非定常船体動揺データの時系列解析について-II. : 多変量時系列データの瞬間クロススペクトル解析

Abstract

The time-varying coefficient vector autoregressive (TVVAR) modeling is applied to the cross-spectral analysis of non-stationary ship motion data. The modeling can be recognized as an extension of the Time-varying coefficient autoregressive (TVAR) modeling examined in the previous report^<(1)>. In this paper, the procedure of TVVAR model is described by contrast with the TVAR modeling. Introducing the instantaneous response, a vector autoregressive model can be reduced to simple autoregressive 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. 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 of ship motions even under non-stationary conditions.