CN106875314A - A kind of Urban Rail Transit passenger flow OD method for dynamic estimation - Google Patents

Abstract

The invention discloses a kind of Urban Rail Transit passenger flow OD method for dynamic estimation, comprise the following steps：It is primarily based on history passenger flow data, it is spaced by setting time, the one-way ticket passenger flow OD matrixes of flow space-time distribution less stable are improved using the method for moving average, passenger flow OD distribution matrixs after generation improvement, passenger flow shunting rate matrix is calculated on this basis, with reference to the journey time regularity of distribution that OD flows, build the dynamic flow relation between OD streams and passenger flow out of the station, OD dynamic estimation state-space models are set up further according to dynamic flow relation and the real-time volume of the flow of passengers information out of the station for uploading, model is solved with kalman filter method, and OD estimated results are modified using Standardization Act, draw optimal estimation value, and the validity to method is tested.The present invention is counted by the real-time transaction data out of the station for uploading and history passenger flow data, establish the state-space model based on Kalman filtering, can be used to estimate real-time passenger flow demand distributed architecture information, supported for the passenger flow dynamic management of track traffic enterprise provides data.

Description

A kind of Urban Rail Transit passenger flow OD method for dynamic estimation

Technical field

The present invention relates to a kind of Urban Rail Transit passenger flow OD method for dynamic estimation.

Background technology

With the fast development of urban track traffic, each big and medium-sized cities progressively stride into networking operation.Rail network structure is answered Hydridization causes passenger's travel behaviour randomness to be strengthened, and mobilism, complication feature are showed on passenger flow demand distributed architecture, right The Transportation Organization of track traffic brings very big challenge, needs badly using appropriate needs estimate model to study in the range of the short period The passenger flow demand regularity of distribution temporally and spatially, should with the mobilism operation management level and system that improve track traffic Change ability.

Since the eighties in last century, domestic and foreign scholars have carried out substantial amounts of research for OD dynamic estimations, form one Serial OD dynamic estimations model.But application of the existing OD methods of estimation in track traffic, mainly also has the following disadvantages：① Existing research focuses primarily upon field of road traffic, Rail traffic network structure and passenger flow feature is not accounted for, in track traffic Gauze passenger flow OD dynamic estimations aspect haves the shortcomings that precision is low, operation efficiency is not high；2. OD streams and collection in existing model Discharge relation between information flow is set up on the basis of section flow is easily obtained mostly, but the real-time section in track traffic Passenger flow information is but difficult to obtain, and is only capable of obtaining passenger flow information out of the station, so gathering the dynamic flow equation of flow based on section It is difficult to be applied to Rail traffic network.Accordingly, it would be desirable to a kind of new method, with reference to Metro Network passenger flow feature and collection number It is believed that breath, realizes the real-time OD estimation of Metro Network passenger flow.

The content of the invention

Goal of the invention：For the deficiencies in the prior art, the present invention provides a kind of Urban Rail Transit passenger flow OD method for dynamic estimation, the method is based on history passenger flow trip data and rail traffic ticket automatic selling and checking system terminal device is real-time The transaction data of upload estimates current passenger flow OD distributed architecture information in real time.

Technical scheme：To achieve the above object, the technical solution adopted by the present invention is：

A kind of Urban Rail Transit passenger flow OD method for dynamic estimation, comprises the following steps：

(1-1) setting time interval of delta t, at timed intervals Δ t daily history passenger flow data is segmented；Statistics is every Stored-value ticket passenger flow data and one-way ticket passenger flow data in its each time period；

(1-2) is improved using the method for moving average to one-way ticket passenger flow data, the one-way ticket passenger flow number after being improved According to for：

In formula, i ≠ j；q_0ijT () represents final slave site j in the passenger entered the station by website i in t-th period after improving Outbound one-way ticket passengers quantity；Represent in the t-a period obtained by history passenger flow data statistics by website Final slave site j outbound one-way ticket passengers quantity in the passenger that i enters the station；R represents the period number of rolling average, and R ＜ t；

(1-3) is calculatedIn formula,Represent to be counted by history passenger flow trip data and obtain T-th period in stored-value ticket passengers quantity final slave site j outbound in the passenger entered the station by website i, q_ijT () is represented the The passenger flow entered the station by website i in t period goes to the outbound total passengers quantities of website j；

According to q_ij(t) build all fronts net entered the station within t-th time period passenger flow OD distribution matrixs A (t) and t-th time Passenger flow streaming rate matrix B (t) in section：

Wherein, n is the sum of website；b_ijT () is passenger flow streaming rate, represent and go in the passenger entered the station by i stations in period t The passenger flow at j stations accounts for i stations and always enters the station the ratio of passenger flow,And

Passenger flow streaming rate matrix B (t) is changed into the form of column vector：

B (t)=[b₁₂(t), b₁₃(t) ..., b_1n(t) ..., b₂₁(t) ..., b_2n(t) ..., b_n(n-1)(t)]^T (1.4)

(1-4) builds the outbound coefficient that reaches of passenger flow：

Wherein,It is the outbound arrival coefficient of passenger flow, represents that slave site i sets out and with station j within the t-m period For the ratio of purpose station j, t >=m are reached in the OD passenger flows of destination in period tu_ijT () represents Passenger's average travel time at j stations is gone to being stood by i in t-th time period,Represent and stood out by i in t-th time period Hair goes to the standard variance of passenger's average travel time at j stations；f_ijX () is probability density function, to represent and go to j being stood by i The passenger flow stood reaches the probability at j stations in moment x；

(1-5) is based on the constraint equation that real-time passenger flow data is set up between OD bus traveler assignments ratio and flow out of the station：

q_ij(t-m)=I_i(t-m)·b_ij(t-m) (1.7)

In formula, I_i(t-m) passengers quantity that always enters the station for i stations within the t-m period；q_ij(t-m) when representing the t-m The passenger flow entered the station by website i in section goes to the total passengers quantities of website j；O_jT () represents that j outbound within t-th period in station multiplies Objective quantity M is hop count when any two time intersegmental passenger's journey time maximum is crossed in gauze；V_ijT () is to set up traffic constraints The outbound amount error produced during equation；

