Identification and Prediction of Internet Traffic Using Artificial Neural Networks

ABSTRACT

This paper presents the development of an artificial neural network (ANN) model based on the multi-layer perceptron (MLP) for analyzing internet traffic data over IP networks. We applied the ANN to analyze a time series of measured data for network response evaluation. For this reason, we used the input and output data of an internet traffic over IP networks to identify the ANN model, and we studied the performance of some training algorithms used to estimate the weights of the neuron. The comparison between some training algorithms demonstrates the efficiency and the accu-racy of the Levenberg-Marquardt (LM) and the Resilient back propagation (Rp) algorithms in term of statistical crite-ria. Consequently, the obtained results show that the developed models, using the LM and the Rp algorithms, can successfully be used for analyzing internet traffic over IP networks, and can be applied as an excellent and fundamental tool for the management of the internet traffic at different times.

This paper presents the development of an artificial neural network (ANN) model based on the multi-layer perceptron (MLP) for analyzing internet traffic data over IP networks. We applied the ANN to analyze a time series of measured data for network response evaluation. For this reason, we used the input and output data of an internet traffic over IP networks to identify the ANN model, and we studied the performance of some training algorithms used to estimate the weights of the neuron. The comparison between some training algorithms demonstrates the efficiency and the accu-racy of the Levenberg-Marquardt (LM) and the Resilient back propagation (Rp) algorithms in term of statistical crite-ria. Consequently, the obtained results show that the developed models, using the LM and the Rp algorithms, can successfully be used for analyzing internet traffic over IP networks, and can be applied as an excellent and fundamental tool for the management of the internet traffic at different times.

Cite this paper

nullS. Chabaa, A. Zeroual and J. Antari, "Identification and Prediction of Internet Traffic Using Artificial Neural Networks,"*Journal of Intelligent Learning Systems and Applications*, Vol. 2 No. 3, 2010, pp. 147-155. doi: 10.4236/jilsa.2010.23018.

nullS. Chabaa, A. Zeroual and J. Antari, "Identification and Prediction of Internet Traffic Using Artificial Neural Networks,"

References

[1] J.-J. Wu, Z.-Y. Gao and H.-J. Sun, “Statistical Properties of Individual Choice Behaviors on Urban Traffic Net-works,” Journal of Transportation Systems Engineering and Information Technology, Vol. 8, No. 2, 2008, pp. 69-74.

[2] R. Albert and A. L. Barabási, “Statistical Mechanics of Complex Networks,” Review Modern Physics, Vol. 74, No. 1, 2002, pp. 47-97.

[3] J.-J. Wu, H.-J. Sun and Z.-Y. Gao, “Cascade and Break-down in Scale-Free Networks with Community Structure”, Physical Review E-Statistical, Nonlinear, and Soft Matter Physics, Vol. 74, No. 6, 2006.

[4] W. E. Leland, M. S. Taqqu, W. Willinger and D. V. Wil-son, “On the Self Similar Nature of Ethernet Traffic,” Proceedings of ACM Sigcomm, San Francisco, 1993, pp. 183-193.

[5] R. Yunhua, “Evaluation and Estimation of Second-Order Self-Similar Network Traffic,” Computer Communications, Vol. 27, No. 9, 2004, pp. 898-904.

[6] B. R. Chang and H. F. Tsai, “Novel Hybrid Approach to Data-Packet-Flow Prediction for Improving Network Traffic Analysis,” Applied Soft Computing, Vol. 9, No. 3, 2009, pp. 1177-1183.

[7] B. R. Chang and H. F. Tsai, “Improving Network Traffic Analysis by Foreseeing Data-Packet-Flow with Hybrid Fuzzy-Based Model Prediction,” Expert Systems with Ap-plications, Vol. 36, No. 3, 2009, pp. 6960-6965.

[8] A. Stathopoulos and M. G. Karlaftis, “A Multivariate State Space Approach for Urban Traffic Flow Modeling and Prediction,” Transportation Research Part C, Vol. 11, No. 2, 2003, pp. 121-135.

[9] D.-C. Park, “Prediction of MPEG video traffic over ATM Networks Using Dynamic Bilinear Recurrent Neural Network,” Applied Mathematics and Computation, Vol. 205, No. 2, 2008, pp. 648-657.

