Page 531 - Practical Design Ships and Floating Structures

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elements), each probably having a small amount of local memory. The processors are linked by
communication channels (synapses), which usually carry numeric data, encoded by any of various
means. The units run only on their local data and on the inputs they receive via the communication
channels.
Most artificial neural networks have some sort of "training" rule whereby the weights of synapses are
adjusted on the basis of data. In other words, artificial neural networks "learn" from examples (as
children learn to recognise cats from examples of cats) and show some capability for generalisation
beyond the training data. Simple linear regression (a minimal feedforward net with only two
processing elements plus bias) is usehlly regarded as special cases of artificial neural networks.
Artificial neural networks are used in many different fields in recent years. A few engineering
application examples:
P Rudder force prediction (Koushan et a1 1998)
P Propeller induced pressure pulses (Koushan 2000)
P Robot control
P Pattern recognition
Figure 1 demonstrates main components of a feed-forward recall artificial neural network. These are
input layer, synapses, one or more hidden layers (mons) and an output layer.

Output Axon

- - -- -_
-
-
' Hidden Layer Synapse Output Layer Synapse Output Data
Figure 1 : Main components of a feed forward recall network with a single hidden layer
Input layer is used to feed the network with data. This layer normalises usually data between 0 and 1 or
between -1 to 1 depending on activation function used. Synapse is connecting different layers. Hidden
layer is made of one or more processing elements and corresponding activation function, which
transforms the input of processing element. Typical activation functions are linear, sigmoid and tanh
functions. Output layer operates usually like a hidden layer and can in addition denormalise the output.

There are different procedures for training the network. Typical procedure is back propagation. In a
backpropagation procedure, network starts with a random set of weights. Then output is compared to
input and the error is verified. Then these errors are propagated backwards through the network to find
better weights. Again there are different ways of reaching optimal weights by means of errors. Apart
from weights and activation functions, number of hidden layers and number of processing elements in
each hidden layer must also be optimised during the training. Usually one half part of database is used
for training whereas the other half is used for verification of the network, i.e. the network does not
"see" verification set during optimisation process.

6 CONCLUSIONS

The method presented is a novel procedure for prediction of total resistance. A reliable prediction
method is presented for the first time for prediction of total resistance of offshore vessels. To keep the
method easy-to-use the number of input parameters are limited. This has the consequence of ignoring