Graph-Based Modelling in Engineering (eBook)

Preface 6
Contents 8
Basics and Theoretical Aspects of Graph and Network Modelling 10
1 Bond Graphs in System Modelling 11
Abstract 11
1 Introduction 11
2 About Power and Energy Variables 12
3 The Bond Graph Elements 14
3.1 Sources of Power 14
3.2 Storage Elements 14
3.3 Dissipative Elements 15
3.4 Transformers and Gyrators 15
3.5 Connection Elements 16
4 Causality in Bond Graphs 17
4.1 Bonds and Ports 17
4.2 Causality Assignment 18
5 Construction of the Bond Graph Model 20
5.1 Construction of Acausal Bond Graph Models for Mechanical Systems 20
5.2 Construction of Acausal Bond Graph Models for Non-mechanical Systems 21
5.3 Construction of the Causal Bond Graph 21
6 Exploitation of Bond Graph as a Meta-Model 22
6.1 Deriving State-Space Models 22
6.2 Deriving Block Diagram Models 23
6.3 Software Environment for the Bond Graph Method 23
7 An Illustrative Example—Use of Bond Graph Method for a Hydro-Mechanical System 24
8 Conclusions 28
References 29
2 Structural Importance and Local Importance in Network Reliability 32
Abstract 32
1 Introduction 32
2 Structural Importance Measures 33
2.1 The Structural Birnbaum Importance 33
2.1.1 Connected Spanning Subgraphs and the Tutte Polynomial 34
2.1.2 Modified Structural Birnbaum Importance 35
2.2 Spanning Trees and Electrical Resistance 36
2.2.1 Spanning Trees 37
2.2.2 Electrical Resistance 37
3 Flow and Distance Related Structural Importance Measures 38
3.1 Stress Centrality 38
3.2 Modified Stress Centrality 39
3.3 Betweenness Centrality 40
3.4 An Importance Measure Based on Distances 40
4 Local Importance Measures 41
5 Summary and Conclusions 43
References 43
3 Access Distribution Scheme to the Computer System Based on Fuzzy Logic 45
Abstract 45
1 Introduction 45
2 RSA is a Modern System of Information Security 49
3 Fuzzy Selection System of Modular Exponentiation Method 51
4 Conclusions 55
References 55
4 Problem of Medicines Distribution on the Example of Pharmaceutical Wholesale 57
Abstract 57
1 Introduction 57
2 Specificity of Distribution in the Pharmaceutical Industry 58
3 Example of Route Optimization of Medicines Physical Distribution 60
3.1 The Mathematical Model of the Traveling Salesman Problem 62
3.2 Route Selection with Branch and Bound Method 67
3.3 Route Selection with Artificial Immune System 68
4 Conclusions 71
References 71
Modelling of Mechanical Systems 72
5 Bond Graph Model of a Robot Leg 73
Abstract 73
1 Introduction 73
2 General Description of the Robot 74
3 Bond Graph Model of a Robot 79
3.1 Graph for a Single Body 80
4 Conclusions 83
References 83
6 Kinematical Analysis of Variants of Wind Turbine Drive by Means of Graphs 85
Abstract 85
1 Introduction 85
2 Kinematical Analysis of Planetary Gear Systems 86
2.1 Classical Analysis of Drive Variants 88
3 Graph-Based Analysis of Planetary Gear Sets 91
3.1 Mixed Multi-graphs Models 91
3.2 Modified Contour Graph Method 94
3.3 Bond Graphs Models 95
4 Conclusions and Final Remarks 98
References 98
7 Graph-Based Algorithm for the Evaluation of the Mechanical Efficiency of Epicyclic Gear Drive in Hybrid Scooters 100
Abstract 100
1 Graph Representation of the Gear Train 102
2 Kinematic and Power Flow Analysis 103
3 PGHT Mechanical Efficiency 105
4 Conclusions 108
References 108
8 Graph-Theoretic Modelling and Sensitivity Analysis of Dynamic Systems 109
Abstract 109
1 Introduction 109
1.1 Graph-Theoretic Modelling of Dynamic Systems 110
1.2 Sensitivity Analysis of Dynamic Systems 111
2 Generation of Governing and Sensitivity Equations 112
3 Example Problem 115
4 Conclusions 117
Acknowledgments 117
References 117
9 Three-Dimensional Analysis of Vehicle Stability Using Graph Theory 119
Abstract 119
1 Introduction 120
2 Static Analysis Tools 120
2.1 Screw Theory 120
2.1.1 Method of Successive Screw Displacements 120
2.1.2 Wrench—Forces and Moments 121
2.2 Graph Theory 121
