CN114254250B - Network vehicle travel demand prediction method considering space-time non-stationarity - Google Patents
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Abstract
The patent belongs to the technical field of intelligent transportation, and discloses a network vehicle travel demand prediction method considering space-time non-stationarity, which comprises the following steps: step one, traffic cell division, step two, network vehicle demand and built environment data extraction; extracting a common factor by a factor analysis method; step four: and (5) calculating a space-time geographic weighted regression model. The method can extract a smaller number of main factors from the original built environment factors, predicts the travel demands of the network about vehicles based on space-time geographic weighted regression, considers the space-time non-stationarity of the network about vehicle demands, retains the information of original variables as much as possible, and simultaneously makes the main factors uncorrelated, thereby avoiding the influence of collinearity among the original independent variables, improving the calculation efficiency of the model, and providing a reference basis for the advance formulation of more targeted strategies of urban traffic managers and network about vehicle companies.
Description
Technical Field
The invention belongs to the field of intelligent transportation, and particularly relates to a network about vehicle travel demand prediction method considering space-time non-stationarity.
Background
Thanks to the popularity of smart phones, internet-based vehicles are rapidly developing in china as an emerging travel mode. By 2021, 6 months, the user scale of the Chinese net about car reaches 3.97 hundred million, more than 400 cities in the whole country are covered, the total order quantity exceeds 43.1 hundred million, and the net about car becomes one of main travel modes of residents in the Chinese city. However, the space-time non-stationarity of the travel demands of the network about vehicles also causes the phenomena of no-load tour of a large number of network about vehicle drivers, no vehicles nearby passengers and the like, seriously influences the operation efficiency of the network about vehicles, and causes social resource waste. The accurate network vehicle travel demand prediction can help the network vehicle company to dispatch drivers in advance, reduce the idle distance of vehicles, reduce tail gas emission, save waiting time of passengers and effectively improve the travel operation efficiency of the network vehicle.
At present, prediction of travel demands of network about vehicles is mainly based on researching factors such as urban building environment, weather and the like. Traditional demand prediction models include least squares, geographically weighted regression, and the like. The partial model considers space non-stationarity, for example, a geographic weighted regression model adds the space position coordinates of variables on the basis of a least square method, so that the influence of different geographic positions is reflected in the model. Although the space non-stationarity is considered by the model, the network about vehicle travel has obvious time non-stationarity, the network about vehicle travel is concentrated in peak time, and the network about vehicle travel requirement is less in peak time. In order to simultaneously consider the space-time non-stationarity, a space-time geographic weighted regression model is applied to the field of traffic demand prediction in recent years, and compared with the traditional least square method and geographic weighted regression, the space-time geographic weighted regression model has higher prediction precision and is more suitable for traffic demand prediction with obvious space-time non-stationarity. Although the current research based on the space-time geographic weighted regression model simultaneously considers the space-time attribute, the problems of inadequate consideration of influence correlation among different independent variables, reduction of model calculation efficiency when the independent variables are too many and the like still exist.
Aiming at the problems, the method comprises the steps of firstly adopting factor analysis to extract common factors of factors such as the built environment influencing the travel demands of the net about vehicles, then selecting main factors as independent variables according to the principle that the accumulated contribution rate is higher than 80%, realizing independent variable dimension reduction, and finally predicting the travel demands of the net about vehicles based on a space-time geographic weighted regression model. The method considers the space-time non-stationarity of the travel of the network about vehicles, can improve the calculation efficiency of the model, avoids the co-linearity influence among the original independent variables, and provides a reference basis for the advance formulation of more targeted strategies of urban traffic managers and network about vehicle companies.
Disclosure of Invention
The invention aims to solve the technical problems that: the defect of the prior art is overcome, and a network vehicle travel demand prediction method is provided.
The technical scheme of the invention is as follows: a network about vehicle travel demand prediction method considering space-time non-stationarity comprises the following steps:
Step one: traffic cell division
Firstly, dividing a research area into a plurality of traffic cells, wherein the dividing mode can be divided into street and village division and grid division.
Step two: network appointment vehicle demand and build environment data extraction
The network vehicle data in this step comes from the network vehicle platform order data, and the data includes: order number, departure time, longitude and latitude and other information. Network taxi data is then used to calculate the network taxi demand for each traffic cell at different time periods, typically one hour or one day in length.
