CN111383452A - A short-term traffic operation state estimation and prediction method for urban road network - Google Patents

Abstract

The invention discloses a method for estimating and predicting short-term traffic running states of an urban road network, which comprises the following steps: (1) acquiring heterogeneous data, preprocessing the data, and reconstructing a speed field of a research unit by using a GASM algorithm by taking a road section between two signalized intersections in a city as the research unit; (2) constructing a spatial weight matrix of an urban road network, calculating the time-space correlation among all road sections, and identifying and quantifying the fragile road sections by adopting TOPSIS (technique for order preference by similarity to similarity); (3) taking the average value of the speeds according to the reconstructed speed field of the research unit and selecting a reasonable and fragile road section to construct a space-time characteristic matrix of the urban road network; (4) and estimating and predicting the traffic state of the whole road network according to the Bi-ConvLSTM. The method has the advantages that the speed field of the research unit is reconstructed by fusing heterogeneous data, the prediction limitation caused by a single data source is solved, meanwhile, Bi-ConvLSTM is adopted to consider the influence of the traffic speed of the upstream and downstream of the research unit, the space-time characteristic of the traffic flow is fully excavated, the prediction accuracy is further improved, and the like.

Description

A short-term traffic operation state estimation and prediction method for urban road network

technical field

The invention belongs to the technical field of intelligent transportation, and in particular relates to a short-term traffic operation state estimation and prediction method of an urban road network.

Background technique

With the rapid development of the social economy and the advent of the 5G information technology revolution, people's lives have become more convenient and new opportunities have been brought to the transportation industry. In particular, the rapid development of the field of intelligent transportation is expected to solve traffic problems such as traffic congestion and traffic environment.

Real-time monitoring of urban road traffic status and accurate traffic status information release are important foundations to ensure traffic safety and operational efficiency. According to the real-time traffic status information of the road, it can realize the rational and scientific management and control of traffic, reduce the occurrence of congestion, give full play to the resources of the road network, and shorten the travel time for road users, which has important practical significance. Therefore, real-time and accurate traffic state information estimation and prediction becomes a crucial link. However, the current research does not fully consider the effect of heterogeneous data on the estimation of the traffic state of the entire road network and the interaction between the upstream and downstream of the traffic flow, resulting in that the prediction accuracy at the road network level cannot meet the requirements.

When predicting the traffic state of the entire road network, the upstream and downstream traffic states between the road segments in the road network cannot be ignored, and the general deep learning method is one-way prediction, such as the Conv-LSTM model, although some studies are carried out Two-way traffic state prediction, but the traffic space features are not well mined, such as the Bidirectional LSTM model, some key information may be filtered out by the model during prediction, resulting in a certain deviation in the final prediction result.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present invention discloses a method for estimating and predicting the short-term traffic operation state of an urban road network, which solves the problem that the existing prediction methods are not comprehensive enough in the space-time dimension, further improves the prediction accuracy, and is very useful for future urban traffic managers. It provides accurate traffic information to users, and is of great significance to the construction of intelligent transportation systems.

For achieving the above object, technical scheme of the present invention is as follows:

A method for estimating and predicting the short-term traffic operation state of an urban road network, comprising the following steps:

(1) Obtain urban taxi GPS data and urban road speed measurement bayonet data, and preprocess heterogeneous data;

(2) Taking the road section between the two intersections as the research unit, by using the generalized adaptive smoothing algorithm (GASM) to fuse the taxi GPS speed and the checkpoint speed, the actual traffic state of the research unit (road section) is reconstructed;

(3) Calculate the average speed of the road section according to the integrated traffic state;

(4) Establish a spatial weight matrix of urban road network;

(5) Calculate the spatiotemporal correlation between road segments;

(6) Identify and quantify vulnerable road sections based on approaching ideal point ranking method (TOPSIS);

(7) Generate input data, that is, the spatiotemporal matrix of the urban road network, an N*D feature matrix, which describes the change of the traffic speed on the road with time. where N is the number of vulnerable road sections, and D is the time interval;

(8) The present invention is based on the respective advantages of the Bi-LSTM and CNN models and combines them, that is, the Bi-ConvLSTM is used to extract the spatiotemporal characteristics of the traffic state of the entire road network, and the traffic state estimation and prediction of the current moment and the next moment of the entire road network are obtained. value.