(1-6) builds passenger flow OD dynamic estimation state-space models, including state using passenger flow streaming rate as state variable Equation of transfer 1.9 and observational equation 1.10：

In formula (1.9), B (t) is actual passenger flow streaming rate b_ijThe R of (t) composition_od× 1 dimension matrix, R_odRepresent OD couples total Number, R_od=n × (n-1)；B^kT () is by the forward direction kth week history passenger flow streaming rate under the conditions of identical passenger flow characteristic dayGroup Into R_od× 1 dimension matrix；F (t) and G^kT () is state-transition matrix, characterize the state evolution feature of system, is by weight system Number γ_kThe R for obtaining_od×R_odDimension scalar matrix；W (t) is to set up the error W produced by systematic state transfer equation_ijT () constitutes White noise matrix；

In formula (1.10), O_j(t) and I_i(t-m) it is real-time passenger flow data out of the station；O (t) is that outbound volume of the flow of passengers square is tieed up in n × 1 Battle array；H (t) is the outbound arrival matrix of passenger flow, and it is characterized between state variable B (t) and observational variable O (t) with period dynamic change Correlation, be n × R_odDimension matrix；Be byThe R of structure_od× 1 dimension matrix,Be comprising present period with And M passenger flow streaming rate average of continuous time section of forward direction；V (t) is to set up the error v produced by systematic observation equation_ij(t) group Into white noise matrix；

(1-7) is solved using kalman filter method to passenger flow OD dynamic estimation state-space models, and using mark Quasi-ization method is modified to OD estimated results；Index is set up according to revised OD estimated results, and is built with the index test Passenger flow OD dynamic estimations state-space model it is whether correct；If assay is correct, passenger flow OD dynamic estimation states are judged Spatial model is correct, exports the estimated result of passenger flow OD dynamic estimation state-space models；If assay is incorrect, again The parameter value of passenger flow OD dynamic estimation state-space models, return to step (1-6) are set；The parameter for resetting includes：It is mobile Average when hop count R and weight coefficient γ_k。

Further, it is the step of structure passenger flow OD dynamic estimation state-space models in the step (1-6)：

(2-1) sets up the intersegmental passenger flow streaming rate relation of adjacent time：

In formula,When being t-th by the history passenger flow data statistics acquisition of identical passenger flow characteristic day ventrocephalad kth week Between section passenger flow streaming rate；γ_kIt is weight coefficient, 0≤γ_k≤ 1, for weighing the preceding reliability to kth week history passenger flow information Property；w_ijT () is normal distribution white Gaussian noise variable, the state produced when building state transition equation for characterizing is shifted to be missed Difference；

(2-2) the intersegmental passenger flow streaming rate relational expression of adjacent time is converted to the matrix form of standard, is obtained state and is turned Moving equation is：

In formula, W (t) is to set up the error w produced by systematic state transfer equation_ijThe white noise matrix of (t) composition, and W T ()~N (0, Q (t)), Q (t) are state Transfer Error variance, the error variance produced during state transition equation, Q are set up in expression T the unbiased esti-mator expression formula of () is as follows：

In formula, W_kT () represents the t-th historic state Transfer Error of period of forward direction kth week under identical passenger flow characteristic day,It is the historic state Transfer Error average of p days；

(2-3) by the approximate passenger flow streaming rate instead of day part of the passenger flow streaming rate average value in adjacent time interval, by formula The expression formula of (1-8) is converted to following form：

The observational equation of state-space model is as available from the above equation：

In formula, V (t) is observational equation error matrix, and V (t)~N (0, R (t)), R (t) are outbound amount error variance square The error variance produced during observational equation is set up in battle array, expression, and the unbiased esti-mator expression formula of R (t) is：

In formula, V_kT () represents t-th observational equation history error matrix of period of kth day,It is the history of continuous n days Observation error average.

Further, kalman filter method is used in the step (1-7) to passenger flow OD dynamic estimation state space moulds Type is solved and OD estimated results are modified using Standardization Act, is the step of draw optimal estimation value：

It is P (t) that (3-1) defines covariance matrix；Initialization t=1；DefinitionP (1)=[1]_n×n；

Wherein, B^k(1) it is by the forward direction kth week history passenger flow streaming rate under the conditions of identical passenger flow characteristic dayComposition R_od× 1 dimension matrix；

(3-2) carries out prior estimate according to state transition equation：

In formula,T-th priori estimates of state variable B (t) of period is represented,Represent t-1 The posterior estimate of the state variable B (t-1) of period；

(3-3) calculates prior estimate covariance matrix；

Wherein,Represent t-th prior estimate covariance matrix of period；After representing the t-1 period Test estimate covariance matrix；

(3-4) calculates Kalman filtering gain；

(3-5) is according to Kalman filtering gain and the residual GM priori estimates of estimate and observationObtain Posterior estimateIt is based on the solution of the standard Kalman filtering method of state-space model：

The constraint amendment of (3-6) standard Kalman filtering method estimate：During OD dynamic estimations, state variable B (t) Equation (1.21) constraint need to be met, formula (1.21) is：

Object function is minimised as with mean square error, can be obtained：

Wherein | | | | represent two norms of vector；Be by correcting after passenger flow streaming rateThe R of composition_od× 1 dimension square Battle array, it is Kalman filtering standard step gained estimateOn the basis of, repaiied by the gained after Mean Square Error adjustment The vector of positive estimate composition；EquationIt is revised state vectorThe equality constraint equation that should be met, Y For scalar matrix is tieed up in n × 1, its element value is 1；X is n × R_odDimension matrix；

For the restricted problem that formula (1.22) is represented builds Lagrange condition function, can obtain：

Wherein, Z is the Lagrange condition function for building；β is Lagrange multiplier vector；P (B (t) | O (t)) it is condition Probability density function；

Assuming that initial system state variable B (1), W (t), V (t) they are joint gaussian variable, with reference to the property of Kalman filtering Matter：When B (1), W (t), V (t) they are joint gaussian variable, Kalman Filter Estimation valueIt is that condition is the B (t) of O (t) Conditional mean, can obtain：

Then respectively in formula (1.23)First derivation is carried out with β, can be solved：

(3-7) updates Posterior estimator covariance matrix；

Further, index is set up according to revised OD estimated results in the step (1-7), and uses the index test The step whether the passenger flow OD dynamic estimations state-space model of structure is correct is：

(4-1) builds Normalized RMSE index：

RMSN values are lower, show to estimate that model is more accurate；

Whether (4-2) judges the value of RMSN less than default threshold value RMSN_minIf meeting RMSN ＜ RMSN_min, then institute is judged State passenger flow OD dynamic estimation state-space models correct；Otherwise, it is determined that the passenger flow OD dynamic estimations state-space model is not just Really.

