Artificial Neural Networks: An Alternative Approach to Risk Based Design

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Artificial Neural Networks An Alternative
Approach toRisk Based Design
By George Mermiris
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Introduction

• Inspiration from the study of the human brain and
  physical neurons
• Response speed for physical neurons is 10-3 s
  compared to electrical circuits with 10-9 s
• Massive parallel structure 1011 neurons with 104
  connections per neuron
• The efficiency of the brain is directly dependent
  on the accumulated experience ? new connections
  are established which determine our capabilities

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The Biological Model
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Artificial Neural Networks (ANN)Basic Forms,
Feed-Forward Networks
General pattern

• p input vector
• w weight matrix
• b bias vector
• n net output of the neuron
• ? activation function
• a output vector of the network

a f(n) f(wp b)
a f(n) f(wp b)
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Multi-Neuron, Single-Layer ANN
a f(n) f(Wp b)
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Multi-Layer, Multi-Neuron Network
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Abbreviated Form of a Network
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Activation Functions
Linear Function
Log Sigmoid Function
Hyperbolic Tangent Sigmoid Function
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Training Neural Networks

• The training of a network has the same concept
  as for humans the larger its experience the
  better its response
• For an ANN the learning is established with
  suitable adjustment of its weights and biases
• Requirements training data and proper algorithm

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The Backpropagation Algorithm

• A three-fold concept
• Performance Index Approximate Square Error F(x)
  (t - a)T(t a) eTe

The Steepest Descent Algorithm for function F and
modifications
g gradient
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The Backpropagation Algorithm

• Chain Rule of Calculus

• Calculation of the first derivatives of the
  performance index starting from the last layer
  and backpropagating to the first (!)

Levenberg Marquardt algorithm Main variation
of the method based on the concept of Newtons
method with small approximation
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Example 1 Resistance Experiment

• Case 1 1 cm wave amplitude
• ANN Architecture
• 1-4-3-1
• Activation Function Log Sigmoid for hidden
  layers and Linear for output layer

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Example 1 Resistance Experiment
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Example 1 Resistance Experiment

• Case 2 2 cm wave amplitude
• ANN Architecture
• 1-3-2-1
• Activation Function Log Sigmoid for hidden
  layers and Linear for output layer

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Example 1 Resistance Experiment
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Example 2 Section Areas Curve

• Input L, Amax, ?, LCB, Cp
• ANN Architecture 5-10-12-21
• Activation Function Log Sigmoid for hidden
  layers and Linear for output layer

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Example 2 Section Areas Curve

• Training Set
• - L153 156 159 180, in m
• - Amax335 345 355 425, in m2
• - ?36000 37000 38000 45000 , in m3
• - LCB-2.4 2.5 2.6 -3.3, in m
• - Cp0.702 0.688 0.660 0.588
• Ordinates of SA curves for each combination
• Generalisation Sets L Amax ? LCB Cp
• - Set1160 360 38500 2.65 0.6664
• - Set2178.5 420 44500 3.25 0.594
• - Set3150 325 35000 2.3 0.718

Network input
Network output
Testing the network
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Example 2 Section Areas Curve (Set1)
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Example 2 Section Areas Curve (Set2)
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Example 2 Section Areas Curve (Set3)
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Strong points of ANN

• Readily applicable to any stage of the design
  process, especially at the preliminary design
  where rough approximations are necessary
• Potential to include different design parameters
  in the training set and avoid iterations
• Results are obtained very fast with high accuracy
• No highly sophisticated mathematical technique is
  involved, only basic concepts of Linear Algebra
  and Calculus
• Very short computer times in common PCs

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Weak points of ANN

• Basic requirement is the existence of historical
  data for the creation of training set
• Not readily applicable to novel ship types
• The results are very sensitive to the networks
  architecture and the training method selected
  each time, although these two parameters are very
  easily adjusted
• There is no specific network architecture for a
  specific calculation different architectures can
  provide the same results. The general rule is to
  use the simplest possible network

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Future Work

• Other networks and training algorithms recurrent
  ANN

• Suitable database for creating the training set
  for different applications

• Application to the Global Ship Design including
  Risk Data and Human Reliability Data

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Thank You!