Multidisciplinary Design Optimization of Launch Vehicles Mathieu Balesdent
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Multidisciplinary Design Optimization of Launch Vehicles Mathieu Balesdent To cite this version: Mathieu Balesdent. Multidisciplinary Design Optimization of Launch Vehicles. Optimization and Control [math.OC]. Ecole Centrale de Nantes (ECN), 2011. English. tel-00659362 HAL Id: tel-00659362 https://tel.archives-ouvertes.fr/tel-00659362 Submitted on 12 Jan 2012 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. ÉCOLE DOCTORALE SCIENCES POUR L’INGÉNIEUR, GÉOSCIENCES, ARCHITECTURE École Centrale de Nantes Année 2011 Thèse de Doctorat Spécialité : Génie Mécanique présentée et soutenue publiquement par Mathieu BALESDENT le 3 novembre 2011 à l’Office National d’Etudes et de Recherches Aérospatiales OPTIMISATION MULTIDISCIPLINAIRE DE LANCEURS (Multidisciplinary Design Optimization of Launch Vehicles) JURY Président : Jean-Antoine Désidéri Directeur de Recherche, INRIA Rapporteurs : David Bassir Docteur, HDR, Université de Technologie de Belfort-Montbéliard Attaché pour la Science et la Technologie, Ministère des Affaires Etrangères Patrick Siarry Professeur, Université Paris-Est Créteil Val-de-Marne Examinateurs : Philippe Dépincé Professeur, Ecole Centrale de Nantes Michèle Lavagna Associate Professor, Politecnico di Milano Rodolphe Le Riche Docteur, HDR, CNRS - Ecole des Mines de Saint-Etienne Invités : Nicolas Bérend Ingénieur, Onera Julien Laurent-Varin Docteur, CNES Directeur de thèse : Philippe DÉPINCÉ Encadrant Onera : Nicolas BÉREND Laboratoires : Office National d’Etudes et de Recherches Aérospatiales Institut de Recherche en Communications et Cybernétique de Nantes N◦ E.D. : 498-196 ACKNOWLEDGMENTS This work has been realized in the Onera’s System Design and Performance Evaluation Department, in collaboration with the CNES Launchers Directorate and the team Systems Engineering Products, Performance and Perceptions of IRCCyN. I would like to thank the director of DCPS, Dr. Donath, for giving me the opportunity to achieve this thesis at Onera. I would like to thank Dr. Désidéri, who did me the honour of chairing my PhD commit- tee. I express my gratitude to Dr. Bassir and Prof. Siarry for reviewing this PhD thesis. I also thank Dr. Laurent-Varin, Prof. Lavagna and Dr. Le Riche for accepting to be part of my PhD committee. I would like to acknowledge Prof. Dépincé for agreeing to be my advisor during these three years. I would like to express my thankfulness to my Onera supervisor, M. Bérend for his comments, suggestions, edits, and advices during the thesis. I would like to thank my CNES supervisor, M. Oswald. I thank also M. Amouroux for his help in the elaboration of the launch vehicle disciplinary models. I owe a great amount of thanks to the people whom I’ve been working with every day at the Onera’s DCPS. Especially, I thank Dr. Piet-Lahanier for her numerous advices all along the thesis. I would also like to thank the Onera PhD students (Dalal, Ariane, Rata, Walid, Julien, Joseph, François, Yohan and Damien) who have provided the most exciting working envi- ronment. Special thanks go to my office mate, Rudy, qui quæsivit rerum causas, for those numerous happy hours spent during the thesis. Last but not least, I would like to thank my parents, who believed in me and always encouraged me. Finally, I would especially like to thank my fiancée Sophie, for all her love and for her understanding when I spent my time working on this thesis. I appreciate her support and her sacrifices very much during this endeavor. This PhD thesis has been co-funded by CNES and Onera. Non est ad astra mollis e terris via. There is no easy way from the earth to the stars. Hercules Furens Seneca the Younger To Sophie, Cécile & Claude Contents Nomenclature 13 Acronyms 15 Introduction 17 I Panorama of Multidisciplinary Design Optimization methods used in Launch Vehicle Design 21 1 Generalities about Multidisciplinary Design Optimization 23 1.1 Introduction . 23 1.2 Mathematical formulation of the general MDO problem . 24 1.2.1 Problem formulation . 25 1.2.2 Types of variables . 25 1.2.3 Types of constraints . 