MicrosoftWord-Text.Artificial.Inteligence

MicrosoftWord-Text.Artificial.Inteligence - CORNELL...

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CORNELL CORNELL U N I V E R S I T Y U N I V E R S I T Y School of Civil and Environmental Engineering CEE – 593 – Engineering Management Methods I A Brief Introduction to Genetic Algorithms, Artificial Neural Networks and Fuzzy Logic Version 1 Donato da Silva Filho Visiting Scholar Prof. Daniel Pete Loucks Ithaca - NY November / 2000
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CEE 593 - Engineering Management Methods I i Index 1. Introduction ______________________________________________________________3 2. Genetic Algorithms_________________________________________________________5 2.1 Example_____________________________________________________________________ 8 2.1.1 Representation____________________________________________________________________9 2.1.2 Initial Population_________________________________________________________________10 2.1.3 Evaluation ______________________________________________________________________11 2.1.4 Selection _______________________________________________________________________12 2.1.5 Crossover_______________________________________________________________________15 2.1.6 Mutation _______________________________________________________________________15 2.2 Matlab and GAs _____________________________________________________________ 16 2.3 River pollutant concentration__________________________________________________ 17 3. Artificial Neural Networks__________________________________________________21 3.1 Fundamental of the biological neuron ___________________________________________ 22 3.2 Modeling a single neuron _____________________________________________________ 23 3.3 Training a single neuron ______________________________________________________ 25 3.3.1 Example________________________________________________________________________27 3.4 Limitation of one single neuron ________________________________________________ 32 3.5 Multilayer networks__________________________________________________________ 33 3.5.1 Nonlinear problems_______________________________________________________________33 3.5.2 The new basic neuron _____________________________________________________________34 3.5.3 The multilayer network model_______________________________________________________35 3.5.4 Backpropagation rule _____________________________________________________________36 3.6 Fitting any set of data ________________________________________________________ 38 3.7 River pollutant concentration__________________________________________________ 42 4. Fuzzy Logic______________________________________________________________47 4.1 Fuzzy Models _______________________________________________________________ 48 4.1.1 Membership Functions ____________________________________________________________48 4.1.2 Linguistic Variables ______________________________________________________________54 4.1.3 Inference Systems ________________________________________________________________54 4.2 Example____________________________________________________________________ 57
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ii CEE 593 - Engineering Management Methods I 5. Some Frequently Asked Questions ___________________________________________59 5.1 What are membership values? _________________________________________________ 59 5.2 What is the origin of the membership functions?__________________________________ 60 5.3 What are Fuzzy Sets in relation to other modeling techniques? ______________________ 60 5.4 Is Fuzzy Logic equal to Probability Theory? _____________________________________ 61 5.5 How fuzzy is a Fuzzy Set? _____________________________________________________ 62 6. Final Comments__________________________________________________________65 7. References_______________________________________________________________67
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Introduction CEE 593 - Engineering Management Methods I 3 1. Introduction This text is a quite brief introduction to three "tools" that have been more and more applied to solve engineering problems: Genetic Algorithms, Artificial Neural Networks and Fuzzy Logic. Each one of these subjects is divided in three topics: theoretical background, one or two numerical examples and a simple engineering application. It is important to reinforce that this text is introductory and aimed at students that are having their "first contact" with this kind of algorithms. So, there is no emphasis on mathematical details. Even the algorithms are not deeply explained; the objective is to make the initial studies motivating and enjoyable rather than boring and cumbersome. However, we also do not want to sell the illusory idea that we are dealing with the simplest and most efficient methods; some regards have to be made concerning the limitations of the present text. The Genetic Algorithms section shows a basic genetic algorithm. The algorithm is applied when the original problem is real valued, but the genetic algorithm works with binary strings. This is the most common algorithm of Genetic Algorithms and most of the engineering applications found in literature use this model. Some experts in Genetic Algorithm can complain against the lack of examples regarding other applications in which this model does not apply. We are conscious of these other applications, but we believe that students specifically interested in Genetic Algorithms can search the references for further details.
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This note was uploaded on 03/29/2009 for the course CEE 5930 taught by Professor Loucks during the Fall '00 term at Cornell University (Engineering School).

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MicrosoftWord-Text.Artificial.Inteligence - CORNELL...

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