Artificial Neural Networks

Artificial Neural Networks for process control

Puneet Kr Singh

Mtech (FT)

What

is a Neural Network?

•Biologically motivated approach to machine learning

Modern digital computers outperform human in the domain of numeric computation & related symbol manipulation

However humans can effortlessly solve complex perceptual problems….

like Recognizing a man in a crowd from a mere

glimpse of his face at such a high speed & extent as to dwarf the world’s fastest computers

NN as an model of brain-like Computer

 An artificial neural network (ANN) is a

massively parallel distributed processor that has a natural propensity for storing

experimental knowledge and making it available for use. It means that:

Knowledge is acquired by the network through a learning (training) process;

ANN as a Brain-Like Computer

through a learning (training) process;

 The strength of the interconnections

between neurons is implemented by means of the synaptic weights used to store the knowledge.

The learning process is a procedure of the adapting the weights with a learning

algorithm in order to capture the knowledge. On more mathematically, the aim of the

learning process is to map a given relation between inputs and output (outputs) of the network.

Brain

The human brain is still not well understood and indeed its

behavior is very complex!

There are about 10 billion

neurons in the human cortex and 60 trillion synapses of connections

The brain is a highly complex, nonlinear and parallel computer (information-processing system)P K Singh, F O E, D E I

A Neuron

1

x

n

x

1

( ,..., )

x

_n

f

x

. . . φ(z) 0 1 1

...

n n

z

 

w

w x

 

w x

1 0 1 1

( ,..., )

_n

(

...

_{n n}

)

f x

x



F w



w x

 

w x

Where f is a function to be earned.

are the inputs.

φ is the activation function.

n

x

z

 

w

₀

w x

_{1 1}

 

...

w x

_{n n}

1

,...,

n

x

x

Z is the weighted sum

 

z z

 

Linear activation Logistic activation

  1 1 z z e    _  z z 1 0

Σ



Artificial Neuron:

Classical Activation Functions

Threshold activation Hyperbolic tangent activation

    e u u tanh u _    1 _2₂      z sign( )z 1, if z 0,   _{ }  z 0

Σ

Neural Network

 Neural Network learns by adjusting the weights so as to be able to

correctly classify the training data and hence, after testing phase, to classify unknown data.

 Neural Network needs long time for training.  Neural Network needs long time for training.

 Neural Network has a high tolerance to noisy and incomplete data

Learning

 The procedure that consists in estimating the parameters of neurons (setting up

the weights) so that the whole network can perform a specific task.

 2 types of learning

 _{Supervised learning}  _{Unsupervised learning}

 Supervised learning which incorporates an external teacher, so that each output  Supervised learning which incorporates an external teacher, so that each output

unit is told what its desired response to input signals ought to be.

 Unsupervised learning uses no external teacher and is based upon only local

self-Threshold Neuron (Perceptron)

• _{Output of a threshold neuron is binary, while inputs may be either}

binary or continuous

• _{If inputs are binary, a threshold neuron implements a Boolean}

function

• _{The Boolean alphabet {1, -1} is usually used in neural networks} • _{The Boolean alphabet {1, -1} is usually used in neural networks}

theory instead of {0, 1}.

• _{Correspondence with the classical Boolean alphabet {0, 1} is}

established as follows:

1 2

(

0

1

1

1

{0

1

}

{1 1}

1)

y

;

-

;

y



,

,

x



,-



x = - y









P K Singh, F O E, D E I

Threshold Boolean Functions: Geometrical

Interpretation

“OR” (Disjunction) is an example of the

threshold (linearly separable) Boolean function: “-1s” are separated from “1” by a line

XOR is an example of the non-threshold (not linearly separable) Boolean function: it is impossible

separate “1s” from “-1s” by any single line

(-1, 1) (1, 1) (-1, 1) (1, 1) 1 1 1 1 1  1 (-1,-1) (1,-1) (-1,-1) (1,-1)

Threshold Neuron: Learning

 A main property of a neuron and of a neural network is their

ability to learn from its environment, and to improve its performance through learning.

 A neuron (a neural network) learns about its environment through A neuron (a neural network) learns about its environment through

an iterative process of adjustments applied to its synaptic weights.

 Ideally, a network (a single neuron) becomes more knowledgeable

about its environment after each iteration of the learning process.

Threshold Neuron: Learning

 Let T be a desired output of a neuron (of a network) for a certain

input vector and

 Y be an actual output of a neuron.  If T=Y, there is nothing to learn.  If T=Y, there is nothing to learn.

 If T≠Y, then a neuron has to learn, in order to ensure that after

adjustment of the weights, its actual output will coincide with a desired output

Error-Correction Learning

 If T≠Y , then is the error .

 A goal of learning is to adjust the weights in such a way that for a new

actual output we will have the following:

 That is, the updated actual output must coincide with the desired

output.

