Designing Input Wave Signals to Achieve Desired Ship Responses Through Linear and Nonlinear Conditioning

We present a new method for generating input wave signals for time-domain ship hydrodynamics simulations which are designed to achieve certain outcomes in ship responses, such as heave, pitch, or roll. By using conditional inputs, this method minimizes guesswork and reduces computation time, especially for predicting rare events. The developed model supports both linear and nonlinear (quadratic) conditioning of ship responses. Linear conditions allow for setting desired amplitude, derivative, and/or average response over a period, while quadratic conditions target specific envelopes and/or spectral moments. Although linear conditions on a Gaussian process preserve the Gaussian nature of the output, quadratic conditions do not, representing an advancement beyond traditional Gaussian approximations. The results demonstrate that the method effectively generates wave signals that meet the desired ship response criteria for both linear and nonlinear conditions.