Short-Term Traffic Flow Forecasting Based on Data-Driven Model

Comments

Responses

The authors have made some text changes to correct some misstatements about ARIMA. They also provided the model form as asked for in review comments on the most recent version. Providing these reveal that they authors used an ARIMA (1,1,1) model. This is not a valid model for traffic condition data. A first ordinary difference will not induce stationarity. A first seasonal (one-week) difference will. The forecasting done on the series transformation that result from a first ordinary difference will be generally biased low during time of the day/week when traffic demand is climbing toward a peak and generally biased high during times of day/week when the traffic demand is falling off following a peak. If the authors include an ARIMA model, it must be a one-week period SARIMA model as described in Williams and Hoel, 2003.

Thanks to the expert for your suggestions on reference to ARIMA and SARIMA model series, but because the contribution of this paper is mainly to improve the original model by using the proposed algorithm, the ARIMA model series is not described as the main content in this paper. Therefore, in the future work, we will focus on SARIMA series methods.

In Section 2.1 of the revised version, the author added a detailed description of SARIMA model and the literature of Williams and Hoel. In the conclusion part, the limitations of this paper and the main work in the future are described. The details are as follows:

In Section 2.1:

 “Some time series are periodic and trendy. The periodicity of the series is caused by seasonal changes or intrinsic factors. When the time series is periodic, this series is seasonal time series. Therefore, seasonal differences can be used to smooth this seasonal time series. This time series can be predicted by the seasonal autoregressive integrated moving average (SARIMA) model. The SARIMA model is a short-term forecasting model formed by adding the seasonal variation of the time series on the basis of the original ARIMA model. It has strong linear modeling capabilities. When there are obvious time trends and seasonal changes in the time series, compared with the ARIMA model, the prediction effect of the SARIMA model is better. Moreover, the SARIMA model does not need to make prior assumptions about the development model of the time series. Therefore, compared with many prediction model methods, SARIMA model has higher prediction accuracy.”

“Williams and Hoel [20] used SARIMA model for univariate traffic condition prediction. The intelligent traffic flow data is used to verify the SARIMA model. The experimental results show that the SARIMA model has a good prediction effect. SARIMA model provides a good prediction benchmark for univariate traffic flow prediction.”

In conclusion:

“Although this paper proposes a traffic flow prediction method based on machine learning theory. But in this paper, time series statistical models (such as ARIMA and SARIMA models) are not studied in depth. In future research, the author will use intelligent optimizer to optimize the super parameters of SARIMA model to achieve the best parameter setting of SARIMA model. In the future, the improved SARIMA model will be applied to the field of traffic flow prediction.”

Comments

Responses

This is a revised paper. The authors have taken reviewers' comments into account and revised the paper well. The paper is now ready for publication.

Thank the expert for your important contribution to the publication of this paper.

(1) Not all used abbreviations are named in the abstract and in the text. It's hard to understand what they mean.

Thanks for the important opinions of the expert. According to the expert's opinion, the author notes the full names of all abbreviations. Detailed modification can be seen in the revised draft.

(2) In abstract from 16 to 18 lines of text make it difficult to understand why it is about food. It should be clarified how this relates to transport flows.

Thanks for the important opinions of the expert. In order to make the reader understand this paper more clearly, the author modified this part according to the expert's opinion. Lines 16 to 18 give a new particle allocation mechanism in the algorithm. The revised content is as follows:

“The first five percent of the particles with better fitness values are selected as producers. The last ten percent of the particles with worse fitness values are selected as beggars.”

(3) Text in the lines from 209 to 219 are almost the same as lines from 149 to 159.

Thanks for the important opinions of the expert. In order to avoid repetition, the author rewrites lines 149-159 according to the expert's opinion. he revised content is as follows:

“Aiming at the defect of BSA optimizer, this study improves the particle allocation mechanism of BSA optimizer. Firstly, the particles are sorted according to the fitness value. Then 5% of the particles with good fitness value are selected as producers, 10% of the particles with poor fitness value are selected as beggars, and the remaining particles are selected randomly. In order to solve the problem that beggars are easy to fall into local optimal value in BSA optimizer, this study improves the position rule of beggars to enhance the convergence ability of particles. Finally, the global and local convergence ability of the optimizer is enhanced by the nonlinear weight coefficient.”