The beneficial effects of the present invention are:

The method for estimating and predicting the short-term traffic operation state of the urban road network in the present invention takes the urban taxi GPS data and the road network speed measurement bayonet data as the basic data, and fuses the taxi data and the taxi data through the generalized adaptive smoothing algorithm (GASM). It reconstructs the actual traffic flow and truly reflects the change of traffic speed in the actual urban road section. This method effectively solves the problems of low accuracy of traffic state estimation and large estimation error from a single data source, effectively improves the traffic operation state of real road sections, and lays a solid foundation for further estimating and predicting the traffic state of the entire road network. By defining the vulnerable road sections in the road network, the bidirectional convolutional long short-term memory neural network is used to accurately estimate and short-term predict the traffic state of the entire urban road network. By accurately reflecting the evolution law of urban road network traffic conditions, it can provide road traffic managers and users with optimal traffic control measures and travel plans.

Description of drawings

FIG. 1 is a flowchart of the method for estimating and predicting the short-term traffic operation state of the urban road network according to the present invention.

Figure 2 is a schematic diagram of the LSTM structure.

Figure 3 is a schematic diagram of the structure of BDC-LSTM.

Detailed ways

The present invention will be further clarified below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and not to limit the scope of the present invention.

Some abbreviations of the present invention are explained:

GASM (General adaptive smoothing method, generalized adaptive smoothing method),

TOPSIS (Technique for Order Preference by Similarity to an IdealSolution),

Bi-ConvLSTM (Bi-directional LSTM, bidirectional long and short-term memory network; CNN, ConvolutionalNeural Network, convolutional neural network, abbreviated Bi-ConvLSTM after fusion, bidirectional convolutional long and short-term memory neural network).

Figure 1 is a flowchart of the method for estimating and predicting the short-term traffic operation state of the urban road network implemented according to the present invention, and the specific steps include:

001, to obtain urban taxi GPS data and urban road speed measurement bayonet data, and preprocess heterogeneous data;

002, taking the road section between the two intersections as the research unit, by using the generalized adaptive smoothing algorithm (GASM) to fuse the GPS speed of the taxi and the speed of the checkpoint, reconstruct the actual traffic state of the research unit (road section);

003, find the average speed of the road section according to the fused traffic state;

004, establish the spatial weight matrix of urban road network;

005, calculate the spatiotemporal correlation between road segments;

006. Identify and quantify vulnerable road sections based on TOPSIS;

007. Generate input data, that is, a spatiotemporal matrix of the urban road network, an N*D feature matrix, which describes the change of the traffic speed on the road with time. where N is the number of vulnerable road sections, and D is the time interval.

008, the present invention is based on the respective advantages of Bi-LSTM and CNN models and combines them, that is, using Bi-ConvLSTM to extract the spatiotemporal characteristics of the traffic state of the entire road network, and obtain the current moment and next moment of the entire road network. Predictive value.

In the above technical solution, the implementation method of step 002 is:

Since the collected traffic data is generally discrete and sparse, it is necessary to reconstruct the continuous velocity field using the generalized adaptive smoothing algorithm (GASM) to achieve accurate traffic states. The input data is a discrete set of data points {x _i ,t _i ,vi }, _i =1,...,n, and the output is a continuous velocity field V(x,t), the formula is as follows:

where: x is the space coordinate; t is the time coordinate; v _i is the velocity value of point i; the smoothing kernel function φ _i (x, t) decreases as |x| and |t| increase.

The kernel function calculation formula is as follows:

where: point (x,t) is the estimated point, (x _i ,t _i ) is the collected data point, σ is half the distance between two adjacent detectors, τ is half the detector sampling time; The transformation function is as follows:

In order to truly reflect the propagation of traffic flow, GASM realizes the speed estimation of congested traffic flow V _cong (x, t) and free flow V _free (x, t) by adjusting the kernel function as follows:

where: c _free and c _cong are the propagation velocities under congestion and free flow, respectively.

