Probability density function methods for uncertainty analysis in underwater acoustics

Abstract

Forward modeling of underwater acoustic propagation is generally successful when environmental parameters and boundary conditions are known. Unfortunately, such information is seldom available at the requisite level of precision, and any imprecision introduces uncertainty into sound field predictions. Quantifying this sound-field uncertainty is important for applications of acoustic propagation models such as matched-field processing. This presentation describes a method for quantifying the underwater-sound-field uncertainty arising from imperfect knowledge of the environment and its boundaries. It is based on formulating and solving a transport equation for the joint probability density function (PDF) of the real and imaginary parts of a harmonic sound field. The appropriate equation is obtained by combining spatial derivatives of the PDF with physical laws drawn from guided wave mechanics. The inputs for solving the PDF-transport equation are known or assumed distributions of the uncertain parameters. Solutions can be readily reduced to expected values, uncertainties, and confidence intervals for the predicted sound field. Results for simple test cases involving range-independent isospeed underwater sound channels are considered, and compared to solutions obtained analytically or through Monte Carlo simulations. [Work sponsored by ONR.]