Machado / Özdemir / Baleanu Mathematical Modelling and Optimization of Engineering Problems

1. Auflage 2020
ISBN: 978-3-030-37062-6
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 30, 204 Seiten

Reihe: Nonlinear Systems and Complexity

This book presents recent developments in modelling and optimization of engineering systems and the use of advanced mathematical methods for solving complex real-world problems. It provides recent theoretical developments and new techniques based on control, optimization theory, mathematical modeling and fractional calculus that can be used to model and understand complex behavior in natural phenomena including latest technologies such as additive manufacturing. Specific topics covered in detail include combinatorial optimization, flow and heat transfer, mathematical modelling, energy storage and management policy, artificial intelligence, optimal control, modelling and optimization of manufacturing systems.  

Jose A. Tenreiro Machado is a Professor at the Institute of Engineering, Polytechnic of Porto, Portugal; Necati Özdemir is a Professor with the Department of Mathematics, Bal?kesir University, Bal?kesir, Turkey; Dumitru Baleanu is a Professor with the Department of Mathematics, Çankaya University, Ankara, Turkey and the Institute of Space Sciences, Magurele-Bucharest, Romania.

Autoren/Hrsg.

Machado, J. A. Tenreiro

Özdemir, Necati

Baleanu, Dumitru

Inhaltsverzeichnis

1;Preface;6
2;Contents;8
3;1 Heuristic Techniques for Real-Time Order Acceptance and Scheduling in Metal Additive Manufacturing;10
3.1;1.1 Introduction;10
3.2;1.2 Literature Review;11
3.3;1.3 Problem Statement;13
3.3.1;1.3.1 Assumptions;14
3.3.2;1.3.2 Notation;14
3.3.2.1;Decision Variables;15
3.3.2.2;Indicators;15
3.3.3;1.3.3 Basic Formulations;15
3.3.4;1.3.4 Objective Function;16
3.3.5;1.3.5 Constraints;16
3.4;1.4 Meta-heuristic Procedures;17
3.4.1;1.4.1 Generation of Feasible Solutions;17
3.4.1.1;1.4.1.1 Single Machine;17
3.4.1.2;1.4.1.2 Multiple Machines;19
3.4.2;1.4.2 Selection Rules;20
3.4.2.1;1.4.2.1 Stochastic Selection;21
3.4.2.2;1.4.2.2 Profit-Time Based Selection;21
3.4.2.3;1.4.2.3 Cost Benefit Based Selection;23
3.5;1.5 Computational Experiments;24
3.5.1;1.5.1 Data Generation;24
3.5.2;1.5.2 Experimental Results and Discussions;25
3.5.2.1;1.5.2.1 The Difference of Stochastic Results;25
3.5.2.2;1.5.2.2 Performance of Non-random Selection Rules;28
3.6;1.6 Conclusions and Future Research;30
3.7;References;32
4;2 Developing a Nationwide Energy Storage Policy by Optimal Size and Site Selection;34
4.1;2.1 Introduction;34
4.2;2.2 Optimization Models in Energy Economics;35
4.2.1;2.2.1 Economic Dispatch Model;35
4.2.2;2.2.2 Unit Commitment Model;36
4.2.3;2.2.3 Energy Storage System Modeling in UC;38
4.2.4;2.2.4 AC Optimal Power Flow Model;39
4.2.5;2.2.5 DC Optimal Power Flow Model;41
4.2.6;2.2.6 Optimal Energy Storage System Placement and Sizing Model;42
4.3;2.3 Optimization of the Nationwide Energy Storage System;43
4.3.1;2.3.1 The Maximum Sizing of Energy Storage Systems;44
4.3.2;2.3.2 Distribution of Energy Storage Systems Within the Network;45
4.3.3;2.3.3 The Proposed Bi-level Optimization for Sizing and Siting of Storage Units;46
4.4;2.4 Case Study: Power Systems in Turkey;47
4.5;2.5 Discussion on a Nationwide Energy Policy;53
4.6;2.6 Conclusion;56
4.7;Nomenclature;56
4.8;References;57
5;3 Pontryagin's Principle for a Class of Discrete Time Infinite Horizon Optimal Growth Problems;59
5.1;3.1 Introduction;59
5.2;3.2 One-Sector Optimal Growth Model;61
5.2.1;3.2.1 Social Planner's Problem of E;62
5.2.2;3.2.2 Necessary and Sufficient Conditions of Optimality;62
5.3;3.3 Optimal Growth Model with an Natural Exhaustible Resource;65
5.3.1;3.3.1 Management Problem of Eenr;66
5.3.2;3.3.2 Necessary and Sufficient Conditions of an Optimal Management of a Natural Resource;67
5.4;3.4 Optimal Growth Model of a Forest: An Optimal Management Model of Forestry;71
5.4.1;3.4.1 Planner's Management Problem;73
5.4.2;3.4.2 Necessary Conditions of Optimality;74
5.5;3.5 Conclusion;77
5.6;References;77
6;4 A Medical Modelling Using Multiple Linear Regression;78
6.1;4.1 Introduction;78
6.2;4.2 Materials and Methods;79
6.2.1;4.2.1 Study Samples;80
