Page 375 - Practical Design Ships and Floating Structures

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1. 1 The Dutubase

The database containing ship characteristics for the world fleet has been purchased from Lloyds'
Maritime Information Services, London (LMIS). Container vessels are chosen as a subject of
investigation in this paper, as they constitute a homogeneous group, which is still sufficiently complex
(e.g. the Panmax size of some container vessels) to show the adaptability of the methods used. To
obtain up-todate estimates of the design parameters, only vessels from 1990 and later are included in
the analyses. Unfortunately, some entries are missing for some vessels and therefore the study is based
on records, for which all of the following data is available: TEU capacity, length, breadth, speed,
draught, height and displacement. This means that 812 container vessels are analysed.

2 DATA ANALYSIS METHODS
2.1 Simple Regresswn

When empirical relations between the main dimensions are established, it is straightforward to use
linear (or piecewise linear) functions to fit the dimensions. Piecewise linear functions require many
subdivisions to yield low error measures and therefore, an alternative representation by power
functions is chosen. This has the additional advantage that derived coefficients (as e.g. CB) are simple
power functions as well.
The loading capacity (e.g. deadweight, TEU or lane metres) can be used as an input for the regression
analyses. These measures indicate the owner's needs and represent in very general terms the
dimensions of the ship. The following power law relation between the loading capacity, LC, and the
main particulars is chosen.

T = a(LC)b (1)

The parameter T is either of the main characteristics, and a and b are determined by use of the least
squares method.

2.2 Neural Network
A feedforward neural network consists of a number of layers each transferring the weighted sum of its
inputs to the next layer through transfer functions. Along with the weighted sum, a constant (also
called bias) enters into the transfer function. The weights and biases are found in the learning phase,
where an optimisation procedure in MATLAB minimises the output error, given known inputs and
outputs.

2.2.1 Neural network topology
Normally, networks with biases, sigmoid layers and a linear output layer can approximate any
continuous function to an arbitrary accuracy. The network used is a two-layer feedforward net with an
input vector, one hidden layer, an output layer and an output vector. See Figure 1. The input vector is
P and has the dimension R. Each of the two layers consist of 5" neurons (outputs), where x refers to the
layer number. The input vector for each layer is connected to the neurons through a weight matrix, V,
and this weighted input is summed by the biases, lbX, to yield the input, d, for the transfer functions, F".
The output is kept in the vector T.