the station arrival passenger flow in the station L; the correction model of the station passenger flow is as follows:
in the formula, H0,H1,H2,...,Hm-1Is a parameter matrix; hi＝[c′1(t),c′2(t),...,c′n(t)](ii) a c is a state variable; v (t) ═ v1(t),v2(t),...,vn(t)]TIs a passenger flow volume vector;
is a predicted inbound passenger volume; w (t) is observation noise, namely an error absolute value of the inbound passenger flow recorded by the video and the inbound passenger flow output by the model, and the covariance matrix of w (t) is R (t);
the following transformations are made:
obtaining:
wherein y (t) is an observation vector; x (t) is a state vector; a (t) is an observation matrix; b (t) is a state transition matrix; b (t) is model noise, u (t-1) is assumed to be zero-mean white noise, and its covariance matrix is Q (t-1);
by using the Kalman filtering theory, the following equation set is obtained:
in the formula,
for updated state estimation, K (t) optimal Kalman gain, P (t | t-1) is the prediction estimation covariance matrix, P (t) is the updated covariance estimation, and P (0|0) is the covariance estimation of the initial state, which is the diagonal matrix;
when in use
After the determination, the corrected value of the station arrival passenger flow is as follows:
the deviation of the actual passenger flow brought by the passenger flow distribution algorithm can be effectively corrected through the process, so that the corrected arrival amount data can be obtained.
5. The time-varying user balanced dynamic network evolution passenger flow prediction method according to claim 2, characterized in that the passenger flow prediction algorithm is a method of fitting and predicting passenger flow data, the passenger flow prediction algorithm divides the passenger flow into a weekday passenger flow of monday to friday and a Saturday break passenger flow for prediction respectively; the passenger flow prediction algorithm comprises the following steps:
(1) constructing a kernel function:
wherein, the polynomial kernel function Kpoly＝[(x·xi)+1]dRadial basis kernel function Krbf＝exp[-||x-xi||2/2σ2]；xiIs the width of the kernel function, x is the input variable, and λ is a constant;
selecting the parameters in the model: the parameters in the model comprise a penalty factor C, an insensitive factor epsilon and a polynomial order d;
selecting an error function, presetting an error, and analyzing the error by adopting a Mean Square Error (MSE):
wherein, yiIs the expected output of the test sample,
is a predicted value, l represents the number of sample points; remove the default error to 10-3；
(2) Constructing parameter pairs: respectively taking the number of hidden layer nodes of different mixed odd functions and radial basis functions to obtain N pairs of different parameters; selecting a pair of parameter pairs, inputting a training sample for training to obtain a prediction function;
(3) testing the model: inputting a test sample, and obtaining actual output data of the test sample through a prediction function;
(5) calculating errors and recording the errors and prediction functions corresponding to the set of parameters: calculating to obtain a corresponding mean square error through an error function by utilizing the expected output of the test sample and the actual output data of the test sample;
(6) recording errors, judging whether the number of the parameter pairs reaches N, if so, performing the next step, and otherwise, returning to the step (3);
(7) selecting a group of parameter pairs to train the model; selecting a parameter pair generating the minimum error, judging whether the error is smaller than a preset error, if so, performing the next step, otherwise, returning to the step (2), and constructing a new two-dimensional network plane by taking the parameter corresponding to the minimum error as a center;
(8) obtaining an optimal parameter pair-level prediction model meeting a preset error;
(9) and inputting passenger flow data by using the prediction model for prediction and obtaining a prediction result.
6. The time-varying user balanced dynamic network evolving passenger flow prediction method according to claim 5, wherein C is 100, e is 0.01, and d is 2.
