Free-Surface Time-Series Generation for Wave Energy Applications

Finite-length, numerical simulations of Gaussian seas are widely used in the wave energy sector. The most common method consists of adding up harmonic sinusoidal components, with random phases and deterministic amplitudes derived from the target wave spectrum [deterministic amplitude scheme (DAS)]. In another approach, the component amplitudes are chosen randomly with a variance depending on the spectrum [random amplitude scheme (RAS)]. It is now generally accepted that only the latter method reproduces the true statistical properties of a Gaussian sea. Compared to previous works, this study clarifies the exact nature of the "statistical properties" that should be represented in the simulation process. Further analysis is carried out to address unanswered questions highlighted in the existing literature, especially with respect to the statistical relationships between discrete successive simulation points, and the probability law governing the average power estimator of a wave energy converter (WEC) simulated with the generated wave time series. It is shown that RAS exactly reflects how the WEC performance, considered over a finite duration, varies with respect to its long-term average, whereas DAS has the advantage of providing accurate estimates of the long-term average values using fewer, or shorter, simulations; in particular, it is demonstrated that only one simulation is sufficient when the WEC model is linear. Furthermore, it is shown why alternative methods, based on nonharmonic superposition of sinusoids, are not recommended. The effects of the simulation method (RAS or DAS) upon the statistics of individual oscillations in the time domain are also explored experimentally. Finally, a table is provided that gives recommendations, depending on the objective of the simulations.