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Mathematical Problems in Engineering
Volume 2014, Article ID 278342, 10 pages
Research Article

A Fuzzy Reliability Model of Blades to Avoid Resonance and Its Convergence Analysis

School of Power and Energy, Northwestern Polytechnical University, Xi’an 710072, China

Received 22 January 2014; Revised 19 July 2014; Accepted 28 July 2014; Published 14 August 2014

Academic Editor: Thomas Hanne

Copyright © 2014 Meng Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The inherent frequencies of blades, especially with friction structure of shroud, are related to many uncertain factors, which include not only random factors but also fuzzy or other uncertain factors. In this paper, the fuzzy reliability model of blades to avoid resonance is investigated. By regarding the inherent frequency as a fuzzy random variable with trapezoidal or flat-normal membership function, a fuzzy reliability model of blades to avoid resonance is proposed based on the fuzzy cut-set theory, and the corresponding numerical solution is given. Further, a theorem is proposed and proved to indicate the deficiency of the previous cut-set distributions on convergence, and, then, a new cut-set distribution is given to cover this shortage and ensure that the model is of good convergence. Finally, the proposed model is applied to evaluate the reliability of one certain blade. Some simulations are carried out to compare the new cut-set distribution with the previous ones and study the influence of fuzzy degree on the reliability.