CN109035761A

CN109035761A - Travel time estimation method based on back-up surveillance study

Info

Publication number: CN109035761A
Application number: CN201810658375.5A
Authority: CN
Inventors: 孙未未; 章瀚元; 吴昊
Original assignee: Fudan University
Current assignee: Fudan University
Priority date: 2018-06-25
Filing date: 2018-06-25
Publication date: 2018-12-18
Anticipated expiration: 2038-06-25
Also published as: CN109035761B

Abstract

The invention belongs to field of intelligent transportation technology, specially a kind of travel time estimation method based on back-up surveillance study.It finds statistical law from magnanimity historical trajectory data, carries out whole estimation by time of the deep learning model end to end to entire stroke；Step includes: feature extraction and expression stage, is pre-processed to track data, extracts its time and space characteristics, driving condition feature, short time and prolonged traffic condition feature respectively；These features extracted are trained and are predicted with unified bidirectional circulating neural network by trained and forecast period；The each step of Recognition with Recurrent Neural Network all exports the time overhead by current area domain；The summation of the time overhead of these zonules is the time overhead of total path.Meanwhile introducing two-way section loss function also to constrain interlude expense.This method can efficiently and accurately estimate the vehicle travel time in city there is preferable effect under practical circumstances.

Description

Travel time estimation method based on auxiliary supervised learning

Technical Field

The invention belongs to the technical field of intelligent transportation, and particularly relates to a travel time estimation method based on auxiliary supervised learning.

Background

Travel time estimation is an essential important technology in the field of urban traffic, can provide help for travel and commute of people, and can also provide support for government planning decisions. However, this is not a simple and small problem, but is influenced by various dynamic factors, such as traffic dynamics, intersection conditions, changes in driver driving behavior, and historical periodic data evolution. These factors contribute to uncertainty and difficulty in the travel time estimate. With the development and popularization of mobile devices supporting GPS, a great amount of trajectory data is continuously generated and covers all corners of a city. With the massive historical track data, the internal rules behind the data can be mined, and the period and the trend of the change of the travel time are learned by constructing an algorithm model, so that the time overhead required by the current query track can be accurately inferred.

Most of the existing methods adopt a divide-and-conquer (divide-and-conquer) method, mainly by decomposing a path into a series of segments or sub-paths.

(1) Single-road-segment-based methods:

the method based on the single road section mainly estimates the average speed of each single road section when the track passes through, calculates the passing average time cost according to the length of the road section, and finally accumulates the time sum of each road section to obtain the total time. This approach does not take into account the intersection time overhead between road segments. In addition, such estimation relies heavily on high quality velocity data, which is often not available in the trajectory data.

(2) The method based on the sub-path comprises the following steps:

the sub-path based approach mainly divides the path into a series of sub-paths, so that the time overhead of the intersection is also considered. The main idea is to splice and mine rich public sub-path information in historical data. Although this approach may overcome many of the drawbacks of the single-route approach, it is still based on heuristic design rather than directly targeting travel time as an algorithm optimization.

In summary, the methods available today fail to achieve satisfactory accuracy for two reasons. One is that they do not see the path as a whole, but split into sub-blocks. During this splitting process, much useful information is lost. And they do not take full advantage of the intermediate surveillance tags that are unique to the trace data, i.e., the time stamp information for each intermediate GPS sample point. On the other hand, with the development and prosperity of deep learning technology, more problems can be solved in an end-to-end integrated manner, and the method is more efficient compared with the traditional heuristic model. In addition, deep learning has strong characterization capability, and compared with a manual model, the deep learning can capture more potential features and can process various complex dynamics in the travel estimation problem.

Disclosure of Invention

The invention aims to provide a travel time estimation method based on a history track of auxiliary supervision learning aiming at the limitations of the traditional two types of travel time estimation technologies so as to overcome the defects of the prior art.

The method searches for a statistical rule from massive historical track data, and integrally estimates the time of the whole travel through an end-to-end deep learning model. The method comprises the following basic steps: a characteristic extraction and representation stage, wherein the track data is preprocessed, and various characteristics of the track data are respectively extracted; training and predicting stage, training and predicting the extracted features with one unified bidirectional circulating neural network; the time cost of passing through the current small area is output by each step of the recurrent neural network; the sum of the time overhead of the small areas is the time overhead of the total path; for more efficient training, a two-way interval loss function is also introduced to constrain the intermediate time overhead.

