Short-term traffic volume prediction using GA-BP based on wavelet denoising and phase space reconstruction

Journal Pre-proof Short-term traffic volume prediction using GA-BP based on wavelet denoising and phase space reconstruction Yanni Peng, Wanli Xiang

PII: DOI: Reference:

S0378-4371(19)32171-5 https://doi.org/10.1016/j.physa.2019.123913 PHYSA 123913

To appear in:

Physica A

Received date : 15 September 2019 Please cite this article as: Y. Peng and W. Xiang, Short-term traffic volume prediction using GA-BP based on wavelet denoising and phase space reconstruction, Physica A (2019), doi: https://doi.org/10.1016/j.physa.2019.123913. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2019 Elsevier Ltd. All rights reserved.

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Short-term traffic volume prediction using GA-BP based on wavelet denoising and phase space reconstruction Yanni Penga,b , Wanli Xianga,b,∗ School of Traffic & Transportation, Lanzhou Jiaotong University, Gansu 730070,PR China b Institute of Modern Logistics,Lanzhou Jiaotong University, Gansu 730070,PR China

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Abstract

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Accurate traffic volume prediction can help traffic managers to control traffic well,and can also provide convenient travel routes for passengers. In order to better describe the non-stationary, complex and spatial correlation of traffic volume, the traffic prediction model is proposed based on wavelet denoising and phase space reconstruction (WD-PSR-GA-BP). Pure traffic volume is firstly preprocessed by wavelet denoising method. Subsequently, the prediction model is built by BP neural network, which is optimized by genetic algorithm. In addition, one-dimensional traffic volume is mapped to high-dimensional space by the theory of phase space reconstruction. The inputs of the prediction model are obtained by the reconstructed traffic volume datasets. In order to verify the effectiveness of the proposed model, two groups of datasets and different models are studied in the experiment of Section 4. The experimental results show that the proposed model is superior to all other competitors in terms of MAPE, RMSE, and MAE. Keywords: Wavelet denoising, Phase space reconstruction, Neural networks, Genetic algorithm, Traffic volume prediction 1. Introduction

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Automobiles have become an indispensable means of transportation for the masses. However, traffic congestion, traffic accidents and other issues are also coming. The Intelligent Transportation Systems(ITS) dedicates to manage information of the traffic and travelers. So that future traffic conditions can be predicted quickly and appropriate actions would be taken [1]. Short-term traffic volume prediction is the basic and key component of the ITS, by which traffic managers can better finish traffic control and management. That is, it can enable the transportation systems to operate orderly[2]. Traffic volume is a complex dynamic system. Its internal periodicity and correlation indicate that traffic volume has some kind of law that can be measured. After years of hard works, the prediction of traffic volume has achieved results both in practice and theory. The methods for predicting traffic volume are mainly divided into two categories: traditional mathematical models and Computational Intelligence (CI). Traditional mathematical model focuses primarily on mathematical statistics and calculus. There are many well-known mathematical approaches, such as Exponential smoothing [3, 4, 5], Kalman filtering [6, 7] and autoregressive integrated moving average(ARIMA) [8, 9]. Statistical models are widely accepted by the researchers owing to its solid mathematical theory and insights [10]. For a simple time series prediction model, the accuracy of its prediction depends on the quality of the training samples in a large extent. However, the traffic volume is often complex and non-linear. So, it can not present a stable and orderly state. In particular, it is easy to gradually expand the error and difficult to achieve high accuracy. ∗

Corresponding author. Email addresses: [email protected] (Yanni Peng), [email protected] (Wanli Xiang)

Preprint submitted to Physica A: Statistical Mechanics and its Applications.

