A stochastic response surface formulation of acoustic propagation through an uncertain ocean waveguide environment

Abstract

Stochastic basis expansions are applied to formulate and solve the problem of including uncertainty in numerical models of acoustic wave propagation within ocean waveguides. As an example, a constrained least-squares approach is used to estimate the intensity of an acoustic field whose waveguide environment has uncertainty in both source depth and sound speed. The mean intensity, a second moment of the field, and its probability distribution are computed and compared with independent Monte-Carlo computations of these quantities. Very good agreement is obtained, indicating the potential of stochastic basis expansions for describing multiple sources of uncertainty and their effect on acoustic propagation.

Hybrid uncertain analysis for structural–acoustic problem with random and interval parameters

“…Traditional approaches for these uncertain problems are probabilistic methods, in which the uncertain parameters are expressed as the random variables whose probability distributions are defined unambiguously [1]. Monte-Carlo method is the simplest and the most versatile method for uncertain problems [2][3][4][5][6]. Whereas, for large industrial scale problems, the computational cost of Monte-Carlo method is prohibitively expensive.…”

“…Whereas, for large industrial scale problems, the computational cost of Monte-Carlo method is prohibitively expensive. Perturbation stochastic method [7][8][9] and spectral stochastic method [10][11][12][13] are the efficient alternatives for stochastic problems. Recently, Bayesian approach has been introduced into uncertain models and has achieved significant successes [14][15][16].…”

Empirical and quadrature approximation of acoustic field and array response probability density functions

“…Creamer 3 investigated the convergence properties of the polynomial chaos expansion for a simplified model of wave propagation in one dimension. Finette 4,5 further developed computation of the polynomial chaos expansion of the acoustic field within the context of stochastic environmental models and parabolic-equation propagation. James and Dowling 6 developed computationally efficient methods for approximating acoustic field pdf's based on approximation of the local variations of the field by spatial shifts.…”

“…Orthogonal polynomial (polynomial chaos) expansion has been applied in the acoustics literature 1,4,5 and in a number of other applications to obtain stochastic-process representations of physical fields as power series in a basis of random variables, based on assumed dynamics (in the acoustics case, an acoustic propagation model). After such construction, Monte Carlo sampling sometimes is applied to the stochastic series representation to obtain an approximation to the pdf of a local value of the stochastic field under consideration, e.g., the pdf of the squared pressure magnitude at a spatial point.…”

Pekeris waveguide comparisons of methods for predicting acoustic field amplitude uncertainty caused by a spatially uniform environmental uncertainty (L)

“…1, and modest Q (<10) may produce reliable results when the uncertain environmental parameter or parameters have finite correlation lengths. The PCE solution method employed here follows that in Finette (2006) (Finette, 2009) may yield a lower computational burden than DS for multiple uncertain variables with finite correlation lengths.…”