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God. NEURAL NETWORKS. M. Alborzi, Ph. D. Petroleum University of Technology October, 2001. OUTLINE. Neural Networks Defined Why Neural Networks Pattern Recognition Neural Networks Application Areas A Brief History of Neural Networks Training Neural Networks

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God

God


God

NEURAL NETWORKS

M. Alborzi, Ph. D.

Petroleum University of Technology

October, 2001


Outline

OUTLINE

  • Neural Networks Defined

  • Why Neural Networks

  • Pattern Recognition

  • Neural Networks Application Areas

  • A Brief History of Neural Networks

  • Training Neural Networks

  • Advantages of Neural Networks

  • A Simple NN Package


Neural networks defined

Neural Networks Defined

  • A Modeling Technique Emulating the Brain


Why neural networks

Why Neural Networks!

  • The Need to Emulate the Brain

  • Facing Complex Problems

  • Limitation of Mathematics

  • Limitation of Serial Computers

  • The Amazing Power of the Brain to Tackle complexities

  • The Parallel Nature and the Network Nature Structure of the Brain


Pattern recognition

Pattern Recognition

  • Mathematical / Statistical

  • Syntactical

  • Neural Networks


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Neural Networks Applications in Pattern Classification

and Pattern Recognition

  • Speech recognition and speech generation

  • Prediction of financial indices such as currency exchange rates

  • Location of radar point sources

  • Optimization of chemical processes

  • Target recognition and mine detection

  • Identification of cancerous cells

  • Recognition of chromosomal abnormalities

  • Detection of ventricular fibrillation

  • Prediction of re-entry trajectories of spacecraft

  • Automatic recognition of handwritten characters

  • Sexing of faces

  • Recognition of coins of different denominations

  • Solution of optimal routing problems such as

    theTraveling Salesman Problem

  • Discrimination of chaos from noise in the prediction of time series


A brief history of neural networks

A Brief History of Neural Networks

  • 1943 McCulloch and Pitts Model

  • 1962 Rosenblatt Perceptron

  • 1969 Miskey and Papert Report on the Shortcomings of Perceptron

  • 1987 Rumelhart and McClleland

    Breakthrough, Multilayer Perceptron (Originally from Werbos),


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Figure 1: The biological neuron


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X1

X2

X3

OUT

Y= fh[sum( wixi)-teta]

fh(x)=1 if x>0

fh(x)=0 if x<0

Figure 2: The McCulloch and Pitts model of a neuron.


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M-P model Biological Neuron

------------------------------------------------------------

Input data xi---------------------------Input signal

Input branches------------------------Dendrites

Weights wji----------------------------Synapses

wjixi-----------------------------------Activation

Threshold L---------------------------Threshold level

Output yj------------------------------Output signal

Output branch------------------------Axon

Figure 3: A comparison between M & P model of a neuron and the biological neuron.


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XOR


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Figure 4: Final connection weights: Positive reinforcing connections: Fixed k.


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Figure 5: The input logs and the output dominant rock lithologies.


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Figure 6: schematic diagram of the initial model


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No.

Log

Unit

Description

1

DT

s/ft

Sonic Velocity

2

ROHB

g/cm3

Bulk Density

3

NPHI

PU

Neutron Porosity

4

PEF

barn/electron

Photoelectric Factor

5

GR

API

Gamma Ray

Table 1: The input logs


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No.

Symbol

Unit

Description

1

DOLO

Fraction

Volume of Dolomite

2

LIME

Fraction

Volume of Limestone

3

SAND

Fraction

Volume of Sandstone

4

ANHY

Fraction

Volume of Anhydrite

5

SHAL

Fraction

Volume of Shale

Table 2: The output rock lithologies.


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Appendix H

A Sample of Log Measurements and PETROS Output for Gachsaran Well No. 6

1) Input Log Measuremwents

Depth

Log Measurements

metres

DT

ROHB

NPHI

PEF

GR

s/ft

g/cm3

PU

barn/electron

API

2505.00

52.700

2.820

1.220

4.820

34.100

2505.15

52.800

2.800

1.470

4.670

33.600

2505.30

52.700

2.790

1.540

4.640

30.400

...

...

...

...

...

...

...

...

...

...

...

...

2667.30

49.200

2.740

3.870

4.590

23.000

2667.46

49.100

2.720

3.880

4.630

23.000

2667.61

49.100

2.720

3.880

4.680

23.000

A Sample of Log Measurements and PETROS Output for Well No. 6

1) Input Log Measuremwents


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Depth

Volume Fractions of the Rock Constituents

metres

DOLO

LIME

SAND

ANHY

SHAL

fraction

fraction

fraction

fraction

fraction

2505.00

0.420

0.000

0.260

0.240

0.080

2505.15

0.500

0.000

0.300

0.120

0.080

2505.30

0.520

0.000

0.300

0.100

0.080

...

...

...

...

...

...

...

...

...

...

...

...

2667.30

0.420

0.580

0.000

0.000

0.000

2667.46

0.380

0.620

0.000

0.000

0.000

2667.61

0.360

0.640

0.000

0.000

0.000

2) PETROS Output Volume Fractions 


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