Cascade Process Modeling with Mechanism-Based Hierarchical Neural Networks

Abstract Cascade process, such as wastewater treatment plant, includes many nonlinear subsystems and many variables. When the number of sub-systems is big, the input-output relation in the first block and the last block cannot represent the whole process. In this paper we use two techniques to overcome the above problem. First we propose a new neural model: hierarchical neural networks to identify the cascade process. Then we use serial structural mechanism model based on the physical equations to connect with neural model. A stable learning algorithm and theoretical analysis are given. Finally, this method is used to model a wastewater treatment plant. Real operational data of wastewater treatment plant is applied to illustrate the modeling approach.

[1]  Peter A Vanrolleghem,et al.  Parallel hybrid modeling methods for a full-scale cokes wastewater treatment plant. , 2005, Journal of biotechnology.

[2]  Xiaoou Li,et al.  Some new results on system identification with dynamic neural networks , 2001, IEEE Trans. Neural Networks.

[3]  Jun Zhou,et al.  Hierarchical fuzzy control , 1991 .

[4]  George Cybenko,et al.  Approximation by superpositions of a sigmoidal function , 1992, Math. Control. Signals Syst..

[5]  Lennart Ljung,et al.  Theory and Practice of Recursive Identification , 1983 .

[6]  Jinn-Wen Wu,et al.  Stability of Neural Field , 2007, Int. J. Neural Syst..

[7]  Marios M. Polycarpou,et al.  Learning and convergence analysis of neural-type structured networks , 1992, IEEE Trans. Neural Networks.

[8]  Jan F Van Impe,et al.  Linearization of the activated sludge model ASM1 for fast and reliable predictions. , 2003, Water research.

[9]  Marco A. Moreno-Armendáriz,et al.  System identification using hierarchical fuzzy neural networks with stable learning algorithm , 2007, J. Intell. Fuzzy Syst..

[10]  Xiao-Jun Zeng,et al.  Approximation Capabilities of Hierarchical Fuzzy Systems , 2005, IEEE Transactions on Fuzzy Systems.

[11]  Claudio Garcia,et al.  Multivariable identification of an activated sludge process with subspace-based algorithms , 2001 .

[12]  Liang Jin,et al.  Stable dynamic backpropagation learning in recurrent neural networks , 1999, IEEE Trans. Neural Networks.

[13]  Mogens Henze,et al.  Activated Sludge Model No.2d, ASM2D , 1999 .

[14]  Witold Pedrycz,et al.  Experience-Consistent Modeling for Radial Basis Function Neural Networks , 2008, Int. J. Neural Syst..

[15]  Thomas J. McAvoy,et al.  Control of an alternating aerobic–anoxic activated sludge system — Part 1: development of a linearization-based modeling approach , 2000 .

[16]  S. Weijers Modelling, identification and control of activated sludge plants for nitrogen removal , 2000 .

[17]  Ming Rao,et al.  An on-line wastewater quality predication system based on a time-delay neural network , 1998 .

[18]  W. Gujer,et al.  Activated sludge model No. 3 , 1995 .

[19]  Wen Yu,et al.  Discrete-time neuro identification without robust modification , 2003 .

[20]  Ch. Venkateswarlu,et al.  Modeling and Optimization of a Pharmaceutical Formulation System Using Radial Basis Function Network , 2009, Int. J. Neural Syst..

[21]  Li-Xin Wang,et al.  Analysis and design of hierarchical fuzzy systems , 1999, IEEE Trans. Fuzzy Syst..

[22]  John Moody,et al.  Fast Learning in Networks of Locally-Tuned Processing Units , 1989, Neural Computation.

[23]  Wen Yu,et al.  Hierarchical Fuzzy CMAC for Nonlinear Systems Modeling , 2008, IEEE Transactions on Fuzzy Systems.

[24]  Tianyou Chai,et al.  Wastewater BOD Forecasting Model for Optimal Operation Using Robust Time-Delay Neural Network , 2005, ISNN.

[25]  R. B. Newell,et al.  Robust model-order reduction of complex biological processes , 2002 .

[26]  Alexander S. Poznyak,et al.  Multilayer dynamic neural networks for non-linear system on-line identification , 2001 .

[27]  I. Takács A dynamic model of the clarification-thickening process , 1991 .

[28]  W. E. Moore,et al.  Hierarchical artificial neural network architecture , 1998, 1998 IEEE International Joint Conference on Neural Networks Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98CH36227).

[29]  Li-Xin Wang,et al.  A Course In Fuzzy Systems and Control , 1996 .

[30]  Guillaume Patry,et al.  Constructing a model hierarchy with background knowledge for structural risk minimization: application to biological treatment of wastewater , 2006, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.