CN110674111A - Tensor decomposition-based vehicle missing travel time filling method - Google Patents
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Abstract
The invention relates to a missing travel time filling method based on tensor decomposition. The method comprises the following steps: firstly, preprocessing original bayonet data; step two, filling up missing travel time; constructing an S201 tensor; s203, calculating an initial solution for the input of the HOOI method by adopting high-order singular value decomposition; s202, Tucker decomposition of the travel time tensor; and S204, iteratively calculating a final solution by adopting an HOOI method. By the method, the filling efficiency is improved, and meanwhile, the filling accuracy is improved.
Description
Technical Field
The invention relates to the field of intelligent transportation, in particular to a missing travel time filling method based on tensor decomposition.
Background
As an important traffic parameter, the travel time can be used as one of the metrics of the travel quality of people, and can also be used as a data support in traffic planning, so that a decision support is provided for a traffic control department to deal with the increasingly severe traffic jam problem. In recent years, with the gradual improvement of a road intersection monitoring system, intersection data plays an increasingly important role in an intelligent transportation system, and travel time can be acquired from the intersection data. However, due to the inherent defects of the equipment and the influence of the environment, the travel time extracted from the original checkpoint data often has the phenomena of abnormality and deficiency, and the overall state of the road network cannot be effectively evaluated, so a method for supplementing the evaluation of the road network state is needed.
In order to solve the problems, the invention provides a tensor decomposition-based vehicle missing travel time filling method in consideration of the multi-dimensional characteristics of traffic data.
Disclosure of Invention
The patent is based on the above requirements of the prior art, and the technical problems to be solved by the invention are as follows: the method for filling the missing travel time of the vehicle based on tensor decomposition is provided, so that the accuracy of filling the travel time is improved.
In order to solve the technical problem, the technical scheme provided by the patent comprises the following steps. A tensor resolution-based method for filling travel time for a vehicle, the method comprising the steps of:
step one, preprocessing original bayonet data
The original data of the card gate comprises original data obtained from card gate points set in a road network; preprocessing the original bayonet data comprises;
and (4) extracting the bayonet A from the original bayonet data during bayonet timing1、A2Obtaining the length L of the road section1(ii) a Extracting all records of vehicles with the same ID from original checkpoint data to obtain travel time T1And calculating the section average speed of the vehicle
If it exceeds 80% of V1According to the average speed of the roadDetermining the time of the bayonet equipment to be accurate, otherwise, recalibrating the time;
extracting three-dimensional data of a bayonet serial number, a license plate number and vehicle passing time in the original data and recording the data into a database; removing unidentified data of license plate numbers in the original data; removing repeated data caused by high-frequency shooting of the red notes;
inquiring road network information covered by all the checkpoints to form a road network section information table, and constructing a road network on the basis of a map;
using the formula
Calculated over a time window T1-T2Average travel time Δ T of inner road section, M represents the number of vehicles, TmRepresents a link travel time of the mth vehicle;
step two, filling up missing travel time
Constructing an S201 tensor; firstly, constructing travel time tensor of current time
N in three dimensions1Is a road section, n2Is the number of days, n3Is a time window; x (n)1,n2,n3) A denotes all vehicles at the n-th2Day time period n3Inner passing road section n1The travel time of (a);
s202, Tucker decomposition of the travel time tensor; travel time tensor X is approximately equal to sigma1R1×2R2×3R3(ii) a Wherein, σ ═ r1×r2×r3Is the core tensor, R1＝r1×n1Factor matrix, R, being road section dimensions2＝r2×n2Factor matrix in the dimension of days, R3＝r3×n3A factor matrix being a dimension of a time window, whereinnIs a modal product, representing the multiplication of a matrix by a tensor;
s203 adopts high-order singular value decomposition to calculate initial solution for input of HOOI method
1) Inputting travel time tensor X and factor matrix R of three dimensions1、R2、R3；
2) For dimension factor matrix Ri(i ═ 1,2,3), there is one decomposition in each case, so thatWherein M isiIs ri×riOrder matrix, NiIs ni×niThe order of the matrix is such that,
is a diagonal matrix and is uniquely determined, wherein i is the dimension of the matrix, and n represents the iteration number; are respectively to R1、R2、R3Performing singular value decomposition to obtain
3) Will be provided with
As an input value for the next operation; update the travel time tensor so that
S204, iterative computation of final solution by adopting HOOI method
1) Inputting the travel time tensor X acquired in the previous step1Obtained by singular value decomposition of a three-factor matrix
Determining the maximum iteration times;
2) let n be 1, n is defined as,
will be provided with
And X1Respectively substituted into to obtain
To pair
Performing singular value decomposition to obtain
Order to
3) Checking the iteration times, and outputting X if the iteration times reach the maximum iteration timesn+1Otherwise go to 4);
4) to XnChecking, if the error is less than 10s, outputting Xn+1Otherwise, go to 5);
5) repeating the calculation in 2) for n ═ n + 1;
x of the final outputn+1I.e. the filling value.
