Estimation of autocorrelation function and spectrum density of wave-induced responses using prolate spheroidal wave functions

Tomoki Takami*, Ulrik Dam Nielsen, Jørgen Juncher Jensen

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

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Abstract

Predicting the wave-induced response in the near-future is of importance to ensure safety of ships. To achieve this target, a possible method for deterministic and conditional prediction of future responses utilizing measured data from the most recent past has been developed. Herein, accurate derivation of the autocorrelation function (ACF) is required. In this study, a new approach for deriving ACFs from measurements is proposed by introducing the Prolate Spheroidal Wave Functions (PSWF). PSWF can be used in two ways: fitting the measured response itself or fitting the sample ACF from the measurements. The paper contains various numerical demonstrations, using a stationary heave motion time series of a containership, and the effectiveness of the present approach is demonstrated by comparing with both a non-parametric and a parametric spectrum estimation method; in this case, Fast Fourier Transformation (FFT) and an Auto-Regressive (AR) model, respectively. The present PSWF-based approach leads to two important properties: (1) a smoothed ACF from the measurements, including an expression of the memory time, (2) a high frequency resolution in power spectrum densities (PSDs). Finally, the paper demonstrates that a fitting of the ACF using PSWF can be applied for deterministic motion predictions ahead of current time.
Original languageEnglish
JournalJournal of Marine Science and Technology
Volume26
Pages (from-to)722-791
ISSN0948-4280
DOIs
Publication statusPublished - 2021

Keywords

  • Autocorrelation
  • Wave-induced response
  • Ship motion
  • Prolate spheroidal wave functions

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