Probability density functions of acoustic modal amplitudes by polynomial chaos expansions

Abstract

Polynomial chaos (PC) expansions have recently been derived to model the statistical behavior of complex modal amplitudes in uncertain waveguides. Here we explore the statistical trajectories of complex modal amplitudes in phase space for one and two degrees freedom (DOF) of waveguide uncertainty. It is shown that for one DOF of uncertainty, the modal amplitudes fall along a trajectory in phase space, while for higher DOFs the phase space of the amplitudes is space filling. Results are compared to phase space characteristics of the adiabatic and saturated limits of waveguide uncertainty, and a discussion of the range progression of the scintillation index of modal amplitude is undertaken. Comparisons between PC estimates of the probability density function of the modal amplitudes and Monte Carlo histograms are also made. [Work supported by ONR.]