Scientific Research

An Academic Publisher

A Comparative Study of Nonlinear Time-Varying Process Modeling Techniques: Application to Chemical Reactor ()

**Author(s)**Leave a comment

This paper proposes the design and a comparative study of two nonlinear systems modeling techniques. These two approaches are developed to address a class of nonlinear systems with time-varying parameter. The first is a Radial Basis Function (RBF) neural networks and the second is a Multi Layer Perceptron (MLP). The MLP model consists of an input layer, an output layer and usually one or more hidden layers. However, training MLP network based on back propagation learning is computationally expensive. In this paper, an RBF network is called. The parameters of the RBF model are optimized by two methods: the Gradient Descent (GD) method and Genetic Algorithms (GA). However, the MLP model is optimized by the Gradient Descent method. The performance of both models are evaluated first by using a numerical simulation and second by handling a chemical process known as the Continuous Stirred Tank Reactor CSTR. It has been shown that in both validation operations the results were successful. The optimized RBF model by Genetic Algorithms gave the best results.

Cite this paper

E. Ayachi, S. Ihsen and B. Mohamed, "A Comparative Study of Nonlinear Time-Varying Process Modeling Techniques: Application to Chemical Reactor,"

*Journal of Intelligent Learning Systems and Applications*, Vol. 4 No. 1, 2012, pp. 20-28. doi: 10.4236/jilsa.2012.41002.Conflicts of Interest

The authors declare no conflicts of interest.

[1] | V. T. S. Elanayar and C. S. Yung, “Radial Basis Function Neural Network for Approximation and Estimation of Nonlinear Stochastic Dynamic,” IEEE Transactions on Neural Networks, Vol. 5, No. 4, 1994, pp. 594-603. doi:10.1109/72.298229 |

[2] | P. Borne, M. Benrejeb and J. Haggege, “Les Réseaux de Neurones. Présentation et Applications,” Editions Ophrys, Paris, 2007. |

[3] | S. Chabaa, A. Zeroual and J. Antari, “Identification and Prediction of Internet Traffic Using Artificial Neural Networks,” Journal of Intelligent Learning Systems & Applications, Vol. 2, No. 3, 2010, pp. 147-155. |

[4] | A. Errachdi, I. Saad and M. Benrejeb, “On-Line Identification Method Based on Dynamic Neural Network,” International Review of Automatic Control, Vol. 3, No. 5, 2010, pp. 474-479. |

[5] | H. Vijay and D. K. Chaturvedi, “Parameters Estimation of an Electric Fan Using ANN,” Journal of Intelligent Learning Systems & Applications, Vol. 2, No. 1, 2010, pp. 43-48. |

[6] | A. Mishra and Zaheeruddin, “Design of Hybrid Fuzzy Neural Network for Function Approximation,” Journal of Intelligent Learning Systems & Applications, Vol. 2, No. 2, 2010, pp. 97-109. |

[7] | A. Errachdi, I. Saad and M. Benrejeb, “Internal Model Control for Nonlinear Time-Varying System Using Neural Networks,” 11th International Conference on Sciences and Techniques of Automatic Control & Computer Engineering, Monastir, 19-21 December 2010, pp. 1-13. |

[8] | Y. Tan, “Time-Varying Time-Delay Estimation for Nonlinear Systems Using Neural Networks,” International Journal of Applied Mathematics and Computer Science, Vol. 14, No. 1, 2004, pp. 63-68. |

[9] | R. Sollacher and H. Gao, “Towards Real-World Applications of Online Learning Spiral Recurrent Neural Networks,” Journal of Intelligent Learning Systems & Applications, Vol. 1, No. 1, 2009, pp. 1-27. |

[10] | S. H. Ling, “A New Neural Network Structure: Node-toNode-Link Neural Network,” Journal of Intelligent Learning Systems & Applications, Vol. 2, No. 1, 2010, pp. 111. |

[11] | J. C. Garcia Infante, J. Jesús Medel Juárez and J. C. Sánchez García, “Evolutive Neural Net Fuzzy Filtering: Basic Description,” Journal of Intelligent Learning Systems & Applications, Vol. 2, No. 1, 2010, pp. 12-18. |

