CN104517159A - Method for predicting short-time passenger flow of bus - Google Patents

Abstract

The invention discloses a method for predicting short-time passenger flow of a bus. The method comprises the following steps of gathering passenger data of IC (integrated circuit) cards of the bus according to a preset time interval (such as 5 minutes); establishing corresponding time sequences on the basis of time scales of weeks, days and time intervals; analyzing stability, seasonality and heteroscedasticity of the time sequences; establishing corresponding time sequence models according to characteristics of the time sequences; and establishing a hybrid model to precisely predict the passenger flow by using a Kalman filtering and interacting multi-model algorithm according to a prediction result of a single model. In the method for predicting the short-time passenger flow of the bus, time varying characteristics of the passenger flow of urban buses on different time scales are considered sufficiently. Compared with the traditional non-parameter model, the time sequence models in the method are high in prediction precision.

Description

The Forecasting Methodology of a kind of public transport passenger flow in short-term

Technical field

What the present invention relates to is traffic system, and what be specifically related to is the Forecasting Methodology of a kind of public transport passenger flow in short-term, belongs to intelligent transport system field.

Background technology

In time, bus passenger flow prediction in short-term plays an important role in the configuration of public transport marshalling, the formulation of transit scheduling and intelligent bus dispatching accurately.Traditional bus passenger flow prediction, the time scale chosen comparatively large (being generally the year, month, day volume of the flow of passengers), the secular trend of main research passenger flow change, are generally used for public bus network planning.Existing passenger flow estimation in short-term mainly based on nonparametric technique, such as K-NN method.The method model is simple, but easily affected by noise, is only applicable to predict comparatively stable bus passenger flow.Artificial Neural Network (ANN) also achieves good effect for passenger flow estimation, but for the passenger flow estimation of larger data amount, the precision of prediction of neural network is lower, and cannot describe the time-varying characteristics of bus passenger flow.Be that the step real-time estimate that the time series models of representative are applied to passenger flow in short-term can obtain higher precision of prediction with arma modeling.But single model only can a kind of feature of matching passenger flow data, is difficult to the different qualities that matching bus passenger flow exists on Different time scales.

Summary of the invention

The object of the invention is to the deficiency overcoming prior art existence, the Forecasting Methodology of a kind of public transport passenger flow is in short-term provided, utilize the historical data of bus passenger flow, set up the time series on Different time scales, by analysis time, the time-varying characteristics of sequence set up corresponding forecast model, Kalman filtering and interacting multiple algorithm is utilized to set up mixture model, to obtain the effect improving predictablity rate.

For reaching above object, solution of the present invention is:

A Forecasting Methodology for public transport passenger flow in short-term, it comprises the following steps:

1) the bus passenger flow historical data obtained from Based on Bus IC Card Data was polymerized by the time interval of specifying;

2) from week, day and the time interval three time scale sequences Time Created;

3) proving time sequence stationarity and seasonality, and further heteroscedasticity is verified to nonstationary time series, sets up corresponding time series predicting model according to seasonal effect in time series time varying characteristic, respectively passenger flow is predicted;

4) predicting the outcome based on single model, utilizes Kalman filtering and interacting multiple algorithm to set up hybrid prediction model;

5) described forecast model is utilized to predict bus passenger flow in short-term.

Further, utilize the bus IC card card reader that bus is installed, read charge time and the circuit ID of passenger, utilize automatic station reporting system of bus (Automated Voice Annunciation System simultaneously, AVAS) bus station data are obtained, take time as critical field, by the card using information of passenger and automatic station name announcing system (Automated Voice AnnunciationSystem, AVAS) site information in carries out Data Matching, the bus passenger flow historical data described in acquisition.

Further, for a certain public bus network, the bus passenger flow historical data in fixed time interval (as 5min) is polymerized, obtains the passenger flow data at this public bus network fixed time interval.