The built environment data is calculated based on urban point of interest (POI) data, and the built environment density of each traffic cell is obtained through calculation.
Step three: factor analysis method for extracting common factor
And extracting the common factors of the original built environment variables in the traffic cell by using a factor analysis method. Assume that there are N traffic cells, each with M build environment variables.
1) Data normalization
The data of the original built environment variables are converted into dimensionless data by using a z-score standardization method, and the standardized formula is as follows:
Where x ij is the ith variable value of the jth traffic cell, For the average value of the ith variable, σ i is the standard deviation of the ith variable, and z ij is the value after normalization of the ith variable of the jth traffic cell.
Average value ofAnd standard deviation sigma i as follows:
2) Calculating a correlation coefficient matrix and checking
After data normalization, correlation coefficients between the variables are calculated for checking the correlation between the variables. The correlation coefficient r ip between the i-th variable and the p-th variable is calculated as follows:
Where z ij is the value after normalization of the ith variable of the jth traffic cell, The mean value after normalization for the ith variable.
Since there are M variables in total, after calculating the correlation coefficient between each variable, the correlation coefficient matrix R of all the variables can be obtained:
The common factors are extracted, a certain correlation exists between variables, and if the correlation is too weak, the common factors cannot be extracted. Therefore, correlation between variables needs to be checked, and if most of the coefficients in the correlation matrix are greater than 0.3 and pass the bat Li Qiuti test, then the description factor analysis is applied to these variables.
3) Calculating the eigenvalue of the correlation coefficient matrix and the contribution rate of the common factors
And obtaining the characteristic value of the matrix through the characteristic equation of the correlation coefficient matrix. The characteristic equation is as follows:
|λI-R|＝0
wherein lambda is a eigenvalue and I is an identity matrix
Through the eigenvalue, λ 1,λ2,…,λM, and M eigenvectors, Y 1,Y2,…,YM, are obtained. Y, the common factor in the variables, is a linear combination of the variables and is independent of each other.
Since λ q is the variance of the common factor Y q, the contribution rate of the q-th common factor Y q to the original data is:
Where d q is the contribution rate of the q-th common factor to the original data, and λ q is the characteristic value of the q-th common factor.
After the contribution rates of all the common factors are calculated, the first m common factors with larger contribution rates are selected as main factors according to the principle that the accumulated contribution rate is higher than 80%.
4) Factor load matrix calculation
Since the common factor Y is a linear combination of variables, the common factor can be represented by M normalized variables Z 1,Z2,…,ZM:
Y1＝a11Z1+a21Z2+…+aM1ZM
Yq＝a1qZ1+a2qZ2+…+aMqZM
YM＝a1MZ1+a2MZ2+…+aMMZM
Wherein a Mq is a vector component corresponding to the q-th common factor in the M-th variable, Y 1,Y2,…,YM is arranged from large to small according to the contribution rate, Y 1 contribution rate is maximum, and Y M contribution rate is minimum.
Since the feature roots are orthogonal to each other, the relationship can be transformed into:
Z1＝a11Y1+…+a1qYq+…+a1MYM
Z2＝a21Y1+…+a2qYq+…+a2MYM
ZM＝aM1Y1+…+aMqYq+…+aMMYM
According to the m main factor results selected in the previous step, the first m common factors of each relation are reserved, and the other common factors are replaced by special factors e. The relationship is obtained as follows:
Z1＝a11Y1+…+a1qYq+…+a1mYm+e1
Z2＝a21Y1+…+a2qYq+…+a2mYm+e2
ZM＝aM1Y1+…+aMqYq+…+aMmYm+eM
where e M is a special factor for the M-th variable.
The coefficient in the relation is taken as a matrix, and a load matrix of M x M of the main factor can be obtained
Step four: space-time geographic weighted regression model calculation
Since there are N traffic cells and M variables in total, a built environment variable matrix can be obtained:
Where B N*M is the as-built environment variable matrix of N x M and z NM is the value after normalization of the mth variable of the nth traffic cell.
Converting the original built environment variable based on the load matrix in the third step, so that the built environment variable input into the space-time geographic weighted regression model is converted into a factor analysis extracted main factor:
Wherein a N*m is a principal factor matrix of n×m.
