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## APPLICATION OF AN EXPERT SYSTEM FOR ASSESSMENT OF THE SHORT TIME LOADING CAPABILITY OF TRANSMISSION

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Title: APPLICATION OF AN EXPERT SYSTEM FOR ASSESSMENT OF THE SHORT TIME LOADING CAPABILITY OF TRANSMISSION

1
Before we start ADALINE
• Test the response of your Hebb and Perceptron on
this following noisy version
• Exercise pp98 2.6(d)

2
• ADAPTIVE LINEAR NEURON
• Typically uses bipolar (1, -1) activations for
its input signal and its target output
• The weights are adjustable, has bias whose
activation is always 1

Architecture of an ADALINE
3
• In general ADALINE can be trained using the delta
rule also known as least mean squares (LMS) or
Widrow-Hoff rule
• The delta rule can also be used for single layer
nets with several output units
• ADALINE a special one - only one output unit

4
• Activation of the unit
• Is the net input with identity function
• The learning rule minimizes the mean squares
error between the activation and the target value
• Allows the net to continue learning on all
training patterns, even after the correct output
value is generated

5
• After training, if the net is being used for
pattern classification in which the desired
output is either a 1 or a -1, a threshold
function is applied to the net input to obtain
the activation
• If net_input 0 then activation 1
• Else activation -1

6
The Algorithm
Step 0 Initialize all weights and
bias (small random values are usually
used0 Set learning rate ? (0 lt ? 1) ?
0 Step 1 While stopping condition is
false, do steps 2-6. Step2For each
bipolar training pair st, do steps 3-5
Step 3. Set activations for input units i
1, , n xi si Step 4.Compute
net input to output unit NET y_in b
? xi wi
7
The Algorithm
Step 5. Update weights and bias i 1, ,
n wi(new) wi(old) ? (t y_in)xi
b(new) b(old) ? (t y_in) else
wi(new) wi(old) b(new) b(old) Step
6. Test stopping condition If the largest
weight change that occurred in Step 2 is
smaller than a specified tolerance, then stop
otherwise continue.
8
Setting the learning rate ?
• Common to take a small value for ? 0.1
initially
• If ? too large, the learning process will not
converge
• If ? too small learning will be extremely slow
• For single neuron, a practical range is
• 0.1 n? 1.0

9
Application
After training, an ADALINE unit can be used to
classify input patterns. If the target values are
bivalent (binary or bipolar), a step function can
be applied as activation function for the output
unit Step 0 Initialize all weights Step
1 For each bipolar input vector x, do steps
2-4 Step 2. Set activations for input units to
x Step 3. Compute net input to output
unit net y_in b ? xi wi Step
4. Apply the activation function

10
Example 1
• ADALINE for AND function binary input, bipolar
targets
• (x1 x2 t)
• (1 1 1)
• (1 0 -1)
• (0 1 -1)
• (0 0 -1)
• Delta rule in ADALINE is designed to find weights
that minimize the total error

Associated target for pattern p
4
E ? (x1(p) w1 x2(p)w2 w0 t(p))2
p1
Net input to the output unit for pattern p
11
Example 1
• ADALINE for AND function binary input, bipolar
targets
• Delta rule in ADALINE is designed to find weights
that minimize the total error
• Weights that minimize this error are w1 1, w2
1, w0 -3/2
• Separating lines x1 x2 3/2 0

12
Example 2
• ADALINE for AND function bipolar input, bipolar
targets
• (x1 x2 t)
• (1 1 1)
• (1 -1 -1)
• (-1 1 -1)
• (-1 -1 -1)
• Delta rule in ADALINE is designed to find weights
that minimize the total error

Associated target for pattern p
4
E ? (x1(p) w1 x2(p)w2 w0 t(p))2
p1
Net input to the output unit for pattern p
13
Example 2
• ADALINE for AND function bipolar input, bipolar
targets
• Weights that minimize this error are w1 1/2, w2
1/2, w0 -1/2
• Separating lines 1/2x1 1/2 x2 1/2 0

14
Example
• Example 3 ADALINE for AND NOT function bipolar
input, bipolar targets
• Example 4 ADALINE for OR function bipolar
input, bipolar targets

15
Derivations
• Delta rule for single output unit
• The delta rule changes the weights of the
connections to minimize the difference between
input and output unit
• By reducing the error for each pattern one at a
time
• The delta rule for Ith weight(for each pattern)
is
• ?wI ? (t y_in)xI