Further, described step 3) further comprising the steps:

A, the hangover of checking time sequence autocorrelation function and partial autocorrelation function, truncation characteristic carry out ADF (AugmentedDickey-Fuller) inspection, the stationarity of proving time sequence, seasonality, the heteroscedasticity of preliminary identification non-stationary series;

B, according to seasonal effect in time series time varying characteristic, arma modeling is set up to stationary time series, SARIMA model is set up to seasonal time series, ARIMA model is set up to nonstationary time series, according to AIC (Akaike InformationCriterion) criterion and SC (Schwarz Criterion) criterion, determine best lag order and the difference order of time series predicting model;

C, carries out ARCH-LM inspection to the nonstationary time series that there is heteroscedasticity, sets up ARIMA-GARCH composite model further;

D, utilizes RLS (Recursive Least Square) algorithm to carry out parameter to the time series models set up and noise is estimated, plant noise is white noise sequence;

E, utilizes the forecast model of Different time scales to carry out passenger flow estimation, exports three groups of sequences that predict the outcome.

Further, described time series predicting model comprises:

A, sets up arma modeling to stable time-of-week sequence:

Wherein, y _wfor bus passenger flow time-of-week sequence; a _wfor white noise sequence; be respectively auto-regressive parameter and running mean parameter;

B, to there is the SARIMA model that the seasonal Time of Day sequence cycle of setting up is 24:

Wherein, y _dfor bus passenger flow Time of Day sequence; a _dfor white noise sequence; be respectively auto-regressive parameter and running mean parameter;

C, sets up ARIMA-GARCH composite model to the non-stationary time interval sequence that there is heteroscedasticity:

${\mathrm{\σ}}_t^2={\mathrm{\θ}}_{m0}+{\mathrm{\θ}}_{m1}*a_m(t-1)+{\mathrm{\ψ}}_{m1}*{\mathrm{\σ}}_{t-1}^2$

Wherein, y _mfor bus passenger flow is by the time series of fixed time interval composition; a _mfor white noise sequence; for auto-regressive parameter; θ _m, ψ _mbe respectively white noise parameter and the variance parameter of GARCH model, for white noise sequence variance.

Further, described step 4) further comprising the steps:

A, according to the validity that single model prediction sequence is predicted at Different periods, computation model probability vector also sets up state-transition matrix;

B, is rewritten as state space form by above-mentioned forecast model:

y(t+1)＝F _j(t)*y(t)+G _j(t)*w(t)

z(t)＝H _j(k)*y(t)+v(t)

Wherein: y is state vector, F _jt () is for corresponding to the state-transition matrix of model j, G _jfor the noise matrix of model j, w is input white noise, and z is observation vector, H _jfor observing matrix, v is observation white noise;

C, utilizes interacting multiple algorithm to set up hybrid prediction model, and wherein utilize Kalman filtering to complete model state and upgrade, utilization state transition matrix implementation model is mutual, exports hybrid predicting result.

Further, described interacting multiple algorithm is further comprising the steps:

A, input is mutual:

Suppose the filter state in known t-1 moment covariance matrix P _i(t|t) and model probability vector μ _i(t-2) known, i, j ∈ [1,3],

${\mathrm{\μ}}_{\mathrm{ij}}(t-1|t-1)=P\left(m_i(t-1)\right|m_j\left(t\right))=\frac{1}{\stackrel{\‾}{c_j}}{\mathrm{\π}}_{\mathrm{ij}}{\mathrm{\μ}}_i(t-1)$

$\stackrel{\‾}{c_j}={\mathrm{\Σ}}_{i=1}^3{\mathrm{\π}}_{\mathrm{ij}}{\mathrm{\μ}}_i(t-1)$

${\hat{\hat{y}}}_j(t-1|t-1)={\mathrm{\Σ}}_{i=1}^3{\hat{y}}_i(t-1|t-1){\mathrm{\μ}}_{\mathrm{ij}}(t-1|t-1)$

