Computer Science

a) For a two input network with two hidden nodes and one output node with both layers using a
logistic activation function we have:
2 11 12
12 12 22
11 11 21
2
1 2
1
b w w
b w w
b w w
x
x

x W1 W
and the Logistic function is ( ) 1
1 ( ) x e
f x
where
=1

2 [ 0.6] 0.2
0.5
1
2 0.2 0.5
0.4 0.2
0.1 0.2
1
0.7
0.4

b b
x w w
Calculate the output of the Network.

b) Describe and sketch the Perceptron and state Hebb’s training rule

c) Describe the two main training methods for Neural Networks?
It is proposed to install a fuzzy speed cruise control system in an automobile. In order to check the efficiency
of the controller a simulation is to be undertaken.
The vehicle dynamics can be simulated using the recursive equations:
v(n) 100v(n 1) 1000TP 0.5 (n 1)
In which v(n) is the current speed , v(n-1) is the value of speed at the previous calculation TP is the value of
the throttle position derived from the fuzzy cruise controller and (n-1) is the angle of the car – uphill
(positive) or downhill (negative)
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The membership functions of the fuzzy speed controller are determined by the setting the cruise controller
for a particular speed. The setting to be considered is 50 mph and the appropriate controller fuzzy sets are
shown in figure Q1 below.
Figure Q1
The Knowledge base for the cruise controller is shown in table Q1 below.
Angle of Incline
Speed
Up Level Down
High
LM LM Low
OK HM Medium LM
Low High HM HM
Table
a) If the initial condition of speed is 52.5 mph and the angle of incline is -50 use the FAM bank to derive
only those rules, in their full “if .. then .. else” form, which contribute to the output of the Throttle
Position.