Filtering algorithm for eigenvalue bounds of fuzzy symmetric matrices

Abstract

Purpose

The solution of dynamic problems of structures using finite element method leads to generalised eigenvalue problem. In general, if the material properties are crisp (exact) then we get crisp eigenvalue problem. But in actual practice, instead of crisp material properties we may have only bounds of values as a result of errors in measurements, observations and calculations or it may be due to maintenance induced error etc. Such bounds of values may be considered in terms of interval or fuzzy numbers. The purpose of this paper is to develop a fuzzy filtering procedure for finding real eigenvalue bounds of different structural problems.

Design/methodology/approach

The proposed fuzzy filtering algorithm has been developed in terms of fuzzy number to solve the fuzzy eigenvalue problem. The initial bounds of fuzzy eigenvalues are filtered to obtain precise eigenvalue bounds which are depicted by fuzzy (Triangular Fuzzy Number) plots using α-cut.

Findings

Previously, bounds of eigenvalues of interval matrices have been investigated by few authors. But when the structural problem consists of fuzzy material properties, then the interval eigenvalue bounds may be obtained for each interval of the fuzzy number. The proposed algorithm has been applied for standard fuzzy eigenvalue problems which may be extended to generalised fuzzy eigenvalue problems for obtaining filtered fuzzy bounds.

Originality/value

The developed fuzzy filtering method is found to be efficient for different structural dynamics problems with fuzzy material properties.

Citation

Mahato, N.R. and Chakraverty, S. (2016), "Filtering algorithm for eigenvalue bounds of fuzzy symmetric matrices", Engineering Computations, Vol. 33 No. 3. https://doi.org/10.1108/EC-12-2014-0255