Response of a Large Spar Platform to Monochromatic Input Wave Excitation

A wavelet analysis of the behavior of a large spar platform model undergoing a monochromatic input wave excitation is presented. Two techniques are involved in this analysis. First, a continuous wavelet transform (CWT) with complex Morlet wavelets is performed. For this transform, special attention is given to the treatment of the signals ends by mean of stating adequate hypotheses on the behavior of the time series at their boundaries. Second, to validate the hypotheses on the boundary extensions made for the CWT analysis and to provide additional insight on the system behavior, a cubic B-spline discrete wavelet transform representation on a bounded interval is performed. This transform relies only on the interval data, giving in this way a truly semi-orthogonal representation of the energy density of the system on a bounded interval. In this manner, it becomes possible the analysis of wave tank experiments with spar platforms in which it is not possible to conduct tests involving long spans of data and making extrapolation assumptions can pose a question on the validity of the analysis.