Laura K. Alford

A Real-Time System for Forecasting Extreme Waves and Vessel Motions

The University of Michigan is leading a team that includes subcontractors Ohio State University, Aquaveo, LLC, and Woods Hole Oceanographic Institute to design, implement, and test an Environmental and Ship Motion Forecasting (ESMF) system. The system has application to many challenges associated with offshore operations, including skin-to-skin transfer of cargo/personnel and extreme wave/response prediction. Briefly, the system uses a modified commercial-off-the-shelf (COTS) Doppler marine radar to determine the wave field surrounding the vessel; nonlinear wave theory to propagate the wave surface forward in time; and seakeeping theory to predict future vessel motions. A major challenge is that all computations must be done in real time. This paper will briefly describe the system and show an example application of predicting extreme waves and motions for a floating offshore type platform.Copyright

Effects of Third-Order Nonlinearities on the Fourier Representation of Deterministic Wave Trains

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.Copyright

Extreme Responses of Bilinear Stiff Systems

A single-point mooring system is modeled as a bilinear-stiff system. Long-term statistics of the nonlinear mooring system are estimated by Monte Carlo computer simulation. In an effort to generate an extreme event in a short time period (as opposed to lengthy Monte Carlo simulations), an equivalent linear system is devised along with an excitation designed to elicit a large, linear response. This design wave and the resulting system excitation are used in simulations to generate both the design nonlinear and equivalent linear responses.Copyright