UNIVERSITY OF TECHNOLOGY, SYDNEY
FACULTY OF ENGINEERING AND INFORMATION TECHNOLOGY
49275 NEURAL NETWORKS AND FUZZY SYSTEMS
ASSIGNMENT 2
QUESTION ONE [ Character recognition ] [ 50 marks ]
This problem is a variation of a pattern recognition problem presented by Widrow
and Hoff in 1960. It is a simple symbol recognition problem with three letters T, G
and F, in an original form and in a shifted form as shown in Figure 1b.
The 6 input vectors x1,x2,x3,x4,x5,x6 and the corresponding target vectors
d1,d2,d3,d4,d5,d6 in the training set are:
1 1
1
1 1 1
1
1 1 1
1
1 1
1 1 1
x1
1
1 1 1
1
1 1 1
1 1 1
1
1
1 1 1
x2
1 1 1
1
1 1 1
1
1 1
1 1
1
1 1 1
x3
1
1
1 1 1
1
1 1 1
1
1 1
1 1 1
1
x4
1 1 1
1
1 1 1
1 1 1
1
1
1 1 1
1
x5
1 1
1
1 1 1
1
1 1
1 1
1
1 1 1
1
x6
1 1
1
d1 ,
1
1
1
d2 ,
1
1 1
d3 ,
1 1
1
d4 ,
1
1
1
d5 ,
1
1 1
d6
Assume that the network has 2 hidden layer neurons and all continuous perceptrons
use the bipolar activation function f e
e
2
1 1
( )
. Note that due to the necessary
augmentation of inputs and of the hidden layer by one fixed input, the trained
network should have 17 input nodes, 3 hidden neurons, and 3 output neurons. Assign
-1 to all augmented inputs.1.1 Assume that the learning constant is 0.2 , and the initial random output
layer weight matrix W( ) 1 and hidden layer weight matrix W ( ) 1 are
0.2137 0.5242 0.6428
0.5377 0.7826 0.9630
0.9003 0.0280 0.0871
W (1)
W (1)
0.2309 0.8436 0.6475 0.8709 0.1795 0.8842 0.6263 0.7222 0.6026 0.4556
0.1106 0.5839 0.4764 0.1886 0.8338 0.7873 0.2943 0.9803 0.5945 0.2076
0.9695 0.1098 0.0680 0.6924 0.5947 0.6762 0.3626
0.6024 0.4936 0.8636 0.1627 0.0503 0.3443 0.9607
Using the error back propagation training, calculate the next weight updates
W( ), ( ) 2 2 . [ 20 marks ] W
1.2 The above training set was trained with the same set of initial random output
layer weight matrix W( ) 1 and hidden layer weight matrix W ( ) 1 as above, and
a learning constant of 2 0. . The training set was recycled when necessary.
Determine the final weight matrices W f W (1201) and W f W (1201) after
200 cycles. Plot the cycle error curve for this training exercise.
[ 20 marks ]
One of the test character, which is shown below, has the following feature
input vector:
1
1 1
1 1 1
1
1 1
1 1
1 1
1 1 1
xCalculate the output vector z which is generated from the above feature input
vector. How would the neural network classify this feature input vector?
Describe how the above character recognition system can be improved using a
validation set. Propose a reasonable validation set.
[ 10 marks ]
Figure 1a Multilayer Neural Network
Figure 1b Training SetQUESTION TWO [Truck-Backer Upper Control] [ 50 marks ]
Backing up a truck to a loading dock is a nonlinear control problem. The truck and
loading zone are shown in Figure 2.1. The truck position is exactly determined by the
three state variables , , x y where is the angle of the truck with the horizontal.
Control to the truck is the angle .
Only backing up is considered. The truck moves backward by a fixed unit distance
every stage. For simplicity, assume that there is enough clearance between the truck
and the loading dock such that y does not have to be considered as an input. The task
here is to design a control system, whose inputs are 90 270 0 20 , , , x and
whose output is 40 40 , such that the final stages will be x f , f 10,90 .