The invention provides a travel time estimation method of a historical track based on auxiliary supervised learning, which comprises the following three stages:

and (I) a characteristic extraction and representation stage, namely preprocessing historical track data and extracting various characteristics (including time characteristics, space characteristics, driving state characteristics, short-time and long-time traffic condition characteristics and the like) of the historical track data. The method comprises the following specific steps:

and (1) carrying out fine-grained division on the grids according to longitude and latitude coordinates in the urban range to form adjacent rectangular small areas. And mapping each coordinate point in the track sequence consisting of the GPS coordinates into a corresponding small area according to the chronological sequence to form a sequence consisting of grid coordinates. For the condition that the adjacent track points are far away and fall into discontinuous small areas, the intermediate passing path can be obtained by algorithms such as map matching and the like, and the discontinuous area information is supplemented.

And (2) mining the characteristics of different aspects of each grid. First, latent semantic information is mined using an embedded vector technique. The embedded vector technology is widely used in the fields of natural language processing, social networks and the like, mainly utilizes low-dimensional real number vectors to represent semantic information of each word or thing, and measures the corresponding relation between real objects through the distance relation in a vector space. The invention utilizes an embedded vector technology to represent semantic information of each grid small region in different spaces and different time periods. The information includes spatial location information of different functional areas (such as residential areas, commercial areas or industrial areas, etc.) of the city, and also includes time information of morning rush hours, weekends, etc. In particular, the space vector V of each mesh is represented by a low-dimensional vector_spDividing a day into a plurality of time buckets (e.g., one bucket per hour), each track obtaining a time vector V according to a specific falling time bucket_tp. To V_spAnd V_tpA random initialization is performed followed by training with the model as it is trained.

And (3) when a driver drives the vehicle, the driving speed and the driving behavior can be changed in different driving states. For example, the vehicle may be more inclined to travel on a road or overhead in the middle of the travel path, where the speed may be faster. When the vehicle starts or arrives at the end, the speed is often reduced because the vehicle travels on a small road or in an area with many people. In particular, a four-dimensional vector V is used_driTo indicate whether the current driving phase is a departure phase, a midway phase, or an end phase, and the proportion of driving that has been performed in each phase. For example, V_driThe value of (1,0,0,0.2) indicates that the driver is driving at the beginning stage, and accounts for 20% of the total travel.

And (4) the traffic condition in one area is changed periodically and regularly along with the time evolution. For example, if a road segment is very congested from 8 o 'clock to 8 o' clock, 8 o 'clock and 35 o' clockIt may also be very clogged. That is, the traffic condition information in the past in a short time is useful for predicting the current traffic state. Defining the short-time traffic condition as V_short. Meanwhile, the long-time periodic traffic condition change can also help to predict the current traffic condition, such as the change rule of the traffic condition on weekdays and weekends. Defining the long-term traffic condition as V_long. In particular, the present invention relates to a method for producing,

defining:

indicating the current small area g in the past jth time interval_iIn which v is_jRepresenting historical average speed, n_jIndicates the amount of historical track data, len_i/v_jRepresenting the roughly estimated transit time. The traffic condition features are input into a sub-cyclic neural network according to the historical time sequence, and the traffic condition features can be extracted.

In addition, since the historical data are unevenly distributed in different spatial regions, the tracks of some regions pass through a small number of regions, which may affect the accuracy of estimation. To solve this data sparseness problem, traffic condition information of neighboring small areas is also taken into account, i.e., traffic condition information of neighboring small areas is taken into account

Defining:

represents the distance g_iAnd collecting the traffic condition characteristics of the grids with the distance not exceeding d in the past short time, and inputting the collected traffic condition characteristics into the neural network together. Wherein x, y represent the coordinates of the grid, g_jRepresents except g_iOther meshes than mesh.

(II) a training stage, inputting the features extracted from the historical track data into a uniform bidirectional recurrent Neural network (bidirectional LSTM, reference: Graves A, Schmidhuber J. frame with photonic classification with bidirectional LSTM and other Neural network architectures [ J ]. Neural Networks,2005,18(5-6): 602-610) for training, and taking a bidirectional interval loss function as the constraint of training; the method comprises the following specific steps:

and (1) constructing a recurrent neural network. Defining a network hidden layer asInput data asThen, the input data of the t step is x_tAnd the calculation result obtained in the t step is h_tThen, there are:

h_t＝φ(x_t·W_x+h_t-1·W_h+b) (3)

wherein,is a weight matrix (weight matrix) of the input data,is a weight matrix of the hidden layer(s),is the bias parameter (bias). Phi denotes a non-linear activation function, which may be a sigmoid function, a ReLU function, a tanh function, etc.