Then, the spatial position, time information and main factor data of the data are input into a space-time geographic weighted regression model, and the formula of the space-time geographic weighted regression model is as follows:
Where F j is the net vehicle demand of the jth sample point, u j is the longitude coordinate of the jth sample point, v j is the latitude coordinate of the jth sample point, t j is the time coordinate of the jth sample point, beta 0(uj,vj,tj) is the intercept of the jth sample point, beta k(uj,vj,tj) is the regression coefficient of the kth main factor at the jth sample point, A jk is the kth main factor of the jth sample point, and epsilon j is the residual term of the jth sample point.
Regression parameters in modelThe calculation formula of (2) is as follows:
Where A T is the transpose of the principal factor matrix and W (u j,vj,tj) is the spatiotemporal matrix of the j-th sample point.
W lj is a space-time decreasing function, and its calculation formula is as follows:
In the method, in the process of the invention, The space-time distance is the space-time bandwidth of the sample point l and the sample point j.
The space-time distance is calculated by the following formula:
where θ is the weight of the spatial distance and μ is the weight of the temporal distance.
The space-time bandwidth is a non-negative variable, typically determined by the minimum cross-validation (CV) value. The calculation formula of CV value is as follows:
Where F j is the actual value of the j-th sample point, and F ≠1 (h) is the predicted value at bandwidth h.
The method can extract a smaller number of main factors from the original built environment factors, predicts the travel demands of the network about vehicles based on space-time geographic weighted regression, considers the space-time non-stationarity of the network about vehicle demands, retains the information of original variables as much as possible, and simultaneously makes the main factors uncorrelated, thereby avoiding the influence of collinearity among the original independent variables, improving the calculation efficiency of the model, and providing a reference basis for the advance formulation of more targeted strategies of urban traffic managers and network about vehicle companies.
Drawings
Fig. 1 is an overall flowchart of a network about vehicle travel demand prediction method considering space-time non-stationarity.
Detailed Description
The invention will be described in further detail with reference to the accompanying drawings. The patent relates to a network about vehicle travel demand prediction method considering space-time non-stationarity, which comprises the following steps.
Step one: traffic cell division
Firstly, dividing a research area into a plurality of traffic cells, wherein the dividing mode can be divided into street and village division and grid division. The distance between the traffic cells takes the distance between the center points of the traffic cells, and the space coordinates of the traffic cells take the coordinates of the center points.
Step two: network appointment vehicle demand and build environment data extraction
The network vehicle data in this step comes from the network vehicle platform order data, and the data includes: order number, departure time, longitude and latitude and other information. Firstly, matching network taxi orders to each traffic cell by using longitude and latitude coordinates in the data, then calculating the number of the network taxi orders of each traffic cell, and finally obtaining the network taxi demands of each traffic cell in different time periods according to the departure time statistics, wherein the time period is usually one hour or one day.
The built environment data is calculated based on urban point of interest (POI) data, firstly, the number of various types of urban POIs in each traffic cell is counted, then the number is divided by the area of the traffic cell, and finally the built environment density of each traffic cell is obtained.
Step three: factor analysis method for extracting common factor
And extracting the original built environment variables in the traffic cell by using a factor analysis method, so that the correlation of the variables in each group after extraction is higher, namely the public factors. The common factors retain as much information as possible of the original variables while being uncorrelated. Assume that there are N traffic cells, each with M build environment variables.
1) Data normalization
The data of the original built environment variables are converted into dimensionless data by using a z-score standardization method, and the standardized formula is as follows:
Where x ij is the ith variable value of the jth traffic cell, For the average value of the ith variable, σ i is the standard deviation of the ith variable, and z ij is the value after normalization of the ith variable of the jth traffic cell.
Average value ofAnd standard deviation sigma i as follows:
2) Calculating a correlation coefficient matrix and checking
After data normalization, correlation coefficients between the variables are calculated for checking the correlation between the variables. The correlation coefficient r ip between the i-th variable and the p-th variable is calculated as follows:
Where z ij is the value after normalization of the ith variable of the jth traffic cell, The mean value after normalization for the ith variable.
Since there are M variables in total, after calculating the correlation coefficient between each variable, the correlation coefficient matrix R of all the variables can be obtained:
The common factors are extracted, a certain correlation exists between variables, and if the correlation is too weak, the common factors cannot be extracted. Therefore, correlation between variables needs to be checked, and if most of the coefficients in the correlation matrix are greater than 0.3 and pass the bat Li Qiuti test, then the description factor analysis is applied to these variables.
