Applied Artificial Neural Network Methods for Engineers and Scientists: Solving Algebraic Equations

Description

The aim of this book is to handle different application problems of science and engineering using expert Artificial Neural Network (ANN). As such, the book starts with basics of ANN along with different mathematical preliminaries with respect to algebraic equations. Then it addresses ANN based methods for solving different algebraic equations viz. polynomial equations, diophantine equations, transcendental equations, system of linear and nonlinear equations, eigenvalue problems etc. which are the basic equations to handle the application problems mentioned in the content of the book. Although there exist various methods to handle these problems, but sometimes those may be problem dependent and may fail to give a converge solution with particular discretization. Accordingly, ANN based methods have been addressed here to solve these problems. Detail ANN architecture with step by step procedure and algorithm have been included. Different example problems are solved with respect to various application and mathematical problems. Convergence plots and/or convergence tables of the solutions are depicted to show the efficacy of these methods. It is worth mentioning that various application problems viz. Bakery problem, Power electronics applications, Pole placement, Electrical Network Analysis, Structural engineering problem etc. have been solved using the ANN based methods. Half Title Page Title Page Copyright Page Contents Preface Acknowledgments Chapter 1: ANN Preliminaries 1.1 Introduction 1.2 ANN Architectures 1.3 Learning Rules 1.3.1 Backpropagation Algorithm or Delta Learning Rule 1.4 Activation Function (or Transfer Function) 1.4.1 Sigmoid function 1.4.2 Tanh function 1.5 Conclusion Chapter 2: Mathematical Preliminaries 2.1 Introduction 2.2 Polynomial Equations 2.3 Transcendental Equations 2.4 Diophantine Equations 2.5 Linear System of Equations (LSEs) 2.6 Systems of Nonlinear Equations 2.7 Eigenvalue Problems 2.8 Nonlinear Eigenvalue Problem (NEP) Chapter 3: Polynomial Equations with application in solving Bakery problem 3.1 Introduction 3.2 General model of a polynomial equation 3.2.1 ANN procedure for solving polynomial equation 3.3 Numerical Examples 3.4 Bakery Problem 3.5 Conclusion Chapter 4: Transcendental equations in power electronics applications 4.1 Introduction 4.2 General model of a transcendental equation 4.3 Numerical Examples 4.4 Application Problem 4.5 Conclusion Chapter 5: Diophantine Equations in Pole placement 5.1 Introduction 5.2 General model of a Diophantine Equation 5.2.1 ANN Procedure for solving Diophantine equation 5.3 Numerical Examples 5.4 Application Problem 5.5 Conclusion Chapter 6: Systems of Linear Equations with application in static structural problems 6.1 Introduction 6.2 ANN-based methodology 6.3 Numerical Examples 6.4 Static Structural Problem 6.5 Conclusion Chapter 7: Systems of Nonlinear Equations in Electrical Network Analysis 7.1 Introduction 7.2 Numerical Examples 7.3 Application Problem 7.4 Conclusion Chapter 8: Eigenvalue Problems with application in structural dynamics 8.1 Introduction 8.2 ANN model for solving eigenvalue problems 8.3 Numerical Examples 8.4 Application Problem 8.4.1 Spring mass system 8.4.2 Multi-storey shear structure 8.5 Conclusion Chapter 9: Nonlinear Eigenvalue Problems with application in structural dynamics 9.1 Introduction 9.2 Nonlinear Eigenvalue Problem (NEP) 9.3 Numerical Example 9.4 Application Problem 9.5 Conclusion Chapter 10: Definite Integrals in the fluid force on a vertical surface 10.1 Introduction 10.2 Preliminaries 10.3 ChNN Methodology 10.4 Numerical Examples 10.5 Application Problem 10.6 Conclusion Chapter 11: Inverse Problems in structural dynamics 11.1 Introduction 11.2 Numerical Examples 11.3 Conclusion