linear conditions, either directly in the frequency domain or indirectly by the analysis of long simulated time traces. Only the nonlinear response in regular waves is required to be known. In this paper, this information was deducted from the regular wave experiments but the results of a set of large amplitude ship motion simulations could be used as well.
The work reported herein was performed during the author's stay at the Laboratory of Ship Hydromechanics of the Delft University of Technology. The author is grateful to professor J.A.Pinkster and staff for inspiring discussions and for their assistance in model testing in particular. The research was financially supported by the Royal Netherlands Navy.
 M.Kac and A.J.F.Siegert. On the theory of noise in radio receivers with square law detecters . Journal of Applied Physics, 18:383– 397, 1947.
 N.Wiener. Nonlinear problems in random theory. M. I. T. Press, Cambridge, Mass., 1958.
 K.Hasselmann. On nonlinear ship motions in irregular waves. Journal of Ship Research, 10:64–68, 1966.
 J.F.Dalzell. The applicability of the functional polynomial input-output model to ship resistance in waves. Technical Report SIT-DL-75–1794, Stevens Inst. of Technology, Hoboken, New Jersey, 1975.
 J.A.Pinkster. Low frequency second order wave exciting forces on floating structures. PhD thesis, Techn. Univ. of Delft, 1980.
 M.H.Kim and D.K.P.Yue. Sum- and difference-frequency wave loads on a body in unidirectional gaussian seas. Journal of Ship Research, 35(2):127–140, 1991.
 J.J.Jensen and P.T.Pedersen. Bending moments and shear forces in ships sailing in irregular waves . Journal of Ship Research, 25:243– 251, 1981.
 M.S.Longuet-Higgins. The effect of nonlinearities on statistical distributions in the theory of sea waves. Journal of Fluid Mechanics, 17:459– 480, 1963.
 T.Vinje and S.O.Skjørdal. On the calculation of the statistical distribution of maxima and minima of slightly non-linear, quadratic, stationary stochastic variables . International Shipbuilding Progress, 22:265–274, 1975.
 J.J.Jensen. Fatigue analysis of ship hulls under non-gaussian wave loads. In Marine Structures, Design, Construction and Safety, pages 279–294. Elsevier Applied Science, 1991.
 J.F.Dalzell. An investigation of the applicability of the third degree functional polynomial model of nonlinear ship motion problems. Technical Report SIT-DL-82–9-2275, Stevens Inst. of Technology, Hoboken, New Jersey, December 1982.
 J.F.Dalzell. Approximations to the probability density of maxima and minima of the response of a nonlinear system. Technical Report EW-22–84, US Naval Academy, Annapolis, Maryland, 1984.
 S.R.Winterstein. Nonlinear vibration models for extremes and fatigue. Journal of Eng. Mech., ASCE, 114(10):1772–1790, 1988.
 J.F.Dalzell. An investigation of midship bending moments experienced in extreme regular waves by a Mariner-type ship and three variants. Technical Report SSC-155, Ship Structure Committee, 1964.
 J.F.Dalzell. An investigation of midship bending moments experienced in extreme regular waves by models of a tanker and a destroyer. Technical Report SSC-156, Ship Structure Committee, 1964.
 D.C.Murdey. An analysis of longitudinal bending moments measured on models in head waves. Transactions of Royal Institute of Naval Architects, 114:221–240, 1972.
 W.C.E.Nethercote. Motions and bending moments of a warship design. Transactions of Royal Institute of Naval Architects, 123:353– 375, 1981.
 J.F.O'Dea, E.Powers, and J.Zselecsky. Experimental determination of nonlinearities in vertical plane ship motions. In Proc. of 19th Symp. on Naval Hydrodynamics, pages 53–70, Seoul, Korea, 1992.