(4) From 129 to 311 lines makes no mention about transport flows. Analyzing methods for flood and bird behavior to predict. It is necessary to explain how these methods relate to transport flows.

Thank the expert for your comments. Lines 129 to 311 mainly introduce the modeling process of IBSAELM model, including basic principles of BSA, IBSA optimizer and ELM model. In the revised version, the author introduces the correlation between these methods and traffic flow prediction. Specific additions are as follows:

In section 3.1: “By enhancing the convergence ability of the IBSA optimizer, the optimal parameters of the ELM model can be better mined, thereby improving the prediction accuracy of the model for traffic flow.”

In section 3.2: “In this study, ELM model is used as the basic model of traffic flow prediction. Through the above analysis of the principle of ELM model, it is found that the super parameters of ELM model are randomly selected. The choice of super parameters has a great influence on the prediction effect of traffic flow. Therefore, this paper uses IBSA optimizer to optimize the super parameters of ELM model to achieve a good effect on traffic flow prediction.”

In section 3.3: “Through the above analysis, it is found that compared with the BSA optimizer, the convergence accuracy and convergence time of the IBSA optimizer are significantly improved. Therefore, the IBSA optimizer can achieve better optimization of model hyper parameters, thereby improving the model's prediction effect on traffic flow.”

Comments

Responses

(1) Introduction section, the literature of traffic flow forecasting should be strengthened. Please refer to recent researchers.

Thank you for your comments. The author added the analysis of literature in the literature review. The newly added literature is as follows:

Williams, Billy M.; Hoel, Lester A. Modeling and Forecasting Vehicular Traffic Flow as a Seasonal ARIMA Process: Theoretical Basis and Empirical Results. Journal of Transportation Engineering. 2003. 129.

Smith, Brian L.; Williams, Billy M.; Keith Oswald, R. Comparison of parametric and nonparametric models for traffic flow forecasting. Transportation Research Part C: Emerging Technologies. 2002, 10, 303-321.

Tselentis, D. I., Vlahogianni, E. I., Karlaftis, M. G. Improving short-term traffic forecasts: to combine models or not to combine? Iet Intelligent Transport Systems. 2015, 9(2), 193-201.

Karlaftis, M. G., Vlahogianni, E. I. Statistical methods versus neural networks in transportation research: Differences, similarities and some insights. Transportation Research Part C-Emerging Technologies. 2011, 19(3), 387-399.

Vlahogianni, E., Karlaftis, M. Comparing traffic flow time-series under fine and adverse weather conditions using recurrence-based complexity measures. Nonlinear Dynamics. 2012, 69(4), 1949-1963.

(2) Why do these measured indexes (Eq. 15-18) be considered in the study? For instance, the MAPE 10% is good performance? How to judgement the performance?

Thank you for your important comments. AE, MAPE and RMSE are commonly used indicators to evaluate the prediction effect of the model. R2 is also a common index in the evaluation of prediction effect model, and R2 is used to evaluate the fitting effect of the model.

SVM model and psosvm model are the existing models. Through comparison, it is found that the prediction accuracy of the model proposed in this paper is higher.

(3) The discussion should be strengthened, and provide more the theoretical implications.

According to the opinions of expert, the author introduces ARIMA model as a comparative model and strengthens the analysis of the model.

Comments

Responses

(1) The authors mention "statistical theory" prediction models but include no references nor discussion of seasonal time series models nor state space methods based on these models. The research in this area is rich, including the following and also many papers by Karlaftis, Vlahogianni, and others --

Modeling and forecasting vehicular traffic flow as a seasonal ARIMA process: Theoretical basis and empirical results. Journal of Transportation Engineering. 2003

Comparison of parametric and nonparametric models for traffic flow forecasting. Transportation Research Part C: Emerging Technologies. 2002

 Thank expert for your important comments on the introduction. According to the expert's opinion, the author has strengthened the summary of the prediction method based on the statistical theory. The following references are cited in the literature review.

