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Parametric and Neural Network Wiener and Hammerstein Models in Fault Detection and Isolation

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Fault Diagnosis
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Abstract

In the last two decades, model-based fault detection and isolation (FDI) has been investigated intensively (Frank, 1990; Chen and Patton, 1999; Patton et al., 1989). These methods require both a nominal model of the system considered, i.e., a model of the system under its normal operating conditions, and models of the system under its faulty conditions. The nominal model is used in the fault detection step to generate residuals, defined as a difference between the output signals of the system and its model. The analysis of these residuals gives an answer to the question whether a fault occurs or not. If it does occur, the fault isolation step is performed in a similar way analyzing residual sequences generated with the models of the system under its faulty conditions (Fig. 10.1).

This work was partially supported by the European Union in the framework of the FP 5 RTN: Development and Application of Methods for Actuators Diagnosis in Industrial Control Systems, DAMADICS (2000–2003), and within the grant of the State Committee for Scientific Research in Poland, KBN, No. 131/E-372/SPUB-M/5 PR UE/DZ 58/200l.

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References

  • Al-Duwaish H., Nazmul K.M. and Chandrasekar V. (1997): Hammerstein model identification by multilayer feedforward neural networks. — Int. J. Systems Science, Vol. 28, No. 1, pp. 49–54.

    Article  MATH  Google Scholar 

  • Billings S.A. and Fakhouri S.Y. (1978a): Identification of a class of nonlinear systems using correlation analysis. — Proc. IEE, Vol. 125, No. 7, pp. 691–697.

    MathSciNet  Google Scholar 

  • Billings S.A. and Fakhouri S.Y. (1978b): Theory of separable processes with applications to the identification of nonlinear systems. — Proc. IEE, Vol. 125, No. 9, pp. 1051–1058.

    MathSciNet  Google Scholar 

  • Billings S.A. and Fakhouri S.Y. (1982): Identification of systems containing linear dynamic and static nonlinear elements. — Automatica, Vol. 18, No. 1, pp. 15–26.

    Article  MathSciNet  MATH  Google Scholar 

  • Carlos A. and Corripio A.B. (1985): Princeples and Pracitice of Automatic Control. — New York: Wiley & Sons.

    Google Scholar 

  • Chang F.H.I. and Luus R. (1971): A noniterative method for identification using Hammerstein model. — IEEE Trans. Automatic Control, Vol. AC-16, No. 5, pp. 464–468.

    Article  Google Scholar 

  • Chen J. and Patton R.J. (1999): Robust Model-based Fault Diagnosis for Dynamic Systems. — London: Kluwer Academic Publishers.

    Book  MATH  Google Scholar 

  • Chung H.-Y. and Sun Y.-Y. (1988): Analysis and parameter estimation of nonlinear systems with Hammerstein model using Taylor series approach. — IEEE Trans. Circuits. Systems, Vol. 35, No. 12, pp. 1539–1540.

    Article  MathSciNet  MATH  Google Scholar 

  • Eskinat E., Johnson S.H. and Luyben W.L. (1991): Use of Hammerstein models in identification of nonlinear systems. — AIChE J., Vol. 37, pp. 255–268.

    Article  Google Scholar 

  • Eykhoff P. (1980): System Identification. Parameter and State Estimation. — London: John Wiley and Sons.

    Google Scholar 

  • Frank P.M. (1990): Fault diagnosis in dynamical systems using analytical and knowledge-based redundancy — A survey of some new results. — Automatica, Vol. 26, pp. 459–474.

    Article  MATH  Google Scholar 

  • Gallman P.G. (1976): A comparison of two Hammerstein model identification algorithms. — IEEE Trans. Automatic Control, Vol. AC-21, No. 1, pp. 124–126.

    Article  Google Scholar 

  • Greblicki W. (1989): Non-parametric orthogonal series identification of Hammerstein systems. — Int. J. Systems Sci., Vol. 20, No. 12, pp. 2355–2367.

    Article  MathSciNet  MATH  Google Scholar 

  • Greblicki W. (1994): Nonparametric identification of Wiener systems by orthogonal series. — IEEE Trans. Automatic Control, Vol. 39, No. 10, pp. 2077–2086.

    Article  MathSciNet  MATH  Google Scholar 

  • Greblicki W. (1997): Nonparametric approach to Wiener system identification. — IEEE Trans. Circuits Syst. I., Vol. 44, No. 6, pp. 538–545. No. 4, pp. 651–677.

