» Download Article

Authors
A. Borowa; M. A. Brdys; K. Mazur

Digital Object Identifier (DOI)
10.3182/20060830-2-SF-4903.00044

Page Numbers:
250-255

Index Terms
neural network models,model approximation,learning algorithms,waste treatment

Abstract
Most of industrial processes are nonlinear, not stationary, and dynamical with at least few different time scales in their internal dynamics and hardly measured states. A biological wastewater treatment plant falls into this category. The paper considers modelling such processes for monitorning and control purposes by using State - Space Wavelet Neural Networks (SSWN). The modelling method is illustrated based on bioreactors of the wastewater treatment plant. The learning algorithms and basis function (multidimensional wavelets) are also proposed. The simulation results based on real data record are presented.

References

[1] Brdys M. A., Grochowski M., Duzinkiewicz K.,
    Chotkowski W., Liu Y. (2002). Design of
    control structure for integrated wastewater
    treatment plant - sewer systems. I
    International Conference on Technolog,
    Automation and Control of Wastewater and
    Drinking WaterSystems TiASWiK'02Gdansk-
    Sobieszewo, June 19-21 2002 - Poland.
[2] Chotkowski W., Makinia J., Brdys M. A.,
    Duzinkiewicz K., Konarczak K. (2001).
    'Mathematical modelling of the processes in
    integrated municipal wastewater systems'. Proc.
    of the 9th IFAC/IFORS/IMACS/IFIP Symposium
    on Large Scale Systems: Theory & Applications,
    Bucharest, July 18-20.
[3] Daubechies I. (1992). Ten Lectures on Wavelets.
    CBMS-NSF Regional Series in Applied
    Mathematics, SIAM, Philadelphia.
[4] Grochowski M., Brdys M. A., Gminski T. (2004).
    Intelligent control structure for control of
    integrated wastewater systems IFAC 10th
    Symposium Large Scale Systems: Theory and
    Applications. July 26-28 2004, Osaka - Japan.
[5] Juditsky A., Zhang Q., Delyon B., Glorennec P-Y.,
    Beneveniste A. (1994). Wavelets in
    identification. Rapport de recherche No. 2315.
[6] Kirkpatrick S., Gelatt C. D., Vecchi M. P. (1983).
    Optimization by Simulated Annealing Science
    vol. 220, pp. 671-680.
[7] Oussar Y., Rivals I., Personnaz L., Dreyfus G.
    (1998). 'Training Wavelet Networks for
    Nonlinear Dynamic Input-Output Modeling'.
    Neurocomputing, vol. 20, pp. 173-188.
[8] Olsson G., Newell R. (1999). Wastewater Treatment
    Systems. Modelling, Diagnosis and Control. IWA
    Publishing, London.
[9] Sanchez E. N., Perez J. P. (1999). 'Input-to-State
    Stability (ISS) Analysis for Dynamic Neural
    Networks' IEEE Transactions On Circuits And
    Systems - I: Fundamental Theory And
    Applications, vol. 46, No. 11 November 1999,
    pp. 1395-1398.
[10] Zamarreno J. M., Pastora V. (1998). 'State space
     neural network. Properties and applications.'
     Neural Networks, vol. 11, pp. 1099-1112.
[11] Zhang Q., Beneveniste A. (1992). 'Wavelet
     Networks'. IEEE Trans. on Neural Networks,
     vol. 3, num. 6, Nov. 1992, pp. 889-898.
[12] Zhang Q. (1992). 'Wavelet Network: the Radial
     Structure and an Efficient Initialization
     Procedure'. Technical Report of Linköping
     University, LiTH-ISY-I-1423. October 1992.
[13] Zhao J., Chen B., Shen J. (1998)., Multidimensional
     non-orthogonal wavelet basis function neural
     network for dynamic process fault diagnosis'.
     Computer and Chemical Engineering vol. 23 s.
     83-92.