Further, in the step (1-7), the method for Reparametrization is：

Calculate：

In formula,It is the when hop count iteration step length for pre-setting, andIt is integer；τ is the weight coefficient iteration for pre-setting Step-length, τ ＜ 1.

It should be noted that when k is small, showing it closer to actual passenger flow data, its γ_kValue resetting When, can increase it, conversely, when k is larger, its γ_kValue when resetting, can reduce it.

If by inspection, it is determined that the gauze passenger flow OD method for dynamic estimation set up is effective, can be used for reality Rail transportation operation is managed.

Beneficial effect：The Urban Rail Transit passenger flow OD method for dynamic estimation that the present invention is provided, combines history visitor The OD regularities of distribution of stream, are processed using the method for moving average one-way ticket passenger flow larger to fluctuation, extract improved going through History passenger flow shunts rate matrix, it is possible to increase model estimated accuracy；The outbound arrival coefficient of passenger flow is constructed, and proposes its double integral Computational methods, for setting up the dynamic flow relation between OD streams and passenger flow out of the station, solve track traffic section passenger flow and are difficult to Collection causes the problem that discharge relation formula greatly reduces；The state-space model based on Kalman filtering algorithm is constructed, to line Netter stream OD carries out dynamic estimation, takes Standardization Act to be modified OD estimated results, further increases OD estimated accuracies； Finally propose to test the validity of model using the standardization weighted root mean square theory of error, it is ensured that the reliability of estimated result Property.The method effectively can carry out real-time OD estimation to Urban Rail Transit passenger flow, be urban track traffic operation pipe Reason decision-making provides data and supports.

Brief description of the drawings

Fig. 1 is method of the present invention operating process schematic diagram.

Specific embodiment

It is as shown in Figure 1 a kind of Urban Rail Transit passenger flow OD method for dynamic estimation operating process schematic diagrams, below The present invention is made further instructions with reference to implementation process.

In the present embodiment, setting time interval of delta t first, at timed intervals Δ t the service time is segmented, due to visitor The real-time upload of flow data be generally 15min interval, therefore, to meet the demand of operation management, can setting time interval of delta t= 15min.History passenger flow trip data is divided into stored-value ticket passenger flow data and one-way ticket passenger flow data, stored-value ticket and one-way ticket is counted The distribution volumes of the flow of passengers of OD at times in passenger flow data, it is contemplated that the spatial distribution less stable of one-way ticket passenger flow and passenger arrives at a station The time difference opposite sex is larger, it is considered to one-way ticket OD passenger flows are improved using the method for moving average.In each time period, perform with Lower step：

Step1：Calculate passenger flow OD distribution matrixs：

Wherein, q_0ijT the subscript 0 of () represents one-way ticket, subscript i and j are site number, q_0ijT () is represented by mobile flat Final slave site j outbound one-way ticket passengers quantity in the passenger entered the station by website i within t-th period after equal method improvement；Represent in the passenger entered the station by website i in the t-a period obtained by original passenger flow data statistics finally slave station Point j outbound one-way ticket passengers quantity；R represents the period number of rolling average, and R ＜ t.

The one-way ticket volume of the flow of passengers after the method for moving average is improved and the stored-value ticket volume of the flow of passengers are added up, all fronts net can be obtained Entered the station within t-th time period OD distribution matrixs A (t) of passenger flow of the same day is：

Wherein, n is the sum of website；q_ijT () represents that the passenger flow entered the station by website i within t-th period is gone to website j and gone out The total passengers quantity stood, and i ≠ j；

Rolling average when hop count R the visitor of same characteristic features day that should be calculated according to history one-way ticket passenger flow data of value Flow distribution fluctuation size and determine.

Step2：Calculate passenger flow shunting rate matrix：The passenger flow shunting in t-th period can be obtained based on OD distribution matrixs A (t) Rate matrix B (t) is：

Wherein, b_ijT () is passenger flow streaming rate, represent that the passenger flow that j stations are gone in the passenger entered the station by i stations in period t accounts for i stations The ratio of the passenger flow that always enters the station, it is known that

For ease of the structure of following model, passenger flow streaming rate matrix B (t) is changed into the form of column vector, it is as follows：

B (t)=[b₁₂(t), b₁₃(t) ..., b_1n(t) ..., b₂₁(t) ..., b_2n(t) ..., b_n(n-1)(t)]^T

Step3：Build the outbound arrival coefficient of passenger flow：Because Rail Transit AFC System have recorded passenger's trip information, together When, the characteristics of track traffic passenger's journey time has reliability high (Subway Tunnel running time is substantially stationary).Therefore, can lead to The passenger's journey time distribution situation between each OD is crossed, for portraying the discharge relation between passenger flow out of the station and OD streams.Assuming that multiplying Visitor's xth minute in arbitrary period t goes to the passenger flow journey time Normal Distribution at j stations, i.e. x ∈ N (u by i stations_ij (t),Wherein, u_ijT () represents passenger's average travel time that j stations are gone to being stood by i in period t；During expression In section k, passenger goes to the standard variance of the average hourage at j stations, u being stood by i_ij(t) andCan be by history visitor Stream OD data carry out statistical analysis and obtain.