That is, the hidden state can be expressed as a function:

h_t＝f(h_t-1,x_t) (4)

on this basis, define forgetting the door to be:

f_t＝σ(W_f·[h_t-1,x_t]+b_f) (5)

the input gates are:

i_t＝σ(W_i·[h_t-1,x_t]+b_i) (6)

the output gate is:

o_t＝σ(W_o[h_t-1,x_t]+b_o) (7)

the memory cell is updated by:

the hidden layer is updated as follows:

h_t＝O_t·tanh(C_t) (10)

wherein, W_f、W_i、W_o、Weight matrices representing forgetting gate, input gate, output gate and memory cell, respectively, b_f、b_i、b_o、Then it is the corresponding bias parameter. σ () is a non-linear activation function, e.g.Is a function of the sigmoid and is,is a hyperbolic tangent function, and f () represents an abstract neural network function containing parameters of each layer. Defining the corresponding parameter of the recurrent neural network as W_Nfrom [ - α, α ]]Is uniformly dividedeach weight parameter in the recurrent neural network is initialized in the method, wherein α is a hyperparameter and is set to be in a range of 0.01 to 1.

The bidirectional recurrent neural network performs calculation by using a forward recurrent neural network and a reverse recurrent neural network simultaneously. The forward circulation neural network inputs the grid features extracted in the previous step according to the sequence of the sequence, and the reverse circulation neural network inputs the grid features after the sequence is in the reverse order. This has the advantage that the neural network can be made to observe the position distances of the current mesh from the start point and the end point simultaneously, thereby having an overall characteristic. Defining its hidden variables as a concatenation of forward and reverse networksWhereinRepresents a hidden layer of the forward recurrent neural network,representing a hidden layer of the inverse recurrent neural network.

Step (2), extracting the characteristics, namely the spatial characteristics, in the historical track dataTemporal characteristicsDriving state characteristicsHistorically short and long term traffic status characteristicsAndare spliced into aOne unified feature vector:

at each small grid passing through, the two-way recurrent neural network is input to obtain the passing time of the grid, namely W^T·h_i+ b. Time overhead of total tripComprises the following steps:

definition ofRespectively, a weight matrix and bias parameters for calculating the total time overhead. W^TRepresenting the transpose of the W matrix.

And (3) defining the real time overhead vector of the track passing through each grid sequence as T. The sequential real time overhead vector is T^fThe real time overhead vector of the reverse order is T^b. The time overhead vector estimated by the neural network is:

and the model is subjected to auxiliary supervised learning by using the bidirectional interval loss function, so that the time overhead of the whole path can be learned, and the transit time of each intermediate stage can be learned. The two-way interval loss function is defined as:

where M denotes whether a trajectory passes through a mask of a small region, [ ] denotes an operation between each element of the vector.

Step (4), the training goal is to minimize the loss function L, i.e.:

where θ represents the training parameters of the model, ε represents the embedding vector in time and space, and S is the size of the training set. Finally, the model is subjected to parameter updating and optimization by using a time sequence-based back propagation algorithm. Back propagation algorithm references: chauvin Y, Rumelhart D E.Backproperation the term, architecures, and applications [ M ]. Psychology Press,2013.

A prediction stage, deducing the features extracted from the query path by using a bidirectional cyclic neural network and estimating the travel time; the method comprises the following specific steps:

and (1) giving a real travel without a timestamp mark as a query path, and obtaining a grid sequence mapped by the real travel according to a passed actual path. For each small grid passing through, using space-time characteristics V obtained by characteristic extraction and expression stage extraction_spAnd V_tpDriving state characteristic V_driAnd historical short and long term traffic condition characteristics V_shortAnd V_longV is indicated as a total feature of the mesh. Wherein the embedded vector of the spatio-temporal features uses vector information updated by parameters of a training process. Short-term and long-term traffic state features are feature mined using a trained sub-cyclic neural network.