March 17, 2008

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In recent years, machine learning receives substantial attention and has been successfully applied in the transportation field. As an important field of machine learning, neural network has unique advantages in the field of prediction. Due to its strong adaptive learning ability, associative and memory ability, large-scale and distributed processing characteristics [11]. Neural networks, such as BP neural network [12, 13, 14], RBF [15], and fuzzy-neural network [16, 17], can approximate nonlinear functions well and perform satisfactorily in specific data and applications. Nevertheless, the neural network has a randomness in the selection of weights and thresholds, which affects the convergence speed and results of the network. Some scholars have used the combination prediction method to apply the genetic algorithm to optimize the weights and thresholds of the neural network. Thus, the model has better generalization ability and convergence speed[18, 19, 20]. Since the traffic volume is easily interfered by various factors such as weather and traffic detectors during the acquisition process. So the data collected is not accurate. Accordingly, it is important to design a data denoising process before the data is predicted. Nourani et al. [21] added the wavelet denoising to the Extreme Learning Machine (ELM) and Least Square Support Vector Machine (LSSVM) models, the results show that data denoising can improve the accuracy of MS-ELM and MS-LSSVM. According to the idea of wavelet denoising “decomposition and integration”, Xu et al. [22] used Echo State Networks(ESNs) to predict the time series after decomposition, then added the outputs of ESNs to reconstruct the overall prediction in order to improve the prediction accuracy. Tang et al. [23] addressed four wavelet denoising functions, i.e., db, haar and sym. Then WD-SVM model is adopted to predict the traffic flow. The experimental results show that the prediction results obtained by using the db function are more accurate than the other three types. Some researches about complex network theory have been applied in different fields on how to describe the dynamic characteristics of time series [24, 25, 26, 27]. After reconstructing the phase space of traffic speed, occupancy and volume, respectively, Li et al. [28] predicted the traffic volume with RBF neural network. The related experimental results demonstrated that the combination method is superior to the single method in the accuracy and timeliness of short-term traffic volume prediction. Furthermore, the reconstructed phase space can be directly implemented as an input to the prediction model, which helps to reduce the error [29]. In this paper, the traffic volume prediction method is proposed based on wavelet denoising and phase space reconstruction. Here, we take the noise and spatio-temporal correlation of the traffic volume into consideration. The wavelet denoising algorithm is adopted to preprocess the traffic volume datasets. According to the phase space reconstruction method, the reconstructed pure datasets are set as the inputs value of the prediction model. Then, GA-BP is executed to forecast the real traffic volume. Recently, another very popular data processing method, EEMD, which is utilized widely with neural networks in many fields. In addition, it has achieved remarkable results [18, 30, 31, 32]. Therefore, the EEMD-GA-BP is also employed to validate the advantage of the proposed model. 2. Description of methods

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2.1. Wavelet-Denoising algorithm The detection results of traffic volume are usually accompanied by a lot of interference data. Wavelet denoising is a common denoising tool for time series, so this technology will be adopted for purpose of training more effective prediction model. According to the wavelet denoising method proposed by Donoho and Johnstone [33], three steps of the wavelet denoising are expressed as follows: (1)Decomposition: determine the decomposition layers N and the wavelet basis function. Then, the noisy data is decomposed into approximate coefficients and detail coefficients. (2)Threshold processing: select threshold function and quantize the coefficients of each layer. (3)Reconstruction: reconstruct data with the processed coefficients.

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Journal Pre-proof The threshold function contains soft threshold and hard threshold, whose definitions are shown in Eq.(1) and Eq.(2) . sgn(y)·(|y| − T ), |y| ≥ T 0 , |y| < T

(1)

ynew =



y, |y| ≥ T 0, |y| < T

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where y is the wavelet coefficient, and T is the threshold. The hard threshold function preserves the peak characteristics of the signal, and the data will produce additional oscillation. However, the soft threshold function obtains better overall continuity of the wavelet coefficients, and also has the smoothness of the original signal [34, 35]. Therefore, soft threshold function is adopted in wavelet denoising method.

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2.2. The GA-BP neural network BP neural network is a multi-layer feedforward neural network. Its working principle is correcting continuously the weight of each layer network through error back propagation, and stopping training once the training times or training precision reached. The prediction result is output by the output layer. BP neural network can get convergence when fitting nonlinear functions. Nevertheless, there is a fatal weakness that it is trap easily in local optimum, because it is based on the gradient descent method to update the weight. To overcome this shortcoming, the BP neural network is improved by taking advantage of the global search of genetic algorithms [36]. The genetic algorithm simulates the law of nature’s ‘natural selection’. First, the weights and thresholds of the BP neural network are encoded as population individuals. Then, in each iteration, according to the preset fitness function, the individual experiences selection, crossover and mutation, so as to get the optimal gene. After multiple iterations, the ’gene’ of weight and threshold will be better and better, the purpose of optimizing BP neural network is achieved.

