The accurate estimation of extreme responses for offshore platforms and supply vessels is critical to the design process. Long time Monte Carlo-type simulations can theoretically capture extreme responses, but this type of simulation is not feasible in the early design process due to the extreme computational expense. An alternative is to use shorter simulations that are tailored to create statistically equivalent extreme responses. The latter requires judicious specification of expected extreme sea conditions.
Extreme responses can be estimated using a variety of processes, including the Design Loads Generator (DLG). Assuming a vessel response is Gaussian, stationary, and ergodic, a given response can be approximated as a sum of Fourier amplitudes with random phase angles. The DLG is a process that can calculate innumerable sets of random phase angles that result in a given extreme response or design event. Using linear-systems theory, the corresponding incident-wave phase angles are calculated from the response phase angles and the incident-wave-train profile is determined.
A fundamental question that must be answered is how can a nonlinear seaway that produces an extreme event be described such that a wave maker or numerical wave boundary condition be controlled to recreate the nonlinear and extreme seaway. A common practice employs linear wave theory to shift the design event in space and time. The shifted phase angles can then be used to drive a wavemaker with the intent of producing the desired wave train at a given point. However, nonlinearities in wave propagation result in an inaccurately generated design wave train. This paper focuses on the role of wave nonlinearity in the evolution of the wave system and how this can be accounted for in the control of a physical or virtual wave maker.