Step (2), inputting the extracted various aspects of characteristics into the trained pairs in each gridObtaining the current hidden variable h in the cyclic neural network_tThen the estimated time to pass through the current region is W^T·h_t+ b. The total time overhead estimate is:

where n represents the total number of grids passed,for the trained results, a weight matrix and bias parameters for the total time overhead are calculated. W^TRepresenting the transpose of the W matrix.

Overall, the process of the invention has several advantages. Firstly, an end-to-end (end-to-end) deep learning method based on historical data training is utilized to directly learn the characteristics of the whole path and estimate the whole transit time. A bidirectional interval loss function is defined, and the time overhead of passing through an intermediate road section can be monitored in an auxiliary mode on the basis of monitoring the whole path time. The method for introducing the auxiliary supervision enriches the sample information of the path and can ensure that the propagation signal can be more accurate when the back propagation algorithm updates the parameters. Secondly, a feature extraction structure is provided, and the passing time of the path can be effectively estimated by extracting dynamic features of different dimensions such as space-time embedded vectors, driving states, short-time and long-time traffic conditions and the like. Finally, the experimental result is better than that of the existing method through experimental verification in the actual environment.

As shown in table 1, we performed experiments with real historical trajectory data, including two cities, boehr diagram and shanghai. The existing methods such as a road section average time method, a sub-path dynamic programming method, a grid full-connection network method, a grid convolution network method and the like are used for comparison. The road section average time method obtains a result by directly accumulating the average passing time of each road section. Dynamic programming of subpaths [ Yilun Wang, Yu Zheng, and Yixing Xue. travel timing of a path using mapping project-ries in Proceedings of the 20th International Conference on Knowledge Discovery and Data Mining (SIGKDD), pages 25-34,2014 ] uses dynamic programming to find the optimal splicing method of subpaths. The grid full-connection Network method and the grid convolution Network method take an NxN whole grid as input, and respectively carry out optimization and estimation by using a full-connection Network (Multi-Layer Perceptin) and a convolution Neural Network (Convolutional Neural Network). We use three error measurement indexes of MAE, RMSE and MAPE to measure the quality of the method.

Wherein, y represents the true value,representing the estimated value, and n represents the total number of samples. As can be seen from the results in Table 1, the method of the present invention is far better than the prior comparative methods in each index. For example, on the Shanghai data set, the method of the present invention estimates MAE error to be only 126 seconds, with MAPE error of 13.3%, whereas the best method has MAE error of 168 seconds and MAPE error of 19.1%.

TABLE 1

Drawings

Fig. 1 shows a real trace sample containing time stamp information for each intermediate GPS trace point, for a total of 720 s.

Fig. 2 shows a path sample that needs to be queried, and only contains specifically-passed path information, and does not contain any timestamp information.

Detailed Description

The following describes the specific implementation process of the present invention with reference to specific examples:

the historical trajectories as in fig. 1 are used for training and the travel times in fig. 2 are estimated.

The method comprises a preprocessing stage and a feature extraction and representation stage, wherein the track data are preprocessed to extract various features of the track data. Taking fig. 1 as an example, the specific steps are as follows:

(1) in the city range, fine-grained grid division is carried out and divided into small areas which are adjacent to each other. As in fig. 1, the map is divided into 5 × 6 meshes. Mapping each coordinate point in the track sequence into a corresponding small area to form a grid sequence, namely g ═ g { (g } {₁,g₂,…,g₁₀}。

(2) For each mesh, features of different aspects of it are mined. For example, for g₁Using random vectorsAndto represent spatiotemporal semantic information. Namely:

second, using a four-dimensional vectorTo indicate whether the current driving phase is a departure phase, a midway phase, or an end phase, and the proportion of the driving that has been performed in each phase, namely:

finally, the past short and long time traffic condition information is used to predict the current traffic condition characteristicsAndin particular, defineFor the past 1 st to 6 th time interval (5min), the current region g₁The traffic situation of (1). For exampleIt is shown that the historical average speed is 10m/s, 8 historical tracks are in total, and the average transit time is estimated to be 20 m/s. Will be provided withInputting the traffic condition characteristics into a subcircular neural network according to historical time sequence, and finally outputting hidden vector h₆As a characteristic of traffic conditions.

II, a training stage, which comprises the following specific steps:

(1) and establishing a Bi-directional circulating neural network (Bi-directional LSTM) model. And randomly initializing various parameters of the model, including matrix parameters and bias parameters of a forgetting gate, an input gate and an output gate.

