Fuzzy Set Methods for Assessing Uncertainty in the Modeling and Control of Space Structures

Abstract

Aerospace institutions such as NASA and the U.S. Air Force have long been interested in the development of methods for evaluating the predictive accuracy of structural dynamic models. This interest is due to the fact that mathematical models are used to evaluate the structural integrity of all aircraft and spacecraft prior to flight. Space structures are often too large and too weak to be tested fully assembled in a ground test laboratory. The predictive accuracy of a model depends on the nature and extent of its experimental verification. The further the test conditions depart from in-service conditions, the less accurate the model is likely be. The best method for quantitatively evaluating the predictive accuracy of a model is to make direct measurements under simulated service conditions. Unfortunately, this method is expensive and fraught with problems in achieving service conditions on earth. This article presents progress made in the combined use of several methods to evaluate the accuracy of dynamic models of large space structures using numerical simulation. Some of these methods involve the theory of fuzzy sets. The fuzzy set methods are shown to be effective and computationally efficient as tools for bounding the range of possible responses, segregating important modal responses from those having less effect on predicted response, reduction of uncertainty in plant models in a control-structure interaction context, and providing the only plausible means of uncertainty prediction at the poles and zeros of the frequency response spectra. The article illustrates these notions with some numerical examples.