Response variance prediction for uncertain vibro-acoustic systems using a hybrid deterministic-statistical method

Imperfections during the manufacturing process can cause significant variations in the noise and vibration levels exhibited by nominally identical structures. Any response calculations employed during the design process should ideally take account of these uncertainties and predict the expected range in performance. Recently a hybrid method has been developed to predict the ensemble average response of a built-up system by combining a deterministic model of parts of the system with a statistical model of other components [Shorter, P. J., and Langley, R. S. (2005) J. Sound. Vib., 288, 669-700]. In this paper the method is extended to predict the ensemble variance of the response. Expressions are derived for the variance of the vibrational energies in the statistical components, and for the variance of the cross spectrum of the response of the deterministic components, which augment the mean values of these quantities predicted by the original theory. The method employs a nonparametric model of uncertainty, in the sense that the statistical components are taken to carry diffuse wave fields, and this obviates the requirement for a detailed description of the system uncertainties. The method is validated by application to a range of coupled plate structures, and good agreement with detailed Monte Carlo simulations is found.