 The error-correction learning rule determines how the weights must

T Y



 

Y  Y   T

The error-correction learning rule determines how the weights must be adjusted to ensure that the updated actual output will coincide with the desired output:

 α is a learning rate (should be equal to 1 for the threshold neuron,

when a function to be learned is Boolean)









0 0 1 1 0 , ,..., ; ,..., ; 1,..., n n i i i W w w w X w w w x x n w x i              P K Singh, F O E, D E I

A Simplest Network

1 x Neuron 1 Neuron 3 2 x Neuron 2

Solving XOR problem using the simplest network

1 x N1 N3 1 -3

)

,

(

)

,

(

_{1 2 2 1 2} 1 2 1 2 1 2 1

x

x

x

x

x

f

x

x

f

x

x

x











2 x N2 N3 3 1 -3 3 3 -1 -1 3 3 P K Singh, F O E, D E I

Solving XOR problem using the simplest network

#

Inputs

Neuron 1 Neuron 2 Neuron 3

XOR= Z Z Z  x1  x2 ) 3 , 3 , 1 ( ~ _{ } W W~  (3,3,1) W~  (1,3,3)

x

x

Z sign z( ) sign z( ) sign z( )

output Z output Z output

1) 1 1 1 1 5 1 5 1 1 2 1 x x   1

Neural Networks

 Components – biological plausibility

 Neurone / node  Synapse / weight

 Feed forward networks

 Unidirectional flow of information  Good at extracting patterns,

generalisation and prediction generalisation and prediction

 _{Distributed representation of data}  _{Parallel processing of data}

 _{Training: Backpropagation}  _{Not exact models, but good at}

demonstrating principles  _{Recurrent networks}

 _{Multidirectional flow of information}  Memory / sense of time

 Complex temporal dynamics (e.g. CPGs)

 Various training methods (Hebbian, evolution)  Often better biological models than FFNs

BACK PROPAGATION

 Back Propagation learns by iteratively processing a set of training data (samples).

 For each sample, weights are modified to minimize the error between network’s classification and actual classification.

Steps in Back propagation Algorithm

 STEP ONE: initialize the weights and biases.

 The weights in the network are initialized to random numbers

from the interval [-1,1].

 Each unit has a BIAS associated with it

 The biases are similarly initialized to random numbers from the

interval [-1,1].

 STEP TWO: feed the training sample.

Steps in Back propagation Algorithm

( cont..)

 STEP THREE: Propagate the inputs forward; we compute the net

input and output of each unit in the hidden and output layers.

 STEP FOUR: back propagate the error.

 STEP FOUR: back propagate the error.

 STEP FIVE: update weights and biases to reflect the propagated

Output nodes Output vector

)

)(

1

(

_k k k k k

O

O

T

O

Err







jk k k j j j O O Err w Err  (1 )



I j O _   1

Back propagation Formula

Input nodes Hidden nodes Input vector: x_i w_ij



  i j i ij j w O I  k i j ij ij w l Err O w   ( ) j j j   (l)Err  j I j e O _   1 P K Singh, F O E, D E I

Example of Back propagation

Initialize weights : Input = 3, Hidden Neuron = 2 Output =1 Random Numbers from -1.0 to 1.0

Example ( cont.. )

 _{Bias added to Hidden}

 + Output nodes

 Initialize Bias

 Random Values from

 -1.0 to 1.0

 -1.0 to 1.0

 _{Bias ( Random )}

θ

4

θ

5

θ

6

Example: Voice Recognition



Task: Learn to discriminate between two different voices

saying “Hello”



Data

 Sources  Sources  _{Steve Simpson}  David Raubenheimer  Format



Network architecture

 Feed forward network

 60 input (one for each frequency bin)  _{6 hidden}

 2 output (0-1 for “Steve”, 1-0 for “David”)



Presenting the data

Steve



Presenting the data (untrained network)

Steve 0.43 0.26 David 0.73 0.55 P K Singh, F O E, D E I



Calculate error

Steve

0.43 – 0 = 0.43

0.26 –1 = 0.74



Backprop error and adjust weights

Steve 0.43 – 0 = 0.43 0.26 – 1 = 0.74 1.17 David 0.73 – 1 = 0.27 0.55 – 0 = 0.55 1.17 0.82 P K Singh, F O E, D E I



Presenting the data (trained network)

Steve

0.01 0.99



Results –Voice Recognition

 Performance of trained network

 Discrimination accuracy between known “Hello”s

 100%

 Discrimination accuracy between new “Hello”’s

 100%

Stabilizing Controller

 This scheme has been applied to the control of robot arm trajectory, where a

proportional controller with gain was used as the stabilizing feedback controller.

 We can see that the total input that enters the plant is the sum of the

feedback control signal and the feed-forward control signal, which is calculated from the inverse dynamics model (neural network).

calculated from the inverse dynamics model (neural network).

