Methodologies Dealing with Uncertainty

Chapter
Part of the Power Systems book series (POWSYS)

Abstract

Uncertainties may arise in complex human thinking processes, which can become particularly challenging in the decision-making context for hard engineering problems with vague, imprecise and incomplete knowledge and information. As an important branch of computational intelligence, the logical approach can be employed to deal with such uncertainties. This chapter presents three mathematical theories, i.e. the Dempster–Shafer theory, the probability theory and the fuzzy logic (FL) theory, to handle different kinds of uncertainties. The FL theory can deal with the imprecision (or vagueness) of defined knowledge, whilst the Dempster–Shafer theory provides two measures (support and plausibility) for formulating a mechanism to represent “ignorance”. As a probabilistic technique, Bayesian networks (BNs) are introduced as graphical representations of uncertain knowledge. In later chapters, the three methodologies are employed to tackle uncertainties arising from complicated condition assessment procedures for detecting transformer faults.

References

  1. 1.
    Finlay J, Dix A (1996) An introduction to artificial intelligence, 3rd edn. UCL Press, LondonGoogle Scholar
  2. 2.
    Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Negnevitsky M (2005) Artificial intelligence: a guide to intelligent systems, 2nd edn. Pearson Education, EnglandGoogle Scholar
  4. 4.
    Ghosh JK, Delampady M, Samanta T (2006) An introduction to bayesian analysis: theory and methods. Springer, New YorkMATHGoogle Scholar
  5. 5.
    Shafer G (1976) A mathematical theory of evidence. Princeton University Press, PrincetonMATHGoogle Scholar
  6. 6.
    Yang JB, Singh MG (1994) An evidential reasoning approach for multiple attribute decision making with uncertainty. IEEE Trans Syst Man Cybern 24(1):1–18CrossRefGoogle Scholar
  7. 7.
    Yang JB, Sen P (1994) A general multi-level evaluation process for hybrid MADM with uncertainty. IEEE Trans Syst Man Cybern 24(10):1458–1473CrossRefGoogle Scholar
  8. 8.
    Tang WH, Wu QH, Richardson ZJ (2004) An evidential reasoning approach to transformer condition monitoring. IEEE Trans Power Deliv 19(4):1696–1703CrossRefGoogle Scholar
  9. 9.
    Spurgeon K, Tang WH, Wu QH, Richardson ZJ, Moss G (2005) Dissolved gas analysis using evidential reasoning. IEE Proc Sci Meas Technol 152(3):110–117CrossRefGoogle Scholar
  10. 10.
    Yang JB, Xu DL (2002) On the evidential reasoning algorithm for multiple attribute decision making under uncertainty. IEEE Trans Syst Man Cybern A Syst Hum 32(3):289–304CrossRefGoogle Scholar
  11. 11.
    Buchanan BG, Shortliffe EH (1984) Rule-based expert systems. Addison-Welsey, ReadingGoogle Scholar
  12. 12.
    Tomsovic K, Tapper M, Ingvarsson T (1993) A fuzzy approach to integrating different transformer diagnostic methods. IEEE Trans Power Deliv 8(3):1638–1646CrossRefGoogle Scholar
  13. 13.
    Yang HT, Liao CC (1999) Adaptive fuzzy diagnosis system for dissolved gas analysis of power transformers. IEEE Trans Power Deliv 14:1342–1350CrossRefGoogle Scholar
  14. 14.
    Huang YC, Yang HZ, Huang CL (1997) Developing a new transformer fault diagnosis system through evolutionary fuzzy logic. IEEE Trans Power Deliv 12(2):761–767CrossRefGoogle Scholar
  15. 15.
    Friedman N, Linial M, Nachman I, Pe’er D (2000) Using Bayesian networks to analyze expression data. J Comput Biol 7:601–620CrossRefGoogle Scholar
  16. 16.
    Pearl J (1988) Probabilistic reasoning in intelligent systems. Morgan Kaufmann Press, San FranciscoGoogle Scholar
  17. 17.
    Korb BK, Nicholson AE (2003) Bayesian artificial intelligence. Chapman & Hall/CRC Press, LondonCrossRefGoogle Scholar
  18. 18.
    Bayes RT (1958) An essay toward solving a problem in the doctrine of chances. Philos Trans R Soc Lond 53:370–418 (1763), reprinted in Biometrika 45:293–315 (1958)Google Scholar

Copyright information

© Springer-Verlag London Limited  2011

Authors and Affiliations

  1. 1.Department of Electrical Engineering and ElectronicsThe University of LiverpoolLiverpoolUK

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