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2.3. Phase space reconstruction Takens [37] proposed embedding theory: as long as the dimension is based on the embedding theory, a phase space with the same topological meaning as the prime dynamical system can be reconstructed. Thus, the analysis and the prediction of time series can be carried out in this reconstructed phase space. In the fact, the embedding dimension m and the delay time τ are the two key parameters of the phase space reconstruction technique. Nevertheless, in Takens’ embedding theory, only the existence of these two parameters are theoretically proved, and no specific expressions are given. Moreover, for taking appropriate value in practical applications, these two parameters should be combined with the characteristics of the time series itself. In this work, the embedding dimension m and the delay time τ are calculated by using the C-C method based on correlation integral[38]. The associated integral can be calculated by the following equation: C (m, N, r, τ ) =

2 M (M − 1)

X

1≤i
θ(r − kX(i ) − X(j)k∞ ), r > 0,

(3)

where N is the size of the dataset, M = N − (m − 1)τ is the number of embedding points, θ(X) = 0, if X < 0, θ(X) = 1, if X ≥ 0, and k ·k∞ denotes the sup-norm. The calculation steps of the C-C method can be divided into the following steps. 3

Journal Pre-proof First, the time series is decomposed into τ disjoint subsequences independently. The statistic S (m, N, r, τ ) is calculated from these sub-sequences as follows:     τ  N N 1X m Cs m, , r, 1 − Cs 1, , r, τ , m = 2, 3, 4, 5 S (m, N, r, τ ) = τ τ τ

(4)

s=1

Next, at the first local minimum point of ∆S (τ ), the delay time τ is obtained. ∆S (τ ) is defined as: ∆S (m, τ ) = max{S(m, rj , τ )} − min{S(m, rj , τ )}

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Scor (t) = ∆S¯ (t) + S¯ (t)

τw = (m − 1)τ

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At the end, the embedding dimension m is computed from the optimal delay time window τw . m and τw are acquired by: (7)

(8)

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X(1 + τ ) X(2 + τ ) .. .

··· ··· .. .

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where τw is the minimum point corresponding to the global Scor (t) . Thus, the reconstructed phase space can be described as : X(1 + (m − 1)τ ) X(2 + (m − 1)τ ) .. .

X(M ) X(M + τ ) · · · X(M + (m − 1)τ )

    

(10)

3. Proposed models

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3.1. WD-PSR-GA-BP In this section, the WD-PSR-GA-BP model is established for short-term traffic volume forecasting. The flowchart of the proposed model is depicted in Fig.1. Accordingly, this model contains the following three steps.

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Algorithm Start Algorithm End InputTraffic volume data Output layer

GA-BP neural network model

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Phase space reconstruction model C-C Method

Traffic volume data after wavelet denosing

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Phase space {X(t),X(t-1),ĂX(t-τ)}

Fig. 1. Proposed framework of the method for short-term traffic volume prediction.

Above all, the wavelet denoising technology is conducted to denoise the traffic volume datasets collected by detectors. Then, the phase space reconstruction method is used to decompose and reconstruct the pure datasets. Finally, the reconstruction pure datasets are input to the GA-BP neural network. The final prediction result can be obtained by the output layer of GA-BP neural network.

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Journal Pre-proof which are divided into the following details. The embedding dimension m and the delay time τ will be employed for this method. Thus, the inputs and outputs of the train datasets  of the neural network are respectively modeled as: Xtrain (i, :) = X1+(i−1)τ , ..., XN 0 −1−(m−i)τ   ,Ytrain = X2+(m−1)τ , ..., XN 0 , where i=1,2,...m, N 0 is the length of the training dataset. The processing method of the testing dataset is the same as mentioned. The selection of the inputs data and outputs data can be illustrated in Fig. 2.

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3.2. Data description The daily real traffic volume datasets are downloaded from the California Department of Transportation (http://www.pems.dot.ca.gov) in 2018. The dataset includes traffic volume, occupancy and average speed of California highways in every 5 minutes. In this experiment, two detectors are selected randomly of main roads from 6th Jan 2018 to 20th Jan 2018, and the detected traffic volume datasets are chose from 06:00-19:00 as the experimental object. In addition, two detectors are named as Site 1 and Site 2 for convenience, respectively. As shown in Fig. 3 , traffic volume has significant differences on workdays and weekends. Therefore, the traffic volume datasets are divided into two groups: workdays and weekends, and predict separately two groups of datasets for a better accuracy. In this experiment, the datasets of two detectors will be used to verify that the proposed model has a better generalization ability. The datasets in Case 1 contain the traffic volume detected by two detectors on the workdays, while the traffic volume detected by the above two detectors on the weekends will be studied in Case 2.