By the method, the filling efficiency is improved, and meanwhile, the filling accuracy is improved.
Drawings
FIG. 1 is a schematic diagram of a Tucker of a travel time tensor X;
FIG. 2 is a flow diagram of missing travel time padding based on the Tucker decomposition;
FIG. 3 is a timing flow chart of a bayonet;
FIG. 4 is a schematic diagram of tensor construction;
FIG. 5 is a road network construction diagram;
FIG. 6 is a flowchart of the HOVSD algorithm;
fig. 7 is a flow chart of the HOOI algorithm.
Detailed Description
The specific embodiment relates to a missing travel time filling method based on tensor decomposition; the method specifically comprises a preprocessing method of checkpoint data, a calculation method of vehicle travel time and a missing travel time filling method based on Tucker decomposition.
Original bayonet data and preprocessing method thereof
(1) The original bayonet data containing information
The method comprises the steps that whether the travel time of a road section is calculated in a city road network or a road network in a partial region, original data required for calculation are obtained from a bayonet point set in the road network, and the quality of bayonet data is difficult to guarantee due to the factors of working defects of bayonet equipment, changeability of traffic conditions, weather conditions and the like, so that the bayonet data are simply verified and cleaned, and if the conditions that a license plate cannot be identified or identified repeatedly and the like occur, the travel time of the road section is greatly influenced.
The original bayonet data information is rich, and the method specifically comprises the following steps: vehicle information such as license plate, vehicle type, traveling direction, vehicle speed, vehicle exterior length, license plate color, and card information such as card slot number and card slot position.
The original bayonet data is stored in a file form, and records generated based on time series are shown in table 1:
bayonet data recording table
(2) Preprocessing method of bayonet data
1) Time correction of bayonet
For the original data obtained from the fixed bayonet, because the fixed-point installation and the starting time of each bayonet are different, the accuracy verification of the bayonet time is needed to be firstly carried out so as to determine whether all the bayonets are at the same time point of the same system. The specific process is as follows:
① extracting Bayonet A from original Bayonet data1、A2Obtaining the length L of the road section1；
② extracting all the records of vehicles with the same ID from the original gate data to obtain the travel time T1And calculating the section average speed of the vehicle:
③ if it exceeds 80% V1According with the range of the average speed of the road section, namely considering the time of the bayonet device as accurate, otherwise returning to the step (1) after calibrating the time;
④ proceed to the next data cleaning after ensuring that all bayonet devices are time accurate.
2) Data cleansing
The bayonet data cleaning refers to checking and cleaning abnormal data, and the specific process is as follows:
①, extracting an effective data sequence, namely extracting three-dimensional data of a bayonet serial number, a license plate number and vehicle passing time in the original data and recording the three-dimensional data into a database;
② removing abnormal records, removing unidentified data of license plate number in the original data;
③, removing the repeated data, namely removing the repeated data caused by the high-frequency shooting of the red note, wherein the repeated data is characterized in that the bayonet data contains completely same records, covers the related attributes such as license plate and passing time, and therefore, in the time sequence, the adjacent records should remove other completely same data except different time.
3) Road network construction
Inquiring the road network information covered by all the checkpoints specifically comprises the following steps: the road length, the driving direction, the road speed limit, the gate position and the number form a road network road information table shown in table 2, and a road network is constructed on the basis of a map.
Road network section information table
| Starting position bayonet number | End position bayonet number | Road section length (meter) |
4) Calculation of link travel time
The average travel time of the road section is the average value of the travel times of vehicles passing through two intersections in sequence in a certain time interval, and the average travel time of the road section is calculated by adopting an average method to establish a time window:
divide a day into 48 time windows, in time window T1-T2Vehicles passing through bayonets 1 and 2 are M, and vehicle n1,n2,…nmRespectively, is t1,t2,…tmThus, the link average travel time is:
lack of travel time
Because of the error of the detector and the deviation of the vehicle passing time, the travel time of vehicles on different road sections in the same time window is lost to different degrees, and the travel time of individual days is completely lost. The traveling time loss ratio calculated by the detection result of the existing bayonet equipment is about 30-40%. Data stuffing calculations are therefore required.
Missing travel time filling based on Tucker decomposition
Aiming at the characteristic of multi-dimensionality of traffic data, the method adopts Tucker decomposition to fill the travel time. The Tucker decomposition decomposes the tensor into 1 set of matrices and 1 core tensor. Each matrix represents a base in 1 direction, and the bases in each direction are related through the core tensor, so that an approximate value of original data can be reconstructed through the matrix in each direction and 1 core tensor.
