Combination of probabilistic and convex models of uncertainty when scarce knowledge is present on acoustic excitation parameters

Abstract

This paper is devoted to a fundamental problem of accounting for parameter uncertainties in random vibrations of structures. In contrast to the overwhelming majority of random vibration studies where perfect knowledge is assumed for the parameters of the excitation, this crucial conjecture is dispensed with. The probabilistic characteristics of the excitation are assumed to be given as depending on some parameters which are not known in advance. We postulate that some imprecise knowledge is available; namely, that these parameters belong to a bounded, convex set. In the case where this convex set is represented by an ellipsoid, closed form solutions are given for the upper and lower bounds of the mean-square displacement of the structures. For the first time in the literature the system uncertainty in the random vibrations is dealt with as an ‘anti-optimization’ problem of finding the least favorable values of the mean-square response. The approach developed here opens a new avenue for tackling parameter uncertainty which is often encountered in various branches of engineering.