Journal of Aerospace Science and Technology

Journal of Aerospace Science and Technology

A surrogate-model multidisciplinary design optimization methodology for trajectory optimization of a launch vehicle

Document Type : Original Article

Authors
1 Faculty of Management & Industrial Engineering, Malek Ashtar University of Technology, Iran
2 Aerospace Research Institute
3 Faculty of Management & Industrial Engineering, Malek Ashtar University of Technology, Iran
Abstract
The present paper tries to optimization of the ascent trajectory of two stages launch vehicle (LV) to achieve a low Earth Orbit (LEO). To this end, the surrogate-model method by utilizing the Design of Experiment (DOE) and the Response Surface Method (RSM) were implemented as two effective means for optimizing. In this paper, the model-based optimization strategy aims to minimize the total mass of the first stage and ultimately reduce the costs of the launch vehicle. Hence, D‐optimal structure has been used for the surrogate-model and 101 different experiments were carried out on the trajectory optimization. The analysis of variance (ANOVA) results indicate that the implemented model is capable to predict the responses adequately within the limits of input parameters. Therefore, the desirability function analysis for LV has been applied to optimize the total mass of the first stage. As a result, the capability of the proposed LV optimization method is 602 kg reduction in total mass. This value is significant in LV design.
Keywords

Subjects


[1] N. P. Zeitlin, G. R. Clements, S. J. Schaefer, M. K. Fawcett, and B. L. Brown, “NASA ground and launch systems processing technology area roadmap,” in IEEE Aerospace Conference, Big Sky, MT. USA, 2012, pp. 1–19, https://doi.org/10.1109/AERO.2012.6187395.
[2] L. Brévault, M. Balesdent, N. Bérend, and R. L. Riche, “Challenges and future trends in uncertainty-based multi-disciplinary design optimization for space transportation system design,” in 5th European Conference for Aeronautics and Space Sciences, Munich, Germany, 2013.
[3] K. Shimoyama, K. Fujii, and H. Kobayashi, “Development of a realistic optimization method for tsto space-plane multi-objective and robust optimization,” in 10th AIAA/ISSMO Multi-disciplinary Analysis and Optimization Conference, Albany, New York, 2004, p. 4475, https://doi.org/10.2514/6.2004-4475.
[4] E. C. Coşkun, “Multistage launch vehicle design with thrust profile and trajectory optimization,” Ph.D. dissertation, Middle East Technical University, Ankara, Turkey, 2014.
[5] M. Balesdent, N. Bérend, and P. Dépincé, “Stagewise multi-disciplinary design optimization formulation for optimal design of expendable launch vehicles,” Journal of Spacecraft and Rockets, vol. 49, no. 2, pp. 720-730, 2012, https://doi.org/10.2514/1.52507.
[6] G. G. Wang and S. Shan, “Review of metamodeling techniques in support of engineering design optimization,” in International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 1: 32nd Design Automation Conference, Parts A and B(ASME),Philadelphia, Pennsylvania, USA. 2006, pp. 415-426, https://doi.org/10.1115/DETC2006-99412.
[7] Z. Lukšič, J. Tanevski, S. Džeroski, and L. Todorovski, “General meta-model framework for surrogate-based numerical optimization,” in Discovery Science, A. Yamamoto, T. Kida, T. Uno, and T. Kuboyama, Eds. Springer Cham, 2017, pp. 51-66, https://doi.org/10.1007/978-3-319-67786-6_4. 
[8] C. J. Park, “Multi-disciplinary simulation for driving performance analysis of an escalator system,” Journal of Mechanical Science and Technology, vol. 32, no. 12, pp. 5615-5621, 2018, https://doi.org/10.1007/s12206-018-1107-7.
[9] Y. Cheng, S. Wang, and D. Yu, “Optimal design of parallel bionic eye mechanism,” Journal of Mechanical Science and Technology, vol. 33 no. 2, pp. 879-887, 2019, https://doi.org/10.1007/s12206-019-0145-0.
