Comparison between Neural Network and Adaptive Neuro-Fuzzy Inference System for Forecasting Chaotic Traffic Volumes

Affiliation(s)

Department of Civil and Ecological Engineering, I-Shou University, Kaohsiung City, Taiwan.

Institute of Civil Engineering Technology, National Kaohsiung University of Applied Sciences, Kaohsiung City, Taiwan..

Department of Civil and Ecological Engineering, I-Shou University, Kaohsiung City, Taiwan.

Institute of Civil Engineering Technology, National Kaohsiung University of Applied Sciences, Kaohsiung City, Taiwan..

ABSTRACT

This paper applies both the neural network and adaptive neuro-fuzzy inference system for forecasting short-term chaotic traffic volumes and compares the results. The architecture of the neural network consists of the input vector, one hidden layer and output layer. Bayesian regularization is employed to obtain the effective number of neurons in the hidden layer. The input variables and target of the adaptive neuro-fuzzy inference system are the same as those of the neural network. The data clustering technique is used to group data points so that the membership functions will be more tailored to the input data, which in turn greatly reduces the number of fuzzy rules. Numerical results indicate that these two models have almost the same accuracy, while the adaptive neuro-fuzzy inference system takes more time to train. It is also shown that although the effective number of neurons in the hidden layer is less than half the number of the input elements, the neural network can have satisfactory performance.

This paper applies both the neural network and adaptive neuro-fuzzy inference system for forecasting short-term chaotic traffic volumes and compares the results. The architecture of the neural network consists of the input vector, one hidden layer and output layer. Bayesian regularization is employed to obtain the effective number of neurons in the hidden layer. The input variables and target of the adaptive neuro-fuzzy inference system are the same as those of the neural network. The data clustering technique is used to group data points so that the membership functions will be more tailored to the input data, which in turn greatly reduces the number of fuzzy rules. Numerical results indicate that these two models have almost the same accuracy, while the adaptive neuro-fuzzy inference system takes more time to train. It is also shown that although the effective number of neurons in the hidden layer is less than half the number of the input elements, the neural network can have satisfactory performance.

Cite this paper

J. Yeh and Y. Chang, "Comparison between Neural Network and Adaptive Neuro-Fuzzy Inference System for Forecasting Chaotic Traffic Volumes,"*Journal of Intelligent Learning Systems and Applications*, Vol. 4 No. 4, 2012, pp. 247-254. doi: 10.4236/jilsa.2012.44025.

J. Yeh and Y. Chang, "Comparison between Neural Network and Adaptive Neuro-Fuzzy Inference System for Forecasting Chaotic Traffic Volumes,"

References

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[15] E. I. Vlahogianni, M. G. Karlaftis and J. C. Golias, “Short-Temporal Short-Term Urban Traffic Volume Forecasting Using Genetically Optimized Modular Networks,” Computer-Aided Civil and Infrastructure Engineering, Vol. 22, No. 5, 2007, pp. 317-325. doi:10.1111/j.1467-8667.2007.00488.x

[16] B. Park, “Hybrid Neuro-Fuzzy Application in Short-Term Freeway Traffic Volume Forecasting,” Transportation Research Record, Vol. 1802, 2002, pp. 190-196.

[17] K. T. Alligood, T. D. Sauer and J. A. Yorke, “Chaos: An Introduction to Dynamical Systems,” Springer-Verlag, New York, 1997.

[18] L. W. Lan, J.-B. Sheu and Y.-S. Huang, “Investigation of Temporal Freeway Traffic Patterns in Reconstructed State Spaces,” Transportation Research Part C, Vol. 16, No. 1, 2008, pp. 116-136. doi:10.1016/j.trc.2007.06.006

[19] J.-S. R. Jang, “ANFIS: Adaptive-Network-Based Fuzzy Inference System,” IEEE Transactions on Systems, Man and Cybernetics, Vol. 23, No. 3, 1993, pp. 665-685. doi:10.1109/21.256541

[20] J.-S. R. Jang, C.-T. Sun and E. Mizutani, “Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence,” Prentice-Hall, Upper Saddle River, 1997.

[21] G. J. Klir and B. Yuan, “Fuzzy Sets and Fuzzy Logic: Theory and Applications,” Prentice-Hall International, Inc., Englewood Cliffs, 1995.

