Properties and approximation of acoustic field and array beam power probability density functions.

Abstract

Recent work [Finette, J. Acoust. Soc. Am. 120] investigated the application of polynomial chaos expansions (PCEs) to the computation of acoustic field uncertainties. In the present work, benchmark studies are performed to investigate the functional properties of acoustic field and array beam power probability density functions (PDFs) in uncertain ocean environments and the convergence and numerical accuracy of PCE based approximations of those PDFs. For these studies, a stratified ocean waveguide model is assumed. The field and beam response PDFs are computed directly from given acoustic parameter PDFs using the normal‐mode expansion and the change of variables theorem of probability theory. For low‐dimensional acoustic parameter uncertainties, the field and beam power PDFs exhibit irregular functional behavior and singularities associated with features of the mapping from the parameter space to the field or beam power space. Computational examples using PCE associate the properties of the PDFs with the convergence rates of the polynomial chaos expansions as a function of range. PDF properties and PCE convergence are then investigated for higher‐dimensional acoustic parameter uncertainties. Finally, results using the parabolic‐equation approximation are compared with the normal‐mode benchmarks. [Work supported by the Office of Naval Research.]