3) Calculating the eigenvalue of the correlation coefficient matrix and the contribution rate of the common factors
And obtaining the characteristic value of the matrix through the characteristic equation of the correlation coefficient matrix. The characteristic equation is as follows:
|λI-R|＝0
wherein lambda is a eigenvalue and I is an identity matrix
Through the eigenvalue, λ 1,λ2,…,λM, and M eigenvectors, Y 1,Y2,…,YM, are obtained. Y, the common factor in the variables, is a linear combination of the variables and is independent of each other.
Since λ q is the variance of the common factor Y q, the contribution rate of the q-th common factor Y q to the original data is:
Where d q is the contribution rate of the q-th common factor to the original data, and λ q is the characteristic value of the q-th common factor.
After the contribution rates of all the common factors are calculated, the first m common factors with larger contribution rates are selected as main factors according to the principle that the accumulated contribution rate is higher than 80%.
4) Factor load matrix calculation
Since the common factor Y is a linear combination of variables, the common factor can be represented by M normalized variables Z 1,Z2,…,ZM:
Y1＝a11Z1+a21Z2+…+aM1ZM
Yq＝a1qZ1+a2qZ2+…+aMqZM
YM＝a1MZ1+a2MZ2+…+aMMZM
Wherein a Mq is a vector component corresponding to the q-th common factor in the M-th variable, Y 1,Y2,…,YM is arranged from large to small according to the contribution rate, Y 1 contribution rate is maximum, and Y M contribution rate is minimum.
Since the feature roots are orthogonal to each other, the relationship can be transformed into:
Z1＝a11Y1+…+a1qYq+…+a1MYM
Z2＝a21Y1+…+a2qYq+…+a2MYM
ZM＝aM1Y1+…+aMqYq+…+aMMYM
According to the m main factor results selected in the previous step, the first m common factors of each relation are reserved, and the other common factors are replaced by special factors e. The relationship is obtained as follows:
Z1＝a11Y1+…+a1qYq+…+a1mYm+e1
Z2＝a21Y1+…+a2qYq+…+a2mYm+e2
ZM＝aM1Y1+…+aMqYq+…+aMmYm+eM
where e M is a special factor for the M-th variable.
The coefficient in the relation is taken as a matrix, and a load matrix of M x M of the main factor can be obtained
Step four: space-time geographic weighted regression model calculation
Since there are N traffic cells and M variables in total, a built environment variable matrix can be obtained:
Where B N*M is the as-built environment variable matrix of N x M and z NM is the value after normalization of the mth variable of the nth traffic cell.
Converting the original built environment variable based on the load matrix in the third step, so that the built environment variable input into the space-time geographic weighted regression model is converted into a factor analysis extracted main factor:
Wherein a N*m is a principal factor matrix of n×m.
Then, the spatial position, time information and main factor data of the data are input into a space-time geographic weighted regression model, and the formula of the space-time geographic weighted regression model is as follows:
Where F j is the net vehicle demand of the jth sample point, u j is the longitude coordinate of the jth sample point, v j is the latitude coordinate of the jth sample point, t j is the time coordinate of the jth sample point, beta 0(uj,vj,tj) is the intercept of the jth sample point, beta k(uj,vj,tj) is the regression coefficient of the kth main factor at the jth sample point, A jk is the kth main factor of the jth sample point, and epsilon j is the residual term of the jth sample point.
Regression parameters in modelThe calculation formula of (2) is as follows:
Where A T is the transpose of the principal factor matrix and W (u j,vj,tj) is the spatiotemporal matrix of the j-th sample point.
W lj is a space-time decreasing function, and its calculation formula is as follows:
In the method, in the process of the invention, The space-time distance is the space-time bandwidth of the sample point l and the sample point j.
The space-time distance is calculated by the following formula:
where θ is the weight of the spatial distance and μ is the weight of the temporal distance.
The space-time bandwidth is a non-negative variable, typically determined by the minimum cross-validation (CV) value. The calculation formula of CV value is as follows:
Where F j is the actual value of the j-th sample point, and F ≠1 (h) is the predicted value at bandwidth h.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the application, and is not meant to limit the scope of the application, but to limit the application to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the application are intended to be included within the scope of the application.
