Chapter XV - Fuzzy Structure Theory

Abstract

This chapter presents the fuzzy structure theory. The objective of this theory is to predict the medium-frequency local dynamical response of a master structure coupled with a large number of complex secondary subsystems, such as equipment units or secondary structures attached to the master structure. These subsystems are called fuzzy substructures due to their structural complexity and because the details of them are unknown, or are not accurately known (the terminology “fuzzy” has nothing to do with the mathematical theory concerning fuzzy sets and fuzzy logic). This fuzzy structure theory is stated as an inverse problem and introduces a random boundary impedance operator to model the effects of the fuzzy substructures on the master structure. As an inverse problem, the random boundary impedance operator is constructed using the concept of a type I or type II homogeneous fuzzy impedance law, which depends on a set of parameters called the mean coefficients and the deviation coefficients of the law. An appropriate method is proposed for identifying these coefficients.