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Fig. 3. Traffic volume of a week.

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4. Experiments

4.1. Comparative analysis of different models Ensemble empirical model decomposition (EEMD) method was proposed by Wu and Huang in 2009 [39]. It is a new time-frequency analysis method, which is widely used in science and engineering. This theory not only improves effectively the problem of empirical modal decomposition (EMD) mode mixing, but also improves the prediction accuracy better than EMD [40, 41]. In this experiment, the Gaussian white noise standard deviation Nstd in EEMD is set as 0.4, the population size is set as 50, and the number of GA iteration is 100, respectively. In this work, to validate the superiority of the proposed model, WD-PSR-GA-BP is compared with the EEMD-GA-BP, PSR-GA-BP, and GA-BP. 6

Journal Pre-proof 4.2. Performance Evaluation To evaluate the result of the proposed model, three error evaluation are utilized to measure the prediction performance. Mean Absolute Percentage Error (MAPE), Root Mean Squard Error (RMSE), and Mean Absolute Error (MAE). MAPE represents the average deviation from the actual predicted results. RMSE is used to measure the deviation between the predicted value and the real value. MAE is the average of absolute errors, and it is more robust to outliers.The three functions are provided as following: N ˆ − Xi 1 X X M AP E = Xi N

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v uN  2 X 1u ˆ i − Xi RM SE = t X N i=1

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(12)

ˆ i are the predicted traffic volume datasets, Xi are the actual traffic volume datasets, where X and N is the length of the datasets. 4.3. Case study In this experiment, each model is run 20 times independently. The minimum, maximum, mean and standard deviation values of the error criteria (MAPE, RMSE, MAE) are recorded for each model. The minimum values of each column are marked in boldface.

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4.3.1. Case 1

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As shown in Fig. 4, traffic volume performs a great similarity in the same period of time. Fig. 5 presents the comparison between two groups of traffic volume datasets after wavelet denoising. At the same time, the delay time τ and the time window τw are calculated by the C-C method, according to Fig. 6. Referring to Eq. (9), the embedding dimension m of Site 1 is 3, and the embedding dimension m of Site 2 is 5. The numbers of hidden layer neurons are set as 7 and 11 in the bp neural network, respectively. Table 1 describes the maximum, minimum, mean and standard deviation of the evaluation index MAPE of the all adopted models. The results of the evaluation index RMSE and MAE are shown in Table 2 and Table 3, respectively.

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Journal Pre-proof Table 1 The comparison of MAPE among different prediction models in Case 1

site 1

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GA-BP PSR-GA-BP EEMD-GA-BP WD-PSR-GA-BP GA-BP PSR-GA-BP EEMD-GA-BP WD-PSR-GA-BP

Min

Max

Mean

Std.a

6.236 6.220 5.325 2.826 6.867 5.956 5.836 4.141

8.007 7.803 6.834 4.888 9.883 9.058 7.443 7.316

7.091 6.869 5.981 3.857 7.929 7.174 6.690 4.945

0.497 0.408 0.407 0.535 0.764 0.714 0.384 0.845

Standard Deviation

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Table 2 The comparison of RMSE among different prediction models in Case 1

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Min

GA-BP PSR-GA-BP EEMD-GA-BP WD-PSR-GA-BP GA-BP PSR-GA-BP EEMD-GA-BP WD-PSR-GA-BP

Standard Deviation

8.401 8.689 7.048 4.523 7.878 7.471 6.885 4.991

Max

Mean

Std.a

10.892 11.249 8.641 7.447 11.569 10.637 8.359 9.255

9.527 9.778 7.633 6.006 9.596 8.606 7.617 6.280

0.674 0.693 0.444 0.887 1.016 0.673 0.381 1.284

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Detector

site 1

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GA-BP PSR-GA-BP EEMD-GA-BP WD-PSR-GA-BP GA-BP PSR-GA-BP EEMD-GA-BP WD-PSR-GA-BP

