A sparse‐grid, nonintrusive formulation of acoustic field uncertainty in ocean waveguides.

Abstract

The inclusion of environmental uncertainty in simulations of acoustic wave propagation in ocean waveguides is important for the development of simulation‐based prediction methods that quantify the influence of multiple sources of incomplete environmental knowledge on the simulation results. Polynomial chaos expansions have been suggested as a natural mathematical framework for describing both environmental and acoustic field uncertainties, their interaction, and propagation through the waveguide [S. Finette, J. Acoust. Soc. Am. 120 (2006)]. Previous research has described the inclusion of these expansions directly into the propagation equation (the intrusive approach), yielding coupled differential equations for the expansion coefficients. The solution for the coefficients contains the statistical properties of the uncertain field. Here we describe an alternative nonintrusive formulation, where existing acoustic propagation codes can be used to estimate the chaos coefficients rather than solve for them via a complex set of coupled differential equations. The nonintrusive formulation involves multiple solutions of an existing deterministic code, e.g., a wide‐angle parabolic equation solver, in conjunction with the Smolyak sparse‐grid interpolation and multidimensional quadrature to obtain uncertainty statistics on the acoustic field. [Research supported by the Office of Naval Research.]