16
Derivations
• The squared error for a particular training
pattern is
• E (t y_in)2.
• E function of all weights wi, I 1, , n
• The gradient of E is the vector consisting of the
partial derivatives of E with respect to each of
the weights
• The gradient gives the direction of most rapid
increase in E
• Opposite direction gives the most rapid decrease
in the error
• The error can be reduced by adjusting the weight
wI in the direction of

- ?E
?wI
17
Derivations
• Since
• y_in ? xi wi ,

-2(t y_in)xI
The local error will be reduced most rapidly by
adjusting the weights according to the delta rule
?wI ? (t y_in)xI
18
Derivations
• Delta rule for multiple output unit
• The delta rule for Ith weight(for each pattern)
is
• ?wIJ ? (t y_inJ)xI

19
Derivations
• The squared error for a particular training
pattern is
• E ?(tj y_inj)2.
• E function of all weights wi, I 1, , n
• The error can be reduced by adjusting the weight
wI in the direction of

- ?E
m
?
(tj y_inj)2
?wIJ
j1
(tJ y_inJ)2
Continued pp 88
20
Exercise
• http//www.neural-networks-at-your-fingertips.com/
• Adaline Network Simulator

21
• MANY ADAPTIVE LINEAR NEURON

Architecture of an MADALINE with two hidden
22
• Derivation of delta rule for several outputs
shows no change in the training process with
several combination of ADALINEs
• The outputs of two hidden ADALINES, z1 and z2 are
determined by signal from input units X1 and X2
• Each output signal is the result of applying a
threshold function to the units net input
• y is the non-linear function of the input vector
(x1, x2)

23
• Why we need hidden units???
• The use of hidden units Z1 and Z2 give the net
• Computational capabilities not found in single
layer nets
• Butcomplicate the training process
• Two algorithms
• MRI only weights for hidden ADALINES are
adjusted, the weights for output unit are fixed
• MRII provides methods for adjusting all weights
in the net

24
ALGORITHM MRI
The weights v1 and v2 and bias b3 that feed
into the output unit Y are determined so that
the response of unit Y is 1 if the signal it
receives from either Z1 or Z2 (or both) is 1
and is -1 if both Z1 and Z2 send a signal of -1.
The unit Y performs the logic function OR on the
signals it receives from Z1 and Z2
Set v1 ½, v2 ½ and b3 ½ see example 2.19
the OR function
25
ALGORITHM MRI
• x1 x2 t
• 1 -1
• 1 -1 1
• -1 1 1
• -1 -1 -1
• Set ? 0.5
• Weights into
• Z1 Z2 Y
• w11 w21 b1 w12 w22 b2 v1
v2 b3
• .05 .2 .3 .1 .2 .15 .5
.5 .5

Set v1 ½, v2 ½ and b3 ½ see example 2.19
the OR function
26
• Step 0 Initialize all weights and bias
• wi 0 (i 1 to n), b0
• Set learning rate ? (0 lt ? 1)
• ? 0
• Step 1 While stopping condition is false,
• do steps 2-8.
• Step2 For each bipolar training pair st, do
steps 3-7
• Step 3. Set activations for input units
• xi si
• Step 4.Compute net input to each hidden ADALINE
unit
• z_in1 b1 x1 w11 x2 w21
• z_in2 b2 x2 w12 x2 w22
• Step 5. Determine output of each hidden ADALINE
• z1 f(z_in1)
• z2 f(z_in2)
• Step 6. Determine output of net

f(x)
27
The Algorithm
• Step 7. Update weights and bias if an error
occurred for this pattern
• If t y, no weight updates are performed
• otherwise
• If t 1, then update weights on ZJ, the unit
whose net input is closest to 0,
• wiJ(new) wiJ(old) ? (1 z_in)xi
bJ(new) bJ(old) ? (1 z_inJ)
• If t -1, then update weights on all units ZK,
that have positive net input,
• wik(new) wik(old) ? (-1 z_in)xi
bk(new) bk(old) ? (-1 z_ink)
• Step 8. Test stopping condition
• Of weight changes have stopped(or reached an
acceptable level), or if a specified maximum
number of weight update iterations (Step 2) have
been performed, then stop otherwise continue