Estimation of autocorrelation function and spectrum density of wave-induced responses using prolate spheroidal wave func
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ORIGINAL ARTICLE
Estimation of autocorrelation function and spectrum density of wave‑induced responses using prolate spheroidal wave functions Tomoki Takami1 · Ulrik Dam Nielsen2,3 · Jørgen Juncher Jensen2 Received: 13 March 2020 / Accepted: 9 September 2020 © The Japan Society of Naval Architects and Ocean Engineers (JASNAOE) 2020
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. Keywords Autocorrelation · Wave-induced response · Ship motion · Prolate spheroidal wave functions
1 Introduction Predicting the wave-induced responses that a ship will encounter in the near-future is important to support ship operation. For instance, various marine operations, such as a helicopter landing on the deck of a ship, and crane and maintenance operations (on deep water) of offshore installations, would benefit highly by a deterministic prediction of the future vessel responses expected a short period (less than a minute) ahead of time. The prediction methods developed in past studies are roughly classified in two categories; (a) those using the wave-excitation input and a hydrodynamic model, e.g. [1], or (b) methods using the correlation structure in the response itself (e.g. AR models), without the need of wave input. As regards (a), although time-domain * Tomoki Takami takami‑[email protected] 1
National Maritime Research Institute, Mitaka, Japan
2
Technical University of Denmark, Lyngby, Denmark
3
Centre of Autonomous Marine Operations and Systems, NTNU AMOS, Trondheim, Norway
numerical methods for computing wave-induced responses have matured, it is still hard to evaluate the response efficiently on board, as the input of the wave elevation sequence, together with design information of the ship, will be required. Thus, utilizing just the
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