Possibilistic interpretation of mistuning in bladed disks by fuzzy algebra

Karataş, Hamit Çağlar
This study aims to define the possibilistic interpretation of mistuning and examine the way of determining the worst case situations and assessing reliability value to that case by using possibilistic methods. Furthermore, in this study, benefits of using possibilistic interpretation of mistuning in comparison to probabilistic interpretation of mistuning are investigated. For the possibilistic analysis of mistuned structures, uncertain mistuning parameters are modeled as fuzzy variables possessing possibility distributions. In this study, alpha-cut representations of fuzzy numbers are used which makes fuzzy variables to be represented by interval numbers at each and every confidence level. The solution of fuzzy equations of motion is governed by fuzzy algebra methods. The bounds of the solution of the fuzzy equation of motion, i.e. fuzzy vibration responses of the mistuned structure, are determined by the extension principle of fuzzy functions. The performance of the method for possibilistic interpretation of mistuning is investigated by comparing it to the probabilistic methods both computational and accuracy wise. For the comparison study, two different optimization tools – genetic algorithm as the global optimization tool and constrained nonlinear minimization method as the gradient based optimization tool- are utilized in possibilistic analysis and they are compared to solutions of probabilistic methods resulted from Monte-Carlo method. The performances of all of the methods are tested on both a cyclically symmetric lumped parameter model and a realistic reduced order finite element model.


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Citation Formats
H. Ç. Karataş, “Possibilistic interpretation of mistuning in bladed disks by fuzzy algebra,” M.S. - Master of Science, Middle East Technical University, 2012.