Abstract
The non-linear ship responses, such as parametric rolling and pure loss of stability in following seas, have become the key issues in the research field of ship stability. In order to investigate these non-linear phenomena, it is well known that the higher order spectral analysis should be introduced and the non-linearity must be treated properly. In this paper, the bispectral analysis, which is the higher order analysis than the power spectral analysis, is introduced to investigate the non-linear ship responses with focusing on the skewness of the data. First of all, characteristics of the bispectra and response functions of the second order Volterra system are investigated using a simple sinusoidal signal and its quadratic response signal. Secondly, the bispectral and cross-bispectral analysis are applied to the time history data that were obtained during on-board tests. The result shows that the non-linear pitching motion and the fluctuating skewness were observed in following seas. Considering the wave pattern and its period of encounter, it is shown that the skewness of the pitching motion is closely related to the non-linear re-storing moment. Furthermore, it is confirmed that the time history data of the main engine load index shows high skewness and two different types of second order response functions can be obtained with considering the pitching motion and the wave height to be the input signals.
