Graph Theory in Modern Engineering: Computer Aided Design, Control, Optimization, Reliability Analysis
Published on 25. May 1973
302 pages
978-0-08-095607-7 (ISBN)
Description
Graph Theory in Modern Engineering: Computer Aided Design, Control, Optimization, Reliability Analysis
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Ernest J. Henley | R. Williams
Graph Theory in Modern Engineering
Book
01/1973
Academic Press
€76.14
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Content
- 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
