APPLICATION OF AN EXPERT SYSTEM FOR ASSESSMENT OF THE SHORT TIME LOADING CAPABILITY OF TRANSMISSION - PowerPoint PPT Presentation

Loading...

PPT – APPLICATION OF AN EXPERT SYSTEM FOR ASSESSMENT OF THE SHORT TIME LOADING CAPABILITY OF TRANSMISSION PowerPoint presentation | free to download - id: 1b07d7-NDM2Z



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

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

Description:

Typically uses bipolar (1, -1) activations for its input signal and its target output ... If the target values are bivalent (binary or bipolar), a step function can be ... – PowerPoint PPT presentation

Number of Views:115
Avg rating:3.0/5.0
Slides: 28
Provided by: EconomicR63
Learn more at: http://www.ftsm.ukm.my
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

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
ADALINE
  • 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
ADALINE
  • 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
ADALINE
  • 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
ADALINE
  • 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.html
  • Adaline Network Simulator

21
MADALINE
  • MANY ADAPTIVE LINEAR NEURON

Architecture of an MADALINE with two hidden
ADALINES and one output ADALINE
22
MADALINE
  • 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
MADALINE
  • 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

About PowerShow.com