Establishment and simulation of RMEA-WNN-LSTM model for short-term traffic flow prediction

Abstract

The research heat of artificial intelligence is increasing, and intelligent transportation is a direction of artificial intelligence. Short-term traffic flow prediction is the embodiment of use of artificial intelligence. In view of the problem that there is no communication between subgroups and the diversity of groups is limited after the convergence operation of mind evolutionary algorithm, this paper introduces learning mechanism and reflection mechanism to improve the mind evolutionary algorithm (RMEA). Through learning mechanism, each subgroup can obtain the winning individual information of all other subgroups on the premise of maintaining its own characteristics, and generating new individuals. After the learning mechanism, the reflection mechanism is used to select the best individuals, and the RMEA-WNN prediction model is constructed. Moreover, taking the prediction residual of model as the data set, the LSTM model is used to forecast the data of traffic flow residual error, and the RMEA-WNN-LSTM prediction model is constructed. The simulation prediction accuracy of the complex model reaches 96.8%, which proves that the model has practical application value.

Keywords

Artificial intelligence RMEA wavelet neural network LSTM traffic flow

1. Introduction

Intelligent transportation originated in the United States and has been popularized all over the world. The research of this technology has always been a research hotspot in the application field of artificial intelligence. In order to achieve the goal of smart city transportation development, building a complete set of intelligent transportation management system is the most effective way. The intelligent transportation system integrates big data and artificial intelligence into a variety of technologies to realize the intelligent management of road traffic. The intelligent transportation system forms memory characteristics through historical data, optimizes model parameters and looks for the optimal scheme, so as to orderly reduce traffic congestion and reduce energy consumption. Intelligent transportation system can bring greater economic benefits and improve transportation production efficiency without affecting the urban environment [1]. Some countries have used intelligent transportation system, which can assist urban managers to master and manage urban traffic conditions, guide and dredge urban traffic. In the smart city, the construction of transportation infrastructure and the development of intelligent transportation system always affect the intelligent transportation system. In the intelligent transportation system, urban traffic control and urban traffic guidance are realized on the premise of traffic flow prediction. The short-term traffic flow data is closely related to the behavior of drivers. The flow is unstable and vulnerable to the influence of the surrounding environment. The data has a nonlinear relationship with time, weather and policy. It is of great significance to select an appropriate prediction model to forecast the data of traffic flow [2]. With the rapid development of urbanization process in China, the wavelet neural network traffic flow prediction (WNN) has a practical application scenario. The advantages of WNN model are gradually known by researchers. The strong self-learning ability has laid the foundation for the popularization of WNN model.

In recent years, the application of short-term traffic flow prediction model in China has gradually increased, and the theory based on WNN model has become one of the branches of research. Many researchers take a single WNN model as the research model prototype and use different intelligent algorithms to optimize the WNN model [3, 4] to improve the forecast accuracy of the prediction model. However, a unified system theory and method has not been formed so far. Since 2008, scholars have used various optimization algorithms to improve the basic WNN model, and the forecast accuracy of the improved WNN model is also gradually improving. These optimization methods include genetic algorithm (GA) [5], particle swarm optimization algorithm (PSO) [6], ant colony algorithm (CA), etc. Since 2014, the paper on the improved WNN short-term traffic flow prediction model has been gradually popularized [7]. In view of the limitations of WNN model, various improved models have also achieved good prediction results. Between 2014 and 2021, intelligent evolutionary algorithms have been widely used to optimize wavelet neural networks, including improved genetic algorithm [8], wolf swarm algorithm [9], improved chicken swarm algorithm [10], improved flower pollination algorithm [11], mind evolutionary algorithm [12], and distributed ant lion algorithm [13]. Different intelligent algorithms have different advantages. Since 2018, the combined forecasting model is the main trend of short-term traffic flow forecasting research [14, 15, 16, 17, 18, 19, 20], and the paper results are gradually increasing. To sum up, using intelligent algorithm to optimize WNN and build combined forecast model is a research trend of traffic flow forecast [21, 22, 23].

