To measure changes in ship motions with respect to the encounter angle of waves, datasets were recorded for analysis during combination maneuvers involving straight sections and changes in course (Table 2). Ship motions were measured using an optical fiber gyro. Data was sampled every 0.5 s and recorded using a PC. Time-histories were analyzed using the proposed on-line algorithm. Off-line analysis was also conducted to obtain a more detailed examination.

　

　

　

　

　

 Figure 4 shows data from run numbers 1 and 2 of the measured time-histories. Data recorded are pitch angle, roll angle and vertical acceleration. This data is composed of two stationary periods and one nonstationary period. The stationary periods were each recorded at a constant speed and course over a period of 360 s, with the nonstationary period recorded during the change in course from one stationary segment to the next. It can be seen that the magnitude of ship motions are easily influenced by changes in the direction of encounter of the waves. In run number 1, the angle of encounter of the waves was 145 degrees (ITTC coordinate system), with relatively large amplitudes of pitching motion and vertical acceleration. After altering course, the angle of encounter was 10 degrees, leading to a drop in the amplitudes of pitch and acceleration variations. In addition, measured roll angles were relatively large during the alteration of course.

　

 Figure 5 shows the autospectra of pitching estimated by instantaneous cross-spectrum analysis based on TVVAR modeling. In this analysis, the optimum hyperparameter τi² was chosen from 20 different values at each time-step based on the maximum likelihood method. The initial values of each covariance were set to σpitch² = 10000 , and a 12th order model was assumed. In this figure, each curve is an estimate of spectral density versus frequency, as a function of time. The autospectrum can be seen to narrow to a sharp peak as time passes.

　

 Figure 6 shows the estimated directional wave spectrum in the first stationary period of Fig.4. The peak of the spectrum can be seen at 160 degrees, corresponding well with the result of visual observation (145 degrees). This estimate was obtained without any time-history data of wave height, indicating the effectiveness of the newly introduced constraint.

　

 As can be seen in Fig.4, ship motions in waves are easily influenced by changes in ship speed and the angle of wave encounter. An attempt to predict the future motions of the ship was then made assuming the directional wave spectrum was stationary in time.

　

 Figure 7 shows the results of predictions of pitching motion compared to measured motion. The horizontal axis gives time-stamps of the measured data and the vertical axis denotes significant value of the pitch angle. Ship course and speed is as summarized in Table 2. Estimates of the significant value were calculated from suitably selected transfer functions and the directional wave spectrum of run number 1. The measured significant values were calculated from standard deviations of the time-histories. This demonstrates that pitching motion can be predicted by the system.

　

 Figure 8 shows one of the comparisons of power spectra of the longitudinal bending stress. The horizontal axis denotes the encounter frequency, the solid line denotes the power spectrum measured by the strain gauge and the broken line denotes the estimated stress that was transformed into encounter frequencies. The total areas of these power spectra are different but the shapes agree well near the peak frequency. The possible causes of the difference are the asymmetry of the ship's hull structure with respect to the centerline, effects of the trans-verse bending stress and the longitudinal axis force.