${\hat{P}}_j(t-1|t-1)={\mathrm{\Σ}}_{i=1}^3[P_i(t-1|t-1)+({\hat{y}}_i(t-1|t-1)-{\hat{\hat{y}}}_j(t-1|t-1)({\hat{y}}_i(t-1|t-1)-{\hat{\hat{y}}}_j{(t-1|t-1)}^T]{\mathrm{\μ}}_{\mathrm{ij}}(t-1|t-1)$

Wherein: μ _ij(t-1|t-1) for the t-1 moment to be transferred to the probability of model j from model i, for the effective probability of model j, for state input value, for covariance input value;

B, model filtering:

${\hat{y}}_i\left(t\right|t-1)=F_i(t-1){\hat{\hat{y}}}_i\left(t\right|t-1)$

$P_i\left(t\right|t-1)=F_i(t-1){\hat{P}}_i(t-1|t-1){\left(F_i(t-1)\right)}^T+G_i(t-1)Q_i(t-1){\left(G_i(t-1)\right)}^T$

Residual error:

${\tilde{z}}_i\left(t\right)=z\left(t\right)-H_i\left(t\right){\hat{y}}_i\left(t\right|t-1)$

Residual covariance:

S _i(t)＝H _i(t)P _i(t|t-1)(H _i(t)) ^T+Q _i(t)

Filter gain:

K _i(t)＝P _i(t|t-1)(H _i(t)) ^T(S _i(t)) ^-1

State-updating:

${\hat{y}}_i\left(t\right|t)={\hat{y}}_i\left(t\right|t-1)+K_i\left(t\right){\tilde{z}}_i\left(t\right)$

Covariance matrix update:

P _i(t|t)＝P _i(t|t-1)-K _i(t)S _i(t)(K _i(t)) ^T

Wherein, Q _ifor the input noise variance matrix of model i;

C, model probability upgrades:

Likelihood function:

${\mathrm{\Λ}}_i\left(t\right)={\left|2\mathrm{\π}{S}_i\left(t\right)\right|}^{-1/2}\exp \{-\frac{1}{2}{\left({\tilde{z}}_i\left(t\right)\right)}^T{\left(S_i\left(t\right)\right)}^{-1}{\tilde{z}}_i\left(t\right)\}$

Model probability upgrades:

${\stackrel{\‾}{c}}_i={\mathrm{\Σ}}_{j=1}^3{\mathrm{\π}}_{\mathrm{ij}}{\mathrm{\μ}}_j(t-1)$

$c={\mathrm{\Σ}}_{j=1}^3{\mathrm{\Λ}}_j\left(t\right){\stackrel{\‾}{c}}_j$

${\mathrm{\μ}}_i\left(t\right)=\frac{1}{c}{\mathrm{\Λ}}_i\left(t\right){\stackrel{\‾}{c}}_i$

D, mixing exports:

T state estimation exports:

${\hat{y}}^{\mathrm{IMM}}\left(t\right|t)={\mathrm{\Σ}}_{i=1}^3{\hat{y}}_i\left(t\right|t){\mathrm{\μ}}_i\left(t\right)$

T covariance matrix:

$P^{\mathrm{IMM}}\left(t\right|t)={\mathrm{\Σ}}_{i=1}^3[P_i\left(t\right|t)+({\hat{y}}^{\mathrm{IMM}}\left(t\right|t)-{\hat{y}}_i\left(t\right|t)){({\hat{y}}^{\mathrm{IMM}}\left(t\right|t)-{\hat{y}}_i\left(t\right|t))}^T]{\mathrm{\μ}}_i\left(t\right)$

E, enters next circulation recurrence calculation.

The present invention sets up the time series of bus passenger flow in short-term with Different time scales, sets up corresponding model and portrays stationarity, periodicity and the heteroscedasticity that data represent on Different time scales, can follow the trail of the data characteristics of bus passenger flow in short-term better; Utilize interacting multiple algorithm implementation model mutual, the advantage of the comprehensive single model of hybrid prediction model energy of foundation simultaneously, and by the adverse effect that Kalman filtering algorithm control abnormal data brings, therefore there is higher precision of prediction and reliability.Application example shows that the inventive method is better than existing method in every evaluation index.