Then the continuous velocity field of the traffic flow is composed as follows:

V(x,t)=w(x,t)V _cong (x,t)+[1-w(x,t)]V _free (x,t) (6)

where w(x,t) is the weight function of congestion and free-flow traffic states, which is represented by a sigmoid nonlinear function:

Therefore, the traffic state based on heterogeneous data is calculated by the following formula:

是数据源j在数据点i相应的核函数(见公式(2))；α^(j)(x,t)是衡量数据源j在点(x,t)的可靠性动态指标的权重因子。α^(j)(x,t)的计算公式如下：Where: z(x,t) is the estimated traffic state based on heterogeneous data;

is the corresponding kernel function of data source j at data point i (see formula (2)); α ^(j) (x, t) is a weight factor to measure the reliability dynamic index of data source j at point (x, t). The calculation formula of α ^(j) (x,t) is as follows:

数据源j的估计平均速度，

数据源j测量误差的标准差，指数k_j反映数据源j的测量误差随平均速度的改变而发生变化。in:

the estimated average velocity of data source j,

The standard deviation of the measurement error of data source j, and the index k _j reflects the change of the measurement error of data source j with the change of the average speed.

In the above technical solution, the implementation method of step 004 is:

The road network spatial adjacency matrix describes the adjacency relationship between different spatial objects from the perspective of network topology. A complex road network is generally abstracted as a directed graph G=(N, L), which consists of N nodes and L edges. In graph theory, the adjacency relationship is expressed by the following formula:

是k阶邻接矩阵中边i和j相邻的权重，并构成N×N空间权重邻接矩阵E_k，路网的综合空间邻接矩阵为

通过行标准化的方法将空间邻接矩阵转化为空间权重矩阵，即

因此，一个含有N个空间单元的研究对象，其空间权重矩阵表达如下：

is the adjacent weight of edges i and j in the k-order adjacency matrix, and constitutes an N×N spatial weight adjacency matrix E _k . The comprehensive spatial adjacency matrix of the road network is

The spatial adjacency matrix is transformed into a spatial weight matrix by row normalization, namely

Therefore, for a research object with N spatial units, the spatial weight matrix is expressed as follows:

In the above technical solution, the implementation method of step 005 is:

作为量化相邻路段的综合速度，其计算公式如下：Traffic states in a road network affect each other, so it is necessary to quantify the spatiotemporal relationship between road segments. Through the Pearson correlation function, the correlation between the two objects in the time series can be measured, and the influence of the spatial relationship can be considered at the same time, and the average speed of the road segment obtained in step 003 can be used to introduce the spatial factor

To quantify the comprehensive speed of adjacent road sections, its calculation formula is as follows:

in: represents the traffic speed of road segment i at time t, w _ij is the adjacent weight of road segment i and j, i∈[1,R]

R is the number of road segments, t∈[1,T], T is the length of the statistical period, t time interval.

The speed correlation between road segment i and its adjacent road segments is as follows:

是路段i在统计时段T内交通速度

的平均值，

综合速度

的平均值，s表示时间延迟。in

is the traffic speed of road segment i in the statistical period T

average of,

Comprehensive speed

, and s represents the time delay.

In the above technical solution, the implementation method of step 006 is:

In order to avoid the large-scale calculation of the traffic status of the urban road network, the effective extraction of vulnerable road sections is crucial to deduce the traffic status of the entire road network. The present invention adopts the TOPSIS method to realize the identification of vulnerable road sections, and its calculation steps are as follows:

①Define the positive ideal scheme ^{A +} and the negative ideal scheme A-

A ⁺ (s)={maxCor _i (s)|s∈(1,2,...,S),1≤i≤R} (14)

A ^- (s)={minCor _i (s)|s∈(1,2,...,S),1≤i≤R} (15)

Among them, A ⁺ (s) and A ^- (s) are the positive and negative ideal schemes, respectively; R is the number of road segments in the road network, and S is the set of values of the time delay s.

②Calculate the weight under each time delay

In order to consider that the traffic states are more similar in similar time intervals, the weights under different time delays are calculated by the Euclidean distance as follows:

Since larger weights are assigned to more similar traffic states, it is transformed as follows:

where max(Ed) and min(Ed) are the maximum and minimum values in the Euclidean distance set, respectively.

③ Calculate the distance

Calculate the distance between the spatiotemporal correlation of each road segment and the positive and negative ideal solutions, and by taking the Euclidean weighted distance, the calculation formula is as follows:

和

分别是路段i与正、负理想方案的加权距离，其他变量与(14)-(15)定义一样。in:

and

are the weighted distances between the road segment i and the positive and negative ideal solutions, respectively, and other variables are the same as those defined in (14)-(15).