 That model uses the desired trajectory as the input and the feedback control

as an error signal. As the NN training advances, that input will converge to zero.

 The neural network controller will learn to take over from the feedback

controller. The advantage of this architecture is that we can start with a stable system, even though the neural network has not been adequately trained.

Image Recognition:

Decision Rule and Classifier

 Is it possible to formulate (and formalize!) the decision rule, using

which we can classify or recognize our objects basing on the selected features?

 Can you propose the rule using which we can definitely decide is

it a tiger or a rabbit?

Image Recognition: Decision Rule and classifier

 Once we know our decision rule, it is not difficult to develop a classifier,

which will perform classification/recognition using the selected features and the decision rule.

 However, if the decision rule can not be formulated and formalized, we

should use a classifier, which can develop the rule from the learning process should use a classifier, which can develop the rule from the learning process

 In the most of recognition/classification problems, the formalization of the

decision rule is very complicated or impossible at all.

Why neural network?

1

( ,..., )

_n

f x

x

- unknown multi-factor decision rule

Learning process using a representative learning set

0 1

( , ,...,

w w

w

_n

)

1 0 1 1

ˆ ( ,..., )

(

...

)

n n n

f x

x

P w

w x

w x





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- a set of weighting vectors is the result of the learning process

- a partially defined function, which is an approximation of the decision rule function

m_p m₁ m₂ m₃ xi y_i n     ft f n p     F : p 

1. Quantization of pattern space into

p decision classes

Mathematical Interpretation of Classification in

Decision Making

m₃

Input Patterns _Response:

2. Mathematical model of quantization: “Learning by Examples”

Application of Artificial Neural Network in Fault

Detection Study of Batch Esterification Process

 The complexity of most chemical industry always tends to create a problem in

monitoring and supervision system.

 Prompt fault detection and diagnosis is a best way to handle and tackle this problem.  There are different methods tackling different angle. One of the popular methods is

artificial neural network which is a powerful tool in fault detection system.

 In this, a production of ethyl acetate by a reaction of acetic acid and ethanol in a

batch reactor is applied. batch reactor is applied.

 The neural network with normal and faulty event is executed on the data collected

from the experiment.

 The relationship between normal-faulty events is captured by training network

topology.

 The ability of neural network to detect any process faults is based on their ability to

learn from example and requiring little knowledge about the system structure.

Temperature control in fermenters: application of

neural nets and feedback control in breweries

 The main objective of on-line quality control in fermentation is to perform the production

processes as reproducible as possible.

 Since temperature is the main control parameter in the fermentation process of beer

breweries, it is of primary interest to keep it close to the predefined set point. Here, we report on a model-supported temperature controller for large production-scale beer fermenters.

 _{The dynamic response of the temperature in the tank on temperature changes in the cooling}  _{The dynamic response of the temperature in the tank on temperature changes in the cooling}

elements has been modeled by means of a difference equation.

 The heat production within the tank Is taken into account by means of a model for the

substrate degradation.

 Any optimization requires a model to predict the consequences of actions. Instead of using a

conventional mathematical model of the fermentation kinetics, an artificial neural network approach has been used.

 The set point profiles for the temperature control have been dynamically optimized in order

to minimize the production cost while meeting the constraints posed by the product quality requirements.

Artificial Intelligent Control s Technical Diagnistic s Intelligent Data Analysis and Signal Advance Robotics Machine Vision

Applications of Artificial Neural Networks

Artificial Intellect with Neural Networks and Signal Processing Vision Image & Pattern Recognition Intelligent Security Systems Devices Intelligent l Medicine Devices Intelligent Expert Systems P K Singh, F O E, D E I

Applications: Classification

Business

•Credit rating and risk assessment •Insurance risk evaluation

•Fraud detection

•Insider dealing detection •Marketing analysis •Signature verification •Inventory control Security •Face recognition •Speaker verification •Fingerprint analysis Medicine •Inventory control Engineering

•Machinery defect diagnosis •Signal processing

•Character recognition

Medicine

•General diagnosis

Applications: Modeling

Business

•Prediction of share and commodity prices •Prediction of economic indicators

•Insider dealing detection •Marketing analysis

•Signature verification

•Inventory control _Science

Engineering

•Transducer linerisation •Colour discrimination

•Robot control and navigation •Process control

•Aircraft landing control

•Car active suspension control •Printed Circuit auto routing •Integrated circuit layout •Image compression

Science

•Prediction of the performance of drugs from the molecular structure •Weather prediction

•Sunspot prediction

Medicine

•. Medical imaging and image processing

Applications: Forecasting

•Future sales •Production Requirements •Market Performance •Economic Indicators •Energy Requirements •Energy Requirements •Time Based Variables

Applications: Novelty Detection

•Fault Monitoring

•Performance Monitoring •Fraud Detection

•Detecting Rate Features •Different Cases

Thank you