Accompanying drawing explanation

Fig. 1 is method flow diagram of the present invention.

Fig. 2 is the predicting the outcome of bus passenger flow in week age in embodiment.

Embodiment

Elaborate to embodiments of the invention below, the present embodiment, premised on invention technical scheme, gives detailed implementation method and specific operation process, but protection scope of the present invention is not limited to following embodiment.

Choosing bus passenger flow in Shenzhen No. 54 bus 6:30-22:45 time period in August, 2013 to November is the embodiment of the present invention.With 15 minutes for time interval polymerization bus passenger flow data, 66 data samples can be obtained every day.Above-mentioned steps 1-5 is utilized to carry out bus passenger flow prediction in short-term.First three time serieses are set up with week, day and 15 minutes for yardstick, the time-varying characteristics of analysis data on Different time scales.Then according to time series characteristic, corresponding ARMA (2,2), SARIMA (2,0,3) (1,0,0) is set up ²⁴and ARIMA (2,1,0)-GARCH (1,1) model, utilize RLS algorithm to carry out parameter and noise estimation, output model predicts the outcome.Finally utilize interacting multiple algorithm to set up mixture model and accurately predicting is carried out to passenger flow.

Fig. 2 illustrates the predicting the outcome of bus passenger flow in week age on November 18 to November 24 of intercepting predicted data from August to November.

In order to the advantage of the inventive method on precision of prediction is described better, adopt mean absolute error (MAE), root-mean-square error (RMSE), average absolute percentage error (MAPE) and absolute percentage error variance (VAPE) to evaluate predicting the outcome, and compare (seeing the following form) with predicting the outcome of traditional K-NN, ARMA and ANN method.

$\mathrm{MAE}=\frac{1}{N}{\mathrm{\Σ}}_1^N|{\hat{y}}_i-y_i|$

$\mathrm{RMSE}=\sqrt{\frac{1}{N}{\mathrm{\Σ}}_1^N{({\hat{y}}_i-y_i)}^2}$

$\mathrm{MAPE}=\frac{1}{N}{\mathrm{\Σ}}_1^N\left|\frac{{\hat{y}}_i-y_i}{y_i}\right|$

$\mathrm{VAPE}=\sqrt{\frac{N{\mathrm{\Σ}}_1^N{\left(\frac{|{\hat{y}}_i-y_i|}{y_i}\right)}^2-{\left[{\mathrm{\Σ}}_1^N\frac{|{\hat{y}}_i-y_i|}{y_i}\right]}^2}{N(N-1)}}$

Precision of prediction comparison sheet

Comparative result shows, the method that the present invention proposes is better than traditional prediction method on precision of prediction.

Above-described specific embodiment; object of the present invention, technical scheme and beneficial effect are further described; be understood that; the foregoing is only specific embodiments of the invention; be not limited to the present invention; within the spirit and principles in the present invention all, any amendment made, equivalent replacement, improvement etc., all should be included within protection scope of the present invention.

Claims (7)

1. a Forecasting Methodology for public transport passenger flow in short-term, is characterized in that: it comprises the following steps:

1) the bus passenger flow historical data obtained from Based on Bus IC Card Data was polymerized by the time interval of specifying;

2) from week, day and the time interval three time scale sequences Time Created;

3) proving time sequence stationarity and seasonality, and further heteroscedasticity is verified to nonstationary time series, sets up corresponding time series predicting model according to seasonal effect in time series time varying characteristic, respectively passenger flow is predicted;

4) predicting the outcome based on single model, utilizes Kalman filtering and interacting multiple algorithm to set up hybrid prediction model;

5) described forecast model is utilized to predict bus passenger flow in short-term.

2. the Forecasting Methodology of public transport according to claim 1 passenger flow in short-term, it is characterized in that, utilize the bus IC card card reader that bus is installed, read charge time and the circuit ID of passenger, utilize automatic station reporting system of bus to obtain bus station data simultaneously, take time as critical field, the site information in the card using information of passenger and automatic station name announcing system is carried out Data Matching, the bus passenger flow historical data described in acquisition.

