An Analysis Method for Fuzzy Natural Frequency using Response Surface Methodology

Abstract

In this paper, we propose an efficient procedure for finding the possible ranges of uncertain natural frequencies of a finite element (FE) model with uncertain parameters. Uncertain model parameters are described by input fuzzy numbers and then output fuzzy numbers are calculated by fuzzy arithmetic. The variation range of natural frequency is obtained from the membership function of output fuzzy number. The fuzzy arithmetic used is based on the α-cut concept and interval analysis. To reduce the computational effort for the interval analysis, the global optimization technique using response surface methodology (RSM) is introduced. Furthermore, we propose an approach for finding the feasible ranges of uncertain model parameters when the ranges of natural frequencies are specified. This is an inverse problem. A simple frame model is used to demonstrate the effectiveness of the proposed procedure and approach. The examples show that the membership functions of uncertain natural frequencies are efficiently and accurately estimated by the proposed procedure. In addition, the ranges of uncertain model parameters are properly evaluated by the proposed approach.