On this basis, it is assumed that the passenger flow for going to website j that entered the station by website i in arbitrary period t is uniform within the period Website i is reached, can be by the passenger's journey time probability density function f between each OD_ij(x), and in the t-m period by I set out at station go to j station passenger flow is reached in period t j stand probability be integrated, so as to calculate the outbound arrival coefficient of passenger flowTo portray the discharge relation between passenger flow out of the station and OD streams, its expression formula is：

Wherein,It is the outbound arrival coefficient of passenger flow, represents that slave site i sets out and with station j within the t-m period For ratio (the outbound passenger flow letter that certain period collects of purpose station j is reached in the OD passenger flows of destination in period t (t >=m) Breath be early stage multiple the periods by other stations enter the station passenger flow reach aggregation result)；

Step4：Build dynamic flow relation：Because track traffic section passenger flow is difficult to gather, it is difficult to use for reference road traffic Field based on the section passenger flow of Real-time Collection section so as to set up dynamic flow relation, therefore, this method is based on time-varying entering The outbound collection volume of the flow of passengers, sets up the constraint equation between OD bus traveler assignments ratio and flow out of the station：

q_ij(t-m)=I_i(t-m)·b_ij(t-m)

Wherein, n represents gauze station sum；I_i(t-m) it is always the enter the station volumes of the flow of passengers of the station i within the t-m period；q_ij (t-m) represent that the passenger flow entered the station by website i in the t-m period goes to the outbound total passengers quantities of website j；b_ij(t-m) it is the The t-m passenger flow separation rate of period, represents that the passenger flow that j stations are gone to being stood by i in the t-m period accounts for station i and always enters standee The ratio of stream；O_jT () represents outbound amounts of the station j in period t；M be in road network between any OD passenger's journey time it is maximum across Hop count when more, the value of hop count M depends on the Network scale of local urban track traffic when maximum is crossed over.；For passenger flow goes out Stand and reach coefficient；V_ijT () is the outbound amount error produced when setting up observational equation.

Step5：Set up state-space model：Station passenger flow streaming rate is chosen as predictor, gauze passenger flow OD is set up Dynamic estimation state-space model.In view of interior passenger flow fluctuation in short-term is not too large, can draw between adjacent time interval passenger flow streaming rate it Between relation meet：

In formula,When being t-th by the history passenger flow data statistics acquisition of identical passenger flow characteristic day ventrocephalad kth week Between section passenger flow streaming rate；γ_kIt is weight coefficient, 0≤γ_k≤ 1, for weighing the preceding reliability to kth week history passenger flow information Property；w_ijT () is normal distribution white Gaussian noise variable, the state produced when building state transition equation for characterizing is shifted to be missed Difference.

The intersegmental passenger flow streaming rate relational expression of adjacent time is converted to the matrix form of standard, state transition equation is obtained For：

In its formula, W (t) is to set up the error w produced by systematic state transfer equation_ijThe white noise matrix of (t) composition, and W (t)~N (0, Q (t)), Q (t) are state Transfer Error variance, and the error variance produced during state transition equation, Q are set up in expression T the unbiased esti-mator expression formula of () is as follows：

In formula, W_kT () represents the t-th historic state Transfer Error of period of forward direction kth week under identical passenger flow characteristic day,It is the historic state Transfer Error average of p days.

From the relational expression between passenger flow streaming rate between adjacent time interval, the state that estimation procedure need to include multiple periods becomes Amount information, estimates t-th passenger flow streaming rate b of period_ij(t) and b_ij(t-1) ..., b_ij(t-m) it is relevant, then, it is necessary to will be many The variable information of individual period is integrated into a period, so as to facilitate model construction.Therefore, assuming the passenger flow in the range of certain hour Fluctuating change is smaller, using the passenger flow streaming rate average in adjacent time intervalBy the b of multiple periods_ijT () is integrated into one Period, the relational expression between passenger flow streaming rate between adjacent time interval can be converted into following form：

Above formula is turned to the matrix form of standard, can obtain systematic observation equation is：

Wherein, O (t) is that outbound moment matrix is tieed up in n × 1；H (t) serves as reasonsThe passenger flow of determination goes out Stand and reach matrix, it characterizes the correlation between state variable and observational variable with period dynamic change, is n × R_odDimension square Battle array；It is by passenger flow streaming rate average in continuous time sectionThe R of structure_od× 1 dimension matrix；V (t) is outbound amount equation Systematic error matrix, and V (t)~N (0, R (t)), R (t) they are outbound amount varivance matrix, expression is produced when setting up observational equation Raw error variance, observation error variance sample value V (t) that can be in historical data carries out statistical analysis and obtains, its nothing Estimate that expression formula is as follows partially：

V_kT () represents t-th history observation error of period of kth day,For the history of continuous n days observe error mean.

Step6：Kalman filtering algorithm is solved：Kalman filtering algorithm is the classical method for solving of state-space model, It is actually a kind of autoregression data processing algorithm of optimization, it is assumed that state vector B (t) of arbitrary period t has two Plant estimate, i.e. priori estimatesAnd posterior estimateThe basic thought of Kalman filtering algorithm is：Arbitrarily The OD estimates of period tIt is in prior estimateOn the basis of, by the further amendment of systematic perspective measured value O (t) And try to achieve, and period t priori estimatesAlways with the posterior estimate of t-1 periodsBased on carry out Improve.Its iteration recursion is concretely comprised the following steps：

1) system initialization：Definition covariance matrix is P (t)；Initialization t=1；DefinitionP(1) =[1]_n×n；Wherein, initial time period t=1 is to run the 1st of day estimation time period, namely [T₀, T₀+ Δ t], T₀Represent subway Run the initial time of day；Initial OD passenger flow streaming rate B (1) can be understood as the 1st posteriority passenger flow streaming rate of estimation period, It is the basis of Kalman filtering iterative algorithm, but B (1) is difficult to be obtained by real-time data collection, generally using historical data In the initial time period passenger flow shunting rate matrix average replacement of continuous k week；B^k(1) it is by the forward direction under the conditions of identical passenger flow characteristic day The all history passenger flow streaming rates of kthThe R of composition_od× 1 dimension matrix；

Initial covariance matrix P (1) can be understood as the 1st posteriority covariance matrix of estimation period, because P (1) is difficult Obtained with by real-time data collection or historical data statistical analysis, therefore, P (1) can be set into unit matrix.