3. the Forecasting Methodology of public transport according to claim 1 passenger flow in short-term, is characterized in that, for a certain public bus network, the bus passenger flow historical data in fixed time interval be polymerized, obtain the passenger flow data at this public bus network fixed time interval.

4. the Forecasting Methodology of public transport according to claim 1 passenger flow in short-term, is characterized in that, described step 3) further comprising the steps:

A, the hangover of checking time sequence autocorrelation function and partial autocorrelation function, truncation characteristic carry out ADF inspection, the stationarity of proving time sequence, seasonality, the heteroscedasticity of preliminary identification non-stationary series;

B, according to seasonal effect in time series time varying characteristic, sets up arma modeling to stationary time series, SARIMA model is set up to seasonal time series, ARIMA model is set up to nonstationary time series, according to AIC criterion and SC criterion, determines best lag order and the difference order of time series predicting model;

C, carries out ARCH-LM inspection to the nonstationary time series that there is heteroscedasticity, sets up ARIMA-GARCH composite model further;

D, utilizes the forecast model of Different time scales to carry out passenger flow estimation, exports three groups of sequences that predict the outcome.

5. the Forecasting Methodology of bus passenger flow in short-term according to claim 1, it is characterized in that, described time series predicting model comprises:

1) arma modeling is set up to stable time-of-week sequence:

Wherein, y _wfor bus passenger flow time-of-week sequence; a _wfor white noise sequence; θ _wbe respectively auto-regressive parameter and running mean parameter;

2) to there is the SARIMA model that the seasonal Time of Day sequence cycle of setting up is 24:

Wherein, y _dfor bus passenger flow Time of Day sequence; a _dfor white noise sequence; θ _dbe respectively auto-regressive parameter and running mean parameter;

3) ARIMA-GARCH composite model is set up to the non-stationary time interval sequence that there is heteroscedasticity:

${\mathrm{\σ}}_t^2={\mathrm{\θ}}_{m0}+{\mathrm{\θ}}_{m1}*a_m(t-1)+{\mathrm{\ψ}}_{m1}*{\mathrm{\σ}}_{t-1}^2$

Wherein, y _mfor bus passenger flow is by the time series of fixed time interval composition; a _mfor white noise sequence; for auto-regressive parameter; θ _m, ψ _mbe respectively white noise parameter and the variance parameter of GARCH model, for white noise sequence variance.

6. the Forecasting Methodology of public transport according to claim 1 passenger flow in short-term, is characterized in that, described step 4) further comprising the steps:

A, according to the validity that single model prediction sequence is predicted at Different periods, computation model probability vector also sets up state-transition matrix;

B, is rewritten as state space form by above-mentioned forecast model:

y(t+1)＝F _j(t)*y(t)+G _j(t)*w(t)

z(t)＝H _j(k)*y(t)+v(t)

Wherein: y is state vector, F _jt () is for corresponding to the state-transition matrix of model j, G _jfor the noise matrix of model j, w is input white noise, and z is observation vector, H _jfor observing matrix, v is observation white noise;

C, utilizes interacting multiple algorithm to set up hybrid prediction model, and wherein utilize Kalman filtering to complete model state and upgrade, utilization state transition matrix implementation model is mutual, exports hybrid predicting result.

7. the Forecasting Methodology of public transport according to claim 1 passenger flow in short-term, it is characterized in that, described interacting multiple algorithm is further comprising the steps:

A, input is mutual:

Suppose the filter state in known t-1 moment covariance matrix P _i(t|t) and model probability vector μ _i(t-2) known, i, j ∈ [1,3],

${\mathrm{\μ}}_{\mathrm{ij}}(t-1|t-1)=P\left(m_i(t-1)\right|m_j\left(t\right))=\frac{1}{\stackrel{\‾}{c_j}}{\mathrm{\π}}_{\mathrm{ij}}{\mathrm{\μ}}_i(t-1)$