[22] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol. 8, No. 3, 1965, pp. 338-353. doi:10.1016/S0019-9958(65)90241-X

[23] P. Grassberger and I. Proccacia, “Characterization of Strange Attractors,” Physical Review Letters, Vol. 50, No. 5, 1983, pp. 346-349. doi:10.1103/PhysRevLett.50.346

[24] F. Takens, “Detecting Strange Attractors in Turbulence,” Lecture Notes in Mathematics, Vol. 898, 1981, pp. 366-381. doi:10.1007/BFb0091924

[25] C. Y. Yang, “Random Vibration of Structures,” John Wiley & Sons, New York, 1986, pp. 44-59.

[26] M. T. Hagan and M. Menhaj, “Training Feedforward Networks with the Marquardt Algorithm,’’ IEEE Transactions on Neural Networks, Vol. 5, No. 6, 1994, pp. 989-993. doi:10.1109/72.329697

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[28] D. Marquardt, “An Algorithm for Least Squares Estimation of Nonlinear Parameters,” SIAM Journal on Applied Mathematics, Vol. 11, No. 2, 1963, pp. 431-441. doi:10.1137/0111030

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[30] W. Mendenhall, R. L. Scheaffer and D. D. Wackerly, “Mathematical Statistics with Applications,” Third Edition, Duxbury Press, Boston, 1986.

[31] M. Sugeno, “Industrial Applications of Fuzzy Control,” Elsevier Science, Amsterdam, 1985.

[32] S. Chiu, “Fuzzy Model Identification Based on Cluster Estimation,” Journal of Intelligent and Fuzzy Systems, Vol. 2, No. 3, 1994, pp. 267-278

[33] H. Demuth, M. Beale and M. Hagan, “Neural Network Toolbox User’s Guide,” The MathWorks Inc., Natick, 2010.

[1] D. C. Gazis, R. Herman and R. W. Rothery, “Nonlinear Follow-the-Leader Models of Traffic Flow,” Operational Research, Vol. 9, No. 4, 1961, pp. 545-567. doi:10.1287/opre.9.4.545

[2] F. C. Moon, “Chaotic and Fractal Dynamics: An Introduction for Applied Scientists and Engineer,” John-Wiley and Sons Inc., New York, 1992.

[3] A. Wolf, J. B. Swift, H. L. Swinney and J. A. Vastans, “Determining Lyapunov Exponents from a Time Series,” Physica D, Vol. 16, No. 3,1985, pp. 285-317.

[4] J. E. Disbro and M. Frame, “Traffic Flow Theory and Chaotic Behavior,” Transportation Research Record, Vol. 1225, 1989, pp.109-115.

[5] P. S. Addison and D. J. Low, “Order and Chaos in the Dynamics of Vehicle Platoons,” Traffic Engineering Control, Vol. 37, No. 7-8, 1996, pp. 456-459.

[6] P. S. Addison and D. J. Low, “A Novel Nonlinear CarFollowing Model,” Chaos, Vol. 8, No. 4, 1998, pp. 791-799. doi:10.1063/1.166364

[7] P. Shang, X. Li and S. Kamae, “Chaotic Analysis of Traffic Time Series,” Chaos, Solitons & Fractals, Vol. 25, No. 1, 2005, pp. 121-128. doi:10.1016/j.chaos.2004.09.104

[8] I. Okutani and Y. J. Stephanedes, “Dynamic Prediction of Traffic Volume through Kalman Filtering Theory,” Transportation Research Part B: Methodological, Vol. 18, No. 1, 1984, pp. 1-11. doi:10.1016/0191-2615(84)90002-X

[9] J. D. Farmer and J. J. Sidorowich, “Predicting Chaotic Time Series,” Physical Review Letters, Vol. 59, No. 8, 1987, pp. 845-848. doi:10.1103/PhysRevLett.59.845

[10] L. A. Aquirre and S. A. Billings, “Validating Identified Nonlinear Models with Chaotic Dynamics,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 4, No. 1, 1994, pp. 109-125. doi:10.1142/S0218127494000095

[11] J. C. Principe, A. Rathie and J. M. Kuo, “Prediction of Chaotic Time Series with Neural Networks and the Issue of Dynamic Modeling,” International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, Vol. 2, No. 4, 1992, pp. 989-996. doi:10.1142/S0218127492000598

[12] A. M. Albano, A. Passamante, T. Hediger and M. E. Farrell, “Using Neural Nets to Look for Chaos,” Physica D, Vol. 58, No. 1-4, 1992, pp. 1-9. doi:10.1016/0167-2789(92)90098-8

[13] G. Deco and B. Schurmann, “Neural Learning of Chaotic System Behavior,” IEICE Transactions, Fundamentals, Vol. E77-A, No. 11, 1994, pp.1840-1845.