[10] B. Zhou, D. He, Z. Sun and W. H. Ng, “Network Traffic Modeling and Prediction with ARIMA/GARTH,” HET- NETs’ 06 Conference, Ilkley, 11-13 September 2006, pp. 1-10.

[11] A. Taraf, I. Habib and T. Saadawi, “Neural Networks for ATM Multimedia Traffic Prediction,” Proceedings of the International Workshop on Applications of Neural Net-works to Telecommunications, Princeton, 1993, pp. 85-91.

[12] P. Chang and J. Hu, “Optimal Non-Linear Adaptive Pre-diction And Modeling Of MPEG Video in ATM Net-works Using Pipelined Recurrent Neural Networks,” IEEE Journal on Selected Areas in Communications, Vol. 15, No. 6, 1997, pp. 1087-1100.

[13] A. Abdennour, “Evaluation of Neural Network Architec-tures for MPEG-4 Video Traffic Prediction,” IEEE Transactions on Broadcasting, Vol. 52, No. 2, pp. 184-192, 2006.

[14] A. F. Atiya, M. A. Aly and A. G. Parlos, “Sparse Basis Selection: New Results and Application to Adaptive Pre-diction of Video Source Traffic,” IEEE Transactions on Neural Networks, Vol. 16, No. 5, 2005, pp. 1136-1146.

[15] Z. Fang, Y. Zhou and D. Zou, “Kalman Optimized Model for MPEG-4 VBR Sources,” IEEE Transactions on Con-sumer Electronics, Vol. 50, No. 2, 2004, pp. 688-690.

[16] V. Alarcon-Aquino and J. A. Barria, “Multi Resolution Fir Neural Network-Based Learning Algorithm Applied to Network Traffic Prediction,” IEEE Transactions on Systems, Man and Cybernetics-Part C: Applications and Reviews, Vol. 36, No. 2, 2006, pp. 208-220.

[17] E. S. Yu and C. Y. R. Chen, “Traffic Prediction Using Neural Networks,” Proceedings of the IEEE Global Tel-ecommunications Conference (GLOBCOM), Vol. 2, 1993, pp. 991-995.

[18] H. Lin and Y. Ouyang, “Neural Network Based Traffic Prediction for Cell Discarding Policy,” Proceedings of IJCNN’97, Vol. 4, 1997.

[19] A. Tarraf, I. Habib and T Saadawi, “Characterization of Packetized Voice Traffic In ATM Networks Using Neural Networks,” Proceeding of the IEEE Global Telecommu-nications Conference (GLOBCOM), Vol. 2, 1993, pp 996-1000.

[20] W. M. Moh, M.-J. Chen, N.-M. Chu and C.-D. Liao, “Traffic Prediction and Dynamic Bandwidth Allocation over ATM: A Neural Network Approach,” Computer Communications, Vol. 18, No. 8, 1995, pp. 563-571.

[21] C. Looney, “Pattern Recognition Using Neural Networks,” Oxford Press, Oxford, 1997.

[22] V. Vemuri and R. Rogers, “Artificial Neural Networks: Forecasting Time Series,” The IEEE Computer Society Press, Los Alamitos, 1994.

[23] D. C. Park, M. A. El-Sharkawi and R. J. Marks II, “Adaptively Trained Neural Network,” IEEE Transactions on Neural Networks, Vol. 2, No. 3, 1991, pp. 34-345.

[24] D. C. Park and T. K. Jeong, “Complex Bilinear Recurrent Neural Network for Equalization of a Satellite Channel,” IEEE Transactions on Neural Networks, Vol. 13, No. 3, 2002, pp. 711-725.

[25] D. C. Park, M. A. El-Sharkawi, R. J. Marks II, L. E. Atlas and M. J. Damborg, “Electronic Load Forecasting Using an Artificial Neural Network,” IEEE Transactions on Power Systems, Vol. 6, No. 2, 1991, pp. 442-449.

[26] D.-C. Park, “Structure Optimization of Bi-Linear Recurrent Neural Networks and its Application to Ethernet Network Traffic Prediction,” Information Sciences, 2009, in press.

