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Similarity measures of generalized trapezoidal fuzzy numbers for fault diagnosis

Methodologies and Application
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Abstract

In this paper, we propose a new similarity measure between generalized trapezoidal fuzzy numbers and several synthesized similarity measures to solve fault diagnosis problem by merging our proposed measures with Dempster–Shafer evidence theory. Firstly, combining the exponential distance with numerical indexes of generalized trapezoidal fuzzy number, such as the span, the center width and the height, etc, we propose a new similarity measure between generalized trapezoidal fuzzy numbers. Secondly, we introduce an evaluation index, distinguish ability, to evaluate the performance of different similarity measures. The experimental results show that our proposed similarity measure can overcome the drawbacks of the existing similarity measures. Thirdly, to solve fault diagnosis problems, we propose three formulas to integrate several single similarity measures to a synthesized one. Finally, based on Dempster–Shafer evidence theory, we transform each similarity measure between fault model and test model, the synthesized similarity measures to their corresponding basic probability assignments to deal with fault diagnosis problem, the results show that our proposed similarity measure is more effective than some other existing similarity measures.

Keywords

Similarity measure Generalized trapezoidal fuzzy number Fault diagnosis Synthesized similarity measure Dempster–Shafer evidence theory 

Notes

Acknowledgements

The authors wish to express their gratitude to the anonymous referees and the Editor-in-Chief, Professor Antonio Di Nola, for their kind suggestions and helpful comments in revising the paper. This study was funded by Grants from the National Natural Science Foundation of China (10971243), Grants from the Key Research Plan of Hebei Province (17210109D), and the Grants from Hebei Normal University (L2015k01, L2017B09, S2016Y13).

Compliance with ethical standards

Conflict of interest

We declare that we have no conflict of interest.

Human ad animal rights

This article does not contain any studies with human participants performed by any of the authors.

