Onboard Analysis of Ship Stability Based on Time-Varying Autoregressive Modeling Procedure

  • Daisuke TeradaEmail author
  • Akihiko Matsuda
Part of the Fluid Mechanics and Its Applications book series (FMIA, volume 119)


In this study, it is clarified that a dynamical system of rolling motion can be approximated by a time-varying autoregressive model, which is a kind of statistical model. As the result, when it is possible to measure the time series of rolling motion, a ship’s stability can be judged based on time series analysis by using a time-varying autoregressive modeling procedure. As for the verification of this method, the results of the model experiment for parametric roll resonance were used. It was confirmed that an evaluation of ship safety is possible based on the proposed procedure.


Time-varying autoregressive model Kalman filter Time-varying characteristic root 



This work was supported by a Grant-in-Aid for Young Scientists (B) from the MEXT (No. 21760672). Authors would like to thank Dr. Hirotada HASHIMOTO (Kobe University), Prof. Naoya UMEDA (Osaka University), Prof. Genshiro KITAGAWA (University of Tokyo) and Prof. Emeritus Kohei OHTSU (Tokyo University of Marine Science and Technology) for helpful suggestions. The authors would like to thank Enago ( for the English language review.


  1. Bartlett, M. S. (1946), “On the Theoretical Specification of Sampling Properties of Autocorrelated Time Series,” Journal of the Royal Statistical Society, Series B8, pp. 27–41.Google Scholar
  2. Hashimoto, H., Matsuda, A. and Umeda, N. (2005), “Model Experiment on Parametric Roll of a Post-Panamax Container Ship in Short-Crested Irregular Seas (in Japanese),” Conference Proceedings of the Japan Society of Naval Architects and Ocean Engineering, Vol. 1, pp. 71–74.Google Scholar
  3. Kitagawa, G. and Gersch, W. (1996) Smoothness Priors Analysis of Time Series, Springer-Verlag, New York.CrossRefGoogle Scholar
  4. Kitagawa, G. (2010) Introduction to Time Series Modeling, Chapman & Hall.Google Scholar
  5. Ozaki, T. (1986), “Local Gaussian Modelling of Stochastic Dynamical Systems in the Analysis of Nonlinear Random Vibrations,” in Essays in Time Series and Allied Processes, Festshrift in honour of Prof. E.J. Hannan, Probability Trust.CrossRefGoogle Scholar
  6. Terada, D., Hashimoto, H. and Matsuda, A. (2016), “Estimation of Parameters in the Linear Stochastic Dynamical System Driven by Colored Noise Sequence,” Proceedings of the ISCIE International Symposium on Stochastic Systems Theory and its Applications, Volume 2016, pp. 125–131.Google Scholar
  7. Umeda, N. and Taguchi, H. (2003), “Parametric Roll Resonance (in Japanese),” Symposium Proceedings of JTTC, pp. 217–235.Google Scholar
  8. Umeda, N. (2007), “Strategy towards Development of Performance-Based Intact Stability Criteria at IMO(in Japanese),” Conference Proceedings of the Japan Society of Naval Architects and Ocean Engineering, Vol. 5E, pp. 19–22.Google Scholar
  9. Yamanouchi, Y. (1956), “On the Analysis of ship’s Oscillations as a Time Series (in Japanese),” Journal of Marine Science and Technology, pp. 47–64.Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Mechanical Systems EngineeringNational Defense AcademyYokosukaJapan
  2. 2.National Research Institute of Fisheries EngineeringHasakiJapan

Personalised recommendations