[27] E. I. Vlahogianni, M. G. Karlaftis and J. C. Golias, “Opti-mized and Meta-Optimized Neural Networks for Short- Term Traffic Flow Prediction: A Genetic Approach,” Transportation Research Part C, Vol. 13, No. 3, 2005, pp. 211-234.

[28] A. Eswaradass, X.-H. Sun and M. Wu, “A Neural Net-work Based Predictive Mechanism for Available Band-width,” Proceeding of 19th IEEE International. Confe-rence on Parallel and Distributed Proceeding Symposium, Denver, 2005.

[29] N. Stamatis, D. Parthimos and T. M. Griffith, “Forecasting Chaotic Cardiovascular Time Series with an Adaptive Slope Multilayer Perceptron Neural Network,” IEEE Transactions on Biomedical Engineering, Vol. 46, No. 2, 1999, pp. 1441-1453.

[30] H. Yousefi’zadeh, E. A. Jonckheere and J. A. Silvester, “Utilizing Neural Networks to Reduce Packet Loss in Self-Similar Tele Traffic,” Proceeding of IEEE Interna-tional. Conference on Communications, Vol. 3, 2003, pp. 1942-1946.

[31] R. Mu?oz, O. Castillo and P. Melin, “Optimization of Fuzzy Response Integrators in Modular Neural Networks with Hierarchical Genetic Algorithms: The Case of Face, Fingerprint and Voice Recognition,” Evolutionary Design of Intelligent Systems in Modeling, Simulation and Control, Vol. 257, 2009, pp. 111-129.

[32] Y. C. Lin, J. Zhang and J. Zhong, “Application of Neural Networks to Predict the Elevated Temperature Flow Be-havior of a Low Alloy Steel,” Computational Materials Science, Vol. 43, 2008, pp. 752-758.

[33] R. Wieland and W. Mirschel, “Adaptive Fuzzy Modeling Versus Artificial Neural Networks,” Environmental Mod-eling & Software, Vol. 23, No. 2, 2008, pp. 215-224.

[34] H. M. Ertunc and M. Hosoz, “Comparative Analysis of an Evaporative Condenser Using Artificial Neural Network and Adaptive Neuro Fuzzy Inference System,” Interna-tional Journal of Refrigeration, Vol. 31, No. 8, 2009, pp. 1426-1436.

[35] C. L. Zhang, “Generalized Correlation of Refrigerant Mass Flow Rate Through Adiabatic Capillary Tubes Using Artificial Neural Network,” International Journal of Reference, Vol. 28, No. 4, 2005, pp. 506-514.

[36] A. Sencan and S. A. Kalogirou, “A New Approach Using Artificial Neural Networks for Determination of the Thermodynamic Properties of Fluid Couples,” Energy Conversion and Management, Vol. 46, No. 15-16, 2005, pp. 2405-2418.

[37] H. Esen, M. Inalli, A. Sengur and M. Esen, “Artificial Neural Networks and Adaptive Neuro-Fuzzy Assessments for Ground-Coupled Heat Pump System,” Energy and Buildings, Vol. 40, No. 6, 2008, pp. 1074-1083.

[38] A. Sang and S.-Q. Li, “A Predictability Analysis of Net-work Traffic,” Computer Networks, Vol. 39, No. 1, 2002, pp. 329-345.

[39] M. ??nar, M. Engin, E. Z. Engin and Y. Z. Ate??i, “Early Prostate Cancer Diagnosis by Using Artificial Neural Networks And Support Vector Machines,” Expert Systems with Applications, Vol. 36, No. 3, 2009, pp. 6357- 6361.

[40] R. Pasti and L. N. de Castro, “Bio-Inspired and Gradient- Based Algorithms to Train Mlps: The Influence of Diver-sity,” Information Sciences, Vol. 179, No. 10, 2009, pp. 1441-1453.

[41] A. Ebrahimzadeh and A. Khazaee, “Detection of Premature Ventricular Contractions Using MLP Neural Networks: A Comparative Study,” Measurement, Vol. 43, No. 1, 2010, pp. 103-112.

[42] D. E. Rumelhart and J. L. McClelland, “Parallel Distri-buted Processing Foundations,” MIT Press, Cambridge, 1986.

[43] Y. Chauvin, D. E. Rumelhart, (Eds.), “Backpropagation: Theory, Architectures, and Applications,” Lawrence Erl- baum Associates, Inc., Hillsdale, 1995.