Claims (3)
1. A network about vehicle travel demand prediction method considering space-time non-stationarity is characterized by comprising the following steps:
dividing a traffic cell into a target area and a plurality of traffic cells;
Step two, extracting network vehicle demand and built environment data; extracting order numbers, departure time and longitude and latitude information in historical network vehicle-contract data; then calculating the network vehicle demand of each traffic cell in different time periods by using the network vehicle data; calculating and building environment data based on the urban interest point data;
Step three, extracting common factors by factor analysis method
Extracting common factors of original built environment variables in a traffic cell by using a factor analysis method; assuming N traffic cells, each traffic cell has M built environment variables;
s3.1, data standardization, converting the original data of each built environment variable into dimensionless data,
S3.2 calculating a correlation coefficient matrix and checking
Calculating correlation coefficients among the variables after data standardization, and checking correlation among the variables; the calculation formula of the correlation coefficient r ip between the ith variable and the p-th variable is as followsWhere z ij is the value after normalization of the ith variable of the jth traffic cell,Mean value normalized for the ith variable; after calculating the correlation coefficient between each variable, the correlation coefficient matrix of all the variables can be obtainedWherein M is the number of variables; then checking the correlation between the variables;
s3.3 calculating the eigenvalues of the correlation coefficient matrix and the contribution rate of the common factors
Obtaining a characteristic value lambda 1,λ2,…,λM of a matrix and M characteristic vectors Y 1,Y2,…,YM through a characteristic equation |lambda I-R|=0 of a correlation coefficient matrix, wherein lambda is a characteristic value, and I is a unit matrix; y is a common factor in the variables; contribution rate of q-th common factor Y q to original dataWherein d q is the contribution rate of the q-th common factor to the original data, and lambda q is the characteristic value of the q-th common factor; after the contribution rates of all the common factors are obtained through calculation, selecting m common factors with the contribution rates as main factors;
s3.4 sub-load matrix calculation
The common factor is represented by the relationship with M normalized variables Z 1,Z2,…,ZM:
Wherein a Mq is a vector component corresponding to the q-th common factor in the M-th variable, Y 1,Y2,…,YM is arranged from large to small according to the contribution rate, the contribution rate of Y 1 is maximum, and the contribution rate of Y M is minimum;
Converting the relation into:
according to the m main factor results selected in the step S3.3, the first m common factors of each relational expression are reserved, and the other common factors are replaced by a special factor e, so that the relational expression is obtained:
wherein e M is a special factor of the M-th variable;
taking the coefficient in the relation as a matrix to obtain a load matrix of M x M of a main factor
Step four, calculating a space-time geographic weighted regression model
And inputting the spatial position, the time information and the main factor data of the data into a space-time geographic weighted regression model, and predicting the travel demand of the network about vehicles.
2. The network about vehicle travel demand prediction method considering space-time non-stationarity according to claim 1, wherein the formula of the space-time geographic weighted regression model is as follows:
Wherein F j is the net vehicle demand of the jth sample point, u j is the longitude coordinate of the jth sample point, v j is the latitude coordinate of the jth sample point, t j is the time coordinate of the jth sample point, beta 0(uj,vj,tj) is the intercept of the jth sample point, beta k(uj,vj,tj) is the regression coefficient of the kth main factor at the jth sample point, A jk is the kth main factor of the jth sample point, and epsilon j is the residual term of the jth sample point;
Regression parameters in model The calculation formula of (2) is as follows:
Wherein A T is the transpose of the principal factor matrix, and W9 (u j,vj,tj) is the space-time matrix of the j-th sample point;
w lj is a space-time decreasing function, and its calculation formula is as follows:
In the method, in the process of the invention, The space-time distance between the sample point l and the sample point j is the space-time bandwidth;
the space-time distance is calculated by the following formula:
wherein θ is the weight of the spatial distance, and μ is the weight of the temporal distance;
The space-time bandwidth is a non-negative variable, typically determined by a minimum cross-validation (CV) value calculated as follows:
Where F j is the actual value of the j-th sample point, and F ≠1 (h) is the predicted value at bandwidth h.
3. The method for predicting travel demand of net car in consideration of space-time non-stationarity according to claim 1, wherein the z-score normalization method is used in step S3.1, and the normalization formula is as follows: Where x ij is the ith variable value of the jth traffic cell, As the average value of the ith variable, σ i is the standard deviation of the ith variable, and z ij is the value after the standardization of the ith variable of the jth traffic cell; average value ofAnd standard deviation sigma i as follows:
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