    Article  MathSciNet  Google Scholar 

  • Greblicki W. and Pawlak M. (1986): Identification of discrete Hammerstein using kernel regression estimates. — IEEE Trans. Automatic Control, Vol. AC-31, No. 1, pp. 74–77.

    Article  Google Scholar 

  • Greblicki W. and Pawlak M. (1987): Hammerstein system identification by nonparametric regression estimation. — Int. J. Control, Vol. 45, No. 1, pp. 343–354.

    Article  MathSciNet  MATH  Google Scholar 

  • Haist N.D, Chang F.H.I. and Luus R. (1973): Nonlinear identification in the presence of correlated noise using a Hammerstein model. — IEEE Trans. Automatic Control, Vol. AC-18, No. 5, pp. 552–555.

    Article  Google Scholar 

  • Ikonnen E. and Najim K. (1999): Identification of Wiener systems with steady-state nonlinearities. — Proc. Europ. Control Conf., ECC, Karlsruhe, Germany, CD-ROM.

    Google Scholar 

  • Janczak A. (1995): Identification of a class of nonlinear systems using neural networks. — Proc. 2nd Int. Symp. Methods and Models in Automation and Robotics, MMAR, Międzyzdroje, Poland, Vol. 2, pp. 697–702.

    Google Scholar 

  • Janczak A. (1996): Recursive identification of Wiener-Hammerstein systems using recurrent neural networks. — Proc. 2nd Conf. Neural Networks and Their Applications, Szczyrk, Poland, pp. 224–229.

    Google Scholar 

  • Janczak A. (1997a): Identification of Wiener models using recurrent neural networks. — Proc. 4th Int. Symp. Methods and Models in Automation and Robotics, MMAR, Międzyzdroje, Poland, Vol. 2, pp. 727–732.

    Google Scholar 

  • Janczak A. (1997b): Recursive identification of Hammerstein systems using recurrent neural models. — Proc. 3rd Conf. Neural Networks and their Applications, Kule, Poland, pp. 517–522.

    Google Scholar 

  • Janczak A. (1998a): Recurrent neural network models for identification of Wiener systems. — Proc. CESA IMACS Multiconference, Nabeul-Hammamet, Tunisia, pp. 965—970, CD-ROM.

    Google Scholar 

  • Janczak A. (1998b): Gradient descent and recursive least squares learning algorithms for on line identification of Hammerstein systems using recurrent neural network models. — Proc. Int. ICSC/IFAC Symp. Neural Computation, NC, Vienna, Austria, pp. 565–571.

    Google Scholar 

  • Janczak A. (1999): Fault detection and isolation in Wiener systems with inverse model of static nonlinear element. — Proc. Europ. Control. Conf., ECC, Karlsruhe, Germany, CD-ROM.

    Google Scholar 

  • Janczak A. (2000a): Parametric and neural network models for fault detection and isolation of industrial process sub-modules. — Prep. 4th IFAC Symp. Fault Detection Supervision and Safety for Technical Processes, SAFEPROCESS, Budapest, Hungary, Vol. 1, pp. 348–351.

    Google Scholar 

  • Janczak A. (2000b): Neural networks in identification of Wiener and Hammerstein systems, In: Biocybernetics and Biomedical Engineering 2000. Neural Networks (W. Duch, J. Korbicz, L. Rutkowski and R. Tadeusiewicz, Eds.).— Warsaw: Akad. Ofic. Wyd. EXIT, Vol. 6, pp. 419–458, (in Polish).

    Google Scholar 

  • Janczak A. (2001): On identification of Wiener systems based on a modified serialparallel model. — Proc. Europ. Control ConE., ECC, Porto, Portugal, pp. 1852–1857, CD-ROM.

    Google Scholar 

  • Janczak A. and Korbicz J. (1999): Neural network models of Hammerstein systems and their application to fault detection and isolation. — Proc. 14th IFAC World Congress, Beijing, P.R.C., Vol. P, pp. 91–96.

    Google Scholar 

  • Kalafatis A.D., Arifin N., Wang L. and Cluett R. (1997): A new approach to the identification of pH processes based on the Wiener model. — Chem. Eng. Sci., Vol. 50, No. 23, pp. 3693–3701.

    Google Scholar 

  • Kalafatis A.D., Wang L. and Cluett R. (1997): Identification of Wiener-type nonlinear systems in a noisy environment. — Int. J. Control, Vol. 66, No. 6, pp. 923–941.