[10] H. Chen, J. Fan, S. Jing, and X. Wang, “Probabilistic design optimization of wind turbine gear transmission system based on dynamic reliability,” Journal of Mechanical Science and Technology, vol. 33 no. 2, pp. 579-589, 2019, https://doi.org/10.1007/s12206-019-0112-9.
[11] S. Wang, K. Hu, and D. Y. Li, “Optimal design method for the structural parameters of hybrid magnetic coupler,” Journal of Mechanical Science and Technology, vol. 33 no. 1, pp. 173-182, 2019, https://doi.org/10.1007/s12206-018-1217-2.
[12] M. N. Mahyari, H. Karimi, H. Naseh, and M. Mirshams, “Numerical investigation of vortex breaker effectiveness on the improvement of launch vehicle ballistic parameters,” Journal of Mechanical Science and Technology, vol. 24, no. 10, pp. 1997-2006, 2010, https://doi.org/10.1007/s12206-010-0618-7.
[13] H. R. Fazeli, H. Taei, H. Naseh, and M. Mirshams, “Multi-objective, multi-disciplinary design optimization methodology for the conceptual design of a spacecraft bipropellant propulsion system,” Journal of Structural and Multi-disciplinary Optimization, vol. 53, no. 1, pp. 145-160, 2015, https://doi.org/10.1007/s00158-015-1304-2.
[14] M. Shafaee, P. Mohammad Zadeh, A. Elkaie, and H. Fallah, “Design optimization of a thrust chamber using a mass-based model to improve the geometrical and performance parameters of low-thrust space propulsion systems,” Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, vol. 233, no. 5, pp. 1820-1837, 2018, https://doi.org/10.1177/0954410018767288.
[15] J. T. Betts, “Survey of numerical methods for trajectory optimization,” Journal of Guidance Control and Dynamics, vol. 21, no. 2, pp. 193-207, 2012, https://doi.org/10.2514/2.4231.
[16] A. Calise, S. Tandon, D. Young, and S. Kim, “Further improvements to a hybrid method for launch vehicle ascent trajectory optimization,” in 18th Applied Aerodynamics Conference, Denver, CO, USA, 2012, p. 4261, https://doi.org/10.2514/6.2000-4261.
[17] N. Yokoyama and S. Suzuki, “Modified genetic algorithm for constrained trajectory optimization,” Journal of Guidance Control and Dynamics, vol. 28, no. 1, pp. 139–144, 2012, https://doi.org/10.2514/1.3042.
[18] M. Pontani and B. A. Conway, “Particle swarm optimization applied to space trajectories,” Journal of Guidance Control and Dynamics, vol. 33, no. 5, pp. 1429–1441, 2012, https://doi.org/10.2514/1.48475.
[19] A. Joshi and B. S. Kumar, “Effect of initial flight path angle error and control constraint on the optimized ascent trajectory of a typical launch vehicle,” in 19th AIAA International Space Planes and Hypersonic Systems and Technologies Conference, Atlanta, GA, 20174, p. 2534, https://doi.org/10.2514/6.2014-2534.
[20] M. Pontani, “Particle swarm optimization of ascent trajectories of multistage launch vehicles,” Acta Astronautica, vol. 94, no. 2, pp. 852–864, 2014, https://doi.org/10.1016/j.actaastro.2013.09.013.
[21] M. V. Dileep, S. Kamath, and V. G. Nair, “Particle swarm optimization applied to ascent phase launch vehicle trajectory optimization problem,” Proceedia of Computer Science, vol. 54, pp. 516–522, 2015, https://doi.org/10.1016/j.procs.2015.06.059.
[22] X. B. Lam, “Multi-disciplinary design optimization for aircraft wing using response surface method, genetic algorithm, and simulated annealing,” Journal of Science and Technology in Civil Engineering, vol. 14, no. 1. pp. 28-41, 2020, https://doi.org/10.31814/stce.nuce2020-14(1)-03.
[23] M. N. P. Meibody, H. Naseh, and F. Ommi, “Developing a multi-objective multi-disciplinary robust design optimization framework,” Scientia Iranica, vol. 28, no. 4, pp. 2150-2163, 2020, https://doi.org/10.24200/sci.2021.55306.4159.