④ Calculate the similarity

Calculate the similarity of road segment i and its adjacent road segments to the ideal solution under all time delays to measure the degree of influence between the traffic state of each road segment and its adjacent road segments. Calculated as follows:

where C _i is the similarity between the road segment i and the ideal solution, that is, the importance of the road segment. C _i =1 indicates that the spatiotemporal correlation of road segment i is the best case, and its influence degree is the greatest, and vice versa. The same as the other variables are defined with equations (18)-(19).

⑤ Sort and extract vulnerable road sections according to the influence degree of C _i on road sections

First, calculate and sort the C _i value of each road section, and then obtain some road sections based on the extraction ratio α, and regard these sections as vulnerable sections, that is, the most easily congested sections are regarded as vulnerable sections, and use the traffic characteristics of vulnerable sections to estimate and predict the traffic status of the entire road network.

In the above technical solution, the implementation method of step 007 is:

Generate the input data, that is, the spatiotemporal feature matrix of the urban road network, an N*D feature matrix, which describes the change of speed on the road over time. Its space-time matrix is generally expressed as the following formula:

where N is the number of vulnerable road segments, D is the number of time delays, and x _it is the average traffic speed of road segment i at time t, that is, the average speed of road segment i based on the fused traffic state.

In the above technical solution, the implementation method of step 008 is:

The present invention is based on the respective advantages of the Bi-LSTM and the CNN model and combines them, that is, the Bi-ConvLSTM is used to realize the estimation and prediction of the traffic state of the entire road network. Through this model, the historical traffic speed data is extracted with spatial correlation features and time correlation features, and finally these features are combined for estimation and prediction.

The above spatial correlation features are extracted from the traffic state of the current road segment and the traffic state sequence of the adjacent road segments of the current road segment through the CNN model, and are used to represent the correlation between the traffic state of the current road segment and the adjacent road segments; The Bi-LSTM model is extracted by considering that the traffic state at each moment is a time series and considering that the current road segment is affected by the upstream and downstream traffic flow, the model finally obtains the forward and reverse traffic state information of the current road segment, which is better Extract actual traffic features, thereby reducing prediction errors.

The Bi-ConvLSTM model is adequately trained on the urban traffic speed data constructed by the above steps. Similar to general LSTM, as shown in Figure 2, in Bi-ConvLSTM model, input x ₁ ,...,x _t , cell output C ₁ ,...,C _t , hidden state h ₁ ,... , h _t are 3D tensors. Each cell contains three parts, namely the input gate it, the forget gate _ft , and the output gate _{ot .} The Bi-ConvLSTM model determines the future state of a cell from the inputs and past states of its local neighbors. The calculation formula of the ConvLSTM model is as follows:

分别表示卷积算子和哈达玛积；W和b表示相应的权重矩阵和偏差。where i _t , f _t , C _t , o _t , h _t , respectively represent the input gate, forget gate, cell state update, output gate and hidden state; σ and tanh represent the activation functions of the sigmoid function and the hyperbolic tangent function, respectively; *and

represent the convolution operator and Hadamard product, respectively; W and b represent the corresponding weight matrix and bias.

是从时间T-n到T-1使用正向输入序列迭代计算，反向输出结果序列

是从时间T-n到T-1使用反向输入序列迭代计算，最终为输出结果向量，在其中每个元素的结果由以下公式进行融合：In Bi-ConvLSTM, as shown in Figure 3, the result sequence is output in the forward direction

It is iteratively calculated from time Tn to T-1 using the forward input sequence, and the reverse output sequence

is iteratively calculated from time Tn to T-1 using the reverse input sequence, and finally is the output result vector, in which the result of each element is fused by the following formula:

The σ _g function is used to fuse the two result vectors of the forward and reverse outputs. The function can be a summation function, an average function, and so on.

When the model Bi-ConvLSTM is applied to actual cases, the time series step size and the number of hidden layers of the Bi-LSTM model involved, the number of network layers of the CNN model, the size of the convolution kernel, the step size, and the fully connected layers These parameters, such as the number of neurons, can be configured by those skilled in the art according to specific requirements, and will not be described one by one here.

A method for estimating and predicting the short-term traffic operation state of an urban road network provided by the embodiments of the present invention has been described above in detail. This article describes the principles and implementations of the present invention. The descriptions of the above embodiments are only used to assist the present invention. At the same time, for those skilled in the art, according to the idea of the present invention, there will be changes in the specific implementation and application scope. In summary, the content of this specification should not be construed as Limitations of the present invention.