Traffic flow forecast is divided into long-term forecast, medium-term forecast and short-term forecast. The main research content of this paper is short-term traffic flow forecast. Many research teams at home and abroad are committed to the short-term traffic flow prediction model. A single research model can not meet the needs of complex data of traffic flow. Generally, a combined prediction model is constructed by combining intelligent algorithms to predict the data of the next period according to the data of the previous period. The research idea of this paper is based on WNN prediction model, using improved mind evolutionary algorithm (RMEA) to optimize WNN model, and using LSTM model to predict the residual value to improve the forecast precision. The combined model can efficiently predict short-time traffic flow data.

2. WNN model

Wavelet neural network is one of the most typical network structures in neural network. In recent years, many scholars use intelligent algorithm to optimize WNN model, so as to improve the WNN short-term traffic flow forecast precision. French scientific institutions invented wavelet neural network [24]. WNN model evolved from BP neural network, and its prediction process is shown in Fig. 1. In the paper, the activation function is wavelet basis function, which has many classifications, including Morlet wavelet function, Gaussian function and Gaussian first-order partial derivative function. The selection of function needs to analyze the characteristics of the adopted data set, and select the most appropriate method function through simulation experiments. This research selects the compact WNN model. The second layer of WNN model is wavelet basis function, which is also an activation function. The activation function can effectively guide the initialization process of weights and parameters of each layer of the network.

As can be seen from Fig. 1, the WNN model is composed of three layers: input layer, hidden layer and output layer. The main calculation formula of the hidden layer is Eq. (1), where $a_{j}$ is the expansion parameter of the basis function, $b_{j}$ is the translation parameter, and $h(j)$ represents the wavelet basis function.

$\displaystyle h(j)=h\left({\frac{\sum\nolimits_{i=1}^{i=m}{w_{ij}x_{i}-b_{j}}}% {a_{j}}}\right),j=1,2,\cdots,m$ (1)

According to the wavelet basis function, the expression of WNN output layer is obtained.

$\displaystyle y_{k}=\sum\limits_{j=1}^{m}{w_{jk}h(j)},k=1,2,\cdots,n$ (2)

Where $y_{k}$ is the output result and $y^{\prime}_{k}$ is the real result. The error value is calculated according to the output result and the real result.

$\displaystyle e_{k}={y}^{\prime}_{k}-y_{k}$ (3)

The error function calculation formula of wavelet neural network is

$\displaystyle E(w,b)=\frac{1}{2}\sum\limits_{j=0}^{n-1}{(y_{k}-y^{\prime}_{k})% ^{2}}$ (4)

Firstly, the paper use Morlet wavelet function for simulation experiment.

Table 1

The Morlet wavelet function simulation results table

Number	EC	Running time
1	0.7541	8.8114
2	0.7533	8.4921
3	0.7419	8.4318
4	0.7603	8.4402
5	0.7608	8.6719

Figure 1.

Wavelet neural network.

Morlet wavelet basis function has strong anti-interference characteristics [25], and its calculation formula is as follows.

$\displaystyle{y}=\cos({1.75x})e^{\frac{x^{2}}{2}}$ (5)

Then, the paper choose Gaussian function for simulation experiments, and obtain the results of five simulation experiments at the same time.

Table 2

The Gaussian function simulation results table

Number	EC	Running time
1	0.7611	8.2275
2	0.7669	8.3976
3	0.7537	8.8482
4	0.7594	8.5617
5	0.7635	8.6759

Compared with Morlet wavelet basis function, Gaussian function has better prediction accuracy and similar time consumption. Finally, the paper choose Gaussian first-order partial derivative function for simulation experiments, and obtain the results of five simulation experiments.

