Abstract
The concept of uncertainty is related to both reducible and irreducible errors that can enter a computer simulation through several channels: modeling errors, discretization of the continuous dynamical system, missing knowledge/information concerning boundary and initial conditions, and selection of parameter values. In ocean waveguide modeling, uncertainty inherent in the lack of knowledge of the sound speed distribution, for example, is mapped into the acoustic field. In a sense, it propagates along with the acoustic field to which it is coupled, though the computed pressure field at a point in the waveguide does not normally include an explicit measure of this uncertainty. This presentation will describe a method for explicitly incorporating uncertainty into the dynamics for acoustic wave propagation in ocean waveguides. In order to quantify uncertainty in numerical simulations for underwater acoustics problems, the application of stochastic basis expansions of random processes that effectively map uncertainty in the parameter input space to uncertainty in the system output space is considered. The relationship to Monte Carlo methods is also discussed. [Work supported by ONR.]
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