The short-term variability of cross-spectral analyses is investigated and its effect on the wave buoy analogy is analysed. Based on the analogy, the sea state can be estimated from the cross-spectra of the ship response, i.e. ship as a wave buoy. In a steady state condition, a certain length of sampled data is required for stable results of the spectral analysis. However, the phase lag between responses, in terms of the phase angle obtained from the coupled cross-spectra, has not been discussed in detail. In a previous study, the authors pointed out that the short-term variability of the relative phase angle of the cross-spectra might be harmful to sea state estimation using the wave buoy analogy. In this paper, using long stationary time series, the transition of estimated wave parameters has been investigated by iterative analyses with a few seconds of time shifting. In the results, the short-term variability of the wave parameters was observed, and the effect was clarified.


Some of the authors of the present paper have made extensive studies about the wave buoy analogy. In this analogy, measured (global) vessel responses from an advancing ship are used together with corresponding transfer functions to obtain estimates, on a continuous basis, of the sea state at the exact position of the ship (Iseki and Ohtsu, 2000; Iseki, 2012; Nielsen and Iseki, 2012). In general, results of the wave buoy analogy compare reasonably well with results of other means for wave estimation (Nielsen and Stredulinsky, 2012; Nielsen, Andersen and Koning, 2013) but observations with poor agreement are also found; not to mention which means are the most accurate. This brings to question how much variation, due to aleatory uncertainty (DNV, 1995), the sea state itself may exhibit on a short-term scale in a 2–5 minutes period.

A direct measure for the aleatory short-term variation of a sea state in time and position could be obtained based on results by the wave buoy analogy. However, an indirect measure can be given in terms of measurements of ship responses, since any change in sea state will be directly observable in the wave-induced responses; assuming other operational parameters (speed, heading, etc.) to be constant and neglecting the fact that a ship is a (linear) wave filter. The advantage by this indirect approach is that modelling ncertainties, of the wave buoy analogy or other similar means for wave measurement, will not influence results. In case of the wave buoy analogy, otably uncertainty related to the transfer functions of the ship could influence results. ‘Modelling uncertainties’ may, in this ense, be viewed as a kind of epistemic uncertainty (DNV, 1995).

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