Introduction to research team 1
Preface 1
Nomenclature 1
Greek symbols 1
Subscripts 1
1．Introduction 1
1.1 Research background 1
1.2 Design process 2
1.3 Optimization algorithm 3
1.4 Classification of optimization problem 5
2．Modeling strategies for optimization 7
2.1 Modeling strategy based on finite concept 7
2.1.1 Introduction to research field 7
2.1.2 Analysis model 8
2.1.3 Development of analysis code suitable for preheating process 9
2.1.3.1 Radiative heat transfer 9
2.1.3.2 Convective heat transfer 14
2.1.3.3 Conductive heat transfer 15
2.1.4 Steady optimization for heater power distribution 17
2.1.5 Summary 22
2.2 Modeling strategy based on design of experiments 22
2.2.1 Introduction to research field 22
2.2.2 Numerical model and analysis conditions 23
2.2.3 Comparison of cases having porous material or not 25
2.2.4 Optimization strategy 27
2.2.4.1 Concept of D-optimal design 27
2.2.4.2 Optimization using DOE method 27
2.2.5 Summary 30
2.3 Modeling strategy based on analysis database 30
2.3.1 Introduction to research field 30
2.3.2 System setup and experimental method 31
2.3.3 Design of baseline vacuum furnace 33
2.3.3.1 Definition of shape 33
2.3.3.2 Comparison of cases nearly vacuum or argon gas 33
2.3.4 Construction of thermal analysis database 35
2.3.4.1 Thermal analysis of vacuum furnace 35
2.3.4.2 Calculation of thermal conductivity 36
2.3.4.3 Thermal analysis database 37
2.3.5 Optimal design strategy 38
2.3.5.1 Classification of problem 38
2.3.5.2 Process using thermal analysis database 38
2.3.6 Optimized results 39
2.3.6.1 Accuracy verification 39
2.3.6.2 Discussion of results 40
2.3.6.3 Feasible optimal design 42
2.3.7 Rebuilding of design method 43
2.3.8 Summary 44
2.4 Modeling strategy based on response surface method 44
2.4.1 Introduction to research field 45
2.4.2 Dynamic model for fuel cell 46
2.4.2.1 Cathode mass flow model 47
2.4.2.2 Anode mass flow model 49
2.4.2.3 Membrane hydration model 50
2.4.2.4 Stack voltage model 50
2.4.2.5 Cathode GDL model 53
2.4.2.6 Anode GDL model 55
2.4.3 Model calibration 55
2.4.4 Optimization design using RSM 58
2.4.4.1 Concept of response surface method 59
2.4.4.2 Construction of response surface 61
2.4.4.3 Optimal design with response surface 64
2.4.5 Summary 65
2.5 Modeling strategy based on analytic method 65
2.5.1 Optimization using analytic method 65
2.5.1.1 1-d analytic solution 65
2.5.1.2 Optimal strategy and results 67
2.5.2 Optimization using finite difference method 72
2.5.2.1 Classification of problem 72
2.5.2.2 Optimal results and discussion 72
2.5.3 Summary 76
3．Global optimization strategy 77
3.1 Global optimization strategy based on genetic algorithm 77
3.1.1 Construction of fitting function 77
3.1.2 Discussion of optimization results 80
3.1.3 Summary 81
3.2 Global optimization strategy based on DOE and GBM 81
3.2.1 Model descriptions 82
3.2.2 Time for obtaining steady state 83
3.2.3 Setup of fitting function 84
3.2.4 Global optimization 87
3.2.5 Summary 90
4．Multi-objective optimal strategy 90
4.1 Multi-objective strategy based on Benson method 90
4.1.1 Parameter study 90
4.1.2 Optimal strategy based on Benson method 92
4.1.3 Summary 93
4.2 Multi-objective strategy based on layered sequence method 93
4.2.1 Construction of fitting function 94
4.2.2 Multi-objective global optimization 96
4.3 Multi-objective strategy based on linear weighted method 99
4.3.1 Construction of response surface 99
4.3.2 Optimal design and discussion 103
4.3.3 Summary 104
4.4 Multi-objective strategy based on ideal point method 105
4.4.1 Optimal heater power distribution 105
4.4.2 Optimal design using ideal point method 107
4.4.2.1 Effect of a damaged heater 107
4.4.2.2 Optimal results and discussion 108
4.4.3 Summary 109
5．Conclusions 110
6．Acknowledgements 111
References 112
Index 116