A Comparison Study of MIMO Water Wall Model with Linear, MFNN and ESN Models

  • Moon, Un-Chul (School of Electrical and Electronic Engineering, Chung-Ang University) ;
  • Lim, Jaewoo (School of Electrical and Electronic Engineering, Chung-Ang University) ;
  • Lee, Kwang Y. (Dept. of Electrical and Computer Engineering, Baylor University)
  • Received : 2015.04.25
  • Accepted : 2015.08.30
  • Published : 2016.03.01


A water wall system is one of the most important components of a boiler in a thermal power plant, and it is a nonlinear Multi-Input and Multi-Output (MIMO) system, with 6 inputs and 3 outputs. Three models are developed and comp for the controller design, including a linear model, a multilayer feed-forward neural network (MFNN) model and an Echo State Network (ESN) model. First, the linear model is developed by linearizing a given nonlinear model and is analyzed as a function of the operating point. Second, the MFNN and the ESN are developed by using training data from the nonlinear model. The three models are validated using Matlab with nonlinear input-output data that was not used during training.


Water wall model;Power plant modelling;Power plant identification;Linearization;Multilayer feed-forward neural network;Echo state network


  1. C. Liu, H. Wang, J. Ding, and C. Zhen, “An Overview of Modelling and Simulation of Thermal Power Plant,” Proc. of the 2011 International Conference on Advanced Systems, pp. 86-91, Zhengzhou, China, 2011.
  2. L. Xueqin, L. Gang, and L. Shangqing, “The development of the boiler Water Wall Tube Inspection,” Third International Conference on Electric Utility Deregulation and Restructuring and Poewer Technologies, pp. 2415-2420, Nanjing, April 2008.
  3. P. B. Usoro, “Modeling and Simulation of a Drum Boiler-Turbine Power Plant Under Emergency State Control,” Master Degree of Massachusetts Institute of Technology, pp.138-139, May 1977.
  4. U.-C. Moon, and K. Y. Lee, “An Adaptive Dynamic Matrix Control with Fuzzy-Interpolated Step-Response Model for a Drum-Type Boiler-Turbine System,” IEEE Transactions on Energy Conversion, Vol. 26, No. 2, pp. 393-401, June 2011.
  5. V. Kecman, Learning and Soft Computing: Support Vector Machines, Neural Networks and Fuzzy Logic Models, Piscataway, NJ: IEEE MIT Press, 2002.
  6. I. Snadburg, J. Lo, C. Fancourt, J. Principe, S. Katagiri, and S. Haykin, Nonlinear Dynamical Systems: Feed-forward Neural Network Perspectives, New York: Wiley, 2001.
  7. F. J. Lin, Y. C. Hung, and S. Y. Chen, “FPGA-Based Computed Force Control System Using Elman Neural Network for Linear Ultrasonic Motor,” IEEE Transactions on industrial electronics, Vol. 56, No. 4, pp. 1238-1253, April 2009.
  8. Ku, C. C. and K. Y. Lee, “Diagonal Recurrent Neural Network for Dynamic Systems Control,” IEEE Transactions on Neural Networks, Vol. 6, pp. 144-156, January 1995.
  9. A. F. Atiya and A. G. Parlos, “New results on recurrent network training: Unifying the algorithms and accelerating convergence,” IEEE Transactions on Neural Networks, vol. 11, no. 3, pp. 697-709, May 2000.
  10. H. Jaeger, “The echo sate approach to analyzing and training recurrent neural networks-with an Erratum note,” Fraunhofer Institute for Autonomous Intelligent Systems (AIS), January 26, 2010.
  11. D. Prokhorov, "Echo state networks: Appeal and challenges," in Proc. IEEE International Conference Neural Networks (IJCNN05), Montreal, PQ, Canada, July 31-August 4, 2005, Vol. 2, pp. 905-910.
  12. H. Jaeger, M. Lukosevicius, D. Popovici and U. Siewert, “Optimization and applications of echo state networks with leaky-integrator neurons,” Neural Networks, Vol. 20, special issue, pp. 335-352, 2007.
  13. X. Lin, Z. Yang, and Y. Song, “Intelligent stock trading system based on improved technical analysis and Echo State Network,” Expert Systems with Applications, Vol. 38, pp. 11347-11354, 2011.
  14. K. Ishii, T. van der Zant, V. Becanovic and P. Ploger, “Optimization of Parameter of Echo State Network and Its Application to Underwater Robot,” SICE Annual Conference in Sapporo, pp. 2800-2805, August 2004.
  15. J. Dai, P. Zhang, J. Mazumdar, R. G. Harley and G. K. Venayagamoorthy “A Comparison of MLP, RNN and ESN in Determining Harmonic Contribution from Nonlinear Loads,” 34th Annual Conference of IEEE on Industrial Electronics, pp. 3025-3032, November 2008.
  16. Y. Pan, and J. Wang, “Model Predictive Control of Unknown Nonlinear Dynamical Systems Based on Recurrent Neural Networks,” IEEE Transactions on Industrial Electronics, Vol. 59, No. 8, pp. 3089-3101, August 2012.
  17. R. Johansson, System Modeling and Identification, Englewood Cliffs, NJ, USA: Prentice-Hall, 1992.
  18. S. Haykin, Neural Networks, Ottawa, On, Canada: Maxwell Macmillan, 1994.
  19. J. Mazumdar, and R. G. Harley, “Utilization of echo state networks for differentiating source and nonlinear load harmonics in the utility network,” IEEE Transactions on power Electronics, Vol. 23, No. 6, pp. 2738-2745, November 2008.
  20. G. Venayagamoorthy, “Online design of an echo state network based wide area monitor for a multimachine power system,” Neural Networks, Vol. 20, No. 3, pp. 404-413, April 2007.
  21. D. Li, M. Han, and J. Wang, “Chaotic time series prediction based on a novel robust echo state network,” IEEE Transactions on Neural Networks and Learning Systems, vol. 23, no. 5, pp. 787-799, May 2012.
  22. H. Jaeger, "A tutorial on training recurrent neural networks, covering BPPT, RTRL, EKF and echo state network approach," GMD-Report 159, German National Research Center for Information Technology, 2002.
  23. B. Zhang, D. J. Miller, and Y. Wang, “Nonlinear system modeling with random matrices: Echo state networks revisited,” IEEE Transactions on Neural Networks and Learning systems, Vol. 23, No. 1, pp. 175-182, January 2012.
  24. A. Millea, "Explorations in echo state networks," Department of Artificial Intelligence, Groningen University, MA, Netherlands, S2064235, June 2014.

Cited by

  1. Practical dynamic matrix control for thermal power plant coordinated control vol.71, 2018,