[44] J. Ramesh, P. T. Vanathi and K. Gunavathi, “Fault Clas-sification in Phase-Locked Loops Using Back Propagation Neural Networks,” ETRI Journal, Vol. 30, No. 4, 2008, pp. 546-553.

[45] D. Panagiotopoulos, C. Orovas and D. Syndoukas, “A Heuristically Enhanced Gradient Approximation (HEGA) Algorithm for Training Neural Networks,” Neurocom-puting, Vol. 73, No. 7-9, 2010, pp. 1303-1323.

[46] A. E. Kostopoulos and T. Grapsa, “Self-Scaled Conjugate Gradient Training Algorithms,” Neurocomputing, Vol. 72, No. 13-15, 2009, pp. 3000-3019.

[47] R. Fletcher and C. M. Reeves, “Function Minimization by Conjugate Gradient,” Computer Journal, Vol. 7, No. 2, 1964, pp. 149-154.

[48] J. Nocedal and S. J. Wright, “Numerical Optimization”, Series in Operations Research, Springer Verlag, Heidel-berg, Berlin, New York, 1999.

[49] E .Polak and G. Ribiéres, “Note sur la convergence de méthodes de directions conjuguées,” Revue Fran?aise d’Informatique et de Recherche Opérationnelle, Vol. 16, 1969, pp. 35-43.

[50] M. J. D. Powell, “Restart Procedures for the Conjugate Gradient Method,” Mathematical Programming, Vol. 12, No. 1, 1977, pp. 241-254.

[51] D. Yuhong and Y. Yaxiang, “Convergence Properties of Beale-Powell Restart Algorithm,” Science in China (Series A), Vol. 41, No. 11, 1998, pp. 1142-1150.

[52] M. Moller, “A Scaled Conjugate Gradient Algorithm for Fast Supervised Learning,” Neural Networks, Vol. 6, No. 4, 1993, pp. 525-533.

[53] S. M. A. Burney, T. A. Jhilani and C. Adril, “Levenberg Mauquardt Algorithm for Karachi Stock Exchange Share Rates Forecasting,” Proceeding of World Academy of Science, Engineering, and Technology, Vol. 3, 2005, pp. 171-176.

[54] R. Battiti, “First- and Second-Order Methods for Learning: Between Steepest Descent and Newton’s Method,” Neural Computation, Vol. 4, No. 2, 1992, pp. 141-166.

[55] M. T. Hagan and M. B. Menhaj, “Training Feed-Forward Networks with the Marquardt Algorithm,” IEEE Trans-action Neural Networks, Vol. 5, No. 6, 1994, pp. 989- 993.

[56] M. I. A. Lourakis and A. A. Argyros, “The Design and Implementation of a Generic Sparse Buddle Adjustment Software Package Based on the Levenberg-Marquardt Algorithmy,” Technical Report FORTH-ICS/TR, No. 340, Institute of Computer Science, August 2004.

[57] K. Levenberg, “A Method for the Solution of Certain Non-linear Problems in Least Squares,” Quarterly of Ap-plied Mathematics, Vol. 2, No. 2, 1944, pp. 164-168.

[58] D. W. Marquardt, “An Algorithm for the Least-Squares Estimation of Non linear Parameters”, SIAM Journal of Applied Mathematics, Vol. 11, No. 2, 1963, pp. 431-441.

[59] M. Riedmiller and H. Braun, “A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP Algo-rithm,” In: H. Ruspini, Ed., Proceeding of the IEEE in-ternational conference on neural networks (ICNN), San Francisco, 1993, pp. 586-591.

[60] M. Riedmiller, “Rprop—Description and Implementation Details,” Technical Report, University of Karlsruhe, Karlsruhe, 1994.

[61] N. K. Treadgold and T. D. Gedeon, “The SARPROP Algorithm: A Simulated Annealing Enhancement to Resi-lient Back Propagation,” Proceedings International Panel Conference on Soft and Intelligent Computing, Budapest, 1996, pp. 293-298.

[62] M. M. Mostafa, “Profiling Blood Donors in Egypt: A Neural Network Analysis,” Expert Systems with Applica-tions, Vol. 36, No. 3, 2009, pp. 5031-5038.