[12] | K. N. Sujatha and K. Vaisakh, “Implementation of Adaptive Neuro Fuzzy Inference System in Speed Control of Induction Motor Drives,” Journal of Intelligent Learning Systems & Applications, Vol. 2, No. 2, 2010, pp. 110118. |

[13] | R. H. Middleton and G. C. Goodwin, “Adaptive Control of Time-Varying Linear Systems,” IEEE Transactions on Automatic Control, Vol. 33, No. 2, 1988, pp. 150-155. doi:10.1109/9.382 |

[14] | F. Giri, M. Saad, J. M. Dion and L. Dugard, “Pole Placement Direct Adaptive Control for Time-Varying Ill-Modeled Plants,” IEEE Transactions on Automatic Control, Vol. 35, 1990, pp. 723-726. doi:10.1109/9.53553 |

[15] | K. S. Tsakalis and P. A. Ioannou, “Linear Time-Varying Systems: Control and Adaptation,” Prentice-Hall, Upper Saddle River, 1993. |

[16] | R. Marino and P. Tomei, “Adaptive Control of Linear Time-Varying Systems,” Automatica, Vol. 39, No. 4, 2003, pp. 651-659. doi:10.1016/S0005-1098(02)00287-X |

[17] | R.-H. Chi, S.-L. Sui and Z.-S. Hou, “A New DiscreteTime Adaptive ILC for Nonlinear Systems with TimeVarying Parametric Uncertainties,” ACTA Automatica Sinica, Vol. 34, No. 7, 2008, pp. 805-808. doi:10.3724/SP.J.1004.2008.00805 |

[18] | M. R. Berthold, “A Time Delay Radial Basis Function Network for Phoneme Recognition,” IEEE Rerthold Intel Corporation, Santa Clara, 1994, pp. 4470-4472. |

[19] | M. Zarouan, J. Haggège and M. Benrejeb, “Anomalies de Fonctionnement de Systèmes Dynamiques et Modélisation par Réseaux de Neurones des Non-Linearités: Cas de la Démultiplication de Fréquence,” Premières Journées Scientifiques des Jeunes Chercheurs en Genie Electrique et Informatique, 23-24 March 2001, Sousse-Tunisie, pp. 123-128. |

[20] | J. Haggège, M. Zarouan and M. Benrejeb, “Anomalies de Fonctionnement et Modélisation de systèMes Dynamiques par réSeaux de Neurones: Cas du Phénomène de Saut,” Premières Journées Scientifiques des Jeunes Chercheurs en Genie Electrique et Informatique, 23-24 March 2001, Sousse-Tunisie, pp. 134-138. |

[21] | S. Allali and M. Benrejeb, “Application des Réseaux de Neurones Multicouches pour le Choix Optimal des Machines Outils,” 4 ème Conférence Internationale JTEA, Hammamet, 12-14 March 2006. |

[22] | H. Bouziane, B. Messabih and A. Chouarfia, “Prédiction de la Structure 2D des Protéines par les Réseaux de Neurones,” Communications of the IBIMA, Vol. 6, 2008, pp. 201-207. |

[23] | J. Park and I. Sandberg, “Universal Approximation Using Radial-Basis-Function Networks,” Neural Computation, Vol. 3, No. 2, 1991, pp. 246-257. doi:10.1162/neco.1991.3.2.246 |

[24] | A. Sifaoui, A. Abdelkrim, S. Alouane and M. Benrejeb, “On new RBF Neural Network Construction Algorithm for Classification,” SIC, Vol. 18, No. 2, 2009, pp. 103110. |

[25] | A. Golbabai, M. Mammadov and S. Seifollahi, “Solving a System of Nonlinear Integral Equations by an RBF Network,” Computer and Mathematics with Applications, Vol. 57, No. 10, 2009, pp. 1651-165. doi:10.1016/j.camwa.2009.03.038 |

[26] | X. Chengying and C. S. Yung, “Interaction Analysis for MIMO Nonlinear Systems Based on a Fuzzy Basis Function Network Model,” Fuzzy Sets and Systems, Vol. 158, No. 18, 2007, pp. 2013-2025. doi:10.1016/j.fss.2007.02.012 |

