Phase-resolved wave estimation during operation of floating structures based on motion measurements provides an efficient, low-cost approach to enhancing operations. Prolate spheroidal wave functions (PSWFs) enable the reconstruction of wave profiles in short time windows with the help of a wave-to-motion response amplitude operator (RAO). Although fully linear hydrodynamic modeling can efficiently derive the RAO of floating structures, its applicability is highly limited to rather linear operation conditions. This study extends the PSWF methodology for wave estimation by combining it with the statistical linearization approach, which allows nonlinearities to be incorporated into the RAO based on the measured motion. The combined methodology is verified with motions for a floating cylinder and sphere, whose motions were calculated using a time domain simulation based on Cummins equation. Viscous drag and nonlinear hydrostatic forces were investigated. The results showed that the combined methodology increased the accuracy of the resulting wave profiles, measured in terms of correlation and spectral differences. Combining PSWFs and statistical linearization reproduced wave profiles with correlation values above 0.9 in waves with periods greater than 9 s. Combining both nonlinear effects for the sphere slightly increased the method’s accuracy due to the reduced motion amplitudes.
Wermbter et al. (Wed,) studied this question.