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An approach to fault diagnosis of nonlinear systems using neural networks with invariance to Fourier transform

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Abstract

A neural network with Gauss-Hermite polynomial activation functions is used for approximating the nonlinear system’s dynamics out of a set of input-output data. Thus the output of the neural network provides a series expansion that takes the form of a weighted sum of Gauss-Hermite basis functions. Knowing that the Gauss-Hermite basis functions satisfy the orthogonality property and remain unchanged under the Fourier transform, subjected only to a change of scale, one has that the considered neural network provides the spectral analysis of the output of the monitored system. Actually, the squares of the weights of the output layer of the neural network denote the distribution of energy into the associated spectral components for the output signal of the monitored nonlinear system. By observing changes in the amplitude of the aforementioned spectral components one can have also an indication about malfunctioning of the monitored system and can detect the existence of failures. Moreover, since specific faults are associated with amplitude changes of specific spectral components of the system fault isolation can be also performed.

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References

  • Abu-Elanien A, Salama M (2010) Asset management techniques for transformers. Electr Power Syst Res 80:456–464

    Article  Google Scholar 

  • Addison PS (2002) The illustrared wavelet transform handbook. Institute of Physics Publishing, Bristol

    Book  Google Scholar 

  • Basseville M, Nikiforov I (1993) Detection of abrupt changes. Prentice Hall, Englewood Cliffs

    Google Scholar 

  • Bernard C, Slotine J (1997) Adaptive Control with multiresolution bases. In: IEEE CDC 97, 36th IEEE International Conference on Decision and Control, San Diego

  • Boukhezzar B, Siguerdidjane H (2009) Nonlinear control with wind estimation of a DFIG variable speed wind turbine for power capture optimization. Energy Convers Manage Elsevier 50:885–892

    Article  Google Scholar 

  • Calderaro V, Galdi V, Piccolo A, Siano P (2008) A fuzzy controller for maximum energy extraction from variable speed wind power generation systems. Electr Power Syst Res Elsevier 78:1109118

    Google Scholar 

  • Cannon M, Slotine J (1995) Space-frequency localized basis function networks for nonlinear system estimation and control. Neurocomputing 9:293–342

    Article  MATH  Google Scholar 

  • Catterson V, Davidson E, McArthur S (2010) Agents for active network management and condition monitoring in the smart grid. In: Proceedings of the First International Workshop on Agent Technologies for Energy Systems, ATES, 2010, Toronto

  • Catterson V, Davidson E, McArthur S (2011) Embedded intelligence for electrical network operation and control. IEEE Intell Syst 26:38–45

    Article  Google Scholar 

  • Forchetti D, Garcia G, Valla M (2009) Adaptive observer for sensorless control of stand-alone doubly-fed induction generator. IEEE Trans Industrial Electron 56:4174–4180

    Article  Google Scholar 

  • Galdi V, Piccolo A, Siano P (2008) Designing an adaptive fuzzy controller for maximum wind energy extraction. IEEE Trans Energy Convers 28:559–569

    Article  Google Scholar 

  • Galdi V, Piccolo A, Siano P (2009) Exploiting maximum energy from variable speed wind power generation systems by using an adaptive Takagi-Sugeno-Kang fuzzy model. Energy Convers Manage 50:413–421

    Article  Google Scholar 

  • Galdi V, Ippolito L, Piccolo A, Vaccaro A (2000) Neural diagnostic system for transformer thermal overload protection. IEE Proc Power Appl 147:415–421

    Article  Google Scholar 

  • Grelle C, Ippolito L, Loia V, Siano P (2006) Agent-based architecture for designing hybrid control systems. Inf Sci 176:1103–1130

    Article  MATH  Google Scholar 

  • Haykin S (1994) Neural networks: a comprehensive foundation. McMillan, New York

    MATH  Google Scholar 

  • Ippolito L, Loia V, Siano P (2003) Extended fuzzy C-means and genetic algorithms to optimize power flow management in hybrid electric vehicles. Fuzzy Optim Decis Mak 2:359–374

    Article  MATH  Google Scholar 

  • Ippolito L, Siano P (2004) Identification of Tagaki-Sugeno-Kang fuzzy model for power transformers predictive overload system. IEE Proc—Gener Transm Distrib 151:582–589

    Article  Google Scholar 

  • Karimi H, Lohmann B (2006) A computational method to robust vibration control of vehicle engine-body system using Haar wavelets. In: Proceedings of the 2006 IEEE International Conference on Control Applications, Munich, pp 169–174

  • Krzyzak A, Sasiadek J (1991) Flexible robot identification using nonparametric techniques. In: Proceedings of the 30th IEEE Conference on Decision and Control, Brighton

  • Lin C (2006) Nonsingular terminal sliding mode control of robot manipulators using fuzzy wavelet networks. IEEE Trans Fuzzy Syst 14:849–859

    Article  Google Scholar 

  • Metwally I (2011) Failures monitoring and new trends of power transformers. IEEE Potentials 30:36–43