[27] | S. S. Chiddarwar and N. R. Babu, “Comparison of RBF and MLP Neural Networks to Solve Inverse Kinematic Problem for 6R Serial Robot by a Fusion Approach,” Engineering Applications of Artificial Intelligence, Vol. 23, No. 7, 2010, pp. 1-10. |

[28] | R. P. Brent, “Fast Training Algorithms for Multilayer Neural Net,” IEEE Transactions on Neural Networks, Vol. 5, No. 6, 1991, pp. 989-993. |

[29] | M. T. Hagan and M. Menhaj, “Training Feedforward Networks with Marquardt Algorithm,” IEEE Transactions on Neural Networks, Vol. 5, No. 6, 1994, pp. 989993. doi:10.1109/72.329697 |

[30] | R. A. Jacobs, “Increased Rates of Converge through Learning Rate Adaptation,” Neural Networks, Vol. 1, No. 4, 1988, pp. 295-307. doi:10.1016/0893-6080(88)90003-2 |

[31] | D. C. Park., M. A. El Sharkawi and R. J. Marks II, “An Adaptively Trained Neural Network,” IEEE Transactions on Neural Networks, Vol. 2, No. 3, 1991, pp. 334-345. doi:10.1109/72.97910 |

[32] | M. Schoenauer and Z. Michalewicz, “Evolutionary Computation,” Control and Cybernetics, Vol. 26, No. 3, 1997, pp. 307-338. |

[33] | A. Errachdi, I. Saad and M. Benrejeb, “Neural Modeling of Multivariable Nonlinear System. Variable Learning Rate Case,” Intelligent Control and Automation, Vol. 2, No. 3, 2011, pp. 165-175. |

[34] | W. L. Cheol and C. S. Yung, “Growing Radial Basis Function Networks Using Genetic Algorithm and Orthogonalization,” International Journal of Innovative Computing, Information and Control ICIC International, Vol. 5, No. 11A, 2009, pp. 3933-3948. |

[35] | G. Lin, H. De-Shuang and Z. Wenbo, “Combining Genetic Optimization with Hybrid Learning Algorithm for Radial Basis Function Neural Networks,” Electronic Letters, Vol. 39, No. 22, 2003, pp. 1600-1601. |

[36] | T. Renato and O. M. J. Luiz, “Selection of Radial Basis Functions via Genetic Algorithms in Pattern Recognition Problems,” 10th Brazilian Symposium on Neural Networks, Salvador, 26-30 October 2008, pp. 71-176. |

[37] | M. L. Huang and Y. H. Hung, “Combining Radial Basis Function Neural Network and Genetic Algorithm to Improve HDD Driver IC Chip Scale Package Assembly Yield,” Expert Systems with Applications, Vol. 34, No. 1, 2008, pp. 588-595. doi:10.1016/j.eswa.2006.09.030 |

[38] | R. Niranjan and G. Ranjan, “Filter Design Using Radial Basis Function Neural Network and Genetic Algorithm for Improved Operational Health Monitoring,” Applied Soft Computing, Vol. 6, No. 2, 2006, pp. 154-169. doi:10.1016/j.asoc.2004.11.002 |

[39] | C. Junghui and H. Tien-Chih, “Applying Neural Networks to On-Line Updated PID Controllers for Nonlinear Process Control,” Journal of Process Control, Vol. 14, No. 2, 2004, pp. 211-230. doi:10.1016/S0959-1524(03)00039-8 |

[40] | J. Van Grop, J. Schoukens and R. Pintelon, “Learning Neural Networks with Noise Inputs Using the Errors in Variables Approach,” IEEE Transactions on Neural Networks, Vol. 11, No. 2, 2000, pp. 402-414. doi:10.1109/72.839010 |

[41] | H. Demuth, M. Beale and M. Hagan, “Neural Network Toolbox 5,” User’s Guide, The MathWorks, Natick, 2007. |

Copyright © 2020 by authors and Scientific Research Publishing Inc.

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.