References

  1. Aydin İ, Karaköse M, Akin E (2014) An approach for automated fault diagnosis based on a fuzzy decision tree and boundary analysis of a reconstructed phase space. ISA Trans 53:220–229CrossRefGoogle Scholar
  2. Babuška R, Verbruggen H (1996) An overview of fuzzy modeling for control. Control Eng Pract 4:1593–606CrossRefGoogle Scholar
  3. Babus̆ka R, Verbruggen H (2003) Neuro-fuzzy methods for nonlinear system identification. Ann Rev Control 27(1):73–85Google Scholar
  4. Chen SM (1996) New methods for subjective mental workload assessment and fuzzy risk analysis. Cybern Syst 27:449–472CrossRefMATHGoogle Scholar
  5. Chen SJ, Chen SM (2003) Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. IEEE Trans Fuzzy Syst 11:45–56CrossRefGoogle Scholar
  6. Chen SH, Hsieh CH (1999) Ranking generalized fuzzy number with graded mean integration representation. In: Proceedings of the 8th international fuzzy systems association world congress, pp 551–555Google Scholar
  7. Couso I, Sanchez L (2017) Additive similarity and dissimilarity measures. Fuzzy Sets Syst 322:35–53MathSciNetCrossRefMATHGoogle Scholar
  8. Dempster AP (1967) Upper and lower probabilities induced by a multivalued mapping. Ann Math Stat 38:325–339MathSciNetCrossRefMATHGoogle Scholar
  9. Escobet A, Nebot À, Mugica F (2014) PEM fuel cell fault diagnosis via a hybrid methodology based on fuzzy and pattern recognition techniques. Eng Appl Artif Intell 36:40–53CrossRefGoogle Scholar
  10. Faisal JU, Patton RJ, Marcin W (2006) A neuro-fuzzy multiple-model observer approach to robust fault diagnosis based on the DAMADICS benchmark problem. Control Eng Pract 14:699–717CrossRefGoogle Scholar
  11. Huang Z, Patton RJ (2015) Output feedback sliding mode FTC for a class of nonlinear inter-connected systems. In: IFAC-Papers Online, the 9th IFAC symposium on fault detection, supervision and safety for technical processes SAFEPROCESS 2015, Paris, 2–4 September, vol 48, pp 1140–1145Google Scholar
  12. Jin M, Li R, Xu ZB, Zhao XD (2014) Reliable fault diagnosis method using ensemble fuzzy ARTMAP based on improved Bayesian belief method. Neurocomputing 133:309–316CrossRefGoogle Scholar
  13. Khorshidi HA, Nikfalazar S (2017) An improved similarity measure for generalized fuzzy numbers and its application to fuzzy risk analysis. Appl Soft Comput 52:478–486CrossRefGoogle Scholar
  14. Lan JL, Patton RJ (2016) A new strategy for integration of fault estimation within fault tolerant control. Automatica 69:48–59MathSciNetCrossRefMATHGoogle Scholar
  15. Lauro F, Moretti F, Capozzoli A, Khan I, Pizzuti S, Macas M, Panzieri S (2014) Building fan coil electric consumption analysis with fuzzy approaches for fault detection and diagnosis. Energy Procedia 62:411–420CrossRefGoogle Scholar
  16. Li JH, Zeng WY (2017) Fuzzy risk analysis based on the similarity measure of generalized fuzzy numbers. J Intell Fuzzy Syst 32:1673–1683CrossRefGoogle Scholar
  17. Li B, Liu PY, Hu RX, Mi SS, Fu JP (2012) Fuzzy lattice classifier and its application to bearing fault diagnosis. Appl Soft Comput 12:1708–1719CrossRefGoogle Scholar
  18. Liu XF, Ma L, Mathew J (2009) Machinery fault diagnosis based on fuzzy measure and fuzzy integral data fusion techniques. Mech Syst Signal Process 23:690–700CrossRefGoogle Scholar
  19. Mitchell HB (2005) Pattern recognition using type-II fuzzy sets. Inf Sci 170:409–418CrossRefGoogle Scholar
  20. Mirea L, Patton RJ (2006) Component fault diagnosis using wavelet neural networks with local recurrent structure. Fault Detect Superv Saf Tech Process 1:78–83Google Scholar
  21. Mirea L, Patton RJ (2007) A new dynamic neuro-fuzzy system applied to fault diagnosis of an evaporation station. Fault Detect Superv Saf Tech Process 6:222–227Google Scholar
  22. Mondal B, Mazumdar D, Raha S (2006) Similarity in approximate reasoning. Int J Comput Cognit 4:46–56Google Scholar
  23. Patra K, Mondal SK (2015) Fuzzy risk analysis using area and height based similarity measure on generalized trapezoidal fuzzy numbers and its application. Appl Soft Comput 28:276–284CrossRefGoogle Scholar
  24. Patton RJ (1995) Robustness in model-based fault diagnosis: the 1995 situation. Ann Rev Control 21(1997):103–123Google Scholar
  25. Patton RJ, Faisal JU, Silvio S et al (2010) Robust FDI applied to thruster faults of a satellite system. Control Eng Pract 18:1093–1109CrossRefGoogle Scholar
  26. Patton RJ, Chen J (1993) Optimal unknown input distribution matrix selection in robust fault diagnosis. Automatica 29:837–841CrossRefMATHGoogle Scholar
  27. Peng H, Wang J, Perez-Jimenez MJ, Wang H, Shao J, Wang T (2013) Fuzzy reasoning spiking neural P system for fault diagnosis. Inf Sci 235:106–116MathSciNetCrossRefMATHGoogle Scholar
  28. Sala A, Guerra TM, Babus̆ka R (2005) Perspectives of fuzzy systems and control. Fuzzy Sets Syst 156:432–444MathSciNetCrossRefMATHGoogle Scholar
  29. Setnes M, Babus̆ka R, Kaymak U, Van Nauta Lemke HR (1998) Similarity measures in fuzzy rule base simplification. IEEE Trans Syst Man Cybern Part B Cybern A Publ IEEE Syst Man Cybern Soc 28:376–386CrossRefGoogle Scholar
  30. Shafer G (1976) A mathematical theory of evidence. Princeton University Press, PrincetonMATHGoogle Scholar
  31. Shaker MS, Patton RJ (2014) Active sensor fault tolerant output feedback tracking control for wind turbine systems via TCS model. Eng Appl Artif Intell 34:1–12CrossRefGoogle Scholar
  32. Simani S, Patton RJ (2008) Fault diagnosis of an industrial gas turbine prototype using a system identification approach. Control Eng Pract 16:769–786CrossRefGoogle Scholar
  33. Simani S, Farsoni S, Castaldi P (2015) Wind turbine simulator fault diagnosis via fuzzy modelling and identification techniques. Sustain Energy Grids Netw 1:45–52CrossRefGoogle Scholar
  34. Tan DL, Patton RJ (2015) Integrated fault estimation and fault tolerant control: a joint design. IFAC Pap Online 48:517–522CrossRefGoogle Scholar
  35. Tan DL, Patton RJ, Wang X (2015) A relaxed solution to unknown input observers for state and fault estimation. IFAC Pap Online 48–51:1048–1053CrossRefGoogle Scholar
  36. Vicente E, Mateos A, Jiménez A (2013) A new similarity function for generalized trapezoidal fuzzy numbers. In: Lecture Notes in Computer Science, vol 7894, pp 400–411Google Scholar
  37. Wang PZ (1983) Fuzzy sets and its applications. Shanghai Science and Technology Press, Shanghai (in Chinese)MATHGoogle Scholar
  38. Wei SH, Chen SM (2009) A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. Expert Syst Appl 36:589–598CrossRefGoogle Scholar
  39. Wen CL, Zhou Z, Xu XB (2011) A new similarity measure between generalized trapezoidal fuzzy numbers and its application to fault diagnosis. Acta Electron Sin 39:1–6 (in chinese)Google Scholar
  40. Witczak M, Korbicz J, Mrugalski M et al (2006) A GMDH neural network-based approach to robust fault diagnosis: application to the DAMADICS benchmark problem. Control Eng Pract 14:671–683CrossRefGoogle Scholar
  41. Yang MS, Lin DC (2009) On similarity and inclusion measures between type-2 fuzzy sets with an application to clustering. Comput Math Appl 57:896–907MathSciNetCrossRefMATHGoogle Scholar
  42. Ye J (2012) The Dice similarity measure between generalized trapezoidal fuzzy numbers based on the expected interval and its multicriteria group decision-making method. J Chin Inst Ind Eng 29:375–382Google Scholar
  43. Zadeh L (1965) Fuzzy sets. Inf Control 8:338–353CrossRefMATHGoogle Scholar
  44. Zhao F, Liu HQ, Jiao LC (2011) Spectral clustering with fuzzy similarity measure. Digit Signal Proc 21:701–709CrossRefGoogle Scholar
  45. Zuo X, Wang L, Yue Y (2013) A new similarity measure of generalized trapezoidal fuzzy numbers and its application on rotor fault diagnosis. Math Probl Eng 7:291–300MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.College of Information Science and TechnologyBeijing Normal UniversityBeijingPeople’s Republic of China
  2. 2.College of Mathematics and Information ScienceHebei Normal UniversityShijiazhuangPeople’s Republic of China

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