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

✍ Scribed by Snehashish Chakraverty, Sumit Kumar Jeswal

• Publisher: WSPC
• Year: 2021
• Tongue: English
• Leaves: 191
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

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