The dynamics of the truck backer-upper procedure can be approximated by:
b
k
k k
y k y k k k k k
x k x k k k k k
2sin[ ( )]
( 1) ( ) sin
( 1) ( ) sin ( ) ( ) sin ( ) cos ( )
( 1) ( ) cos ( ) ( ) sin ( ) sin ( )
1
where b is the length of the truck. Assume that b 4.
Fuzzy logic is required for this truck backer-upper control. In this simple fuzzy logic
controller, a set of linguistic variables is chosen to represent 5 degrees of truck angle
error 90 70 90 110 270 , , , , , 5 degrees of truck position x error
0 7 10 13 20 m m m m m , , , , , and 5 degrees of control angle 40 10 0 10 40 , , , ,
as shown in Figure 2.2. The generic rule set in the form of "Fuzzy Associative
Memories" is shown in Figure 2.3.
The initial states of this truck are assumed to be ) ((1), x(1), y(1)) (75,12.5m,10m .
2.1 If the Centre of Area (COA) defuzzification strategy is used with the fire
strength i of the i-th rule calculated from
i X X
i i
min( ( ), ( )) x x
1 2 1 2
determine the defuzzified control angle ) (1 and the next state
[(2), x(2), y(2)] .
[ 20 marks ]2.2 If the Mean of Maximum (MOM) defuzzification strategy is used with the fire
strength i of the i-th rule calculated from
i X1i (x1).X 2i (x2)
determine the defuzzified control angle (1) and the next state
[(2), x(2), y(2)] . Then continue and calculate (2) and [x(3),(3), y(3)].
Write a computer program to calculate the system state vector
[x(k 1),(k 1), y(k 1)] and the defuzzified control angle ) (k for 100
consecutive sampling points. Plot the corresponding vertical truck position
y(k) against the horizontal truck position ) x(k for these 100 sampling points.
Plot the defuzzified control angle ) (k for these 100 sampling points.
[ 20 marks ]
Find the dominant rule which contributes the highest fire strength to the
control action for the defuzzified control angle ) (1 . If softer control action
(for slower response) is required, modify this dominant rule and recalculate
the new defuzzified control angle ) *(1 and the next state vector
[(2), x(2), y(2)] . Using the modified FAM table, plot the corresponding
vertical truck position ) y(k against the horizontal truck position ) x(k for
these 100 sampling points. Plot the new defuzzified control angle ) *(k for
these 100 sampling points.
[ 10 marks ]
Figure 2.1 Diagram of truck and loading zoneFigure 2.2 Membership functions of a truck backer-upper system
Figure 2.3 Generic Fuzzy Associative Memories
H.T. NGUYEN
April 2017MARKING SCHEME
Assignment 2: Neural Networks and Fuzzy Logic
Student Name: ____________________ Mark: ___________
Requirement Criteria Comment
Standard “Declaration of
Originality” cover page
as provided by the
Faculty
At front of report, completed and
signed
Yes/no
Question 1
1.1 Neural Network:
Back Propagation
Presentation
W (2)
W (2)
Calculation/software code
/20
Question 1
1.2 Neural Network:
Training and Test
Presentation
W (1201)
W (1201)
Cycle error curve
Software code
Classify the test character
Discussion
/30
Section 2
2.1 Fuzzy Logic: COA
defuzzification
Fuzzification
Combined fuzzy inference
Moment calculation
Area calculation
Defuzzified control angle
(1)
Next state vector
[(2), x(2), y(2)]
/20
Section 2
2.2 Fuzzy Logic: MOM
defuzzification
Fuzzification
Defuzzified control angle
(1) and next state vector
[(2), x(2), y(2)]
(2) and [(3), x(3), y(3)]
Truck position plot and
defuzzified control angle
plot (100 points)
Software code
Dominant rule
Modified FAM Table
New defuzzified control
angle *(1)
New truck position plot and
defuzzified control angle
plot (100 points)
Software code
/30