[63] S. Chabaa, A. Zeroual and J. Antari, “MLP Neural Net-works for Modeling non Gaussian Signal,” Workshop STIC Wotic’09 in Agadir, 24-25 December 2009, p. 58.

[64] H. Demuth and M. Beale, “Neural Network Toolbox for Use with MATLAB: Computation, Visualization, Pro-gramming, User’s Guide, Version 3.0,” The Mathworks Inc., Asheboro, 2001.

[65] V. Karri, T. Ho and O. Madsen, “Artificial Neural Net-works and Neuro-Fuzzy Inference Systems as Virtual Sensors for Hydrogen Safety Prediction,” International Journal of Hydrogen Energy, Vol. 33, No. 11, 2008, pp. 2857-2867.

[66] J. Antari, R. Iqdour and A. Zeroual, “Forecasting the Wind Speed Process Using Higher Order Statistics and Fuzzy Systems,” Review of Renewable Energy, Vol. 9, No. 4, 2006, pp. 237-251.

[1] J.-J. Wu, Z.-Y. Gao and H.-J. Sun, “Statistical Properties of Individual Choice Behaviors on Urban Traffic Net-works,” Journal of Transportation Systems Engineering and Information Technology, Vol. 8, No. 2, 2008, pp. 69-74.

[2] R. Albert and A. L. Barabási, “Statistical Mechanics of Complex Networks,” Review Modern Physics, Vol. 74, No. 1, 2002, pp. 47-97.

[3] J.-J. Wu, H.-J. Sun and Z.-Y. Gao, “Cascade and Break-down in Scale-Free Networks with Community Structure”, Physical Review E-Statistical, Nonlinear, and Soft Matter Physics, Vol. 74, No. 6, 2006.

[4] W. E. Leland, M. S. Taqqu, W. Willinger and D. V. Wil-son, “On the Self Similar Nature of Ethernet Traffic,” Proceedings of ACM Sigcomm, San Francisco, 1993, pp. 183-193.

[5] R. Yunhua, “Evaluation and Estimation of Second-Order Self-Similar Network Traffic,” Computer Communications, Vol. 27, No. 9, 2004, pp. 898-904.

[6] B. R. Chang and H. F. Tsai, “Novel Hybrid Approach to Data-Packet-Flow Prediction for Improving Network Traffic Analysis,” Applied Soft Computing, Vol. 9, No. 3, 2009, pp. 1177-1183.

[7] B. R. Chang and H. F. Tsai, “Improving Network Traffic Analysis by Foreseeing Data-Packet-Flow with Hybrid Fuzzy-Based Model Prediction,” Expert Systems with Ap-plications, Vol. 36, No. 3, 2009, pp. 6960-6965.

[8] A. Stathopoulos and M. G. Karlaftis, “A Multivariate State Space Approach for Urban Traffic Flow Modeling and Prediction,” Transportation Research Part C, Vol. 11, No. 2, 2003, pp. 121-135.

[9] D.-C. Park, “Prediction of MPEG video traffic over ATM Networks Using Dynamic Bilinear Recurrent Neural Network,” Applied Mathematics and Computation, Vol. 205, No. 2, 2008, pp. 648-657.

[10] B. Zhou, D. He, Z. Sun and W. H. Ng, “Network Traffic Modeling and Prediction with ARIMA/GARTH,” HET- NETs’ 06 Conference, Ilkley, 11-13 September 2006, pp. 1-10.

[11] A. Taraf, I. Habib and T. Saadawi, “Neural Networks for ATM Multimedia Traffic Prediction,” Proceedings of the International Workshop on Applications of Neural Net-works to Telecommunications, Princeton, 1993, pp. 85-91.

[12] P. Chang and J. Hu, “Optimal Non-Linear Adaptive Pre-diction And Modeling Of MPEG Video in ATM Net-works Using Pipelined Recurrent Neural Networks,” IEEE Journal on Selected Areas in Communications, Vol. 15, No. 6, 1997, pp. 1087-1100.

[13] A. Abdennour, “Evaluation of Neural Network Architec-tures for MPEG-4 Video Traffic Prediction,” IEEE Transactions on Broadcasting, Vol. 52, No. 2, pp. 184-192, 2006.