Claims (7)

1. A method for estimating and predicting short-term traffic running states of an urban road network is characterized by comprising the following steps: the method comprises the following steps:

(1) acquiring urban taxi GPS data and urban road speed measuring card port data, and preprocessing heterogeneous data;

(2) the method comprises the steps that a road section between two intersections serves as a research unit, and the GPS speed and the gate speed of a taxi are fused by using a GASM (generalized adaptive smoothing algorithm), so that the actual traffic state of the research unit is reconstructed;

(3) solving the average speed of the road section according to the fused traffic state;

(4) establishing a spatial weight matrix of an urban road network;

(5) calculating the space-time correlation between road sections;

(6) identifying and quantifying vulnerable road sections based on a TOPSIS method, namely an approximate ideal point sorting method;

(7) input data, i.e. a spatio-temporal matrix of the urban road network, a N x D characteristic matrix is generated, which describes the traffic speed over the road as a function of time. Wherein N is the number of vulnerable segments and D is the time interval;

(8) based on the respective advantages of the Bi-LSTM and the CNN models, the Bi-ConvLSTM is used for extracting the space-time characteristics of the traffic state of the whole road network, and the estimation and prediction values of the traffic state of the whole road network at the current moment and the next moment are obtained.

2. The method for estimating and predicting the short-term traffic operation state of the urban road network according to claim 1, wherein the method comprises the following steps: the implementation method of the step (2) comprises the following steps:

the input data is a discrete set of data points { x }_i,t_i,v_i1, the output is a continuous velocity field V (x, t), which is calculated as follows:

wherein: x is the spatial coordinate, t time coordinate, v_iIs the velocity value of point i, smoothing kernel function phi_i(x, t) decreases as | x | and | t | increase;

the kernel function calculation formula is as follows:

wherein: point (x, t) is the evaluation point, (x)_i,t_i) For the collected data points, σ is half the distance between two adjacent detectors, and τ is half the sampling time of the detectors; the normalization function is also defined as follows:

GASM realizes congestion traffic flow V by adjusting kernel function_cong(x, t) and free stream V_freeThe velocity estimates of (x, t) are respectively as follows:

wherein: c. C_freeAnd c_congPropagation speeds under congested and free-flow conditions, respectively;

the continuous speed field of the traffic flow then consists of:

V(x,t)＝w(x,t)V_cong(x,t)+[1-w(x,t)]V_free(x,t) (6)

where w (x, t) is a weighted function of congestion and free stream traffic conditions, which is represented by an S-shaped nonlinear function:

thus, the traffic state based on heterogeneous data is calculated by the following formula:

wherein: z (x, t) is the traffic state estimated based on the heterogeneous data;

is the corresponding kernel function of the data source j at the data point i α^(j)(x, t) is a measure of the reliability dynamics of the data source j at point (x, t)

Weighting factor of index α^(j)The calculation formula of (x, t) is as follows:

wherein:

the estimated average velocity of the data source j,

standard deviation of measurement error of data source j, index k_jThe measurement error reflecting data source j varies with the change in average velocity.

3. The method for estimating and predicting the short-term traffic operation state of the urban road network according to claim 1, wherein the method comprises the following steps: the implementation method of the step (4) comprises the following steps:

the complex road network is abstracted into a directed graph G (N, L) to express the topological relation of the road network, a directed graph consisting of N nodes and L edges is established, and the adjacency relation in the graph theory is expressed by the following formula:

is the weight of the adjacent edges i and j in the k-order adjacency matrix and forms an N × N space weight adjacency matrix E_kThe comprehensive space adjacent matrix of the road network is

Converting the spatial adjacency matrix into a spatial weight matrix by means of row normalization, i.e.

Thus, a subject with N spatial elements has a spatial weight matrix expressed as follows:

4. the method for estimating and predicting the short-term traffic operation state of the urban road network according to claim 1, wherein the method comprises the following steps: the implementation method of the step (5) comprises the following steps:

the correlation of two objects on a time sequence can be measured through a Pearson correlation function, meanwhile, the influence of a spatial relation is considered, and a spatial factor is introduced by utilizing the road section average speed obtained in the step (3)

As a comprehensive speed for quantifying the adjacent links, the calculation formula is as follows:

wherein:

representing the traffic speed, w, of the section i at time t_ijFor the weight adjacent to the road sections i and j, i ∈ [1, R]R is the number of road segments, T ∈ [1, T]T is the length of the statistical time period, T time interval;

the speed correlation of the road section i and its adjacent road sections is shown as follows:

wherein

Is the traffic speed of the road section i in the statistical time period T

Is determined by the average value of (a) of (b),

integrated speed

S represents a time delay.

