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Artificial Neural Networks for Decision Support in Copper Smelting Process

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Ivan S. Živković. Mathematical Institute of the Serbian Academy of Sciences and Arts. Artificial Neural Networks for Decision Support in Copper Smelting Process. 1. Introduction. Considerable development of pyrometallurgical copper smelting process

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ivan s ivkovi
Ivan S. Živković

Mathematical Institute of the Serbian Academy of Sciences and Arts

Artificial Neural Networks for Decision Support in Copper Smelting Process

Ivan S. Živković

1 introduction
Ivan S. Živković1. Introduction

Considerable development of pyrometallurgical copper smelting process

Enlargement of production plants capacities

Increase of entirecopper production in the world

Increasing problems due to environmental pollution

1 introduction1
Ivan S. Živković1. Introduction

Smelting plants with old technologies emit PM10 and SO2 far above the limited values

World Health Organization (WHO, 2001) has prescribed limited values of SO2, PM10 content and heavy metals' content in the air

EU standardized limits of these polluters in the air by their regulations

1 introduction2
Ivan S. Živković1. Introduction

Multi-Criteria Decision Making (MCDM)methods in the analysis of problems of air pollution and soil

The integration of the analysis:

technological criteria

social criteria

environmental criteria

economicalcriteria

2 the blending problem
Ivan S. Živković2. The blending problem

K1,...,Kmconcentrates

Determining the amount of each of the available raw materials (concentrates) K1,...,Km which will be used for obtaining the useful products

GOAL:achieve the greatest difference betweenprofit from useful products salesand costs for obtaining specified quantities of raw materials.

2 the blending problem1
Ivan S. Živković2. The blending problem

Take into account :

interactive relations between the quality of raw materials,

economical criteria,

the influence of the environmental criteria in the production process.

2 the blending problem3
Ivan S. Živković2. The blending problem

Maximize the goal function F(x1,...xn)

3 neural network model
Ivan S. Živković3. Neural network model

F(x1,...,xn) = ?

F(x1,...,xn) = Artificial Neural Network (ANN)

4 neural network training
Ivan S. Živković4. Neural network training

Generate training data

Combination of concentrate amount in mixture (x1,...,x14)

Calculate profit for combination

Back propagation algorithm

The trained network stores the nonlinear relationships between amounts of concentrates in mixture

5 optimization
Ivan S. Živković5. Optimization

Complex Method for Constrained Optimization (Richardson and Kuester)

Sequential search technique

No derivatives are required

The initial set of points is randomly scattered throughout the feasible region

5 optimization1
Ivan S. Živković5. Optimization

x1 = 0.0011503862654742391

x2 = 0.0000044659968334488122

x3 = 0.33686567686323504

x4 = 0.000065479997370932846

x5 = 0.000005457597151501704

x6 = 0.14504843643625098

x7 = 0.0031948514922107056

x8 = 0.073478464846484792

x9 = 0.00043238651034418812

x10 = 0.00046832857651410561

x11 = 0.00011146905884013261

x12 = 0.43769285709204886

x13 = 0.00043421539040961333

x14 = 0.000063306618389357238

Profit = 581.19142562842535

6 advantage
Ivan S. Živković6. Advantage
  • No need for explicit form of the goal function
  • No derivatives are required
  • Network can learn nonlinear relationships between amounts of concentrates in mixture
  • Easy to implement
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