Table 3

The Gaussian first-order partial derivative function simulation results table

Number	EC	Running time
1	0.7704	8.7374
2	0.7693	8.5207
3	0.7765	8.8367
4	0.7781	8.3376
5	0.7806	8.2743

According to the result data, the prediction fitting degree of Gaussian first-order partial derivative function is better than the other two functions, and its formula is as follows.

$\displaystyle{y}={xe}^{-\frac{{x}^{2}}{2}}$ (6)

In this paper, Gaussian first-order partial derivative function is selected as the excitation function of WNN. The number of hidden layer nodes is calculated as follows.

$\displaystyle n=\sqrt{a+b}+m$ (7)

Among them, $n$ is hidden layer nodes number of the WNN model, $a$ is input layer nodes number of the WNN model, $b$ is output layer nodes number of the WNN, $m$ is an integer, and the value range is [1, 10]. Firstly, with the increase of hidden layer nodes, the prediction fitting degree of WNN model is also gradually increasing, and the time complexity is also increasing. When the hidden layer nodes number increases to 8, the prediction accuracy is no longer improved, but the overall time complexity is still increasing. According to the simulation experimental data, the optimal nodes number of hidden layer is 8, the nodes number of input layer is based on the current data and prediction data, the nodes number of input layer is 2, and the nodes number of output layer is 1.

3. RMEA

Mind evolutionary algorithm (MEA) was proposed by Sun Chengyi [30] and others in 1998. MEA is applied to optimize various artificial intelligence prediction models, such as BP, WNN, SVM (support vector machine) [31, 32], etc. Its application fields include dam deformation prediction [26], prediction of temporal and spatial distribution of groundwater depth [27], sparse antenna array synthesis [28], numerical control thermal compensation [29], etc.

Like genetic algorithm, mind evolutionary algorithm also has basic definitions such as population, individual and environment, but its specific content is different from genetic algorithm. The group forms a new group through evolutionary iteration. The group is divided into temporary subgroup and winning subgroup. The individuals in the temporary subgroup compete, and the excellent individuals are recorded by the winning subgroup.

The process of convergence operation is also divided into two cases. One is that an individual becomes an excellent individual through competition in the temporary subgroup, and the convergence operation ends when the last excellent individual is produced. The other is that the subgroup has been conducting the convergence operation until there are no more excellent individuals, indicating that this temporary subgroup has matured, marking the completion of the convergence operation. In the whole solution space constructed, competitive optimization can be carried out within subgroups, and competitive optimization also needs to be carried out among subgroups. This process is an alienation operation. The fitness function of mind evolutionary algorithm is more like a record version. The fitness function provides the basis of information reference between individuals and groups.

The convergence operation and alienation operation of traditional mind evolutionary algorithm make each subgroup compete with each other and guide the group to evolve in the optimal direction. However, in the process of evolution, each subgroup can not obtain the information of other subgroups, and there is no opportunity to cooperate among subgroups, so as to update the information of subgroups and increase the diversity of groups. RMEA introduces learning and reflection mechanisms on the basis of traditional mind evolutionary algorithm. After the convergence operation, through learning, each subgroup can obtain the winning individual information of all other subgroups on the premise of maintaining its own characteristics, and producing new individuals. After learning, use reflection to judge whether the learning result is desirable. Avoid the algorithm search falling into local optimization, increase the diversity of the population as a whole and improve the search efficiency.

After the convergence operation, the subgroups exchange information, and each subgroup obtains the information of the winning individuals in other subgroups through learning, so as to obtain new individuals. $X_{i}^{r}$ is the new individual obtained after the i-th subgroup learning, and the learning function is

$\displaystyle X_{i}^{r}=wX_{i}+cr\sum\limits_{j=1}^{i-1}{X_{j}}+cr\sum\limits_% {j=i+1}^{N}{X_{j}}$ (8)