2) prior estimate is carried out according to state transition equation；

Wherein,The priori estimates of state variable B (t) of period t are represented,Represent the shape of period t-1 The posterior estimate of state variable B (t-1)；

3) prior estimate covariance matrix is calculated；

Wherein,Represent the prior estimate error variance of period t；Represent the Posterior estimator of period t-1 Error variance；

4) Kalman filtering gain is calculated；

5) according to Kalman filtering gain and the residual GM priori estimates of estimate and observationAfter obtaining Test estimateIt is based on the solution of the standard Kalman filtering method of state-space model：

6) Posterior estimator covariance matrix is updated；

Above step is the standard step of kalman filter method.It should be noted that in Metro Network passenger flow OD During dynamic estimation, the estimate of state variable B (t) need to meet equality constraintTherefore, can be in step 6) before performing, using Standardization Act to step 5) the OD estimated results that obtain are modified：

In formula,It is state variable passenger flow streaming rate b_ijThe posterior estimate of (t),It is to be entered using Standardization Act The revised passenger flow streaming rate estimate of row.

Obtain concretely comprising the following steps for correction result：

Object function is minimised as with mean square error, can be obtained：

Wherein | | | | represent two norms of vector；Be by correcting after passenger flow streaming rateThe R of composition_od× 1 dimension square Battle array, it is Kalman filtering standard step gained estimateOn the basis of, repaiied by the gained after Mean Square Error adjustment The vector of positive estimate composition；EquationIt is revised state vectorThe equality constraint equation that should be met, Y For scalar matrix is tieed up in n × 1, its element value is 1；X is n × R_odDimension matrix, its element value is as follows：

In above formula, zeros functions are the matrix for producing element value to be all 0.

For object function builds Lagrange condition function, can obtain：

Wherein, Z is the Lagrange condition function for building；β is Lagrange multiplier vector；P (B (t) | O (t)) it is condition Probability density function.

Here, it will be assumed that initial system state variable B (1), W (t), V (t) are joint gaussian variable, with reference to Kalman The property of filtering：When B (1), W (t), V (t) are joint gaussian variable, then Kalman Filter Estimation valueIt is that condition is The conditional mean of the B (t) of O (t), can obtain：

Then respectively in formula (1.24)First derivation is carried out with β, can be solved：

Then, amendment step is achieved that the amendment of standard Kalman filtering algorithm estimated result more than.In every meter Calculate the passenger flow streaming rate estimate of some period tAfterwards, then it is modified using above method, to ensure Passenger flow streaming rate estimate meets equality constraint.

Step7：Method of estimation is checked：The estimate that Step6 is obtained is tested using sample data, if failing to pass through Inspection, then in returning to abovementioned steps, reset rolling average when hop count R, the isoparametric values of weight coefficient α；If by inspection Test, it is determined that the time series predicting model set up is effective, can be used for actual track traffic operation and management.

Using standardization weighted root mean square error criterion (Weighted Root Mean Square Error Normalized, WRMSN) validity for estimating model is assessed, WRMSN index expression formulas are as follows：

Wherein, R_odRepresent network OD sums；N is station sum；b_ij(t) andGauze passenger flow in respectively period t Streaming rate actual value and gauze passenger flow streaming rate estimate average；RMSN values are lower, show to estimate that model is more accurate.

When the RMSN achievement datas calculated according to sample data actual value and estimate in allowed limits (such as Then think that method is feasible during RMSN≤20%), can apply to actual rail transportation operation management；If RMSN values are excessive Then reset the when hop count R and weight coefficient γ of rolling average_kValue, repeat set up estimate model the step of until model By validity check.

The method of Reparametrization is：

Calculate：

In formula,It is the when hop count iteration step length for pre-setting, andIt is integer；τ is the weight coefficient iteration for pre-setting Step-length, τ ＜ 1.

It should be noted that when k is small, showing it closer to actual passenger flow data, its γ_kValue resetting When, can increase it, conversely, when k is larger, its γ_kValue when resetting, can reduce it.

The above is only the preferred embodiment of the present invention, it should be pointed out that：For the ordinary skill people of the art For member, under the premise without departing from the principles of the invention, some improvements and modifications can also be made, these improvements and modifications also should It is considered as protection scope of the present invention.

Claims (5)

1. a kind of Urban Rail Transit passenger flow OD method for dynamic estimation, it is characterised in that：Comprise the following steps：

(1-1) setting time interval of delta t, at timed intervals Δ t daily history passenger flow data is segmented；Statistics is each daily Stored-value ticket passenger flow data and one-way ticket passenger flow data in time period；

(1-2) is improved using the method for moving average to one-way ticket passenger flow data, and the one-way ticket passenger flow data after being improved is：

$q_{0ij}\left(t\right)=\frac{\underset{a=0}{\overset{R}{\Σ}}{q}_{0ij}^{*}(t-a)}{R}---\left(1.1\right)$

In formula, i ≠ j；q_0ijFinal slave site j is outbound t () represents the passenger entered the station by website i in t-th period after improving in One-way ticket passengers quantity；Represent and entered by website i in the t-a period obtained by history passenger flow data statistics Final slave site j outbound one-way ticket passengers quantity in the passenger for standing；R represents the period number of rolling average, and R ＜ t；

(1-3) is calculatedIn formula,Represent the t obtained by history passenger flow trip data statistics Final slave site j outbound stored-value ticket passengers quantity, q in the passenger entered the station by website i in the individual period_ijT () is represented at t-th The passenger flow entered the station by website i in section goes to the outbound total passengers quantities of website j；

According to q_ij(t) build all fronts net entered the station within t-th time period passenger flow OD distribution matrixs A (t) and t-th time period in Passenger flow streaming rate matrix B (t)：

$A\left(t\right)=\left\{\begin{array}{cccc}0& q_{12}\left(t\right)& \mathrm{...}& q_{1n}\left(t\right)\\ q_{21}\left(t\right)& 0& \mathrm{...}& \mathrm{...}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ q_{n1}\left(t\right)& \mathrm{...}& \mathrm{...}& 0\end{array}\right\}---\left(1.2\right)$

$B\left(t\right)=\left\{\begin{array}{cccc}0& b_{12}\left(t\right)& \mathrm{...}& b_{1n}\left(t\right)\\ b_{21}\left(t\right)& 0& \mathrm{...}& \mathrm{...}\\ \mathrm{...}& \mathrm{...}& \mathrm{...}& \mathrm{...}\\ b_{n1}\left(t\right)& \mathrm{...}& \mathrm{...}& 0\end{array}\right\}---\left(1.3\right)$