[24] H. R. Alimohammadi, H. Naseh, and F. Ommi, “New synthetic meta-model methodology for liquid propellant engine’s cooling system optimization,” Heat Transfer, vol. 50, no. 1, pp. 907-941, 2021, https://doi.org/10.1002/htj.21911.
[25] H. R. Alimohammadi, H. Naseh, and F. Ommi, “A novel framework for liquid propellant engine’s cooling system design by sensitivity analysis based on RSM and multi-objective optimization using PSO,” Advances in Space Research, vol. 67, no. 5, pp. 1682-1700, 2021, https://doi.org/10.1016/j.asr.2020.11.018.
[26] R. Zardashti, S.A. Saadatdar Arani, and S. M. Hosseini, “Robust Optimal Trajectory Design of a Launch Vehicle Using Particle Swarm Optimization,” Journal of Computational Methods in Engineering, Vol. 41, Issue 1, 2022, 175-192, https://doi.org/10.47176/jcme.41.1.8761.
[27] S. Swaminathan, U.P. Rajeev, and D. Ghose, “Robust Launch Vehicle Trajectory Optimization with Stage Impact and Heat Flux Constraints,” Journal of Spacecraft and Rockets, 2023, https://doi.org/10.2514/1.A35562.
[28] U. Aksen, A.R. Aslan, and U.D. Goker, “Comprehensive Six-Degrees-of-Freedom Trajectory Design and Optimization of a Launch Vehicle with a Hybrid Last Stage Using the PSO Algorithm,” Applied Sciences, vol. 14, no. 9, 2024. https://doi.org/10.3390/app14093891.
[29]  J. Ko, J. Kim, J. Choi, and J. Ahn, “Simultaneous Optimization of Launch Vehicle Stage and Trajectory Considering Flight-Requirement Constraints,” Journal of Aeronautical and Space Sciences, vol 25, 2024, pp. 1563–1573, https://doi.org/10.1007/s42405-024-00737-1.
[30] J. Philippine, A. G. D. Buttes, B. Jeanneret, R. Trigui, F. Deneve, and F. Pereyron, “Engine cooling system optimization for fuel consumption reduction,” in IEEE Vehicle Power and Propulsion Conference, Hanoi, Vietnam, 2019, https://doi.org/10.1109/VPPC46532.2019.8952496.
[31] T. Long, J. Liu, G. Gary Wang, L. Liu, R. L. Shi, and  X. Guo, “Discussion on approximate optimization strategies using design of computer experiments and meta-models for flight vehicle design,” Journal of Mechanical Engineering, vol. 52, no. 14, pp. 79–105, 2016, (in Chinese), https://doi.org/10.3901/JME.2016.14.079.
[32] M. Mirshams, J. Roshniyan, S. Yadgari Dehkordi, and A. A. Bataleblo, “Optimal multi-subject design of space carrier using genetic algorithm and modeled refrigeration algorithm and comparison of results,” in 14th International Conference of the Iranian Aerospace Association, Tehran, Iran, 2015.
[33] L. He, Launch Vehicles Design, Beijing hang kong hang tian da xue chu ban she, 2002.
[34] R. H. Myers and D. C. Montgomery, Response Surfaces Methodology: Process and Product in Optimization Using Designed Experiments, 2nd ed. New York, NY: John Wiley & Sons, Inc., 2002, pp. 303-328.
[35] R. H. Myers, D. C. Montgomery, G. Geoffrey Vining, C. M. Borror, and S. M. Kowalski, “Response surface methodology: retrospective and literature survey,” Journal of Quality Technology, vol. 36, no. 1, pp. 53–77, 2004, https://doi.org/10.1080/00224065.2004.11980252.
[36] M. Naghikhani and H. R. Ali Mohammadi, “Using response surface methodology (rsm) in optimal tolerance allocation,” Journal of Space Science and Technology, vol. 4, no. 1, pp. 61–67, 2011, https://www.jsstpub.com/article_14417.html
[37] R. H. Myers, D. C. Montgomery, and C. M. Andersson-Cook, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, 3rd ed. Hoboken, New Jersey, USA: Wiley, 2008.
[38] A. B. Ryberg, R. Domeij Bäckryd, and L. Nilsson, “Metamodel-based multi-disciplinary design optimization for automotive applications,” Engineering with Computers, vol. 31, no. 4, pp. 711-728, 2015,  https://doi.org/10.1007/s00366-014-0381-y.
Volume 18, Issue 1
2025
Pages 28-43

  • Receive Date 24 May 2024
  • Revise Date 18 February 2025
  • Accept Date 02 March 2025
  • First Publish Date 01 April 2025