$X_{i}$ is the winning individual of the ith sub population after convergence, and $X_{j}$ is the winning individual of each sub population, where $j=1,2,3,\ldots,N$ and $j\neq i$ . N is the number of sub populations, $r$ is the random number distributed between [0, 1], $w$ and $c$ are inertia weight and learning factor, respectively, and their different values produce different learning results. $w$ reflects the degree of inheritance from the original individual, and $c$ reflects the degree of learning. In this experiment, $w$ and $c$ are set to a fixed value of 1. After learning, the desirability of learning results is judged through the reflection mechanism. Calculate the fitness value of the new individual. If $f(X_{i}^{r})<f(X_{i})$ , the winning individual of the sub population is replaced by $X_{i}^{r}$ . If $f(X_{i}^{r})<f(X_{i})$ , the winning individual is still $X_{i}$ .

4. RMEA-WNN prediction model

In thesis, the RMEA is used to optimize the WNN model, and the RMEA-WNN model is constructed to forecast the short-term traffic flow data. The steps of the RMEA-WNN model are as follows.

Step 1: Set data preprocessing. Including data repair and data normalization [12, 32].

Step 2: Determine the basic hierarchical structure of wavelet neural network.

Step 3: Determine the WNN structure and initialize the parameters of MEA. The solution space is the coding space, and each coding is an answer, or a solution. The length calculation formula of the code is

$\displaystyle S=s_{1}\ast s_{2}+s_{2}\ast s_{3}+\ldots s_{n-1}\ast s_{n}+s_{2}% +\ldots+s_{n}$ (9)

Step 4: Form initial subgroups, winning subgroups and temporary subgroups. Iter is the number of iterations, Popsize is the population size, Bestsize is the size of allocated winning sub population, and Tempsize is the size of temporary sub population. The calculation formula of subgroup SG is as follows.

$\displaystyle SG=\textit{Popsize}/(\textit{Bestsize}+\textit{Tempsize})$ (10)

Step 5: Perform convergence operation. Select the optimal sub group, and then stop the internal convergence process. Or stop the convergence process after the group reaches the maturity times.

Step 6: Learn and reflect. Through the learning mechanism, each sub group can obtain the winning individual information of all other sub groups on the premise of maintaining its own characteristics, and generating new individuals. The learning function refers to Eq. (8).

After learning, the reflection mechanism is used to judge whether the learning results are desirable, so as to avoid the search falling into local optimization, increase the diversity of the group as a whole and improve the search efficiency.

Figure 2.

The flow chart of RMEA-WNN.

Step 7: Alienation operation. Sub groups are constantly competing to select the best individual, but also constantly exploring new areas, increasing the diversity of groups. Obtain the score function of each individual and population $\textit{Score}=1/SE$ .

$\displaystyle SE=\textit{mse}(T-A2)$ (11)

where $A2$ is the output value, $T$ is the expected output value, and $S E$ is the mean square deviation.

Step 8: Judge whether the end conditions are met. If satisfied, the optimal individual is analyzed to obtain the weights and parameters of WNN. Otherwise, return to step 5.

Step 9: Decode the optimal individual and apply it to the constructed WNN model. Train the RMEA-WNN model and input the training data set for model training. When the model is mature, stop training.

Step10: Forecast traffic flow on the fourth day. Calculate the prediction error.

5. RMEA-WNN-LSTM prediction model

In thesis, the LSTM model is used to forecast the residual data, which is obtained by subtracting the predicted value of RMEA-WNN model from the real value. The principle is to take the residual data as the training data of LSTM, and predict the residual after the LSTM training is mature. The overall structure of LSTM is shown in Fig. 3.

Figure 3.

Overall structure of LSTM.

Since the residual data of traffic flow is time series data, the residual data prediction uses the sliding time series (residual data of the first three days) to forecast the future data (data of the fourth day). The sliding time series is the input characteristic data. Firstly, the residual data feature vector $X_{t-1}$ at time $t$ is predicted, and the residual data value $x_{t}$ at time $t$ is the label $Y_{t}$ corresponding to $X_{t-1}$ .