Wherein, n is the sum of website；b_ijT () is passenger flow streaming rate, to represent and go to j stations in the passenger entered the station by i stations in period t Passenger flow account for i stations and always enter the station the ratio of passenger flow,And

Passenger flow streaming rate matrix B (t) is changed into the form of column vector：

B (t)=[b₁₂(t), b₁₃(t) ..., b_1n(t) ..., b₂₁(t) ..., b_2n(t) ..., b_n(n-1)(t)]^T (1.4)

(1-4) builds the outbound coefficient that reaches of passenger flow：

${\mathrm{\δ}}_{ij}^{t-m}\left(t\right)=\underset{0}{\overset{\mathrm{\Δ}t}{\∫}}\underset{(m-1)\mathrm{\Δ}t+y}{\overset{m\mathrm{\Δ}t+y}{\∫}}\frac{f_{ij}\left(x\right)}{\mathrm{\Δ}t}dxdy=\frac{1}{\mathrm{\Δ}t}\underset{0}{\overset{\mathrm{\Δ}t}{\∫}}\underset{(m-1)\mathrm{\Δ}t+y}{\overset{m\mathrm{\Δ}t+y}{\∫}}\frac{1}{\sqrt{2\mathrm{\π}}\mathrm{\δ}}{e}^{-\frac{{\[x-u_{ij}(t-m)\]}^2}{2{z_{ij}}^2\left(t\right)}}dxdy---\left(1.5\right)$

Wherein,It is the outbound arrival coefficient of passenger flow, represents that slave site i sets out and with station j as mesh within the t-m period Ground OD passenger flows in the ratio of purpose station j, t >=m are reached in period t；u_ijT () represents t Passenger's average travel time at j stations is gone to being stood by i in the individual time period,Represent and left for by i stations in t-th time period Toward the standard variance of passenger's average travel time at j stations；f_ijX () is probability density function, represent and j stations are gone to being stood by i Passenger flow reaches the probability at j stations in moment x；

(1-5) is based on the constraint equation that real-time passenger flow data is set up between OD bus traveler assignments ratio and flow out of the station：

$I_i(t-m)=\underset{j=1,j\≠i}{\overset{n}{\Σ}}{q}_{ij}(t-m)---\left(1.6\right)$

q_ij(t-m)=I_i(t-m)·b_ij(t-m) (1.7)

$O_j\left(t\right)=\underset{m=0}{\overset{M}{\Σ}}\underset{i=1,i\≠j}{\overset{n}{\Σ}}{I}_i(t-m)\·b_{ij}(t-m)\·{\mathrm{\δ}}_{ij}^{t-m}\left(t\right)+V_{ij}\left(t\right)---\left(1.8\right)$

In formula, I_i(t-m) passengers quantity that always enters the station for i stations within the t-m period；q_ij(t-m) represent in the t-m period The passenger flow entered the station by website i goes to the total passengers quantities of website j；O_jT () represents outbound passenger numbers of the station j within t-th period Amount；M is hop count when any two time intersegmental passenger's journey time maximum is crossed in gauze；V_ijT () is to set up traffic constraints side The outbound amount error produced during journey；

(1-6) builds passenger flow OD dynamic estimation state-space models, including state transfer using passenger flow streaming rate as state variable Equation 1.9 and observational equation 1.10：

$\left\{\begin{array}{c}B\left(t\right)=F\left(t\right)B(t-1)+G^1\left(t\right)B^1+G^2\left(t\right)B^2\left(t\right)+\mathrm{...}{G}^p\left(t\right)B^p\left(t\right)+W\left(t\right)\\ =F\left(t\right)B(t-1)+\underset{k=1}{\overset{p}{\Σ}}{G}^k\left(t\right)B^k\left(t\right)+W\left(t\right)\\ B\left(t\right)={\[b_{ij}\left(t\right)\]}_{R_{od}\×1},B^k\left(t\right)={\[b_{ij}^k\left(t\right)\]}_{R_{od}\×1}\\ F\left(t\right)=(1-{\mathrm{\γ}}_1-{\mathrm{\γ}}_2-\mathrm{...}-{\mathrm{\γ}}_k)I_{R_{od}\×R_{od}},G^k\left(t\right)={\mathrm{\γ}}_k{I}_{R_{od}\×R_{od}}\\ W\left(t\right)={\[w_{ij}\]}_{R_{od}\×1}\end{array}\right.---\left(1.9\right)$

$\left\{\begin{array}{c}O\left(t\right)=H\left(t\right)\stackrel{\‾}{B}\left(t\right)+V\left(t\right)\\ O\left(t\right)={\[O_j\left(t\right)\]}_{n\×1}\\ H\left(t\right)={\[h_{ij}\]}_{n\×R_{od}},h_{ij}=\underset{m=0}{\overset{M}{\Σ}}\underset{i=1,i\≠j}{\overset{n}{\Σ}}{I}_i(t-m)\·{\mathrm{\δ}}_{ij}^{t-m}\left(t\right)\\ \stackrel{\‾}{B}\left(t\right)={\[{\stackrel{\‾}{b}}_{ij}\left(t\right)\]}_{R_{od}\×1},{\stackrel{\‾}{b}}_{ij}\left(t\right)=\underset{m=0}{\overset{M}{\Σ}}{b}_{ij}(t-m)/(M+1)\\ V\left(t\right)={\[v_{ij}\left(t\right)\]}_{n\×1}\end{array}\right.---\left(1.10\right)$

In formula (1.9), B (t) is actual passenger flow streaming rate b_ijThe R of (t) composition_od× 1 dimension matrix, R_odRepresent the sum of OD pairs, R_od =n × (n-1)；B^kT () is by the forward direction kth week history passenger flow streaming rate under the conditions of identical passenger flow characteristic dayComposition R_od× 1 dimension matrix；F (t) and G^kT () is state-transition matrix, characterize the state evolution feature of system, is by weight coefficient γ_kThe R for obtaining_od×R_odDimension scalar matrix；W (t) is to set up the error w produced by systematic state transfer equation_ij(t) composition White noise matrix；

