COHERENCY 
WITHOUT BLK. 
_|v=o 
SPECTRUM II 
Fig. 3.7. Frequency responses of rol--waves (run 832). 
(From Yamanouchi.3") 
IG(@)I, i.e., the amplitude gain, from these different methods is very similar. From the 
time history of inputs X, of the waves, and the use of Eq. 3.5 which neglects the noise 
N,, the output Y, was synthesized, using values of g,, u =—90 to 90, as shown in Fig. 
3.11. These results show that this method gives reasonably good results. 
This example is for the roll of a model ship where, because of the small damping of 
the motion, the impulse response function g,, is slow to decay. We need a larger number of 
terms, i.e., g, for a longer range of u. With much larger damping, as with the heave or 
pitch response of a real ship, this author believes we will get better results. 
Here the more statistical, stricter estimation of reliability or confidence in the results 
is lacking. This author found later that the procedure was the same as that to solve the 
Yule—Walker equations used for the AR—model fitting, that will be mentioned in Part II. 
Accordingly, the above mentioned belief was more strictly examined statistically as the 
choice of order in AR—model fitting, as mentioned in Section 5.5. 
3.4 EXAMPLE OF MULTIPLE INPUT ANALYSIS, A TRIAL FOR 
NONLINEAR ANALYSIS OF SHIP’S RESPONSE 
Here a multiple input analysis of a ship’s behavior at sea, performed by this author 
[Yamanouchi>}], will be shown to demonstrate the usefulness of the method. Often, one 
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