$\displaystyle[{x_{t-n},x_{t-n-1},\ldots x_{t-2},x_{t-1}}]$ (12)

When LSTM predicts the residual data, select the sliding time length $N$ and cut the preprocessed residual data into feature vector set $X{\_}\textit{flow}=[Y,X]$ . $Y$ is the target variable column and $X$ is the eigenvector matrix of $Y$ . Suppose the LSTM has n-th nodes of input layer, m-th nodes of hidden layer and one output layer node. After the LSTM network model is expanded, when the time is $t-1$ , the inputs of forgetting gate, input gate and output gate are $x^{i,t-1}$ , $h_{t-2}$ and $c_{t-2}$ respectively. The formula is as follows.

$\displaystyle x^{i,t}=\sigma(W_{hc}\cdot h_{t-1}+b_{hc})$ (13)

$W_{hc}$ is the weight between the output layer and the hidden layer, and $\sigma$ represents the activation function. The formula is as follows.

$\displaystyle f(h_{t-2},c_{t-2},x^{i,t-1})$ (14)

$h_{t-2}$ is the implicit cell output at $t-2$ time. $x^{i,t-1}$ is the residual data input at time $t-1$ , and $b_{hc}$ is the LSTM paranoid term. $W_{hc}$ and $b_{hc}$ are randomly selected. The expanded network diagram is as follows.

Figure 4.

Internal structure diagram of the LSTM.

The main steps of RMEA-WNN-LSTM model are as follows.

Step 1: Data preprocessing. Firstly, the short-term traffic flow data is repaired and normalized, and the training data set is input into the RMEA-WNN prediction model.

Step 2: Initialize the RMEA-WNN model, train the RMEA-WNN model until it is mature, and obtain the prediction result $y_{\textit{test}}$ .

Step 3: After the RMEA-WNN model is mature, forecast the traffic flow data of the first three days, and calculate the residual $\textit{error}_{\textit{train}}$ according to the predicted value and real result.

Step 4: The residual data $\textit{error}_{\textit{train}}$ can be used as the training data set er1 ${}_{\textit{train}}$ of LSTM, and it can be used to train the LSTM model until it is mature.

Step 5: Test the RMEA-WNN model, output the test data value, calculate the residual between the output result and the real result, and record it as error ${}_{\textit{test}}$ as the test sample data set er2 ${}_{\textit{test}}$ of LSTM.

Step 6: Use the mature LSTM model to predict the residual value er2 ${}_{\textit{test}}$ to obtain the predicted value $y_{\textit{er2}}$ . $y_{\textit{test}}$ and $y_{\textit{er2}}$ are superimposed to obtain the final prediction result.

6. Simulation experiment

The platform is MATLAB 2015b and PyCharm 2021.1.2 x64. The computer’s memory is 16 GB. The main hard disk is Samsung nvme mzvlv256 (256GB/SSD). The evaluation indexes mainly include mean absolute error (MAE), mean absolute percentage error (MAPE), root mean square error (RMSE) and fitting degree ( $EC_{\textit{error}}$ ). Their formula is as follows.

$\displaystyle\textit{MAE}=\frac{1}{n}|x_{ir}-x_{\textit{ipre}}|$ (15) $\displaystyle\textit{MAPE}=\frac{1}{n}\sum\nolimits_{t}{\left|{\frac{x_{ir}-x_% {\textit{ipre}}}{x_{ir}}}\right|}\times 100\%$ (16) $\displaystyle\textit{RMSE}=\sqrt{\frac{\sum\nolimits_{t}{({x_{ir}-x_{\textit{% ipre}}})^{2}}}{n}}$ (17) $\displaystyle EC_{\textit{error}}=1-\frac{\sqrt{\sum\nolimits_{i=1}^{n}{(x_{ir% }-x_{\textit{ipre}})^{2}}}}{\sqrt{\sum\nolimits_{i=1}^{n}{x_{ir}^{2}}}+\sqrt{% \sum\nolimits_{i=1}^{n}{x_{\textit{ipre}}^{2}}}}$ (18)