$\stackrel{\‾}{c_j}={\mathrm{\Σ}}_{i=1}^3{\mathrm{\π}}_{\mathrm{ij}}{\mathrm{\μ}}_i(t-1)$

${\hat{\hat{y}}}_j(t-1|t-1)={\mathrm{\Σ}}_{i=1}^3{\hat{y}}_i(t-1|t-1){\mathrm{\μ}}_{\mathrm{ij}}(t-1|t-1)$

${\hat{P}}_j(t-1|t-1)={\mathrm{\Σ}}_{i=1}^3[P_i(t-1|t-1)+({\hat{y}}_i(t-1|t-1)-{\hat{\hat{y}}}_j(t-1|t-1)({\hat{y}}_i(t-1|t-1)-{\hat{\hat{y}}}_j{(t-1|t-1)}^T]{\mathrm{\μ}}_{\mathrm{ij}}(t-1|t-1)$

Wherein: μ _ij(t-1|t-1) for the t-1 moment to be transferred to the probability of model j from model i, for the effective probability of model j, for state input value, for covariance input value;

B, model filtering:

${\hat{y}}_i\left(t\right|t-1)=F_i(t-1){\hat{\hat{y}}}_i\left(t\right|t-1)$

$P_i\left(t\right|t-1)=F_i(t-1){\hat{P}}_i(t-1|t-1){\left(F_i(t-1)\right)}^T+G_i(t-1)Q_i(t-1){\left(G_i(t-1)\right)}^T$

Residual error:

${\tilde{z}}_i\left(t\right)=z\left(t\right)-H_i\left(t\right){\hat{y}}_i\left(t\right|t-1)$

Residual covariance:

S _i(t)＝H _i(t)P _i(t|t-1)(H _i(t)) ^T+Q _i(t)

Filter gain:

K _i(t)＝P _i(t|t-1)(H _i(t)) ^T(S _i(t)) ^-1

State-updating:

${\hat{y}}_i\left(t\right|t)={\hat{y}}_i\left(t\right|t-1)+K_i\left(t\right){\tilde{z}}_i\left(t\right)$

Covariance matrix update:

P _i(t|t)＝P _i(t|t-1)-K _i(t)S _i(t)(K _i(t)) ^T

Wherein, Q _ifor the input noise variance matrix of model i;

C, model probability upgrades:

Likelihood function:

${\mathrm{\Λ}}_i\left(t\right)={\left|2\mathrm{\π}{S}_i\left(t\right)\right|}^{-1/2}\exp \{-\frac{1}{2}{\left({\tilde{z}}_i\left(t\right)\right)}^T{\left(S_i\left(t\right)\right)}^{-1}{\tilde{z}}_i\left(t\right)\}$

Model probability upgrades:

${\stackrel{\‾}{c}}_i={\mathrm{\Σ}}_{j=1}^3{\mathrm{\π}}_{\mathrm{ij}}{\mathrm{\μ}}_j(t-1)$

$c={\mathrm{\Σ}}_{j=1}^3{\mathrm{\Λ}}_j\left(t\right){\stackrel{\‾}{c}}_j$

${\mathrm{\μ}}_i\left(t\right)=\frac{1}{c}{\mathrm{\Λ}}_i\left(t\right){\stackrel{\‾}{c}}_i$

D, mixing exports:

T state estimation exports:

${\hat{y}}^{\mathrm{IMM}}\left(t\right|t)={\mathrm{\Σ}}_{i=1}^3{\hat{y}}_i\left(t\right|t){\mathrm{\μ}}_i\left(t\right)$

T covariance matrix:

$P^{\mathrm{IMM}}\left(t\right|t)={\mathrm{\Σ}}_{i=1}^3[P_i\left(t\right|t)+({\hat{y}}^{\mathrm{IMM}}\left(t\right|t)-{\hat{y}}_i\left(t\right|t)){({\hat{y}}^{\mathrm{IMM}}\left(t\right|t)-{\hat{y}}_i\left(t\right|t))}^T]{\mathrm{\μ}}_i\left(t\right)$

E, enters next circulation recurrence calculation.