    Article  Google Scholar 

  • Piccolo A, Siano P, Rigatos G (2010) An adaptive framework for power components dynamic loadability. In: Rigatos GG (ed) Modelling and automation of intelligent industrial systems. IGI Publications, Hershey

  • Refregier A (2003) Shapelets—I. A method for image analysis. Mon Not R Astron Soc 338:35–47

    Article  Google Scholar 

  • Rigatos G, Tzafestas S (2006) Feed-forward neural networks using Hermite polynomial activation functions. Lecture Notes in Artificial Intelligence, Springer 3925:323–333

    Google Scholar 

  • Rigatos G, Tzafestas S (2006) Neural structures using the eigenstates of the Quantum Harmonic Oscillator. Open Systems and Information Dynamics, Springer 13:27–41

    Article  MathSciNet  MATH  Google Scholar 

  • Rigatos G, Zhang Q (2009) Fuzzy model validation using the local statistical approach. Fuzzy Sets Syst Elsevier 60:882–904

    Article  MathSciNet  Google Scholar 

  • Rigatos G, Siano P, Piccolo A (2009) A neural network-based approach for early detection of cascading events in electric power systems. IET Gener Transm Distrib 3:650–665

    Article  Google Scholar 

  • Rigatos G, Siano P (2011) Sensorless control of electric motors with Kalman Filters: applications to robotic and industrial systems. Int J Adv Robot Syst 8:62–80 (Special Issue Robot Manipulators)

    Google Scholar 

  • Rigatos G, Siano P (2011) Design of robust electric power system stabilizers using Kharitonov’s theorem. Math Comput Simul 82:181–191

    Article  MathSciNet  MATH  Google Scholar 

  • Rigatos G, Siano P (2012) Sensorless nonlinear control of induction motors using Unscented Kalman Filtering. In: Proceedings of the IEEE IECON 2012, 38th International Conference of the Industrial Electronics Society, Montreal

  • Rigatos G, Siano P (2012) DFIG control using differential flatness theory and extended Kalman filtering. IFAC INCOM 2012, 14th IFAC International Conference on Information Control Problems in Manufacturing, Bucharest

  • Rigatos G, Siano P, Zervos N (2012) A distributed state estimation approach to condition monitoring of nonlinear electric power systems. Asian J Control 15:1–12

    MathSciNet  Google Scholar 

  • Rigatos G, Siano P, Piccolo A (2012) Incipient fault detection for electric power transformers using neural modeling and the local statistical approach to fault diagnosis. IEEE SAS 2012, 2012 IEEE Sensors Applications Symposium, University of Brescia, Brescia

  • Sureshbabu N, Farell J (1999) Wavelet-based system identification for nonlinear control. IEEE Trans Autom Control 44:412–417

    Article  MATH  Google Scholar 

  • Velasquez-Contreras J, Sanz-Bobi M, Arellano S (2011) General asset management model in the context of an electric utility: application to power transformers. Electr Power Syst Res Elsevier 81:2015–2037

    Article  Google Scholar 

  • Yang S, Cheng C (1996) An orthogonal neural network for function approximation. IEEE Trans Syst Man Cybern—Part B: Cybern 26:779–784

    Article  Google Scholar 

  • Zhang Q, Benveniste A (1993) Wavelet networks. IEEE Trans Neural Netw 4:889–898

    Google Scholar 

  • Zhang Q, Basseville M, Benveniste A (1994) Early warning of slight changes in systems. Automatica 30:9513 (special issue on Statistical Methods in Signal Processing and Control)

    MathSciNet  Google Scholar 

  • Zhang Q, Basseville M, Benveniste A (1998) Fault detection and isolation in nonlinear dynamic systems: a combined inpututput and local approach. Automatica, Elsevier 34:1359373

    Google Scholar 

  • Zuo W, Zhu Y, Cai L (2009) Fourier-Neural-Network-Based Learning control for a class of nonlinear systems with flexible components. IEEE Trans Neural Netw 20:139–151

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Unit of Industrial Automation, Industrial Systems Institute, 26504, Rion Patras, Greece

    Gerasimos Rigatos

  2. Department of Industrial Engineering, University of Salerno, Fisciano, 84084, Italy

    Pierluigi Siano

  3. Unit of Digital Communications, Industrial Systems Institute, 26504, Rion Patras, Greece

    Nikolaos Zervos

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  1. Gerasimos Rigatos
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  2. Pierluigi Siano
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  3. Nikolaos Zervos
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Correspondence to Gerasimos Rigatos.

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Rigatos, G., Siano, P. & Zervos, N. An approach to fault diagnosis of nonlinear systems using neural networks with invariance to Fourier transform. J Ambient Intell Human Comput 4, 621–639 (2013). https://doi.org/10.1007/s12652-012-0173-4

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  • DOI: https://doi.org/10.1007/s12652-012-0173-4

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