(1) Tensor construction
Firstly, constructing travel time tensor of current time
N in three dimensions1Is a road section, n2Is the number of days, n3Is a time window; x (n)1,n2,n3) A denotes all vehicles at the n-th2Day time period n3Inner passing road section n1The travel time of (a);
since most vehicles pass through only a part of the road links in the road network in each time slot, tensor X obtained by extracting travel time from missing datanIs a sparse tensor, with non-zero elements only accounting for a very small fraction. Then we propose a method using tensor decomposition to fill the tensor of travel time, and then obtain the travel time of all vehicles passing any link in any time period.
(2) Tucker decomposition of travel time tensors
X≈σ×1R1×2R2×3R3
Wherein, σ ═ r1×r2×r3Is the core tensor, R1＝r1×n1Factor matrix, R, being road section dimensions2＝r2×n2Factor matrix in the dimension of days, R3＝r3×n3A factor matrix being a dimension of a time window, whereinnThe representation matrix is a modal product multiplied by the tensor.
(3) Computing an initial solution using a HOSVD method
1) Inputting travel time tensor X and factor matrix R of three dimensions1、R2、R3；
2) For dimension factor matrix Ri(i ═ 1,2,3), there is one decomposition, so thatTo obtain
Wherein M isiIs ri×riOrder matrix, NiIs ni×niThe order of the matrix is such that,
is a diagonal matrix and is uniquely determined, wherein i is the dimension of the matrix and n represents the iteration number.
Are respectively to R1、R2、R3Performing singular value decomposition to obtain
3) Because the predicted value obtained by the HOSVD method has lower precision, but can be used as the initial solution of the HOOI iterative algorithm
As an input value for the next operation. Update the travel time tensor so that
(4) Calculating the final solution by using HOOI method
1) Inputting the travel time tensor X acquired in the previous step1Obtained by singular value decomposition of a three-factor matrix
Determining the maximum iteration times;
2) let n be 1, n is defined as,
will be provided withAnd X1Respectively substituted into to obtain
To pair
Performing singular value decomposition to obtain
Order to
3) Checking the iteration times, and outputting X if the iteration times reach the maximum iteration timesn+1Otherwise go to 4)
4) To XnChecking, if the error is less than 10s, outputting Xn+1Otherwise, go to 5);
5) the calculation in 2) is repeated for n ═ n + 1.
X of the final outputn+1I.e. the filling value.
The method for filling the missing travel time of the vehicle based on tensor decomposition is further explained by combining with an example. Let's data in Ruian city, Zhejiang province be taken as an example.
(1) The system time of the card port data is calibrated, and the calibration process is shown in fig. 2, and the specific operations are as follows:
① extracting Bayonet A from original Bayonet data1、A2Obtaining the length L of the road section1；
② extracting all the records of vehicles with the same ID from the original gate data to obtain the travel time T1And calculating the section average speed of the vehicle:
③ if it exceeds 80% V1In accordance with the range of average speeds of the road section, i.e. when considered as a bayonet deviceThe time is accurate, otherwise, returning to (1) after the calibration time;
④ proceed to the next data cleaning after ensuring that all bayonet devices are time accurate.
(2) And cleaning the data, extracting an effective data sequence and removing abnormal records and repeated data.
(3) The road network is reconstructed according to the road section length, the driving direction, the road section speed limit, the gate position and the serial number according to the electronic map, as shown in fig. 3.
(4) Consider a first time window, using
And calculating the average travel time of the road section to obtain the travel time of the road section. To verify the accuracy of the data population, a relatively complete piece of data was selected, some of which were set to 0, and the following table 3 was obtained (original data in parentheses):
road average travel time table (part)
| Day1 | Day2 | Day3 | Day4 | Day5 | |
| Section a | 77.1667 | 77.25 | 0(78.83) | 89.3529 | 0(69.9545) |
| Section b | 0(75) | 103.125 | 99 | 97.3333 | 106 |
| Section c | 101.9 | 0(100) | 102 | 101 | 92.7 |
| Section d | 0(83.75) | 83.4167 | 75.8667 | 0(81.4524) | 76.0909 |
Regarding 0 as a numerical value missing, the next filling is performed.
① constructing the travel time tensor of the current time
In FIG. 4, the three dimensions are n1(road section), n2(days) and n3(time window);
② As shown in FIG. 1, the travel time tensor X is subjected to a Tucker decomposition:
X≈σ×1R1×2R2×3R3
wherein, σ ═ r1×r2×r3Is the core tensor, R1＝r1×n1Factor matrix, R, being road section dimensions2＝r2×n2Factor matrix in the dimension of days, R3＝r3×n3A factor matrix being a dimension of a time window, whereinnThe representation matrix is a modal product multiplied by the tensor.
