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10.2.1 Fuzzy Inference Model Based on Simulated
and Experimental Data
The model based on experiments with ideal waves consists of three fuzzy inference
systems (Santos et al.
2006
). Each of them gives the heave and pitch motion (both,
amplitude and phase), and the final pitch moment. The fuzzy inputs are: the Sea
State Number, SSN (given by the modal frequency of the waves); the ship speed, U;
and the heading angle,
. They have been represented by five Gaussian membership
functions uniformly distributed in their corresponding universe of discourse: [0.9,
7.7] (m) for the waves height, [20, 40] (knots) for the speed, and [0, 180] (
◦
)for
the angle. The output is a non-linear function of the input variables, and it gives
the amplitude and phase of the vertical signals (heave, x
3
; pitch, x
5
), and the pitch
moment, M
5
.
The neuro-fuzzy model has been tested by introducing simulated regular waves
as another input to the model. Figure
10.1
shows the results of the model performing
at 40 knots, SSN of 5 (H
1
/
3
=
μ
180
◦
). The encounter
frequency in this case is 1.255 rad/s (upper graphic). The behavior of the fuzzy model
is compared to the experimental model obtained by Precal (Esteban et al.
2000
)for
the same conditions. The comparison shows good results.
3.78 m) and heading seas (
μ
=
Fig. 10.1
Fuzzy model (
solid line
) and simulated data (
diamonds line
) of pitch and heave signals,
and pitch moment, at SSN 5, 40 knots,
μ
=
180
◦
(Santos et al.
2006
)
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