Min

Max

Mean

Std.a

6.910 7.062 5.648 3.310 6.427 5.548 5.275 3.651

8.976 8.645 7.035 5.513 9.126 8.578 6.514 7.254

7.907 7.699 6.177 4.452 7.558 6.769 5.833 4.838

0.566 0.430 0.386 0.632 0.713 0.613 0.336 0.957

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site 2

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Table 3 The comparison of MAE among different prediction models in Case 1

Standard Deviation

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Compared with GA-BP, PSR-GA-BP obtains decreased MAPE values by 9.52%, and 3.13% in site 1 and Site 2, respectively. In addition, from the observation of PSR-GA-BP and WD-PSR-GA-BP in each error evaluation result, the values of MAPE, RMSE and MAE of WDPSR-GA-BP all decreased significantly. Especially, compared with PSR-GA-BP, the improved percentages of WD-PSR-GA-BP in MAPE are 43.85%, 31.07% in Table 1, and the RMSE are decreased by 38.58% and 27.03% in Table 2. This indicates that the prediction of the traffic volume datasets can enhance the accurate of results after wavelet denoising. It is clear to see that EEMD-GA-BP behaves well in Tables 1, 2, and 3 of the Site 1. The mean values of MAPE, RMSE, and MAE are 5.981, 7.633, 6.177, respectively. We can conclude that it is better than GA-BP and PSR-GA-BP. Comparison GA-BP, PSR-GA-BP, and EEMD-GA-BP, the WD-PSR-GA-BP proposed performs best among all these adopted models, its the mean of MAPE, RMSE, MAE are 3.857, 6.006 and 4.452 in Site 1, respectively.Compared 10

Journal Pre-proof with EEMD-GA-BP, it obtains decreased MAPE, RMSE, and MAE values by 35.5%, 21.32% and 27.93%, respectively. Meanwhile, Fig. 7 draws the mean values of MAPE, RMSE and MAE after each model carries out for 20 times, which can describe the comparison results more clearly. Therefore, the above results indicate that the proposed model is better than other competitive models in accuracy and robustness.

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Fig. 7. The 3 evaluation index of models in Case 1.

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Fig. 8. Two original traffic volume time series in Case 2.

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In Case 2, the traffic volume over weekends is collected to analyze. In order to obtain sufficient data samples, the traffic volume is selected in each weekends, from 6th Jan 2018 to 20th Jan 2018. As shown in Fig.8, it can be clearly seen that the distribution of traffic on each weekend is very similar in time. Compared with the traffic volume on workdays in Case 1, the traffic volume on the weekend is less than those on workdays. Fig.9 presents the wavelet denoising of the traffic volume datasets of Case 2. The delay time τ and the time window τw are show in Fig.10. Similarly, according to Eq. (9), it can be calculated that the embedding dimension m of the Site 1 is 4, and the embedding dimension m of the Site 2 is 2. The numbers of hidden layer neurons are set as 9 and 5, respectively. Tables 4, 5, and 6 describe the maximum, minimum, mean and standard deviation of the three error criteria (MAPE, RMSE, MAE) of Case 2, respectively. The meanvalues of the three error criteria for each model are shown in Fig.11. For the single prediction model of GA-BP, the other models all outperform it in each error index. For example, compared with GA-BP, the mean of MAPE, RMSE, MAE of PSR-GA-BP are decreased by 33.69%, 10.93%, and 11.46%, according to Tables 4, 5, and 6 of Site 1. It is obvious that EEMD-GA-BP provides the better prediction accuracy. For instance, compared with GA-BP, EEMD-GA-BP obtains decreased the mean of MAPE, RMSE, and MAE values by 14.90%, 11.48%, 14.53%, respectively. Not only that, the improvement of the proposed model in MAPE, RMSE and MAE is the most significant. It can also be seen from the Fig.11 that the three error indicators of WD-PSR-GA-BP are the lowest. In summary, the experimental results clearly indicate that the proposed model is better than the rest of the benchmark models in accuracy and stability. Thus, the same experimental conclusion as in Case 1 can be drawn , i.e., the proposed model has a better predictive effectiveness.

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Fig. 10. The delay time τ and time window τw obtained in Case 2.