In formula (1.10), O_j(t) and I_i(t-m) it is real-time passenger flow data out of the station；O (t) is that outbound passenger flow moment matrix is tieed up in n × 1；H T () is the outbound arrival matrix of passenger flow, it characterizes the phase between state variable B (t) and observational variable O (t) with period dynamic change Mutual relation, is n × R_odDimension matrix；Be byThe R of structure_od× 1 dimension matrix,It is comprising present period and preceding To the M passenger flow streaming rate average of continuous time section；V (t) is to set up the error v produced by systematic observation equation_ij(t) composition White noise matrix；

(1-7) is solved using kalman filter method to passenger flow OD dynamic estimation state-space models, and using standardization Method is modified to OD estimated results；Index is set up according to revised OD estimated results, and the visitor built with the index test Whether stream OD dynamic estimations state-space model is correct；If assay is correct, passenger flow OD dynamic estimation state spaces are judged Model is correct, exports the estimated result of passenger flow OD dynamic estimation state-space models；If assay is incorrect, reset The parameter value of passenger flow OD dynamic estimation state-space models, return to step (1-6)；The parameter for resetting includes：Rolling average When hop count R and weight coefficient γ_k。

2. a kind of Urban Rail Transit passenger flow OD method for dynamic estimation according to claim 2, it is characterised in that institute Stating the step of step (1-6) is middle to build passenger flow OD dynamic estimation state-space models is：

(2-1) sets up the intersegmental passenger flow streaming rate relation of adjacent time：

$\begin{array}{c}{b}_{ij}\left(t\right)=(1-{\mathrm{\γ}}_1-{\mathrm{\γ}}_2-...{\mathrm{\γ}}_n)b_{ij}(t-1)+{\mathrm{\γ}}_1{b}_{ij}^1\left(t\right)+{\mathrm{\γ}}_2{b}_{ij}^2\left(t\right)+...{\mathrm{\γ}}_n{b}_{ij}^k\left(t\right)+w_{ij}\left(t\right)\\ =(1-{\mathrm{\γ}}_1-{\mathrm{\γ}}_2-...{\mathrm{\γ}}_n)b_{ij}(t-1)+\underset{k=1}{\overset{p}{\Σ}}{\mathrm{\γ}}_k{b}_{ij}^k\left(t\right)+w_{ij}\left(t\right)\end{array}---\left(1.11\right)$

In formula,It is t-th time period obtained by identical passenger flow characteristic day ventrocephalad kth week history passenger flow data statistics Passenger flow streaming rate；γ_kIt is weight coefficient, 0≤γ_k≤ 1, for weighing the preceding reliability to kth week history passenger flow information；W_ij T () is normal distribution white Gaussian noise variable, the state Transfer Error produced when building state transition equation for characterizing；

(2-2) the intersegmental passenger flow streaming rate relational expression of adjacent time is converted to the matrix form of standard, obtains state transfer side Cheng Wei：

$\begin{array}{c}B\left(t\right)=F\left(t\right)B(t-1)+G^1\left(t\right)B^1\left(t\right)+G^2\left(t\right)B^2\left(t\right)+\mathrm{...}{G}^p\left(t\right)B^p\left(t\right)+W\left(t\right)\\ =F\left(t\right)B(t-1)+\underset{k=1}{\overset{p}{\Σ}}{G}^k\left(t\right)B^k\left(t\right)+W\left(t\right)\end{array}---\left(1.12\right)$

In formula, W (t) is to set up the error w produced by systematic state transfer equation_ijThe white noise matrix of (t) composition, and W (t)~ N (0, Q (t)), Q (t) are state Transfer Error variance, and the error variance produced during state transition equation is set up in expression, Q's (t) Unbiased esti-mator expression formula is as follows：

$Q\left(t\right)=\frac{1}{p-1}\underset{k=1}{\overset{p}{\Σ}}\[W_k\left(t\right)-\stackrel{\‾}{W}\left(t\right)\]{\[W_k\left(t\right)-\stackrel{\‾}{W}\left(t\right)\]}^T---\left(1.13\right)$

In formula, W_kT () represents the t-th historic state Transfer Error of period of forward direction kth week under identical passenger flow characteristic day, It is the historic state Transfer Error average of p days；

(2-3) by the approximate passenger flow streaming rate instead of day part of the passenger flow streaming rate average value in adjacent time interval, by formula (1-8) Expression formula be converted to following form：

$O_j\left(t\right)=\[\underset{m=0}{\overset{M}{\Σ}}\underset{i=1,i\≠j}{\overset{n}{\Σ}}{I}_i(t-m)\·{\mathrm{\δ}}_{ij}^{t-m}\left(t\right)\]\·{\stackrel{\‾}{b}}_{ij}\left(t\right)+v_{ij}\left(t\right)---\left(1.14\right)$

The observational equation of state-space model is as available from the above equation：

$O\left(t\right)=H\left(t\right)\stackrel{\‾}{B}\left(t\right)+V\left(t\right)---\left(1.15\right)$

In formula, V (t) is observational equation error matrix, and V (t)~N (0, R (t)), R (t) are outbound amount varivance matrix, table Show the error variance produced when setting up observational equation, the unbiased esti-mator expression formula of R (t) is：

$R\left(t\right)=\frac{1}{p-1}\underset{k=1}{\overset{P}{\Σ}}\[V_k\left(t\right)-\stackrel{\‾}{V}\left(t\right)\]\[{\left(V_k\right(t)-\stackrel{\‾}{V}(t)\]}^T---\left(1.16\right)$

In formula, V_kT () represents t-th observational equation history error matrix of period of kth day,For the history of continuous n days are observed Error mean.

