Artificial Neural Networks: An Alternative Approach to Risk – Based Design

1. Artificial Neural Networks:An Alternative Approach toRisk – Based Design By George Mermiris

2. 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

3. Dendrites Axon Synapses Cell Body The Biological Model

4. 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)

5. Multi-Neuron, Single-Layer ANN a =f(n) =f(Wp + b)

6. Multi-Layer, Multi-Neuron Network

7. Abbreviated Form of a Network

8. Activation Functions Linear Function Log – Sigmoid Function Hyperbolic Tangent Sigmoid Function

9. 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

10. 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

11. 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 Newton’s method with small approximation

12. 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

13. Example 1: Resistance Experiment

14. 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

15. Example 1: Resistance Experiment

16. a (101) a (121) a (211) p W (105) W (1210) W (2110) logsig purelin logsig + + + b (101) b (121) b (211) 51 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

17. Example 2: Section Areas Curve Training Set - L=[153 156 159 … 180], in m - Amax=[335 345 355 … 425], in m2 - =[36000 37000 38000 … 45000] , in m3 - LCB=[-2.4 –2.5 –2.6 … -3.3], in m - Cp=[0.702 0.688 0.660 …0.588] Ordinates of SA curves for each combination Generalisation Sets [L Amax  LCB Cp] - Set1=[160 360 38500 –2.65 0.6664] - Set2=[178.5 420 44500 –3.25 0.594] - Set3=[150 325 35000 –2.3 0.718] “Network input” “Network output” “Testing the network”

18. Example 2: Section Areas Curve (Set1)

19. Example 2: Section Areas Curve (Set2)

20. Example 2: Section Areas Curve (Set3)

21. 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 PC’s

22. 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 network’s 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

23. 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

24. Thank You!