[14] A. F. Atiya, M. A. Aly and A. G. Parlos, “Sparse Basis Selection: New Results and Application to Adaptive Pre-diction of Video Source Traffic,” IEEE Transactions on Neural Networks, Vol. 16, No. 5, 2005, pp. 1136-1146.

[15] Z. Fang, Y. Zhou and D. Zou, “Kalman Optimized Model for MPEG-4 VBR Sources,” IEEE Transactions on Con-sumer Electronics, Vol. 50, No. 2, 2004, pp. 688-690.

[16] V. Alarcon-Aquino and J. A. Barria, “Multi Resolution Fir Neural Network-Based Learning Algorithm Applied to Network Traffic Prediction,” IEEE Transactions on Systems, Man and Cybernetics-Part C: Applications and Reviews, Vol. 36, No. 2, 2006, pp. 208-220.

[17] E. S. Yu and C. Y. R. Chen, “Traffic Prediction Using Neural Networks,” Proceedings of the IEEE Global Tel-ecommunications Conference (GLOBCOM), Vol. 2, 1993, pp. 991-995.

[18] H. Lin and Y. Ouyang, “Neural Network Based Traffic Prediction for Cell Discarding Policy,” Proceedings of IJCNN’97, Vol. 4, 1997.

[19] A. Tarraf, I. Habib and T Saadawi, “Characterization of Packetized Voice Traffic In ATM Networks Using Neural Networks,” Proceeding of the IEEE Global Telecommu-nications Conference (GLOBCOM), Vol. 2, 1993, pp 996-1000.

[20] W. M. Moh, M.-J. Chen, N.-M. Chu and C.-D. Liao, “Traffic Prediction and Dynamic Bandwidth Allocation over ATM: A Neural Network Approach,” Computer Communications, Vol. 18, No. 8, 1995, pp. 563-571.

[21] C. Looney, “Pattern Recognition Using Neural Networks,” Oxford Press, Oxford, 1997.

[22] V. Vemuri and R. Rogers, “Artificial Neural Networks: Forecasting Time Series,” The IEEE Computer Society Press, Los Alamitos, 1994.

[23] D. C. Park, M. A. El-Sharkawi and R. J. Marks II, “Adaptively Trained Neural Network,” IEEE Transactions on Neural Networks, Vol. 2, No. 3, 1991, pp. 34-345.

[24] D. C. Park and T. K. Jeong, “Complex Bilinear Recurrent Neural Network for Equalization of a Satellite Channel,” IEEE Transactions on Neural Networks, Vol. 13, No. 3, 2002, pp. 711-725.

[25] D. C. Park, M. A. El-Sharkawi, R. J. Marks II, L. E. Atlas and M. J. Damborg, “Electronic Load Forecasting Using an Artificial Neural Network,” IEEE Transactions on Power Systems, Vol. 6, No. 2, 1991, pp. 442-449.

[26] D.-C. Park, “Structure Optimization of Bi-Linear Recurrent Neural Networks and its Application to Ethernet Network Traffic Prediction,” Information Sciences, 2009, in press.

[27] E. I. Vlahogianni, M. G. Karlaftis and J. C. Golias, “Opti-mized and Meta-Optimized Neural Networks for Short- Term Traffic Flow Prediction: A Genetic Approach,” Transportation Research Part C, Vol. 13, No. 3, 2005, pp. 211-234.

[28] A. Eswaradass, X.-H. Sun and M. Wu, “A Neural Net-work Based Predictive Mechanism for Available Band-width,” Proceeding of 19th IEEE International. Confe-rence on Parallel and Distributed Proceeding Symposium, Denver, 2005.

[29] N. Stamatis, D. Parthimos and T. M. Griffith, “Forecasting Chaotic Cardiovascular Time Series with an Adaptive Slope Multilayer Perceptron Neural Network,” IEEE Transactions on Biomedical Engineering, Vol. 46, No. 2, 1999, pp. 1441-1453.

[30] H. Yousefi’zadeh, E. A. Jonckheere and J. A. Silvester, “Utilizing Neural Networks to Reduce Packet Loss in Self-Similar Tele Traffic,” Proceeding of IEEE Interna-tional. Conference on Communications, Vol. 3, 2003, pp. 1942-1946.