(2) Extracting the feature in the historical track data, namely the spatial feature V_spTime characteristic V_spDriving state characteristic V_driHistorically short and long time traffic status features V_shortAnd V_longAnd splicing the two into a uniform feature vector. With a grid g₁For example, as

(3) At each small grid passing through, the two-way recurrent neural network is input to obtain the passing time of the grid, namely W^T·h_i+ b. The total travel time overhead is:

for example, W is defined as (0.1, 0.3., 0.7), and 10 mesh hidden layer variable values are defined as h₁＝(0.8,0.3,…,0.2),…,h₁₀When the offset value b is equal to 0.7, (0.7, 0.4.. 0.5) then:

(4) the real time cost vector of the trajectory through each grid sequence is defined as T. The sequential real time overhead vector is T^fTrue time cost vector in reverse order of (70,120, …,720) is T^b(720,640, …, 50). The time overhead vector estimated by the neural network is:

(5) Minimize the loss function L, i.e.:

where θ represents the training parameters of the model, ε represents the embedding vector in time and space, and S is the size of the training set. Finally, the model is subjected to parameter updating and optimization by using a time sequence-based back propagation algorithm.

The prediction stage comprises the following specific steps (taking fig. 2 as an example):

(1) giving a real trip without timestamp marking as query path g ═ g₁,g₂,…,g₈And obtaining a grid sequence mapped by the actual path according to the actual path. For each small grid g of passes₁～g₈Using spatio-temporal features V extracted in the feature extraction and representation stages_spAnd V_tpDriving state characteristic V_driAnd historical short and long term traffic condition characteristics V_shortAnd V_longV is indicated as a total feature of the mesh. Wherein the embedded vector of the spatio-temporal features uses vector information updated by parameters of a training process. Short and long term traffic condition characterizationAnd performing feature mining by using the trained sub-cycle neural network.

(2) Inputting the extracted various aspects of characteristics into the trained bidirectional cyclic neural network in each passing grid to obtain the current hidden variable h_tThen the estimated time to pass through the current region is W^T·h_t+ b. The total time overhead estimated value is;

where both W and b are parameters obtained from previous training procedures.

Claims

1. A travel time estimation method based on auxiliary supervised learning is characterized by comprising three stages:

the method comprises the steps of (I) feature extraction and representation, wherein historical track data are preprocessed, and various features of the historical track data are extracted;

in the training stage, the features extracted from the historical track data are input into a uniform bidirectional cyclic neural network for training, and a bidirectional interval loss function is used as the constraint of training;

a prediction stage, deducing the features extracted from the query path by using a bidirectional cyclic neural network and estimating the travel time;

the specific steps of the characteristic extraction and representation stage are as follows:

step (1), in an urban area, carrying out fine-grained division on grids according to longitude and latitude coordinates to form adjacent rectangular small areas; mapping each coordinate point in a track sequence consisting of historical GPS coordinates sequenced according to a time sequence into a corresponding small region to form a sequence consisting of grid coordinates;

step (2), for each grid, excavating the characteristics of different aspects of the grid; firstly, representing semantic information of each grid small region in different spaces and different time periods by using an embedded vector technology; the information comprises space location information of different functional areas of a city and also comprises time information such as early peak, weekend and the like; in particular, the space vector V of each mesh is represented by a low-dimensional vector_spDividing a day into a plurality of time buckets, and obtaining a time vector V according to the time bucket in which each track falls_tp(ii) a To V_spAnd V_tpCarrying out random initialization, and then training the model along with the model during model training;

step (3) of using the four-dimensional vector V_driTo indicate whether the current driving phase is a starting phase, a midway phase or an ending phase, and the proportion of driving in each phase;

step (4), defining the short-time traffic condition characteristic as V_shortDefining a long-term traffic condition characteristic as V_longIn the case of a liquid crystal display device, in particular,

defining:

indicating the current small area g in the past jth time interval_iIn which v is_jRepresenting historical average speed, n_jIndicates the amount of historical track data, len_i/v_jRepresenting a coarse estimated transit time; inputting the traffic condition characteristics into a subcircular neural network according to historical time sequence for extractingTaking out the traffic condition characteristics;

in addition, traffic condition information of adjacent small areas is taken into account, i.e.