7. The time-varying user-balanced dynamic network evolving passenger flow prediction method according to claim 2, characterized in that the random user-balanced traffic distribution model is:
in the case of an emergency, the transit time of a path is a random variable; under the condition, the travel time of the route and the probability distribution thereof become the selection basis of travelers; each feasible path corresponds to an actual travel utility variable x and a probability function p thereof; according to the principle of a foreground theory, a traveler is limited under the condition that the road network transit time is uncertain, the basis for selecting behaviors is the perception utility of a trip path, and the perception utility is obtained by depending on a subjective utility function and a subjective probability function:
(a) the subjective utility function v (x) is subjective utility formed by the traveler according to the actual utility of each path, and represents the influence of the actual utility level on the psychology of the traveler;
(b) the subjective probability function w (p) is the subjective occurrence probability formed by the traveler according to the actual occurrence probability of the path utility, and represents the influence of the actual utility probability function p on the perception utility;
the travel utility of the path is used for replacing the generalized time used in the traditional passenger distribution as the impedance in the path selection;
when a traveler makes a decision, the traveler has a requirement on the probability of arriving at a destination on time, and the required probability can be regarded as the requirement of the traveler on the reliability of the path traveling time;
reliability of travel time:
the psychologically expected time for a traveler to wish to reach a destination is expressed as:
since the path travel time is continuously and randomly distributed, the above formula is converted into:whereinIs the inverse of the path travel time distribution function, and therefore,
the travel time is a function of the traffic flow of the road section, namely the expected value of the travel time of the psychological path of the travelers is the travel time of the rho percentile of the path k; from the cumulative distribution function of the normal distribution:
the traveler determines a reference point of the path perception travel time between the OD pairs according to the existing travel experience so as to ensure that the traveler can arrive at the destination on time; under the condition that the departure time is determined, dividing the route travel time into an early arrival time and a late arrival time by a reference point; since there are many different travel paths between OD pairs; the expected travel time of each path is taken as the reference time
OD versus inter-r trip reference time is its minimum expected travel time for the path, i.e. <math>
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in the formula,
lagrange multiplier as constraint condition
When a traveler selects a route to travel, the traveler can obtain a balanced distribution result of traffic flow by taking the maximum perceived travel utility as a target; before a traveler decides a traveling path, the traveling utility of each path is evaluated, the foreground utility curve of the path is steeper in a loss area than in a benefit area, the characteristic that the current loss has larger influence on the traveler than the potential income is shown, the traveler is shown as risk avoidance in the benefit area, and the traveler is shown as risk seeking in the loss area;
according to the Theory of Cumulative Prospect (CPT), the subjective probability w in earnings+The calculation formula of (p) is:
at loss, subjective probabilityThe calculation formula of (A) is as follows:
setting the reference point of the travel time of the path between OD and r as xrAnd then, the perceived path travel time of the path k is:
wherein:
in the formula, x is the actual path travel time,
is the perceived travel time, x, of the OD to the inter-r path kmAnd xrRespectively an upper limit and a lower limit of travel time on the path k, wherein alpha and beta are constants;
seeking the balance state of the final user of the traffic network by utilizing a balance passenger flow analysis module in combination with the established utility function;
in determining whether to be in traffic network [ N, A]The set of all the link flows v ═ v (v ═ v)1,…,va,…v|A|)TAnd the relationship between the path flow and the road section flow
Wherein N and A are respectively a node and a road section in a rail transit road network, vaIs the traffic flow on the road segment a, where | represents the cardinality of the set,
belongs to K for path KrF is the set of traffic flows on all paths, KrFor the set of all paths, r represents the starting point,
the correlation matrix is the incidence matrix of the path flow and the road section flow; r and S represent a set of OD pairs in the network, QrsDenotes the random traffic volume, p, starting from the origin R ∈ R to S ∈ SrsAll paths from r to s are represented, and since the travel requirements are random, the path p ∈ p from r to srsAnd the traffic volume q on the road section a ∈ ApAnd q isa；
After learning the traveling utility of the traveler, carrying out user-balanced passenger flow distribution: all kinds of tripsThe perceived travel utility of OD to r path k is
The traffic network user equilibrium state based on the accumulated prospect theory is represented as follows:
in the formula,
for traffic flow for class j users on path k,
the conditions for user equalization are as follows:
the reference points for travel utility are selected as follows:
the calculation formula of the utility of the path perception travel is as follows:
in the above formula, the first and second carbon atoms are,
for the travel demand of OD on j-th class passengers between r, the nonlinear equation is solved by using the variational inequality transformation to obtain the optimal solution, namely, the balanced passenger flow distribution of users is achieved, so that the final road network passenger flow prediction result is obtained and is output through a human-computer interaction terminal.
8. The time-varying user balanced dynamic network evolution passenger flow prediction method according to claim 7, characterized in that when the random user balanced traffic distribution model is calculated, a convergence check error is given first, the corrected passenger flow data is used for calculating the traffic flow and travel time distribution of a path, then the corresponding reference points are calculated by using formulas (6) - (9), the perceived travel utility of each path is calculated by using formulas (10) and (11), the current passenger flow distribution and the perceived travel utility are used for calculating the steepest descent direction and step length, then the path passenger flow is updated, and the process is repeated until the error is within the convergence check error, and the model reaches the optimal result; and finally, carrying out statistical calculation on data such as station entrance and exit amount, number of detained people, transfer amount, cross section passenger flow and the like of each station to obtain a final result and sending the final result to the man-machine interaction terminal.
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