Model test estimation of quadratic transfer functions (QTFs) is investigated for slowly varying wave drift excitation on a large moored ship in shallow water. Cross-bi-spectral analysis in irregular waves is used. A numerical study is run first, with a known, synthetical QTF model characterized by a strong off-diagonal variation, combined with a very lightly damped linear slow-drift dynamical system. The purpose is to check the accuracy of the analysis. For this simple model, a good accuracy is obtained in the estimated QTF. This is because of a refined noise reduction method which works well in this case. The wave frequency range of valid estimates is where the wave spectrum S(f) is higher than 7% of the spectral peak. Without the refinement, the useful range is reduced to where S(f) is higher than 15% of the spectral peak, based on a 3-hour sea state simulation. The method is then applied on experimental surge motion records from 1:50 scaled model tests carried out in an offshore basin, simulating 15m water depth. It is found that the QTF estimation procedure works reasonably well, but the accuracy is lower than that in the numerical study because the refined noise reduction could not be used due to the particular characteristics of the QTF. Therefore a basic version without the refinement had to be used. Still, results appear to be fairly reliable in the reduced wave frequency range with S(f) > 15% of the spectral peak, i.e. from 0.07Hz to 0.10Hz in this case.
Spatial-phase-modulation-based study of polyvinyl-alcohol/acrylamide photopolymers in the low spatial frequency range