③ the HOSVD method is used to calculate the initial solution:
1) inputting travel time tensor X and factor matrix R of three dimensions1、R2、R3；
2) For dimension factor matrix Ri(i ═ 1,2,3), there is one decomposition in each case, so that
Wherein M isiIs ri×riOrder matrix, NiIs ni×niThe order of the matrix is such that,
is a diagonal matrix and is uniquely determined, wherein i is the dimension of the matrix and n represents the iteration number.
Are respectively to R1、R2、R3Performing singular value decomposition to obtain
3) Because the predicted value obtained by the HOSVD method has lower precision, but can be used as the initial solution of the HOOI iterative algorithm
As an input value for the next operation. Update the travel time tensor so that
④ the HOOI method is used to calculate the final solution:
1) inputting the travel time tensor X acquired in the previous step1Obtained by singular value decomposition of a three-factor matrixDetermining the maximum iteration times;
2) let n be 1, n is defined as,
will be provided with
And X1Respectively substituted into to obtain
To pair
Performing singular value decomposition to obtain
Order to
3) Checking the iteration times, and outputting X if the iteration times reach the maximum iteration timesn+1Otherwise go to 4)
4) To XnChecking, if the error is less than 10s, outputting Xn+1Otherwise, go to 5);
5) the calculation in 2) is repeated for n ═ n + 1.
X of the final outputn+1I.e. the filling value.
The filling results are shown in table 4:
data fill results
Mean error
The method is verified to be accurate, wherein the average error rate in a single time window is 5.1735s, and the error rate is 5.88%.
Claims (1)
1. A tensor decomposition-based vehicle travel time filling method, comprising the steps of:
step one, preprocessing original bayonet data
The original data of the card gate comprises original data obtained from card gate points set in a road network; preprocessing the original bayonet data comprises;
and (4) extracting the bayonet A from the original bayonet data during bayonet timing1、A2Obtaining the length L of the road section1(ii) a Extracting all records of vehicles with the same ID from original checkpoint data to obtain travel time T1And calculating the section average speed of the vehicle
If it exceeds 80% of V1According with the range of the average speed of the road section, namely judging that the time of the gate equipment is accurate, otherwise, recalibrating the time;
extracting three-dimensional data of a bayonet serial number, a license plate number and vehicle passing time in the original data and recording the data into a database; removing unidentified data of license plate numbers in the original data; removing repeated data caused by high-frequency shooting of the red notes;
inquiring road network information covered by all the checkpoints to form a road network section information table, and constructing a road network on the basis of a map;
using the formula
Calculated over a time window T1-T2Average travel time Δ T of inner link, M representsNumber of vehicles, tmRepresents a link travel time of the mth vehicle;
step two, filling up missing travel time
The second step comprises the steps of,
s201 tensor construction, namely constructing the travel time tensor of the current time
N in three dimensions1Is a road section, n2Is the number of days, n3Is a time window; x (n)1,n2,n3) A denotes all vehicles at the n-th2Day time period n3Inner passing road section n1The travel time of (a);
s202 Tucker decomposition of travel time tensor, X ≈ sigma-1R1×2R2×3R3(ii) a Wherein, σ ═ r1×r2×r3Is the core tensor, R1＝r1×n1Factor matrix, R, being road section dimensions2＝r2×n2Factor matrix in the dimension of days, R3＝r3×n3A factor matrix being a dimension of a time window, whereinnIs a modal product, representing the multiplication of a matrix by a tensor;
s203 adopts high-order singular value decomposition to calculate initial solution for input of HOOI method
1) Inputting travel time tensor X and factor matrix R of three dimensions1、R2、R3；
2) For dimension factor matrix Ri(i ═ 1,2,3), there is one decomposition in each case, so that
Wherein M isiIs ri×riOrder matrix, NiIs ni×niThe order of the matrix is such that,
is a diagonal matrix and is uniquely determined, itWherein i is the dimension of the matrix, and n represents the iteration times; are respectively to R1、R2、R3Performing singular value decomposition to obtain
3) Will be provided with
As an input value for the next operation; update the travel time tensor so that
S204, iterative computation of final solution by adopting HOOI method
1) Inputting the travel time tensor X acquired in the previous step1Obtained by singular value decomposition of a three-factor matrix
Determining the maximum iteration times;
2) let n be 1, n is defined as,
will be provided with
And X1Respectively substituted into to obtain Y1 1、Y1 2、Y1 3(ii) a To pair
Performing singular value decomposition to obtain
Order to
3) Checking the iteration times, if soOutputting X to the maximum iteration numbern+1Otherwise go to 4);
4) to XnChecking, if the error is less than 10s, outputting Xn+1Otherwise, go to 5);
5) repeating the calculation in 2) for n ═ n + 1;
x of the final outputn+1I.e. the filling value.
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