Closed-form Approximations and Series Representations for Partially Saturated Ocean Acoustic Processes

Abstract

An approximate, closed‐form expression for the value of the integral encountered in the calculation of the probability density function (PDF) of the envelope of a partially saturated ocean acoustic process is obtained. Furthermore, an expression of this PDF as a series of modified Bessel functions is presented. The results may also be directly applied to the evaluation of the PDF encountered in the structural reliability analysis of rotating machinery components. Numerical applications show that the closed‐form expression is always within 1%2% of the exact result. The required computational effort is substantially lower than that required by direct numerical integration.