Study on real-time estimation of the ship motion cross spectra

 Time-varying coefficient vector autoregressive (T-VVAR) modeling with instantaneous responses is applied to spectrum analysis based on the nonstationary motion data of ships. Because of the ship's maneuvers, changes such as course and speed, the ship motions in waves are regarded as a nonstationary random process, although the seaway can be considered as a stationary stochastic process. The T-VVAR model is transformed into a state space model, and the time-varying coefficients can be evaluated by using the Kalman filter algorithm. Using the estimated time-varying coefficients, the instantaneous cross spectra of the ship motions can be calculated at every moment. In order to examine the reliability of the proposed procedure, on-board tests were carried out. Under stationary conditions, at a constant speed and course, the proposed method shows good agreement with stationary vector autoregressive (SVAR) modeling analysis. Moreover, it is confirmed that the proposed method can estimate the instantaneous cross spectra of the ship motions even under nonstationary conditions, showing that this is a powerful tool for on-line analysis of the nonstationary motion data of ships. Received: August 2, 2002 / Accepted: November 28, 2002 Acknowledgments. The authors thank the captain and crew of the training ship Shioji Maru, Tokyo University of Mercantile Marine. Address correspondence to: T. Iseki (iseki@ipc.tosho-u.ac.jp) Updated from the Japanese original, which won the 2002 SNAJ prize (J Soc Nav Archit Jpn 2001;190:161–168)