Instantaneous Spectral Analysis of Non-Stationary Ship Motion Data

The time varying coefficient vector autoregressive (TVVAR) modeling is applied to the cross-spectral analysis of non-stationary ship motion data. Introducing the instantaneous response, a vector autoregressive model can be reduced to simple time varying coefficient autoregressive (TVAR) models for each ship motion and the required CPU time is effectively reduced. The TVVAR model and stochastic perturbed difference equations are transformed into a state space model. The vector-valued unknown coefficients can be evaluated and the instantaneous cross spectra of ship motions can be calculated at every moment. The results showed good agreements with one of the TVAR modeling and also with the stationary autoregressive (SAR) modeling analysis under stationary conditions. Furthermore, the instantaneous relative noise contribution was also estimated using the TVVAR coefficients and illustrated how the structure of a spectrum changed according to the ship manoeuvres for the first time. Optimum order of the model and Akaike’s information criterion were also examined for several changes of parameters. Moreover, it is confirmed that the TVVAR modeling can estimate the instantaneous cross spectra and relative noise contribution of ship motions even under non-stationary conditions.