2.3 Davies Method for Statics 122
3 Two-Dimensional Model of Vehicle Stability 123
4 Three-Dimensional Model of Vehicle Stability 123
4.1 Kinematic Chain 124
4.2 Mechanism Position Kinematics 125
4.3 Direct Coupling Graph 125
4.4 The Mechanism Statics 126
4.5 Equation System Solution 127
5 Result Analysis 128
6 Conclusions 129
Acknowledgments 129
Appendix A. Wrench Parameters of the Mechanism 129
Appendix B. The Equations System from the Statics of the Mechanism 130
References 130
10 Analysis of the Kinematics of Planar Link Mechanism with Non-stationary Motion of Crank 132
Abstract 132
1 Introduction 132
2 Equations of the Contour Graph Method [4] 133
3 Problem Description 135
4 Derivation of the Vector Equation System for Velocities 137
5 Generation of a System of Vector Equations for the Accelerations of Mechanism Links 138
6 Analysis of the Results 140
7 Conclusions 141
References 141
Modeling of Production Processes 142
11 Petri Nets for Computer Aided Group Technology 143
Abstract 143
1 Petri Nets as a Formal Language for Conditions and Events System Specification 143
2 Process Planning in the Group Technology Conditions 145
3 Petri Nets Class for Modeling the Performance of Manufacturing Group Process 147
4 Petri Net for Group Manufacturing Process 149
4.1 Production Task Module 149
4.2 Raw Material Availability Control (RMAC) 150
4.3 The Module for the Fixture Element Selection 153
4.4 Manufacturing Processes Module 155
4.5 Tools Module 157
5 Optimization of Production Program Realization in Automatic Manufacturing Cell 160
6 Summary 163
References 163
12 Graph Theory in Product Development Planning 165
Abstract 165
1 Introduction 165
2 GERT 166
3 Risk in Product Development 167
4 Risk Management and the GERT Method: A Joint Example 169
5 Conclusions 172
References 172
13 A Digital Pattern Approach to 3D CAD Modelling of Automotive Car Door Assembly by Using Directed Graphs 174
Abstract 174
1 Introduction 174
2 The Digital Pattern Approach to 3D CAD Modelling 176
3 The DP of an Automotive Car Door Assembly 177
3.1 Discussion 181
4 Conclusions 183
Acknowledgments 183
References 183
Graph-Based Aid and Modelling of Design Tasks 185
14 Application of Game Graphs to Describe the Inverse Problem in the Designing of Mechatronic Vibrating Systems 186
Abstract 186
1 Introduction 186
2 Application of Dependence Graphs and Parametric Game Trees in a Discrete Description of Mechatronic Systems 187
3 The Inverse Problem in the Designing of Mechatronic Vibrating Systems 189
4 Conclusions 194
References 195
15 Graphic Matrix Formalization of Logical Decision Trees in the Optimization of Machine Systems 197
Abstract 197
1 Introduction 197
2 Graphic Matrix Formalization of Logical Decision Trees 198
2.1 Example 198
3 Application of the Graphic Matrix Formalization in the Optimization of Machine Systems 199
3.1 Analysis of a Degree of Importance of Construction Parameters of the Overflow Valve 199
4 Conclusions 204
References 204
16 The Class of Objects Graph Model as Dataware of Structural Synthesis System 206
Abstract 206
1 Introduction 206
2 Preparation of the Initial Set of Modules 207
3 Synthesis Algorithm of Generalized Model 209
4 Further Steps 213
References 214
Miscellaneous 215
17 Search Module as a Tool for Improvement of Classifier 216
Abstract 216
1 Introduction 216
2 Classifier as a Database of Search Module 217
3 Information Search Algorithm 220
4 Conclusion 223
References 223
18 Kazimierz Kuratowski—Biography and Genesis of the Theorem on Planar Graphs 225
Abstract 225
1 Introduction 225
1.1 General Historical Background 227
2 Mathematics in New Established Poland 227
2.1 Methods of Working and the Scottish Book 229
2.2 Journals 230
2.3 Congresses, Conferences and Visits 230
3 Short Kuratowski’s Biography (1896–1980) 231
4 Proof of Kuratowski’s Theorem—Genesis 233
5 Conclusions 236
References 236
Author Index 239