    Article  MathSciNet  MATH  Google Scholar 

  • Korbicz J. and Janczak A. (1996): A neural network approach to identification of structural systems. — Proc. IEEE Int. Symp. Industr. Electronics, ISIE, Warsaw, Poland, pp. 97–103.

    Google Scholar 

  • Kung F.-C. and Shih D.-H. (1986): Analysis and identification of Hammerstein model non-linear delay systems using block-pulse function expansions. — Int. J. Control, Vol. 43, No. 1., pp. 141–147.

    Article  Google Scholar 

  • Lang Z.-Q. (1994): On identification of controlled plants described by Hammerstein system. — IEEE Trans. Automatic Control, Vol. 39, No. 3, pp. 569–573.

    Article  MATH  Google Scholar 

  • Lang Z.-Q. (1997): A nonparametric polynomial identification algorithm for the Hammerstein system. — IEEE Trans. Automatic Control, No. 10, Vol. 42, pp. 1435–1441.

    Google Scholar 

  • Ling W.-M. and Rivera D. (1998): Nonlinear black-box identification of distillation column models—design variable selection for model performance enhancement. — Appl. Math. Comp. Sci., Vol. 8, No. 4, pp. 794–813.

    Google Scholar 

  • Lissane Elhaq S., Giri F. and Unbehauen H. (1999): Modelling, identification and control of sugar evaporation — theoretical design and experimental evaluation. — Control Engineering Practice, Vol. 7, No. 8, pp. 931–

    Article  Google Scholar 

  • Ljung L. (1999): System Identification. Theory for the User. — Upper Saddle River: Prentice Hall.

    Google Scholar 

  • Marciak C., Latawiec K., Rojek R. and Oliveira H.C. (2001): Adaptive least-squares parameter estimation of OBF-based models. — Proc. 7th IEEE Int. Conf. Methods and Models in Automation and Robotics, MMAR, Międzyzdroje, Poland, Vol. 2, pp. 965–969.

    Google Scholar 

  • Narendra K.S. and Gallman P.G. (1966): An iterative method for the identification of nonlinear systems using Hammerstein model. — IEEE Trans. Automatic Control, Vol. AC-11, No. 3, pp. 546–550.

    Article  Google Scholar 

  • Nie J. and Lee T.H. (1998): Rule-based control of Wiener-type nonlinear processes through self-organizing. — Int. J. Systems Sci., Vol. 29, No. 3, pp. 275–286.

    Article  Google Scholar 

  • Patton R.J., Frank M. and Clark R.N. (1989): Fault Diagnosis in Dynamic Systems. Theory and Applications. — New York: Prentice-Hall.

    Google Scholar 

  • Pawlak M. (1991): On the series expansion to the identification of Hammerstein systems. — IEEE Trans. Automatic Control, Vol. 36, No. 6, pp. 763–767.

    Article  MathSciNet  Google Scholar 

  • Pearson R.K. and Pottmann M. (2000): Gray-box identification of block-oriented nonlinear models. — J. Process Control, Vol. 10, No. 4, pp. 301–315.

    Article  Google Scholar 

  • Söderström T. and Stoica P. (1994): System Identification. — London: Prentice Hall.

    Google Scholar 

  • Su Hong-Te and McAvoy T. (1993): Integration of multilayer perceptron networks and linear dynamic models: A Hammerstein modeling approach. — Ind. Eng. Chem. Res., Vol. 32, pp. 1927–1936.

    Article  Google Scholar 

  • Thathachar M.A.I. and Ramaswamy S. (1973): Identification of a class of non-linear systems. — Int. J. Control, Vol. 18, No. 4, pp. 741–752.

    Article  MATH  Google Scholar 

  • Wigren T. (1993): Recursive prediction error identification using the nonlinear Wiener model. — Automatica, Vol. 39, No. 4, pp. 1011–1025.

    Article  MathSciNet  Google Scholar 

  • Wigren T. (1994): Convergence analysis of recursive identification algorithms based on the nonlinear Wiener model. — IEEE Trans. Automatic Control, Vol. 39, No. 11, pp. 2191–2206.

    Article  MathSciNet  MATH  Google Scholar 

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Janczak, A. (2004). Parametric and Neural Network Wiener and Hammerstein Models in Fault Detection and Isolation. In: Korbicz, J., Kowalczuk, Z., Kościelny, J.M., Cholewa, W. (eds) Fault Diagnosis. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18615-8_10

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  • DOI: https://doi.org/10.1007/978-3-642-18615-8_10

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