26 1.2.4 Types of functions . 26 1.2.5 Disciplinary equations . 26 1.2.6 Coupling . 27 1.2.7 Multidisciplinary analysis . 28 1.3 Feasibility concepts in MDO . 28 1.3.1 Individual disciplinary feasibility . 28 1.3.2 Multidisciplinary feasibility . 29 1.4 Description of the Launch Vehicle Design problem . 29 1.4.1 Disciplines and variables . 29 1.4.2 Constraints . 30 1.4.3 Objective functions . 30 1.4.4 Specificities of the Launch Vehicle Design problem . 30 1.5 Conclusion . 31 2 Classical MDO methods 33 2.1 Introduction . 33 2.2 Single level methods . 34 2.2.1 Multi Discipline Feasible . 34 1 2.2.2 Individual Discipline Feasible . 36 2.2.3 All At Once . 38 2.3 Qualitative comparison of the single level methods . 39 2.4 Multi level methods . 40 2.4.1 Collaborative Optimization . 40 2.4.2 Modified Collaboration Optimization . 42 2.4.3 Concurrent SubSpace Optimization . 44 2.4.4 Bi-Level Integrated Systems Synthesis . 46 2.4.5 Analytical Target Cascading . 49 2.4.6 Other multi level methods . 51 2.5 Conclusion . 52 3 Optimization algorithms and optimal control techniques 53 3.1 Introduction . 53 3.2 Optimization algorithms used in MDO . 54 3.2.1 Gradient-based algorithms . 54 3.2.2 Gradient-free algorithms . 55 3.3 Optimal control . 62 3.3.1 Direct methods . 64 3.3.2 Indirect methods . 65 3.3.3 Single vs multiple shooting methods . 66 3.3.4 Collocation methods . 68 3.3.5 Dynamic Programming . 69 3.4 Conclusion . 69 4 Analysis of the MDO method application in the Launch Vehicle Design 71 4.1 Introduction . 71 4.2 Different study cases and optimization criteria . 72 4.2.1 MDO methods and optimization algorithms . 72 4.2.2 Optimization criteria and different study cases . 73 4.3 Trajectory handling . 73 4.4 Comparison of the main MDO methods in a common application case . 74 4.4.1 Presentation of the optimization problem . 74 4.4.2 Comparison of AAO, MDF and CO . 74 4.4.3 Comparison of FPI, AAO, BLISS2000 and MCO . 75 4.5 Comparative synthesis of the main MDO methods . 76 4.5.1 Calculation costs and convergence speed . 76 4.5.2 Considerations about optimality conditions . 76 4.5.3 Method deftness . 77 4.6 Conclusion and ways of improvement . 78 4.6.1 Inclusion of design stability aspects in the optimization process . 78 4.6.2 Trajectory optimization in the design process . 79 4.6.3 Heuristics and gradient-based algorithms coupling . 79 4.6.4 Another subdivision of the optimization process . 79 II Multidisciplinary Design Optimization formulations using a stage-wise decomposition 81 5 Presentation of the stage-wise decomposition formulations 83 5.1 Introduction . 83 5.2 Decomposition of the problem and identification of the couplings . 85 5.2.1 Definition of the launch vehicle design problem . 85 5.2.2 Decomposition of the state vector dynamics . 87 5.2.3 Determination of the coupling variables . 88 5.2.4 Proposition of the optimization strategy . 89 5.3 Stage-wise decomposition formulations . 91 5.3.1 First formulation . 91 5.3.2 Second formulation . 93 5.3.3 Third formulation . 95 5.3.4 Fourth formulation . 96 5.4 Conclusion . 98 6 Application case : optimization of a three-stage-to-orbit launch vehicle 99 6.1 Introduction . 99 6.2 Description of the disciplines . 100 6.2.1 Propulsion . 100 6.2.2 Aerodynamics . 102 6.2.3 Trajectory . 102 6.2.4 Mass budget and geometry design . 106 6.3 Optimization variables and disciplinary interactions . 109 6.3.1 Optimization variables . 109 6.3.2 Interactions between the different disciplines . 109 6.4 MDO problem formulation . 110 6.4.1 Initial formulation . 110 6.4.2 MDF formulation . 110 6.5 Stage-wise decomposition formulations . 111 6.5.1 First formulation . 111 6.5.2 Second formulation . 113 6.5.3 Third formulation . 114 6.5.4 Fourth formulation . 115 6.6 Conclusion . 116 7 Comparison of the different formulations 117 7.1 Introduction . 117 7.2 Analysis of the problem dimensionality and the number of constraints . 118 7.3 Qualitative comparison of proposed formulations . 120 7.4 Numerical comparison of the formulations . 122 7.4.1 Context . 122 7.4.2 Adaptation of stage-wise formulations to genetic algorithm . 124 7.4.3 Results and analysis . 125 7.4.4 Limitations of the numerical comparison ..