6.2.2;4.2.2 Multiple Linear Regression Analysis;81
6.2.3;4.2.3 Test for the Model;83
6.2.4;4.2.4 Residual Analysis;84
6.3;4.3 Building Regression Analysis Model;85
6.4;4.4 Discussion and Analysis;87
6.5;4.5 Conclusions and Recommendations;90
6.6;References;92
7;5 Lie Group Method Solution for Two-Dimensional Heat and Viscous Flow Driven by Injection Through a Deformable Rectangular Channel with Porous Walls;95
7.1;5.1 Introduction;95
7.2;5.2 Mathematical Modelling of the Problem;97
7.2.1;5.2.1 Problem Statement;97
7.2.2;5.2.2 Flow Configuration;98
7.2.3;5.2.3 Forces Affecting the Dynamics of the Flow;98
7.2.3.1;5.2.3.1 Surface Force;98
7.2.3.2;5.2.3.2 Body Forces;101
7.2.4;5.2.4 Derivation of Governing Equations;104
7.2.4.1;5.2.4.1 Conservation of Mass;104
7.2.4.2;5.2.4.2 Conservation of Momentum;104
7.2.4.3;5.2.4.3 Conservation of Energy;105
7.2.4.4;5.2.4.4 Boundary Conditions;105
7.3;5.3 Mathematical Representation of Problem;106
7.3.1;5.3.1 Governing Equations and Boundary Conditions;106
7.4;5.4 Solution of the Problem;108
7.4.1;5.4.1 Lie Group Analysis;108
7.4.2;5.4.2 Semi-Analytical Solution;111
7.5;5.5 Results and Discussion;113
7.5.1;5.5.1 Effects of Wall Dilation;113
7.5.2;5.5.2 Effects of Reynolds number inside the Filtration Chamber;114
7.5.3;5.5.3 Effects of Porosity Variable Inside the Filtration Chamber;116
7.5.4;5.5.4 Effects of Stuart Number Inside the Filtration Chamber;116
7.5.5;5.5.5 Temperature Distribution Inside the Chamber;116
7.6;5.6 Concluding Remarks;117
7.7;References;119
8;6 Optimal Siting of Wind Turbines in a Wind Farm;121
8.1;6.1 Introduction;121
8.2;6.2 Numerical Methods of the Present Study;124
8.2.1;6.2.1 Wake Model;124
8.2.2;6.2.2 Power Model;127
8.3;6.3 Methodology;127
8.3.1;6.3.1 Problem Formulation;127
8.3.2;6.3.2 Initial Population Based on Elevation Values;130
8.3.3;6.3.3 Genetic Algorithm for Optimization;132
8.3.3.1;6.3.3.1 Population Formation;132
8.3.3.2;6.3.3.2 Selection;134
8.3.3.3;6.3.3.3 Crossover;135
8.3.3.4;6.3.3.4 Mutation;136
8.3.3.5;6.3.3.5 Genetic Algorithm Parameters;136
8.4;6.4 Results and Discussion;139
8.5;6.5 Conclusion;141
8.6;References;142
9;7 RSM-Based Optimization of Excitation Capacitance and Speed for a Self-Excited Induction Generator;144
9.1;7.1 Introduction;144
9.2;7.2 Modelling of SEIG;146
9.3;7.3 Voltage Build-up process;147
9.4;7.4 Analysis;148
9.5;7.5 Response Surface Method;150
9.6;7.6 Results and Discussions;151
9.7;7.7 Conclusion;158
9.8;References;158
10;8 Distance-Constrained Vehicle Routing Problems: A Case Study Using Artificial Bee Colony Algorithm;161
10.1;8.1 Introduction;161
10.2;8.2 Research Background;162
10.3;8.3 Artificial Bee Colony (ABC) Algorithm;165
10.3.1;8.3.1 Initialization of the Population;166
10.3.2;8.3.2 Initialization of the Bee Phase;167
10.3.3;8.3.3 Onlooker Bee Phase;167
10.3.4;8.3.4 Scout Bee Phase;168
10.3.5;8.3.5 Stopping Phase;168
10.4;8.4 Case Study;168
10.5;8.5 Results and Discussion;171
10.6;8.6 Conclusion;175
10.7;References;175
11;9 Fractional Model for Type 1 Diabetes;178
11.1;9.1 Introduction;178
11.1.1;9.1.1 Some Concepts of Fractional Calculus;179
11.2;9.2 Description of the Model;180
11.3;9.3 Model Analysis;181
11.4;9.4 Global Stability of the Disease-Free Equilibrium;182
11.5;9.5 Numerical Results;184
11.6;9.6 Conclusion;186
11.7;References;187
12;10 Mathematical Modelling and Additive Manufacturingof a Gyroid;189
12.1;10.1 Infinite Periodic Minimal Surfaces (IPMS) Without Self-intersections: Gyroid;189
12.2;10.2 Additive Manufacturing Technology;190
12.3;10.3 3D Printing Process of an IPMS Gyroid;191
12.3.1;10.3.1 Creating the 3D Mathematical Model of the IPMS Gyroid with K3DSurf Program;191
12.3.2;10.3.2 Converting the CAD Model Data to ``.obj'' or ``.stl'' File Format;192
12.3.3;10.3.3 Generating a Solid, Thickened Shell or Hollow CAD Model;193
12.3.4;10.3.4 Slice the Model into Layers, Generate the Travel Movements and Support Structure;194
12.3.5;10.3.5 3D Printing of the Model;195
12.3.5.1;10.3.5.1 Fused Deposition Modelling;195
12.3.5.2;10.3.5.2 3D Printing of the IPMS Gyroid;196
12.3.6;10.3.6 Removing the Support Material If Any and Apply Finishing Process;196
12.4;10.4 Conclusion;196
12.5;References;197
13;Index;199