Defining:

represents the distance g_iCollecting the traffic condition characteristics of the grid set with the distance not exceeding d in the past short time, and inputting the traffic condition characteristics into the neural network together; wherein x, y represent the coordinates of the grid, g_jRepresents except g_iOther meshes than the mesh;

the second training stage comprises the following specific steps:

step (1), constructing a recurrent neural network; defining a network hidden layer asInput data asThen, the input data of the t step is x_tAnd the calculation result obtained in the t step is h_tThen, there are:

h_t＝φ(x_t·W_x+h_t-1·W_h+b) (3)

wherein,is a weight matrix (weight matrix) of the input data,is a weight matrix of the hidden layer(s),is the bias parameter (bias);

i.e. the hidden state is represented as a function:

h_t＝f(h_t-1,x_t) (4)

on this basis, define forgetting the door to be:

f_t＝σ(W_f·[h_t-1,x_t]+b_f) (5)

the input gates are:

i_t＝σ(W_i·[h_t-1,x_t]+b_i) (6)

the output gate is:

o_t＝σ(W_o[h_t-1,x_t]+b_o) (7)

the memory cell is updated by:

the hidden layer is updated as follows:

h_t＝O_t·tanh(C_t) (10)

wherein, W_f,W_i,W_o,Weight matrices representing forgetting gate, input gate, output gate and memory cell, respectively, b_f,b_i,b_o,Then it is the corresponding bias parameter; σ () is a nonlinear activation function; f () represents an abstract neural network function containing parameters of each layer, and the corresponding parameter of the recurrent neural network is defined as W_Nfrom [ - α, α]initializing each element in the uniform distribution, wherein α is a hyper-parameter and is set to be in a range of 0.01 to 1;

the bidirectional cyclic neural network simultaneously uses the forward cyclic neural network and the reverse cyclic neural network for calculation; the forward circulation neural network inputs the grid features extracted in the previous step according to the sequence in turn and reversesInputting the grid characteristics to a recurrent neural network after reversing the sequence; its hidden variables are defined as the concatenation of the forward and reverse networks, i.e.:

step (2), extracting the feature in the historical track data, namely the spatial feature V_spTime characteristic V_spDriving state characteristic V_driHistorically short and long time traffic status features V_shortAnd V_longAnd splicing into a unified feature vector:

V＝(V_sp，V_sp，V_dri，V_short，V_long) (11)

at each small grid passing through, the two-way recurrent neural network is input to obtain the passing time of the grid, namely W^T·h_i+ b, total travel time overheadComprises the following steps:

to calculate the weight matrix and bias parameters for the total time overhead, W^TRepresents the transpose of the W matrix;

step (3), defining the real time overhead vector of the track passing through each grid sequence as T; the sequential real time overhead vector is T^fThe real time overhead vector of the reverse order is T^b(ii) a The time overhead vector estimated by the neural network is:

the model is subjected to auxiliary supervised learning by using a bidirectional interval loss function, so that the time overhead of the whole path can be learned, and the transit time of each intermediate stage can be learned; the two-way interval loss function is defined as:

wherein, M represents whether the track passes through the mask of a small region, and [ ] represents the operation among each element of the vector;

step (4), the goal of training is to minimize the loss function L, i.e.:

wherein, theta represents the training parameter of the model, epsilon represents the embedding vector on time and space, and S is the size of the training set; finally, updating and optimizing parameters of the model by using a time sequence-based back propagation algorithm;

the third step of the prediction stage comprises the following steps:

step (1), a real travel without a timestamp mark is given as a query path, and a grid sequence mapped by the real travel is obtained according to a passed actual path; for each small grid passing through, using space-time characteristics V obtained by characteristic extraction and expression stage extraction_spAnd V_tpDriving state characteristic V_driAnd historical short and long term traffic condition characteristics V_shortAnd V_longV is represented as a total feature of the mesh; the embedded vector of the space-time characteristics uses vector information updated by parameters in a training process; carrying out feature mining on the traffic state features of short time and long time by using the trained sub-cycle neural network;

step (2), inputting the extracted various aspects of characteristics into the trained bidirectional cyclic neural network in each passing grid to obtain the current timeHidden variable h of front_tThen the estimated time to pass through the current region is W^T·h_t+ b, and the total time overhead estimate is:

where n represents the total number of grids passed,for the trained weight matrix and bias parameters, W, of the total time overhead^TRepresenting the transpose of the W matrix.