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.
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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 53:220–229
Babuška R, Verbruggen H (1996) An overview of fuzzy modeling for control. Control Eng Pract 4:1593–606
Babus̆ka R, Verbruggen H (2003) Neuro-fuzzy methods for nonlinear system identification. Ann Rev Control 27(1):73–85
Chen SM (1996) New methods for subjective mental workload assessment and fuzzy risk analysis. Cybern Syst 27:449–472
Chen SJ, Chen SM (2003) Fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. IEEE Trans Fuzzy Syst 11:45–56
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 551–555
Couso I, Sanchez L (2017) Additive similarity and dissimilarity measures. Fuzzy Sets Syst 322:35–53
Dempster AP (1967) Upper and lower probabilities induced by a multivalued mapping. Ann Math Stat 38:325–339
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 36:40–53
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 14:699–717
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 1140–1145
Jin M, Li R, Xu ZB, Zhao XD (2014) Reliable fault diagnosis method using ensemble fuzzy ARTMAP based on improved Bayesian belief method. Neurocomputing 133:309–316
Khorshidi HA, Nikfalazar S (2017) An improved similarity measure for generalized fuzzy numbers and its application to fuzzy risk analysis. Appl Soft Comput 52:478–486
Lan JL, Patton RJ (2016) A new strategy for integration of fault estimation within fault tolerant control. Automatica 69:48–59
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 62:411–420
Li JH, Zeng WY (2017) Fuzzy risk analysis based on the similarity measure of generalized fuzzy numbers. J Intell Fuzzy Syst 32:1673–1683
Li B, Liu PY, Hu RX, Mi SS, Fu JP (2012) Fuzzy lattice classifier and its application to bearing fault diagnosis. Appl Soft Comput 12:1708–1719
Liu XF, Ma L, Mathew J (2009) Machinery fault diagnosis based on fuzzy measure and fuzzy integral data fusion techniques. Mech Syst Signal Process 23:690–700
Mitchell HB (2005) Pattern recognition using type-II fuzzy sets. Inf Sci 170:409–418
Mirea L, Patton RJ (2006) Component fault diagnosis using wavelet neural networks with local recurrent structure. Fault Detect Superv Saf Tech Process 1:78–83
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 6:222–227
Mondal B, Mazumdar D, Raha S (2006) Similarity in approximate reasoning. Int J Comput Cognit 4:46–56
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 28:276–284
Patton RJ (1995) Robustness in model-based fault diagnosis: the 1995 situation. Ann Rev Control 21(1997):103–123
Patton RJ, Faisal JU, Silvio S et al (2010) Robust FDI applied to thruster faults of a satellite system. Control Eng Pract 18:1093–1109
Patton RJ, Chen J (1993) Optimal unknown input distribution matrix selection in robust fault diagnosis. Automatica 29:837–841
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 235:106–116
Sala A, Guerra TM, Babus̆ka R (2005) Perspectives of fuzzy systems and control. Fuzzy Sets Syst 156:432–444
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 28:376–386
Shafer G (1976) A mathematical theory of evidence. Princeton University Press, Princeton
Shaker MS, Patton RJ (2014) Active sensor fault tolerant output feedback tracking control for wind turbine systems via TCS model. Eng Appl Artif Intell 34:1–12
Simani S, Patton RJ (2008) Fault diagnosis of an industrial gas turbine prototype using a system identification approach. Control Eng Pract 16:769–786
Simani S, Farsoni S, Castaldi P (2015) Wind turbine simulator fault diagnosis via fuzzy modelling and identification techniques. Sustain Energy Grids Netw 1:45–52
Tan DL, Patton RJ (2015) Integrated fault estimation and fault tolerant control: a joint design. IFAC Pap Online 48:517–522
Tan DL, Patton RJ, Wang X (2015) A relaxed solution to unknown input observers for state and fault estimation. IFAC Pap Online 48–51:1048–1053
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 400–411
Wang PZ (1983) Fuzzy sets and its applications. Shanghai Science and Technology Press, Shanghai (in Chinese)
Wei SH, Chen SM (2009) A new approach for fuzzy risk analysis based on similarity measures of generalized fuzzy numbers. Expert Syst Appl 36:589–598
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)
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 14:671–683
Yang MS, Lin DC (2009) On similarity and inclusion measures between type-2 fuzzy sets with an application to clustering. Comput Math Appl 57:896–907
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 29:375–382
Zadeh L (1965) Fuzzy sets. Inf Control 8:338–353
Zhao F, Liu HQ, Jiao LC (2011) Spectral clustering with fuzzy similarity measure. Digit Signal Proc 21:701–709
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 7:291–300
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).
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Xie, J., Zeng, W., Li, J. et al. Similarity measures of generalized trapezoidal fuzzy numbers for fault diagnosis. Soft Comput 23, 1999–2014 (2019). https://doi.org/10.1007/s00500-017-2914-y
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DOI: https://doi.org/10.1007/s00500-017-2914-y