On the calculation of the statistical distribution of maxima of slightly non-linear, quadratic, stationary stochastic variables

Article type: Research Article

Authors: Vinje, T. | Skjørdal, S.O.

Affiliations: Division of Ship Hydrodynamics, Norwegian Institute of Technology, University of Trondheim, Trondheim, Norway

Abstract: A method for calculation of the statistical distribution of maxima of stochastic variables of the type: Y=αiXi+aijXiXj where {aij} is ‘small’ and {Xi} is a Gaussian distributed stationary stochastic process, is shown. This method is based on an asymptotic series expansion of the probability density function for {aij}→0, which is compared to the exact solution for: Y=X+εX2 and the validity of the asymptotic series is discussed. The statistical distribution of the combined stresses at the deck corner of a ship is calculated according to the present method and some characteristic parameters of the extreme-value statistics are given. These parameters are compared to some standard estimates, which are found to be conservative. At last the possibility of calculating the long-term distribution of maxima of non-linear variables is discussed.

DOI: 10.3233/ISP-1975-2225201

Journal: International Shipbuilding Progress, vol. 22, no. 252, pp. 265-274, 1975