Thermal System Design and Optimization

✍ Scribed by C. Balaji

• Publisher: Springer
• Year: 2021
• Tongue: English
• Leaves: 385
• Category: Library

✦ Synopsis

This highly informative and carefully presented textbook introduces the general principles involved in system design and optimization as applicable to thermal systems, followed by the methods to accomplish them. It introduces contemporary techniques like Genetic Algorithms, Simulated Annealing, and Bayesian Inference in the context of optimization of thermal systems. There is a separate chapter devoted to inverse problems in thermal systems. It also contains sections on Integer Programming and Multi-Objective optimization. The linear programming chapter is fortified by a detailed presentation of the Simplex method. A major highlight of the textbook is the inclusion of workable MATLAB codes for examples of key algorithms discussed in the book. Examples in each chapter clarify the concepts and methods presented and end-of-chapter problems supplement the material presented and enhance the learning process.

✦ Table of Contents

Preface to the Second Edition
Preface to the First Edition
Contents
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About the Author
1 Introduction to Design and System Design
1.1 Introduction
1.2 Design Analysis Through a Flowchart
1.2.1 Identifying the Need
1.2.2 Some Key Considerations in the Techno-Economic Feasibility Study
1.2.3 Research and Development
1.2.4 Flow Loop and Iterations
1.3 Optimization
1.4 Analysis and Design
1.4.1 Difference Between Design and Analysis
1.4.2 Constraints in Design
1.5 Workable System and Optimum System
1.5.1 Features of a Workable System
1.6 Optimum Design
Reference
2 System Simulation
2.1 Introduction
2.2 Some Uses of Simulation
2.3 Different Classes of Simulation
2.4 Information Flow Diagrams
2.5 Techniques for System Simulation
2.5.1 Successive Substitution Method
2.5.2 The Newton–Raphson Method
2.5.3 Newton–Raphson Method for Multiple Unknowns
2.5.4 System of Linear Equations
3 Curve Fitting
3.1 Introduction
3.1.1 Uses of Curve Fitting
3.2 Exact Fit and Its Types
3.2.1 Polynomial Interpolation
3.2.2 Lagrange Interpolating Polynomial
3.2.3 Newton's Divided Difference Method
3.2.4 Spline Approximation
3.3 Best Fit
3.4 Strategies for Best Fit
3.4.1 Least Square Regression (LSR)
3.4.2 Performance Metrics of LSR
3.4.3 Linear Least Squares in Two Variables
3.4.4 Linear Least Squares with Matrix Algebra
3.5 Nonlinear Least Squares
3.5.1 Introduction
3.5.2 Gauss–Newton Algorithm
Reference
4 Optimization—Basic Ideas and Formulation
4.1 Introduction
4.2 General Representation of an Optimization Problem
4.2.1 Properties of Objective Functions
4.2.2 Cardinal Ideas in Optimization
4.2.3 Flowchart for Solving an Optimization Problem
4.2.4 Optimization Techniques
5 Lagrange Multipliers
5.1 Introduction
5.2 The Algorithm
5.2.1 Unconstrained Optimization Problems
5.2.2 Constrained Optimization Problems
5.3 Graphical Interpretation of the Lagrange Multiplier Method
5.4 Mathematical Proof of the Lagrange Multiplier Method
5.5 Economic Significance of the Lagrange Multipliers
5.6 Tests for Maxima/Minima
5.7 Handling Inequality Constraints
5.8 Why Should U Be Positive?
Reference
6 Search Methods
6.1 Introduction
6.1.1 A Smarter Way of Solving Example 6.1
6.2 Monotonic and Unimodal Functions
6.2.1 Monotonic Function
6.2.2 Unimodal Function
6.3 Concept of Global and Local Minimum
6.3.1 Global and Local Minimum
6.3.2 Concept of Elimination and Hill Climbing
6.4 Elimination Method
6.4.1 The Two Point Test
6.4.2 The Dichotomous Search Method
6.4.3 The Fibonacci Search Method
6.4.4 A Critical Assessment of the Fibonacci Search From the Previous Example
6.4.5 The Golden Section Search
6.4.6 Improvements in Single Variable Searches
6.5 Search Methods for Multivariable Unconstrained Optimization Problem
6.5.1 Cauchy's Method: The Method of Steepest Ascent/Descent
6.5.2 How Does the Cauchy's Method (Steepest Descent) Work?
6.5.3 Conjugate Gradient Method
6.6 Constrained Multivariable Optimization Problems
6.7 Multi-objective Optimization
6.7.1 TOPSIS Method
7 Linear Programming and Dynamic Programming
7.1 Introduction
7.2 Linear Programming or LP
7.2.1 Formulation of an LP Problem
7.2.2 Advantages of LP Method Over Lagrange Multiplier Method
7.2.3 Key Differences with Respect to the Lagrange Multiplier Method
7.2.4 Why Is Everybody so Fond of Linear Programming?
7.2.5 Graphical Method of Solving an LP Problem
7.2.6 Simplex Method
7.2.7 Integer Programming
7.3 Dynamic Programming (DP)
References
8 Nontraditional Optimization Techniques
8.1 Introduction
8.2 Genetic Algorithms (GA)
8.2.1 Principle Behind GA
8.2.2 Origin of GA
8.2.3 Robustness of GA
8.2.4 Features of Biological Systems that Are Outstanding
8.2.5 Conclusions About Living and Artificial Systems
8.2.6 Why Would We Want to Use Genetic Algorithms?
8.2.7 What Are the Mathematical Examples for Multi-Modal Functions?
8.2.8 Efficiency of the Optimization Technique Versus the Kind of Problem
8.2.9 Philosophy of Optimization
8.2.10 Key Differences Between GA and Traditional Optimization Methods
8.2.11 The Basic GA
8.2.12 Elitist Strategy
8.2.13 Some Doubts About GA?
8.2.14 The Main Features of GA
8.2.15 A Research Example
8.3 Simulated Annealing (SA)
8.3.1 Basic Philosophy
8.3.2 Key Point in Simulated Annealing (SA)
8.3.3 Steps Involved in SA
8.4 Hybrid Optimization Techniques
Reference
9 Inverse Problems
9.1 Introduction
9.1.1 Parameter Estimation by Least Squares Minimization
9.2 The Bayesian Approach to Inverse Problems
9.2.1 Bayesian Inference
9.2.2 Steps Involved in Solving a Problem Using Bayesian Approach
Appendix Summary
Appendix
Random Number Table
Bibliography
Index