Where the true value is $x_{ir}$ , the predicted value of WNN is $x_{\textit{ipre}}$ , and the number of predicted samples of WNN is $n$ . Generally speaking, the smaller the MAE, MAPE and RMSE, the higher the forecast precision. The closer the value of EC is to 1, the closer the predicted value is to the real value, but the fitting value is always infinitely close to 1, but between 0 and 1. The simulation experiment environment is divided into Matlab 2015b and Pycharm 2021.1.2 x64. RMEA-WNN runs in MATLAB 2015b and LSTM runs in Pycharm 2021.1.2 x64. The $EC_{\textit{error}}$ value of WNN model is 0.775. The $EC_{\textit{error}}$ value of GA-WNN model is 0.856. The $EC_{\textit{error}}$ value of IGA-WNN model is 0.902. The prediction value and error are as follows.

Figure 5.

WNN model prediction.

Figure 6.

WNN model predictive error.

Figure 7.

GA-WNN model prediction.

Figure 8.

GA-WNN model predictive error.

Figure 9.

IGA-WNN model prediction [15].

Figure 10.

IGA-WNN model predictive error [15].

Figure 10 shows that the error of the IGA-WNN model decreases significantly, and the prediction effect of the optimized model is significantly improved. Among them, in the RMEA-WNN prediction model, the data set is the traffic flow data of a single intersection, and the data time span is 15 minutes. The data set has 384 groups of data, which are divided into 4 groups, that is four days of data. 288 groups of data in the first three days are set as training samples, and 96 groups of data in the fourth day are set as prediction samples. Initialization parameter setting: the group size is 100, the temporary group is 8, the winning group is 8, the training is 100 times, the learning rate is 0.05, the learning rate of translation parameters and expansion parameters is 0.005, and the momentum parameter is 0.5.

Figure 11.

The prediction result of RMEA-WNN-LSTM.

In the LSTM model, the training data is the residual data of the first three days, a total of 288 groups of data. The prediction data is the residual data of the fourth day, a total of 96 data. The random seed is 7, the training time is 100, the step size is 1, and the predicted residual value is output. Figure 11 shows the prediction results of RMEA-WNN-LSTM short-term traffic flow prediction model. The evaluation indexes are calculated according to Eqs (15) to (18). The MAE value is 9.175, the MAPE value is 0.0477, the RMSE value is 11.904, and the $EC_{\textit{error}}$ value is 0.968.

Figure 12.

The prediction error of RMEA-WNN-LSTM.

In Fig. 11, the error of RMEA-WNN-LSTM prediction model fluctuates a little. From the index comparison, RMEA-WNN-LSTM model has higher overall forecast accuracy compared with other models. From the perspective of time complexity, because the residual prediction of RMEA-WNN-LSTM model uses LSTM model, it needs to be trained and takes some time, so the overall time complexity is more than twice that of IGA-WNN model. According to the comprehensive analysis, the RMEA-WNN-LSTM prediction model has better accuracy, and the prediction EC reaches 96.8%.

7. Conclusion

In view of the problem that there is no communication between subgroups and the diversity of groups is limited after the convergence operation of mind evolutionary algorithm, this paper introduces the learning mechanism and reflection mechanism to improve mind evolutionary algorithm. Through learning, each subgroup can obtain the winning individual information of all other subgroups and generate new individuals on the premise of maintaining its own characteristics. After the learning, use the reflection mechanism to select the best individual, and use improve the mind evolutionary algorithm to optimize the WNN model, and construct the RMEA-WNN prediction model of short-term traffic flow. Meantime, taking the prediction residual of the RMEA-WNN model as the data set, the LSTM model is used to forecast the traffic flow residual data, and the short-term traffic flow RMEA-WNN-LSTM prediction model is constructed. The simulation prediction accuracy of the model reaches 96.8%, which proves that the model has practical application value.

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