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Abstract In order to overcome the limitations of the ordinary convex set in expressing the uncertainty of the actual parameters, a fuzzy set model for fatigue life parameters and method for fatigue life estimation were proposed. The scale parameter of the hyper ellipsoid model was considered to be a positive fuzzy number. The inner and outer ellipsoid model on the basis of the interval model were the inside and outside edge the fuzzy set, and the membership function of the scale parameter was determined. Thus the fuzzy constraint set for fatigue life was built. Based on the Taylor series and Lagrange multiplier method, an approach for estimating the extreme values of fatigue lifetime in the ordinary set was proposed. The fuzzy maximal set and fuzzy minimal set were constructed. Through the normalization of the hyper ellipsoid model and spherical coordinate conversion, the sample points inside the fuzzy set can be extracted and estimation of fatigue life under fuzzy constraints can be realized. In a project example, the proposed method was compared with the convex set method and the probabilistic method. The results illustrated that the fuzzy set method is closer to the engineering practice and can provide more reasonable solutions, so it is a development and improvement of previous methods.
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Received: 16 February 2012
Published: 28 April 2013
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2013, Vol. 34 
