Reconstruction of Incident Wave Profiles Based on Short-Time Ship Response Measurements

Tomoki Takami*, Ulrik Dam Nielsen, Chen Xi, Jørgen Juncher Jensen, Masayoshi Oka

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


This paper presents a new approach to attain estimates of the sea state based on short-time sequences of wave-induced ship responses. The present sea state estimation method aims at reconstructing the incident wave profiles in time domain. In order to identify phase components of the incident waves, the Prolate Spheroidal Wave Functions (PSWF) are employed. The use of PSWF offers an explicit expression of phase components in the measured responses and incident waves, indicating that estimations can be efficiently attained. A method to estimate the relative wave heading angle based on the response measurements and pre-computed transfer functions of the responses is also proposed. The method is tested with numerical simulations and experimental measurements of ship motions, i.e. heave, pitch, and roll, together with vertical bending moment and local pressure in a post-panamax size containership. Validation is made by comparing the reconstructed wave profiles with the incident waves. The accuracy and efficiency of the present approach are promising. At the same time, it is shown that the use of responses, which are more broad-banded in their frequency characteristics, is an effective means to cope with high frequency noise in reconstructed waves.
Original languageEnglish
Article number103183
JournalApplied Ocean Research
Number of pages21
Publication statusPublished - 2022


  • Sea state estimation
  • Wave reconstruction
  • Prolate spheroidal wave functions
  • Short-time measurements


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