Williams, Billy M.; Hoel, Lester A. Modeling and Forecasting Vehicular Traffic Flow as a Seasonal ARIMA Process: Theoretical Basis and Empirical Results. Journal of Transportation Engineering. 2003. 129.

Smith, Brian L.; Williams, Billy M.; Keith Oswald, R. Comparison of parametric and nonparametric models for traffic flow forecasting. Transportation Research Part C: Emerging Technologies. 2002, 10, 303-321.

Tselentis, D. I., Vlahogianni, E. I., Karlaftis, M. G. Improving short-term traffic forecasts: to combine models or not to combine? Iet Intelligent Transport Systems. 2015, 9(2), 193-201.

Karlaftis, M. G., Vlahogianni, E. I. Statistical methods versus neural networks in transportation research: Differences, similarities and some insights. Transportation Research Part C-Emerging Technologies. 2011, 19(3), 387-399.

Vlahogianni, E., Karlaftis, M. Comparing traffic flow time-series under fine and adverse weather conditions using recurrence-based complexity measures. Nonlinear Dynamics. 2012, 69(4), 1949-1963.

(2) Another significant weakness in the paper is the lack of parametric and heuristic benchmarking. The forecasts put forward by the authors should be compared to at least two heuristic benchmarks, specifically a random walk forecast where FlowEstimate_t+1=FlowObserved_t and a historically informed forecast where FlowEstimate_t+1=SmoothedFlowEstimate_t+1

*FlowObserved_t-1/SmoothedFlowEstimate_t-1). This last forecast benchmark is described in the last paper in the list above. Also, a parametric benchmark based on a properly formed and fitted seasonal ARIMA model should be included in the comparisons. The next to last paper above provides the details necessary for this model.

Thanks to the important opinions of experts, the author introduces ARIMA model as the comparison model in the revised version, and modifies the data in Figures 4 to 7, with detailed comparison results in the revised version.

Comments

Responses

(1) The authors did not do enough literature review. Check in Google and Google scholar, it can be seen so many similar and important studies in the past that did not get cited. For instance, time series analysis based on George Box and Jenkin’s work, HMM, and so on. Check also review by Lee, J. B. and Teknomo, K. (2014) A review of various short-term traffic speed forecasting models.

Thanks for the important opinions of the expert, the following important references are cited in the literature review.

Williams, Billy M.; Hoel, Lester A. Modeling and Forecasting Vehicular Traffic Flow as a Seasonal ARIMA Process: Theoretical Basis and Empirical Results. Journal of Transportation Engineering. 2003. 129.

Smith, Brian L.; Williams, Billy M.; Keith Oswald, R. Comparison of parametric and nonparametric models for traffic flow forecasting. Transportation Research Part C: Emerging Technologies. 2002, 10, 303-321.

Tselentis, D. I., Vlahogianni, E. I., Karlaftis, M. G. Improving short-term traffic forecasts: to combine models or not to combine? Iet Intelligent Transport Systems. 2015, 9(2), 193-201.

Karlaftis, M. G., Vlahogianni, E. I. Statistical methods versus neural networks in transportation research: Differences, similarities and some insights. Transportation Research Part C-Emerging Technologies. 2011, 19(3), 387-399.

Vlahogianni, E., Karlaftis, M. Comparing traffic flow time-series under fine and adverse weather conditions using recurrence-based complexity measures. Nonlinear Dynamics. 2012, 69(4), 1949-1963.

(2) Instead, the paper poorly only cite a few not so important studies in order to frame the reviewers to think their own study as important. So what’s wrong with the existing studies that you need to propose the study using new methods? No comparisons to the existing study means very poor results.

Thank expert for your important comments. According to the expert's opinion, the author replaced the unimportant literature and cited the latest references and strengthened the comparison between the literatures.

“Statistical regression model is based on time series, when the nonlinearity of time series increases, the prediction error of the model increases. Compared with statistical regression method, machine learning model has stronger nonlinear mapping ability.”

“The gradient descent method is used in the artificial neural network, which is easy to cause the network to fall into the local minimum.”

“By decomposing the dimension of time series, then using the model to predict separately, and finally synthesizing the prediction results, this method can improve the prediction accuracy but also increase the calculation amount.”