Reliability of Vibrating Structures with Uncertain Inputs

Abstract

10 6 Summary 12 Abstract We evaluate the reliability of vibrating systems subject to severely deficient information about the dynamic loads. We stress non-probabilistic information-gap models of uncertainty, which are adapted to severe lack of information. When some probabilistic information avail- able, we show how it can be incorporated in a hybrid probabilistic/info-gap analysis. We outline the theory of robust reliability, which replaces probabilistic reliability in those situations where prior information insufficient to verify the choice of a probability density. We also illustrate a hybrid probabilistic/info-gap reliability analysis. Finally, we use the gambler's theorem and the idea of aversion to risk to provide an overall quantitative assessment of the performance of a system in an uncertain environment. 1 Modelling the Unknown Prediction, said Niels Bohr, is always difficult, especially of the future. But we act all the time on suppositions extrapolated from incomplete information. From coin-flips to international conflicts, we predict outcomes based on partial information. When we have extensive experience, like in ambient vibrations under known and controlled conditions, we can make reliable asser- tions. But in unique and unfamiliar circumstances we have severely limited prior knowledge, so we must be much more circumspect. In analyzing the reliability of critical components and systems with respect to rare and extraordinary events, about which we know very little, we must avoid unverifiable assumptions as much as possible. In particular, we must represent the uncertainties as reliably as possible, without extraneous assumptions. In this paper we discuss a method of reliability analysis which developed for this purpose. There no free lunch, informationally speaking, so an analysis based on limited prior information will be able to make only modest predictions. However, the crucial point that the analysis itself be reliable and not illusory.