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Journal Pre-proof Table 4 The comparison of MAPE among different prediction models in Case 2

site 1

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GA-BP PSR-GA-BP EEMD-GA-BP WD-PSR-GA-BP GA-BP PSR-GA-BP EEMD-GA-BP WD-PSR-GA-BP

Min

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Std.a

9.248 5.435 7.739 2.696 8.879 5.069 7.809 1.948

11.168 8.162 9.800 4.649 10.564 6.529 10.201 4.063

10.308 6.835 8.772 3.835 9.502 5.777 8.823 2.743

0.596 0.738 0.521 0.499 0.455 0.396 0.662 0.521

Standard Deviation

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a

Model

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Detector

Table 5 The comparison of RMSE among different prediction models in Case 2

site 1

site 2

a

Model

Min

GA-BP PSR-GA-BP EEMD-GA-BP WD-PSR-GA-BP GA-BP PSR-GA-BP EEMD-GA-BP WD-PSR-GA-BP

Std means Standard Deviation

8.388 6.238 7.441 2.929 6.313 4.465 6.149 1.513

Max

Mean

Std.a

10.566 9.707 8.885 6.671 7.729 5.656 7.585 3.144

9.259 8.247 8.196 4.339 6.989 4.969 6.632 2.333

0.599 0.910 0.414 0.910 0.411 0.373 0.357 0.438

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Detector

site 1

a

GA-BP PSR-GA-BP EEMD-GA-BP WD-PSR-GA-BP GA-BP PSR-GA-BP EEMD-GA-BP WD-PSR-GA-BP

Min

Max

Mean

Std.a

6.727 5.228 5.734 2.473 5.069 3.634 4.791 1.280

8.426 7.620 6.919 4.879 6.152 4.585 6.149 2.571

7.442 6.589 6.361 3.490 5.470 4.103 5.203 1.830

0.487 0.682 0.301 0.617 0.335 0.262 0.339 0.342

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site 2

Model

urn

Detector

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Table 6 The comparison of MAE different prediction models in Case 2

Standard Deviation

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WD-PSR-GA-BP

EEMD-GA-BP

PSR-GA-BP

GA-BP

12.000 10.308

10.000

9.259

8.772

8.196 8.247 7.442

8.000

6.835

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6.361 6.589

6.000 4.339 3.835

3.490

p ro

4.000 2.000 0.000

MAPE

RMSE

MAE

Pr e-

(a) Site 1

WD-PSR-GA-BP

9.502

10.000 8.823

9.000 8.000

EEMD-GA-BP

5.777

6.000

al

4.000 2.000 1.000

0.000

2.743

4.103

2.333

urn

3.000

5.470

5.203

4.969

5.000

GA-BP

6.989

6.632

7.000

PSR-GA-BP

MAPE

1.830

RMSE

MAE

(b) Site 2

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Fig. 11. The 3 evaluation index of models in Case 2.

5. Conclusion

At present, the prediction of short-term traffic volume has become a hotspot. The prediction method of accurate and generalization ability is more than significant in traffic control and management. For the WD-PSR-GA-BP, wavelet denoising preprocessing is employed firstly on the traffic volume datasets. Then the embedding dimension m and delay time τ of the pure datasets are calculated by the C-C method. GA-BP is utilized to forecast the real traffic volume. The reconstructed pure datasets can be regarded directly as the inputs of the GA-BP. The outputs of the GA-BP are the predicted traffic volumes. In this work, the datasets are collected 16

Journal Pre-proof by two detectors for experiments. Divide the data into two groups, i.e., site 1 and site 2. Based on the distribution characteristics of the traffic volume, the study is divided into Case 1 and Case 2 (workingdays and weekends). The experimental results show that the proposed model performs best in the three error evaluation of MAPE, RMSE and MAE. It can be concluded that the WD-PSR-GA-BP has significant effects when compared with other competitive models in short-term traffic volume prediction. In the future, the visualization of traffic flow prediction will be a very useful research direction.

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Acknowledgement

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This work is supported by the National Natural Science Foundation of China (Grant No. 61563028) and Foundation of A Hundred Youth Talents Training Program of Lanzhou Jiaotong University (Grant No.1520220203) and Innovative Foundation of Lanzhou Jiaotong UniversityTianjin University (Grant No.2018065). References

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Highlights:

  

The GA-BP prediction model combining wavelet denoising and phase space reconstruction to predict the short-term traffic volume. The prediction effectiveness of four forecast methods including EEMD-GA-BP are compared. Traffic volume collected two detectors from the California are used in model validation. Experiments verify the outperformance of the proposed model.

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