[14] R. Bakker, J. C. Schouten, F. Takens and C. M. van den Bleek, “Neural Network Model to Control an Experimental Chaotic Pendulum,” Physical Review E, Vol. 54A, No. 4, 1996, pp. 3545-3552. doi:10.1103/PhysRevE.54.3545

[15] E. I. Vlahogianni, M. G. Karlaftis and J. C. Golias, “Short-Temporal Short-Term Urban Traffic Volume Forecasting Using Genetically Optimized Modular Networks,” Computer-Aided Civil and Infrastructure Engineering, Vol. 22, No. 5, 2007, pp. 317-325. doi:10.1111/j.1467-8667.2007.00488.x

[16] B. Park, “Hybrid Neuro-Fuzzy Application in Short-Term Freeway Traffic Volume Forecasting,” Transportation Research Record, Vol. 1802, 2002, pp. 190-196.

[17] K. T. Alligood, T. D. Sauer and J. A. Yorke, “Chaos: An Introduction to Dynamical Systems,” Springer-Verlag, New York, 1997.

[18] L. W. Lan, J.-B. Sheu and Y.-S. Huang, “Investigation of Temporal Freeway Traffic Patterns in Reconstructed State Spaces,” Transportation Research Part C, Vol. 16, No. 1, 2008, pp. 116-136. doi:10.1016/j.trc.2007.06.006

[19] J.-S. R. Jang, “ANFIS: Adaptive-Network-Based Fuzzy Inference System,” IEEE Transactions on Systems, Man and Cybernetics, Vol. 23, No. 3, 1993, pp. 665-685. doi:10.1109/21.256541

[20] J.-S. R. Jang, C.-T. Sun and E. Mizutani, “Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence,” Prentice-Hall, Upper Saddle River, 1997.

[21] G. J. Klir and B. Yuan, “Fuzzy Sets and Fuzzy Logic: Theory and Applications,” Prentice-Hall International, Inc., Englewood Cliffs, 1995.

[22] L. A. Zadeh, “Fuzzy Sets,” Information and Control, Vol. 8, No. 3, 1965, pp. 338-353. doi:10.1016/S0019-9958(65)90241-X

[23] P. Grassberger and I. Proccacia, “Characterization of Strange Attractors,” Physical Review Letters, Vol. 50, No. 5, 1983, pp. 346-349. doi:10.1103/PhysRevLett.50.346

[24] F. Takens, “Detecting Strange Attractors in Turbulence,” Lecture Notes in Mathematics, Vol. 898, 1981, pp. 366-381. doi:10.1007/BFb0091924

[25] C. Y. Yang, “Random Vibration of Structures,” John Wiley & Sons, New York, 1986, pp. 44-59.

[26] M. T. Hagan and M. Menhaj, “Training Feedforward Networks with the Marquardt Algorithm,’’ IEEE Transactions on Neural Networks, Vol. 5, No. 6, 1994, pp. 989-993. doi:10.1109/72.329697

[27] K. Levenberg, “A Method for the Solution of Certain Problems in Least Squares,” Quarterly of Applied Mathematics, Vol. 2, 1994, pp. 164-168.

[28] D. Marquardt, “An Algorithm for Least Squares Estimation of Nonlinear Parameters,” SIAM Journal on Applied Mathematics, Vol. 11, No. 2, 1963, pp. 431-441. doi:10.1137/0111030

[29] D. J. C. MacKay, “Bayesian Interpolation,” Neural Computation, Vol. 4, No. 3, 1992, pp. 415-447. doi:10.1162/neco.1992.4.3.415

[30] W. Mendenhall, R. L. Scheaffer and D. D. Wackerly, “Mathematical Statistics with Applications,” Third Edition, Duxbury Press, Boston, 1986.

[31] M. Sugeno, “Industrial Applications of Fuzzy Control,” Elsevier Science, Amsterdam, 1985.

[32] S. Chiu, “Fuzzy Model Identification Based on Cluster Estimation,” Journal of Intelligent and Fuzzy Systems, Vol. 2, No. 3, 1994, pp. 267-278

[33] H. Demuth, M. Beale and M. Hagan, “Neural Network Toolbox User’s Guide,” The MathWorks Inc., Natick, 2010.