An Efficient Numerical Method for Calculating the Statistical Distribution of Combined First-Order and Wave-Drift Response

Abstract

The paper describes an efficient and accurate numerical procedure for calculating the probability distribution function of combined first-order and slowly varying, second-order hydrodynamic loads and response of compliant offshore structures. No approximations are made except those inherent in the numerical calculations. The method does not require extensive computer capacity; in fact it can be implemented on any standard PC. Several example calculations serve to illustrate the method, and its accuracy is demonstrated by comparison with cases where exact analytical results are available. The accuracy of previously proposed approximations are also discussed.

Joint statistics of combined first- and second-order random processes

“…For the main body of the distribution, the FFT algorithm provides an accurate and efficient solution. However, at the tails of the distribution a much more accurate and efficient solution is obtained by using saddle-point integration techniques [12].…”

“…Given that the characteristic function and the pdf form a Fourier transform pair, the pdf can be calculated. For most situations this must be achieved numerically using either the Fast Fourier Transform (FFT) algorithm or saddlepoint integration techniques [12].…”

Numerical calculation of the level crossing rate of second order stochastic Volterra systems

“…The problem of determining the probability distribution function of such response processes has been solved in the sense that computer programs are available that allow very accurate numerical calculations of these functions [7]. These programs are all based on the use of the characteristic function of the stationary response process at an arbitrary fixed point in time.…”