Research on Traffic Parameter Measurement Methods for Intelligent Transportation Systems

1)

Coil detector

The coil detector is a detection device based on the principle of electromagnetic induction, which realizes the collection of traffic flow data by detecting the inductance change of the induction coil, and consists of a frame, a base plate, a processor, a detection card, and a terminal block. The coil detector can determine the inductance change by detecting the phase change through the phasor, and it can also determine the inductance change by detecting the oscillation frequency through the coupling circuit. When the vehicle passes through the two induction coils respectively, it will cause the coil inductance to change, and then it can detect the passing state of the vehicle, and then transmit the state signal to the detector to realize data acquisition.

Considering the data demand of the study, this paper decides to select 8 sections of GY highway in a city as the object of traffic flow data collection.The 8 sections of GY highway are numbered Section 1~Section 8, respectively, in which the first 4 sections use coil detector to collect the data, and the last 4 sections use microwave detector to collect the data.

In order to make full use of the time-related features such as between daily and weekly traffic flow data, the weekdays from 2023-12-01 to 2023-12-25 were selected as the collection time, totaling 25 days, in which the time interval of data collection was 5 minutes. In order to make full use of the traffic flow data between types and other related features, traffic volume, speed and occupancy were selected as the data collection types, totaling three types of data.

1)

Time correlation of traffic volume

In this paper, the traffic volume is analyzed by using the data of 2023.12.04-2023.12.08 for inter-weekday correlation, and by using the data of 2023.12.04, 2023.12.11, 2023.12.18 for weekly period correlation. The traffic inter-weekday correlation coefficients are shown in Figure 3, and the traffic week-period correlations are shown in Figure 4. The correlation coefficients between weekdays and between week periods are all greater than 0.88, indicating the existence of very strong temporal correlation. Through the weekly period correlation analysis of the data of 12.04, 12.11 and 12.18 time nodes, it is found that the correlation between the two of them shows a bimodal normal distribution.

Figure 3.

The correlation coefficient of the traffic volume of the working day

Figure 4.

Correlation between periodic traffic volume

Figure 5.

The correlation coefficient of speed between weekdays

Figure 6.

The correlation coefficient of the velocity within the period

The data of GY highway 2023.12.08 was selected to carry out the study of spatial correlation of traffic volume, speed and occupancy. 1)

Spatial correlation of traffic volume

In this paper, the traffic volume analyzes the spatial correlation between lanes (L1~L4) using the data of section Section 1, and analyzes the spatial correlation between sections using the data of L1 lanes in 8 sections. The correlation coefficients between traffic volume lanes are shown in Figure 7, and the correlation coefficients between traffic volume sections are shown in Figure 8. The correlation coefficients of the traffic volume data of each lane and the traffic volume data of each cross-section are greater than 0.85, which is extremely strong correlation.

Figure 7.

The correlation coefficient between traffic lanes

Figure 8.

Correlation coefficient of traffic volume between sections

Figure 9.

Correlation coefficient of speed between lanes

Figure 10.

Correlation coefficient of speed between sections

The basic framework of a graph convolutional neural network consists of an input layer, a graph convolutional layer, and an output layer. 1)

Input layer

The input layer is used to receive a representation of the graph structure data, which usually consists of node information and adjacency matrix. The node information contains the feature vectors of each node, while the adjacency matrix contains the connection relationships between nodes and their respective connection strengths or weights.

The Fourier transform is a classical method for achieving graph convolution. Specifically, the graph Fourier transform is used to perform feature extraction and frequency domain filtering operations on the graph signal. Before performing the graph Fourier transform, it is necessary to obtain the graph Laplacian matrix L corresponding to the target graph, and perform the singular value decomposition operation on L to obtain the eigenvector matrix U and the eigenvalue diagonal matrix Λ, which is calculated as follows: (8)L=D−A$$L = D - A$$ (9)L=UΛUT$$L = U\Lambda {U^T}$$

where D∈ℝN×N$$D \in {\mathbb{R}^{N \times N}}$$ is the diagonal matrix and Dii=∑jAij$${D_i}i = \sum\limits_j {{A_{ij}}}$$.

Using the eigenvector matrix U of L as the base of the graph Fourier transform, the graph Fourier transform operation of the graph signal f on the null domain can be defined as: (10)f=UTf$$f = {U^T}f$$

where f is the graph signal converted to the spectral domain after performing the graph Fourier transform.

The graph convolution operation is equivalent to applying a convolution filter to the graph signal f on the spectral domain with respect to the eigenvalues of the graph Laplacian matrix L, which is defined as follows: (11)y=ω(L)f=ω(UΛUT)f=Uω(Λ)UTf$$y = \omega (L)f = \omega (U\Lambda {U^T})f = U\omega (\Lambda ){U^T}f$$

where y denotes the output signal obtained from the graph convolution operation and ω(Λ) denotes the convolution filter function, which can be expressed as: (12)ω(Λ)=diag(ω(λ0),ω(λ1),...,ω(λN−1))$$\omega (\Lambda ) = diag(\omega ({\lambda _0}),\omega ({\lambda _1}),...,\omega ({\lambda _{N - 1}}))$$

where λ_i denotes the ird eigenvalue in Λ.