[31] R. Mu?oz, O. Castillo and P. Melin, “Optimization of Fuzzy Response Integrators in Modular Neural Networks with Hierarchical Genetic Algorithms: The Case of Face, Fingerprint and Voice Recognition,” Evolutionary Design of Intelligent Systems in Modeling, Simulation and Control, Vol. 257, 2009, pp. 111-129.

[32] Y. C. Lin, J. Zhang and J. Zhong, “Application of Neural Networks to Predict the Elevated Temperature Flow Be-havior of a Low Alloy Steel,” Computational Materials Science, Vol. 43, 2008, pp. 752-758.

[33] R. Wieland and W. Mirschel, “Adaptive Fuzzy Modeling Versus Artificial Neural Networks,” Environmental Mod-eling & Software, Vol. 23, No. 2, 2008, pp. 215-224.

[34] H. M. Ertunc and M. Hosoz, “Comparative Analysis of an Evaporative Condenser Using Artificial Neural Network and Adaptive Neuro Fuzzy Inference System,” Interna-tional Journal of Refrigeration, Vol. 31, No. 8, 2009, pp. 1426-1436.

[35] C. L. Zhang, “Generalized Correlation of Refrigerant Mass Flow Rate Through Adiabatic Capillary Tubes Using Artificial Neural Network,” International Journal of Reference, Vol. 28, No. 4, 2005, pp. 506-514.

[36] A. Sencan and S. A. Kalogirou, “A New Approach Using Artificial Neural Networks for Determination of the Thermodynamic Properties of Fluid Couples,” Energy Conversion and Management, Vol. 46, No. 15-16, 2005, pp. 2405-2418.

[37] H. Esen, M. Inalli, A. Sengur and M. Esen, “Artificial Neural Networks and Adaptive Neuro-Fuzzy Assessments for Ground-Coupled Heat Pump System,” Energy and Buildings, Vol. 40, No. 6, 2008, pp. 1074-1083.

[38] A. Sang and S.-Q. Li, “A Predictability Analysis of Net-work Traffic,” Computer Networks, Vol. 39, No. 1, 2002, pp. 329-345.

[39] M. ??nar, M. Engin, E. Z. Engin and Y. Z. Ate??i, “Early Prostate Cancer Diagnosis by Using Artificial Neural Networks And Support Vector Machines,” Expert Systems with Applications, Vol. 36, No. 3, 2009, pp. 6357- 6361.

[40] R. Pasti and L. N. de Castro, “Bio-Inspired and Gradient- Based Algorithms to Train Mlps: The Influence of Diver-sity,” Information Sciences, Vol. 179, No. 10, 2009, pp. 1441-1453.

[41] A. Ebrahimzadeh and A. Khazaee, “Detection of Premature Ventricular Contractions Using MLP Neural Networks: A Comparative Study,” Measurement, Vol. 43, No. 1, 2010, pp. 103-112.

[42] D. E. Rumelhart and J. L. McClelland, “Parallel Distri-buted Processing Foundations,” MIT Press, Cambridge, 1986.

[43] Y. Chauvin, D. E. Rumelhart, (Eds.), “Backpropagation: Theory, Architectures, and Applications,” Lawrence Erl- baum Associates, Inc., Hillsdale, 1995.

[44] J. Ramesh, P. T. Vanathi and K. Gunavathi, “Fault Clas-sification in Phase-Locked Loops Using Back Propagation Neural Networks,” ETRI Journal, Vol. 30, No. 4, 2008, pp. 546-553.

[45] D. Panagiotopoulos, C. Orovas and D. Syndoukas, “A Heuristically Enhanced Gradient Approximation (HEGA) Algorithm for Training Neural Networks,” Neurocom-puting, Vol. 73, No. 7-9, 2010, pp. 1303-1323.

[46] A. E. Kostopoulos and T. Grapsa, “Self-Scaled Conjugate Gradient Training Algorithms,” Neurocomputing, Vol. 72, No. 13-15, 2009, pp. 3000-3019.

[47] R. Fletcher and C. M. Reeves, “Function Minimization by Conjugate Gradient,” Computer Journal, Vol. 7, No. 2, 1964, pp. 149-154.