5. The method for estimating and predicting the short-term traffic operation state of the urban road network according to claim 1, wherein the method comprises the following steps: the implementation method of the step (6) comprises the following steps:

the TOPSIS method is adopted to realize the identification of the fragile road section, and the calculation steps are as follows:

① define Positive Ideal solution A⁺And negative ideal scheme A^-

A⁺(s)＝{maxCor_i(s)|s∈(1,2,...,S),1≤i≤R} (14)

A^-(s)＝{minCor_i(s)|s∈(1,2,...,S),1≤i≤R} (15)

Wherein A is⁺(s) and A^-(s) are positive and negative ideal schemes, respectively; r is the number of road sections in the road network, and S is a value set of time delay S;

② calculating the weight at each time delay

Considering that traffic conditions are more similar in close time intervals, the weights at different time delays are calculated from the euclidean distance as follows:

since greater weight is assigned to more similar traffic states, it is translated as follows:

wherein max (ed) and min (ed) are the maximum and minimum values, respectively, in the Euclidean distance set;

③ calculating distance

And calculating the distance between the space-time correlation of each path segment and the positive and negative ideal schemes, and taking the Euclidean weighted distance to calculate the following formula:

wherein:

and

the weighted distances of the road section i and the positive and negative ideal schemes respectively, and other variables are defined as (14) - (15);

④ calculating similarity

Calculating the similarity between the road section i and the adjacent road sections thereof and the ideal scheme under the condition of all time delay so as to measure the influence degree between the traffic states of each road section and the adjacent road sections thereof; the calculation formula is as follows:

wherein C is_iThe similarity of the road section i and the ideal scheme, namely the importance degree of the road section; c_i1 represents that the space-time correlation of the road section i is the best case, the influence degree is the greatest, and vice versa; as defined for other variables and equations (18) - (19);

⑤ according to C_iSequencing road section influence degrees and extracting fragile road sections

First according to C of each road section_iThe values are sorted, partial road sections are obtained based on the extraction proportion α, the partial road sections are regarded as weak road sections, and the traffic state of the whole road network is estimated and predicted by using the traffic characteristics of the weak road sections.

6. The method for estimating and predicting the short-term traffic operation state of the urban road network according to claim 1, wherein the method comprises the following steps: the implementation method of the step (7) comprises the following steps:

generating input data, namely a space-time characteristic matrix of the urban road network, and an N-D characteristic matrix, wherein the N-D characteristic matrix describes the change of speed on a road along with time; the time-space matrix is generally expressed as follows:

where N is the number of weak segments, D is the number of time delays, x_itThe average traffic speed of the road section i at the time t is the average speed of the road section i according to the fused traffic state in the step (3);

7. the method for estimating and predicting the short-term traffic operation state of the urban road network according to claim 1, wherein the method comprises the following steps: the implementation method of the step (8) comprises the following steps:

training a Bi-ConvLSTM model by using the urban traffic speed tensor data generated in the step (7); similar to general LSTM, in the Bi-ConvLSTM model, x is input₁,...,x_tCell output C₁,...,C_tHidden state h₁,...,h_tAre all 3D tensors; each cell comprises three parts, namely input gates i_tForgetting door f_tOutput gate o_t(ii) a The Bi-ConvLSTM model determines the future state of a certain cell by the inputs of its local neighbors and the past state; the formula for the ConvLSTM model is as follows:

wherein i_t,f_t,C_t,o_t,h_tRespectively showing an input gate, a forgetting gate, a cell state updating gate, an output gate and a hidden state; sigma and tanh respectively represent activation functions of a sigmoid function and a hyperbolic tangent function; a and

respectively representing a convolution operator and a Hadamard product; w and b represent the respective weight matrix and bias;

in Bi-ConvLSTM, the result sequence is output in the forward direction

Is to use the forward input sequence to iterate calculation from time T-n to T-1 and output the result sequence reversely

Is iteratively computed from time T-n to T-1 using an inverse input sequence, eventually an output result vector in which the results for each element are fused by the following formula:

wherein sigma_gThe function is used to fuse the two result vectors output in the forward and reverse directions.

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