Considering that the computational cost required to directly compute all the eigenvectors of the graph Laplacian matrix is too expensive, the filter function ω(Λ) is simplified by using the Kth order Chebyshev polynomials, which enables fast localization and achieves a reduction in computational overhead. The simplified function ω(Λ) can be expressed as: (13)ω(Λ)=∑k=0KθkTk(Λ˜)$$\omega (\Lambda ) = \sum\limits_{k = 0}^K {{\theta _k}} {T_k}(\tilde \Lambda )$$

where Λ˜=(2Iλmax)Λ−I$$\tilde \Lambda = (2I{\lambda _{{\text{max}}}})\Lambda - I$$, λ_max denote the largest eigenvalues of the Laplace matrix L and I denotes the unit matrix. θ denotes the coefficients of the Chebyshev polynomials. T_k( · ) denotes the Chebyshev polynomial of the kth order, which is defined as follows: (14){ T0(u)=1 T1(u)=u Tk(u)=2u Tk−1(u)−Tk−2(u)$$\left\{ {\begin{array}{l} {{T_0}(u) = 1}&{{T_1}(u) = u} \\ {{T_k}(u) = 2u}&{{T_{k - 1}}(u) - {T_{k - 2}}(u)} \end{array}} \right.$$

where u denotes the real independent variable.

By combining Eq. (11) and Eq. (14), the graph convolution operation can be simplified as: (15)y = U∑k=0KθkTk(Λ˜)UTf = ∑k=0KθkTk(L˜)f$$\begin{array}{rcl} y &=& U\sum\limits_{k = 0}^K {{\theta _k}} {T_k}(\tilde \Lambda ){U^T}f \\ &=& \sum\limits_{k = 0}^K {{\theta _k}} {T_k}(\tilde L)f \\ \end{array}$$

where L˜=(2Iλmax)L−I$$\tilde L = (2I{\lambda _{\max }})L - I$$.

Considering that the maximum eigenvalue of the graph Laplacian matrix is approximately equal to 2, i.e., λ_max ≈ 2, and that the symmetrically normalized graph Laplacian matrix L^xym is often used instead of the original L, this paper further simplifies the graph convolution operation and generalizes the inputs to the graph-structured data equipped with N nodes and each node has a feature dimension of D. Thus, the graph convolution operation used in this paper is shown below: (16)graph_conv(X,A) = ∑k=0KθkTk(Lsym−I)X = ∑k=0Kθk′Tk(D− 12AD−12)X$$\begin{array}{rcl} graph\_conv(X,A) &=& \sum\limits_{k = 0}^K {{\theta _k}} {T_k}({L^{sym}} - I)X \\ &=& \sum\limits_{k = 0}^K {\theta _k^\prime } {T_k}({D^{ - \frac{1}{2}}}A{D^{ - \frac{1}{2}}})X \\ \end{array}$$

where graph_conv(·) denotes the graph convolution operation and θ′ = − θ.

Long Short-Term Memory (LSTM) neural network is a special type of recurrent neural network that addresses the drawbacks of long term dependencies by introducing gate mechanisms and memory cells that allow to maintain long term dependent information and mitigate gradient vanishing and gradient explosion. Each LSTM node consists of at most a set of data flow units responsible for storage delivery, with an upper line in each unit connecting the model as a transportation line to pass data from the past to the present, and the independence of the units helps the model to handle filters that add values from one unit to another. Ultimately, the -shaped neural network layers that make up the gate drive the units to optimal values by processing or letting data pass through.

The LSTM expression is as follows, which describes the update process of the memory storage structure in the LSTM layer. Where, x is the input vector of the LSTM model, h is the output vector of the model, f, i, o denotes the activation values of the forgetting, input and output gates, respectively, C and C˜$$\tilde C$$ denote the cell states and their candidate values, the subscript t denotes the time, σ, tach denotes the sigmoia and tach activation functions, respectively, and w and b denote the weights and the bias matrices, respectively.

In the first step, the LSTM layer decides which information will be discarded from the previous unit state C_t−1. Therefore, the activation value f_t of the forgetting gate at moment t is computed based on the inputs x_t at moment t, the outputs h_t−1 at moment (t − 1). As well as the deviation matrix of the forgetting gate b_f. The Sigmoid function norms all the activation values between 0 (all forgotten) and 1 (all remembered): (17)ft=σ(wf[ht−1,xt]+bf)$${f_t} = \sigma ({w_f}[{h_{t - 1}},{x_t}] + {b_f})$$

In the second step, the LSTM layer decides which information will be added to the cell state C_t. This step consists of two steps: first, computing C˜t$${\tilde C_t}$$, who may be added to the cell state, and second, computing the activation value of the input gate i_t: (18)it=σ(wi[ht−1,xt]+bi)$${i_t} = \sigma ({w_i}[{h_{t - 1}},{x_t}] + {b_i})$$ (19)C˜t=tach(wC[ht−1,xt]+bC)$${\tilde C_t} = tach({w_C}[{h_{t - 1}},{x_t}] + {b_C})$$

