Bayesian Estimation of Directional Wave-Spectrum Using Vessel Movements and Wave-Probes: Proposal and Preliminary Experimental Validation

Abstract

The measurement of the directional wave spectrum in oceans has been done by different approaches, mainly wave-buoys, satellite imagery and radar technologies; these methods, however, present some inherent drawbacks, e.g., difficult maintenance, low-resolution around areas of interest and high-cost. In order to overcome those problems, recent works in the area proposed a motion-based estimation procedure using the vessel, or the floating facility, as a wave sensor, what was called wave-buoy analogy. Despite of solving the issues, the solution is still incomplete, since it suffers from low estimation capabilities of the spectral energy below the cut-off period of the systems, around eight seconds, a frequency range that is responsible for the drift effects, that are critical for operation planning and dynamic positioning. This work studies the usage of wave-probes installed on the hull of a moored vessel to enhance the estimation capabilities of the motion-based strategy, using a high-order estimation method based on Bayesian statistics. The proposal is founded on the asymptotical response of the oceanic systems facing low period waves, which starts to behave like a wall, reflecting all the incoming energy, i.e., the worst the motion-based estimation is, the better the wave-elevation based estimation should be. Firstly, the measurements from the wave-probes are incorporated to the dynamic system of the vessel as new degrees-of-freedom, using a linear model extension, thus the Bayesian method can be expanded without additional reasoning. Secondly, the linear model hypothesis and the possible improvements are validated by experiments conducted in a wave-basin with a scale model of a moored FPSO-VLCC, concluding that the approach is able to improve not only the estimation of spectra with low peak period, but also the estimation in the entire range of expected spectra, mainly the significant height and the peak period properties. Lastly, some drawbacks are discussed, as the effect of the non-linear roll movement, which must be taken in account when calculating the wave-probe response; and the poor mean-direction estimation capability in some particular wave directions and low peak periods, in which even the vessel motions allied with the wave-probe response are not able to provide the proper direction discrimination.