Graph Theory in Modern Engineering: Computer Aided Design, Control, Optimization, Reliability Analysis

Front Cover
Graph Theory in Modern Engineering
Copyright Page
Contents
Preface
Acknowledgments
Nomenclature
Chapter 1. Basic Concepts
	Directed Graphs
	Flow Graphs for Differential Equations
	Further Terminology
Chapter 2. Construction and Analysis of Signal Flow Graphs
	Signal-Flow-Graph Reduction and the Solution of Equations
	Flow-Graph Algebra
	Loop Elimination and Equation Solving by Equation Reduction
	Mason’s Rule
	Applying Mason’s Rule
	Application of Mason’s Rule to Dynamic Systems
	References
Chapter 3. Systematic Analysis of Large Flow Graphs
	Determining Specific Paths and Loops
	Determining Specific Paths
	List Processing Approach to Determining Paths
	Evaluation of Gains
	Removing Unnecessary Paths from the List Structure
	Evaluating Determinants in Mason’s Formula
	Computing the Determinants Corresponding to Specific Paths as Required by Mason’s Rule
	Computing Transmittances
	Implementing the Algorithms
	References
Chapter 4. Frequency Response Analysis
	Final Value Theorem
	Initial Value Theorem
	Substitution Rule
	Bode Diagrams
	A Typical Application
	Other Stability Criteria
	Reference
Chapter 5. Sensitivity Analysis
	Sensitivity Analysis in General
	Derivation of Network Functions
	Deriving Sensitivity Functions
	Applying Sensitivity Functions to Structural Analysis
	Gain and Phase Sensitivity
	Pole and Zero Sensitivity
	Sensitivities via Structural Methods
	Sensitivities for Large Parameter Variations
	Transfer Functions and Sensitivities in Static Systems
	References
Chapter 6. Examples and Further Applications
	Closed-Form Solution of an Absorption Column
	Sensitivity Analysis of a Heat Exchanger Network
	Continuous Stirred Tank Reactor
	Eigenvalue Problems
	Ordering Recycle Calculations
	Transportation Problems
	References
Chapter 7. Linear and Nonlinear Programming
	General Form of LP Problems
	Simplex Solution by Signal-Flow-Graph Methods
	Example Problems
	Discussion of Solution Procedure (MASNLP)
	An Advantage of MASNLP
	Dual Simplex Method
	Postoptimal Analysis
	Sensitivity Analysis
	Nonlinear Systems
	Method of Feasible Directions
	A Heat Exchanger Problem
	Solution to the Heat Exchanger System
	Results and Discussion
	References
Chapter 8. Ranking by Flow-Graph Methods
	Tennis Rankings
	Implementation Difficulties
	A Solution to the Implementation Problem
	Reference
Chapter 9. Undirected Graphs
	Undirected Graphs
	Trees
	Logic Trees
	Branch and Bound Methods
	Trees-Further Theorems and Definitions
	Disconnecting Sets and Cut-Sets
	Bipartite Graphs
	Assigning Output Sets
	References
Chapter 10. Matrix Representation of Graphs
	Nondirected Graphs
	Digraphs
	References
Chapter 11. Branch and Eound. Search Tree Methods
	Formal Definition of the Branch and Bound Technique
	The Traveling Salesman Problem
	Integer Programming and Pseudo-Boolean Progrhmming
	Generalization of the Branch and Bound Method
	Bidding Contest Problem
	Conclusion
	References
Chapter 12. Process Reliability Analysis by Flow-Graph Methods
	Module Representation of Reliability Graphs
	Principle of Path Enumeration and Sensitivity Calculation Methods
	Basic Algorithm
	Path Finding Algorithm
	System Reliability
	Comparison with State Enumeration Algorithm
	Examples
	Extension to System MTBF Calculation
	Conclusions
	References
Appendix A. Matrix Theory
Appendix B. Linearization of Equations
Appendix C. Derivation of Mason’s Rule
Appendix D. Boolean and Modulo-2 Algebra
Appendix E. Linear Programming
Appendix F. The Coates Flow Graph
Appendix G. The Fibonacci Search Method
Appendix H. Glossary of Graph Nomenclature
Appendix I. Computer Programs for Chapters 1-6
Appendix J. Computer Programs for Chapter 7
BIBLIOGRAPHY
INDEX