In the third step, the new cell state C_t is computed: (20)Ct=ftCt−1+itC˜t$${C_t} = {f_t}{C_{t - 1}} + {i_t}{\tilde C_t}$$

In the last step, the output value h_t is obtained by the following two equations: (21)Ot=σ(wO[ht−1,xt]+bO)$${O_t} = \sigma ({w_O}[{h_{t - 1}},{x_t}] + {b_O})$$ (22)ht=Ottach(Ct)$${h_t} = {O_t}tach({C_t})$$

In usual time series processing, LSTM tends to ignore future information. Bidirectional Long Short-Term Memory Neural Network (BiLSTM) uses two separate hidden layers on top of LSTM to process the sequence data in both forward and backward directions.Connecting the two hidden layers to the same output layer stores both previous and later information as the current time base of the time series data, so the Theoretically the prediction performance will be better than one-way LSTM.The hidden layer output of BiLSTM includes the activation output of the forward hidden layer and the activation output of the backward hidden layer.The BiLSTM expression is as follows, where σ is the activation function, H_t is the hidden layer output, and the outputs are generated by updating the forward structure h→t$${\vec h_t}$$ and the backward structure h←t$${\overleftarrow h_t}$$: (23)ht→=σ(Wxh→xt+Wh→h→ht−1→+bh→)$$\overrightarrow {{h_t}} = \sigma ({W_{x\vec h}}{x_t} + {W_{\vec h\vec h}}\overrightarrow {{h_{t - 1}}} + {b_{\vec h}})$$ (24)ht←=σ(Wxh←xt+Wh←h←ht−1←+bh¯)$$\overleftarrow {{h_t}} = \sigma ({W_{x\overleftarrow{h} }}{x_t} + {W_{\overleftarrow{h} \overleftarrow{h} }}\overleftarrow {{h_{t - 1}}} + {b_{\bar h}})$$ (25)Ht=Wxh→h→+Wh→yht←+by$${H_t} = {W_{x\vec h}}\vec h + {W_{\vec hy}}\overleftarrow {{h_t}} + {b_y}$$

In summary, LSTM deep neural networks can effectively take into account the temporal order of the input data, which can solve the problems of gradient recursion and gradient explosion that traditional RNNs are prone to.Bi LSTM deep neural networks are able to take future data into account on the basis of LSTM. However, due to the complexity of the deep neural network structure, its training often requires various optimization techniques to speed up the training process and solve the overfitting problem.

The experimental software environment of this paper is completed using the MATLAB2017b platform. The experimental data is selected from the coil and microwave detection data of the GY expressway in a city, which is the same source of experimental data as in the previous chapter, including flow, speed, and occupancy. Parameters of model input and output: the experiment is for traffic flow prediction to study the application of input traffic speed and occupancy, and the output is traffic flow.

In this paper, GCN-LSTM, GCN and LSTM algorithms are selected for research and analysis to illustrate the advantages of the GCN-BiLSTM traffic parameter measurement model, and the four methods are used to conduct comparative experiments to verify the superiority of the GCN-BiLSTM model.

The traffic flow is predicted for the whole day on weekdays by observing the changes in data and the actual traffic state. The data collection time is from 6:00 to 22:00 for 25 consecutive days, with a 5-minute interval between the collection time, the data collected on the first 20 days of the road section is used as a learning sample, and the data on the 5th day of the road section is used as a testing sample. Traffic flow parameters based on the GCN-BiLSTM model, the comparison algorithms are GCN-LSTM, GCN and LSTM three baseline models, respectively, GCN-BiLSTM, GCN-LSTM, GCN and LSTM model of the traffic flow prediction effect is shown in Fig. 11 to Fig. 14. It can be seen that the GCN-BiLSTM model in this paper has the closest predicted value curve and true value curve for the traffic flow parameters, followed by the GCN-LSTM model, and the predicted and true value errors of the GCN and LSTM models are relatively large.

Figure 11.

The traffic flow prediction of GCN-BiLSTM model

Figure 12.

The traffic flow prediction of GCN-LSTM model

Figure 13.

The traffic flow prediction of GCN model

Figure 14.

The traffic flow prediction of LSTM model

By outputting the comparison graphs of data points and also analyzing and comparing the error as well as accuracy of the output results of the two groups of models at the same time, the three evaluation indexes selected are:

MAE indicates the mean absolute error, which is the average of the absolute error between the true value and the predicted value.

MAXRE is the maximum relative error, which is the magnitude of the deviation between the predicted value and the actual value.

MSE indicates the mean square error, which is a measure of the deviation between the predicted value and the observed value.

The results of the comparison of traffic flow prediction error results are shown in Figure 15. The average absolute error, mean square error and maximum relative error of the GCN-BiLSTM model among the methods for performing traffic flow parameter prediction are superior to the prediction error results of the GCN-LSTM, GCN and LSTM models, and the error results are 1.027, 1.606 and 0.511, respectively, which also proves that the overall prediction effect of the GCN-BiLSTM is closer to the true value, through the error illustrates the availability and superiority of the GCN-BiLSTM model in the field of traffic parameter measurement.

Figure 15.

Comparison results of traffic flow prediction error results