Underwater acoustic field prediction is a mature field of research, with many applications in Naval and ocean engineering. However, existing prediction models rely on accurate information about the underwater environment, which is seldom available.
For many applications of acoustic field prediction, it is useful to know both the accuracy of the prediction, and the possible range of values the field may take as a result of uncertainty in the environment. Such information is not provided by existing deterministic acoustic-field-prediction models.-This thesis explores three methods for quantifying the uncertainty in acoustic field predictions, based on the uncertainty in environmental parameters.
(1) The PDF propagation method develops governing equations for the probability distribution of the field which are mathematically exact, but cannot be solved in closed form without further modeling or approximation of several terms. (2) The field shifting method approximates the relationship between the field and all environmental variables, by assuming that small changes in any parameter result in small spatial shifts of the field on a local scale. (3) The polynomial chaos method expresses the uncertain field as a weighted sum of orthogonal polynomials, then solves for the unknown weighting coefficients to obtain a distribution for the field.-The latter two techniques are compared to direct numerical simulations in a Pekeris waveguide using an L1-error norm of the predicted-fields probability density function to gauge accuracy.
It is found that 95% of the field-shifting approximation results calculated in environments with a 10 m/s uncertainty in sound speed exhibit L1 errors lower than 0.40, indicative of acceptable approximation accuracy for many applications. When the polynomial chaos truncation order is chosen iteratively, 95% of the approximations for the same cases exhibit L1 errors below 0.09, indicating a very high degree of accuracy. However, for a single uncertain variable, determining the appropriate truncation order for polynomial chaos is far less computationally efficient than direct simulation, potentially requiring thousands of field calculations, compared to 20-100.
In contrast, field shifting is shown to be the most efficient approximation in this research, requiring only N + 1 field calculations for N uncertain environmental parameters.