With the variation of the 6. THE NETWORK Figure 3: Variation of Depth (Maxsurf)
Further evaluation of the basis yachts shows that the displacement cannot easily be expressed as a linear function of the length. Therefore it is decided to generate the hulls of all standard yachts in the CAD software Maxsurf which includes a tool to calculate the displacement of a generated hull. It is decided to use the same hull form for all variations which is adjusted to the desired dimensions. The hull form that is chosen is that of a 40’ cruising yacht, that is introduced in Principles of Yacht Design [1].
The ratio between the sail area and the Di .spl is a commonly used parameter in sailing yacht
23 design.
Therefore it is chosen to derive a formula for calculating the sail area. The sail area is also chosen to be one of the varying parameters. The factors are derived as described above.
A bDispl with 1
Si . b 18 , 2
23 b 21 and 3 b 24 .
For each value of the sail area three different aspect ratios are applied to generate the training data set. The values for the aspect ratio are
AR 3 , AR 4.5 1 2 and AR 6 . 3 ANN Out-In
The choice of these values seems to be reasonable, based on experimental data published by Marchaj [2].
With these values for the aspect ratio the mast height can be calculated using the formula introduced further above.
MH ARA 1.1
S (3)
For each length over all in the training data three different Dellenbaugh angles are applied - a stiff yacht, a tender yacht and one mean value.
The metacentric height GM for each Dellenbaugh angle can be calculated with [1]:
GM
Displ DA
279
A HA .
S (4)
With the value for GM the vertical centre of gravity can be derived.
Displ. [t]
Dellenbaugh Angle [°] Aspect Ratio Sails [-] Sail Area
Figure 5: [m²]
Arithmetic Mean Variation 0.04 0.32
-0.14 2.79
Validation of ANN Out-In
The network reproduces the trained data very accurately. The training of the network can be considered successful.
7. TEST DESIGN CASES
The quality of results derived by an ANN can only be as good as the quality of the training data. As elaborated in the previous chapter the network is able to reproduce the training data accurately. Now it has to be checked if the network produces valid unknown input data.
results for B-36 ©2007: Royal Institution of Naval Architects
The ANN for this application is generated with the software Labview. The network is a fully connected feed forward ANN with one hidden layer. The hidden layer and the output layer use sigmoidal activation functions of the following form:
output For training 1 1expinput the backpropagation algorithm is applied.
To verify the performance of the trained network for reproducing the training data, ten randomly chosen training data sets are applied to the network and the results are evaluated. This is made both for the In-Out approach and the Out-In approach. The results are displayed in the Figures 4 and 5.
ANN In-Out
Loa Boa
Mast Height above Deck
VCG above Water line
Figure 4:
[m] [m]
T [m]
Arithmetic Mean Variation 0.01
-0.01 -0.17
[m] -0.10 [m] 0.07
Validation of ANN In-Out (5) network a conventional
different parameters as
described above a training data set of 486 different cases is derived.
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