3. a kind of Urban Rail Transit passenger flow OD method for dynamic estimation according to claim 3, it is characterised in that institute Use kalman filter method is solved and is used standard to passenger flow OD dynamic estimation state-space models in stating step (1-7) Change method is modified to OD estimated results, is the step of draw optimal estimation value：

It is P (t) that (3-1) defines covariance matrix；Initialization t=1；DefinitionP (1)=[1]_n×n；

Wherein, B^k(1) it is by the forward direction kth week history passenger flow streaming rate under the conditions of identical passenger flow characteristic dayThe R of composition_od× 1 dimension matrix；

(3-2) carries out prior estimate according to state transition equation：

${\hat{B}}^{-}\left(t\right)=F\left(t\right){\hat{B}}^{+}(t-1)+\underset{k=1}{\overset{p}{\Σ}}{G}^k\left(t\right)B^k\left(t\right)+W\left(t\right)---\left(1.17\right)$

In formula,T-th priori estimates of state variable B (t) of period is represented,Represent the t-1 period The posterior estimate of state variable B (t-1)；

(3-3) calculates prior estimate covariance matrix；

${\hat{P}}^{-}\left(t\right)=F\left(t\right){\hat{P}}^{+}(t-1)F^T\left(t\right)+Q\left(t\right)---\left(1.18\right)$

Wherein,Represent t-th prior estimate covariance matrix of period；Represent that the posteriority of the t-1 period is estimated Meter covariance matrix；

(3-4) calculates Kalman filtering gain；

$K\left(t\right)={\hat{P}}^{-}\left(t\right)H^T\left(t\right){\[H\left(t\right){\hat{P}}^{-}\left(t\right)H^T\left(t\right)+R\left(t\right)\]}^{-1}---\left(1.19\right)$

(3-5) is according to Kalman filtering gain and the residual GM priori estimates of estimate and observationObtain posteriority Estimate It is based on the solution of the standard Kalman filtering method of state-space model：

${\hat{B}}^{+}(t-1)={\hat{B}}^{-}\left(t\right)+K\left(t\right)\[O\left(t\right)-H{\hat{B}}^{-}\left(t\right)\]---\left(1.20\right)$

The constraint amendment of (3-6) standard Kalman filtering method estimate：During OD dynamic estimations, state variable B (t) need to expire Sufficient equation (1.21) constrains, and formula (1.21) is：

$\underset{j=1,j\≠i}{\overset{n}{\Σ}}{b}_{ij}\left(t\right)=1---\left(1.21\right)$

Object function is minimised as with mean square error, can be obtained：

$\left\{\begin{array}{c}\min E\left(\right|\left|B\right(t)-\tilde{B}(t\left)\right|{|}^2\left|O\right(t\left)\right),\tilde{B}\left(t\right)={\[{\tilde{b}}_{ij}\left(t\right)\]}_{R_{od}\×1}\\ X\tilde{B}\left(t\right)=Y\end{array}\right.---\left(1.22\right)$

Wherein | | | | represent two norms of vector；Be by correcting after passenger flow streaming rateThe R of composition_od× 1 dimension matrix, it It is Kalman filtering standard step gained estimateOn the basis of, estimate by the gained amendment after Mean Square Error adjustment The vector of evaluation composition；EquationIt is revised state vectorThe equality constraint equation that should be met, Y be n × 1 dimension scalar matrix, its element value is 1；X is n × R_odDimension matrix；

For the restricted problem that formula (1.22) is represented builds Lagrange condition function, can obtain：

$\begin{array}{c}Z=E\left(\right|\left|B\right(t)-\tilde{B}(t\left)\right|{|}^2\left|O\right(t\left)\right)-2{\mathrm{\β}}^T\left(X\tilde{B}\right(t)-Y)\\ =\∫B^T\left(t\right)B\left(t\right)P\left(B\right(t\left)\right|O\left(t\right))dB\left(t\right)-2\tilde{B}\left(t\right)\∫B\left(t\right)P\left(B\right(t\left)\right|O\left(t\right))dB\left(t\right)\\ +{\[\tilde{B}\left(t\right)\]}^T\tilde{B}\left(t\right)+2{\mathrm{\β}}^T\left(X\tilde{B}\right(t)-Y)\end{array}---\left(1.23\right)$

Wherein, Z is the Lagrange condition function for building；β is Lagrange multiplier vector；P (B (t) | O (t)) it is conditional probability Density function；

Assuming that initial system state variable B (1), W (t), V (t) they are joint gaussian variable, with reference to the property of Kalman filtering：Work as B (1) when, W (t), V (t) they are joint gaussian variable, Kalman Filter Estimation valueBe condition be O (t) B (t) condition it is equal Value, can obtain：

${\hat{B}}^{+}\left(t\right)=\∫B\left(t\right)P\left(B\right(t\left)\right|O\left(t\right))dB\left(t\right)---\left(1.24\right)$

Then respectively in formula (1.23)First derivation is carried out with β, can be solved：

$\tilde{B}\left(t\right)={\hat{B}}^{+}\left(t\right)-X^T{\left(XX\right)}^{-1}\left(X{\hat{B}}^{+}\right(t)-Y)---\left(1.25\right)$

(3-7) updates Posterior estimator covariance matrix；

${\hat{P}}^{+}\left(t\right)=\[I-K\left(t\right)H\left(t\right)\]{\hat{P}}^{-}\left(t\right)---\left(1.26\right)$

4. a kind of Urban Rail Transit passenger flow OD method for dynamic estimation according to claim 3, it is characterised in that institute State in step (1-7) and index is set up according to revised OD estimated results, and dynamically estimated with the passenger flow OD that the index test builds Whether counting the correct step of state-space model is：

(4-1) builds Normalized RMSE index：

$RMSN=\sqrt{R_{od}\underset{i=1}{\overset{n}{\Σ}}\underset{j=1}{\overset{n}{\Σ}}{\[b_{ij}\left(t\right)-{\tilde{b}}_{ij}\left(t\right)\]}^2}/\[\underset{i=1}{\overset{n}{\Σ}}\underset{j=1}{\overset{n}{\Σ}}{b}_{ij}\left(t\right)\]---\left(1.26\right)$

RMSN values are lower, show to estimate that model is more accurate；

Whether (4-2) judges the value of RMSN less than default threshold value RMSN_minIf meeting RMSN ＜ RMSN_min, then the visitor is judged Stream OD dynamic estimation state-space models are correct；Otherwise, it is determined that the passenger flow OD dynamic estimation state-space models are incorrect.

5. a kind of Urban Rail Transit passenger flow OD method for dynamic estimation according to claim 4, it is characterised in that institute State in step (1-7), the method for Reparametrization is：

Calculate：

In formula,It is the when hop count iteration step length for pre-setting, andIt is integer；τ is the weight coefficient iteration step for pre-setting It is long, τ ＜ 1.