[48] J. Nocedal and S. J. Wright, “Numerical Optimization”, Series in Operations Research, Springer Verlag, Heidel-berg, Berlin, New York, 1999.

[49] E .Polak and G. Ribiéres, “Note sur la convergence de méthodes de directions conjuguées,” Revue Fran?aise d’Informatique et de Recherche Opérationnelle, Vol. 16, 1969, pp. 35-43.

[50] M. J. D. Powell, “Restart Procedures for the Conjugate Gradient Method,” Mathematical Programming, Vol. 12, No. 1, 1977, pp. 241-254.

[51] D. Yuhong and Y. Yaxiang, “Convergence Properties of Beale-Powell Restart Algorithm,” Science in China (Series A), Vol. 41, No. 11, 1998, pp. 1142-1150.

[52] M. Moller, “A Scaled Conjugate Gradient Algorithm for Fast Supervised Learning,” Neural Networks, Vol. 6, No. 4, 1993, pp. 525-533.

[53] S. M. A. Burney, T. A. Jhilani and C. Adril, “Levenberg Mauquardt Algorithm for Karachi Stock Exchange Share Rates Forecasting,” Proceeding of World Academy of Science, Engineering, and Technology, Vol. 3, 2005, pp. 171-176.

[54] R. Battiti, “First- and Second-Order Methods for Learning: Between Steepest Descent and Newton’s Method,” Neural Computation, Vol. 4, No. 2, 1992, pp. 141-166.

[55] M. T. Hagan and M. B. Menhaj, “Training Feed-Forward Networks with the Marquardt Algorithm,” IEEE Trans-action Neural Networks, Vol. 5, No. 6, 1994, pp. 989- 993.

[56] M. I. A. Lourakis and A. A. Argyros, “The Design and Implementation of a Generic Sparse Buddle Adjustment Software Package Based on the Levenberg-Marquardt Algorithmy,” Technical Report FORTH-ICS/TR, No. 340, Institute of Computer Science, August 2004.

[57] K. Levenberg, “A Method for the Solution of Certain Non-linear Problems in Least Squares,” Quarterly of Ap-plied Mathematics, Vol. 2, No. 2, 1944, pp. 164-168.

[58] D. W. Marquardt, “An Algorithm for the Least-Squares Estimation of Non linear Parameters”, SIAM Journal of Applied Mathematics, Vol. 11, No. 2, 1963, pp. 431-441.

[59] M. Riedmiller and H. Braun, “A Direct Adaptive Method for Faster Backpropagation Learning: The RPROP Algo-rithm,” In: H. Ruspini, Ed., Proceeding of the IEEE in-ternational conference on neural networks (ICNN), San Francisco, 1993, pp. 586-591.

[60] M. Riedmiller, “Rprop—Description and Implementation Details,” Technical Report, University of Karlsruhe, Karlsruhe, 1994.

[61] N. K. Treadgold and T. D. Gedeon, “The SARPROP Algorithm: A Simulated Annealing Enhancement to Resi-lient Back Propagation,” Proceedings International Panel Conference on Soft and Intelligent Computing, Budapest, 1996, pp. 293-298.

[62] M. M. Mostafa, “Profiling Blood Donors in Egypt: A Neural Network Analysis,” Expert Systems with Applica-tions, Vol. 36, No. 3, 2009, pp. 5031-5038.

[63] S. Chabaa, A. Zeroual and J. Antari, “MLP Neural Net-works for Modeling non Gaussian Signal,” Workshop STIC Wotic’09 in Agadir, 24-25 December 2009, p. 58.

[64] H. Demuth and M. Beale, “Neural Network Toolbox for Use with MATLAB: Computation, Visualization, Pro-gramming, User’s Guide, Version 3.0,” The Mathworks Inc., Asheboro, 2001.

[65] V. Karri, T. Ho and O. Madsen, “Artificial Neural Net-works and Neuro-Fuzzy Inference Systems as Virtual Sensors for Hydrogen Safety Prediction,” International Journal of Hydrogen Energy, Vol. 33, No. 11, 2008, pp. 2857-2867.

[66] J. Antari, R. Iqdour and A. Zeroual, “Forecasting the Wind Speed Process Using Higher Order Statistics and Fuzzy Systems,” Review of Renewable Energy, Vol. 9, No. 4, 2006, pp. 237-251.