EXAMPLE NEURAL NETWORK

By.Mat

Example Neural network

Input

3 2 1 2

3

Output

9 4

1 4

9

X^2

Example Neural network

1 1.5 2 2.5 3 3.5 4 4.5 51

2

3

4

5

6

7

8

9

Input

Output

Example

Example Neural network

Input

3 2 1 2

3

Output

9 4

1 4

9

Example Neural network

Input

3 2 1 2

3

Output

9 4

1 4

9

w1

w2

v2

w1’

w2’

v1’

Z1

Z2

input output

bias bias

v1

Example Neural network

Input

3 2 1 2

3

Output

9 4

1 4

9

45.154

44.7552

-2.84

0.8996

1.0645

-1.70386’

Z1

Z2

input output

bias bias

-6.194/16

*16

tansig

tansig

logsig

oz

Example Neural network

a = tansig(n) = (2/(1+exp(-2*n)))-1 logsig(n) = 1 / (1 + exp(-n))

Example Neural networkInput = 3 ====================

output 9

NormalizationNormalization

3/16= 0.1875 9/16= 0.5625

Bias value is always “one”Z1=(0.1875 *45.154)+(1*-6.194) = 2.2723Z2=(0.1875 *44.7552)+(1*-2.84 = 5.5512

Z1’=tansig(Z1)=0.979Z2’=tansig(Z2)=1.000

Example Neural networkOz=(0.979*0.8991)+(1*1.0645)+(1*-1.70386)= 0.2412

Output= logsig(oz)=0.5600So.. NN output is 0.5600*16 (denormalization) = 8.96And Real output is 0.5625*16 (denormalization) = 9.00

Error=9.00-8.96 = 0.04;Error limits are determined at the time of training

process, The smaller constraint error on the training process, then NN will produce more accurate output.

but the training process will become more difficult.

Example Neural network

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