Transformation of a wave energy spectrum from encounter to absolute domain when observing from an advancing ship

Abstract

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Ship Motion-Based Wave Estimation Using a Spectral Residual-Calculation

“…Thus, the whole set of estimated encounter-wave spectra are shown in Figures 5 and 6. Obviously, the corresponding wave spectra -in absolute domain -seen previously in Figures 2 and 3 have been obtained by transformation of the encounter-wave spectra by applying the particular transformation algorithm [15], specifically developed to transform a spectrum from encounter to absolute domain, but not the "other way". The reason to transform to absolute domain is that the estimated encountered wave spectrum cannot be used to deduce any consequence of speed or heading changes of the vessel, which is the objective of decision support systems and also in more general response calculations.…”

“…[12]- [14], but giving no solution on how to deal with the problem in practice, when a wave spectrum (or a response spectrum) shall be transformed from encounter frequencydomain to absolute frequency-domain; a process that theoretically cannot be uniquely solved as it relates one single encounter frequency to three absolute frequencies in following seas. On the other hand, an interrelated study by Nielsen [15] outlines explicitly an elaborate and practical solution strategy for this problem. The details of the particular work will not be covered herein, but later additional referencing will be made to the study [15].…”

“…On the other hand, an interrelated study by Nielsen [15] outlines explicitly an elaborate and practical solution strategy for this problem. The details of the particular work will not be covered herein, but later additional referencing will be made to the study [15]. The main (mathematical) task of the wave estimation problem is to solve Eq.…”

“…Basically, the postprocess consists of two steps: Firstly, a corresponding match of the optimum wave direction and an associated set of wave spectra (composed by all signal-combinations) is selected through a minimisation of a metric based on an energy-variance between the individual wave spectra. Secondly, for the particular wave direction, the mean wave spectrum of the set of wave spectra is calculated and, lastly, this spectrum is transformed [15] to the absolute (frequency) domain.…”

Estimation of on-site directional wave spectra using measured hull stresses on 14,000 TEU large container ships

“…Nielsen et al suggested a new method in 2015 which is to make the fitting of the measured response and the corresponding theoretically calculated one directly in the time domain [15,16]. Subsequently, Nielsen has proposed a practical approach which is a transformation from encounter to an absolute domain of wave spectral densities, and it is considered that this method is satisfactory through numerical simulation and experimental verification [17]. Brodtkorb et al developed a simple method to solve the wave spectrum by using the iteration method.…”