Statistics of extreme values of stochastic processes generated by rotating machines and associated probabilistic reliability model

Abstract

The random stress processes recorded on the mechanical structures of rotating machines have non-Gaussian structure. These processes are logically composed of a deterministic periodic process, centred on the harmonics of the rotor rotation frequency, on which is routinely superposed a Gaussian zero-mean random process. This article first presents the mathematical principles of extreme value models, adapted to their specific nature. The proposed probabilistic models are then compared with each other in order to examine their degree of similarity and conservatism. On the basis of Gumbel's theory, adopted as an asymptotic approach to extreme values, a statistical model of extreme values of sine plus noise composite random processes is proposed and discussed.