Large-Scale Multidisciplinary Optimization of a Small Satellite’s Design and Operation
Abstract
The design of satellites and their operation is a complex task that involves a large number of variables and multiple engineering disciplines. Thus, it could benefit from the application of multidisciplinary design optimization, but previous efforts have been hindered by the complexity of the modeling and implementation, discontinuities in the design space, and the wide range of time scales. We address these issues by applying a new mathematical framework for gradient-based multidisciplinary optimization that automatically computes the coupled derivatives of the multidisciplinary system via a generalized form of the adjoint method. The modeled disciplines are orbit dynamics, attitude dynamics, cell illumination, temperature, solar power, energy storage, and communication. Many of these disciplines include functions with discontinuities and nonsmooth regions that are addressed to enable a numerically exact computation of the derivatives for all of the modeled variables. The wide-ranging time scales in the design problem, spanning 30 s to one year, are captured through a combination of multipoint optimization and the use of a small time step in the analyses. Optimizations involving over 25,000 design variables and 2.2 million state variables require 100 h to converge three and five orders of magnitude in optimality and feasibility, respectively. The results show that the geometric design variables yield a 40% improvement in the total data downloaded, which is the objective function, and the operational design variables yield another 40% improvement. This demonstrates not only the value in this approach for the design of satellites and their operation, but also promise for its application to the design of other large-scale engineering systems.
References
[1] , “Cubesat Investigating Atmospheric Density Response to Extreme Driving (CADRE),” Proceedings of the 25th Small Satellite Conference, Logan, UT, Aug. 2011.
[2] , “Small Satellite Structural Optimisation Using Genetic Algorithm Approach,” Proceedings of the 3rd International Conference on Recent Advances in Space Technologies, Istanbul, Turkey, 2007, pp. 398–406.
[3] , “Spacecraft Thermal Design with the Generalized Extremal Optimization Algorithm,” Inverse Problems in Science and Engineering, Vol. 15, No. 1, 2007, pp. 61–75. doi:https://doi.org/10.1080/17415970600573924
[4] , “Genetic Algorithm Based Charge Optimization of Lithium-Ion Batteries in Small Satellites,” Proceedings of the 19th Annual AIAA/USU Conference on Small Satellites, Logan, UT, Aug. 2005.
[5] , “Sizing/Optimization of a Small Satellite Energy Storage and Attitude Control System,” Journal of Spacecraft and Rockets, Vol. 44, No. 4, 2007, pp. 940–952. doi:https://doi.org/10.2514/1.25134 JSCRAG 0022-4650
[6] , “Layout Optimization of Satellite Module Using Soft Computing Techniques,” Applied Soft Computing, Vol. 8, No. 1, Jan. 2008, pp. 507–521. doi:https://doi.org/10.1016/j.asoc.2007.03.004 1568-4946
[7] , “SPIDR: Integrated Systems Engineering Design-to-Simulation Software for Satellite Build,” Proceedings of the 7th Annual Conference on Systems Engineering Research, Loughborough, England, U.K., 2009.
[8] , “Automating the Process of Optimization in Spacecraft Design,” Proceedings of the 1997 IEEE Aerospace Conference, Vol. 4, IEEE Publ., Piscataway, NJ, 1997, pp. 411–427.
[9] , “Multidisciplinary Integrated Design Assistant for Spacecraft (MIDAS),” Proceedings of the 36th Structures, Structural Dynamics, and Materials Conference, AIAA Paper 1995-1372, 1995.
[10] , “Spacecraft Design Using a Genetic Algorithm Optimization Approach,” Proceedings of the 1998 IEEE Aerospace Conference, Vol. 3, IEEE Publ., Piscataway, NJ, 1998, pp. 123–134.
[11] , “Trade Space Exploration of Satellite Datasets Using a Design by Shopping Paradigm,” Proceedings of the 2004 IEEE Aerospace Conference, Vol. 6, IEEE Publ., Piscataway, NJ, 2004, pp. 3885–3895.
[12] , “Multidisciplinary Design of a Small Satellite Launch Vehicle Using Particle Swarm Optimization,” Structural and Multidisciplinary Optimization, Vol. 44, No. 6, 2011, pp. 773–784. doi:https://doi.org/10.1007/s00158-011-0662-7 1615-147X
[13] , “Collaborative Optimization of Remote Sensing Small Satellite Mission Using Genetic Algorithms,” Iranian Journal of Science and Technology—Transactions of Mechanical Engineering, Vol. 36, No. 2, 2012, pp. 117–128.
[14] , “Satellite Multidisciplinary Design Optimization with a High-Fidelity Model,” Journal of Spacecraft and Rockets, Vol. 50, No. 2, 2013, pp. 463–466. doi:https://doi.org/10.2514/1.A32309 JSCRAG 0022-4650
[15] , “Development and Application of the Collaborative Optimization Architecture in a Multidisciplinary Design Environment,” Multidisciplinary Design Optimization: State of the Art, edited by Alexandrov N. and Hussaini M. Y., Society for Industrial and Applied Mathematics, Philadelphia, 1997, pp. 98–116.
[16] , “Multidisciplinary Design Optimization: A Survey of Architectures,” AIAA Journal, Vol. 51, No. 9, 2013, pp. 2049–2075. doi:https://doi.org/10.2514/1.J051895 AIAJAH 0001-1452
[17] , “Extensions to the Design Structure Matrix for the Description of Multidisciplinary Design, Analysis, and Optimization Processes,” Structural and Multidisciplinary Optimization, Vol. 46, No. 2, Aug. 2012, pp. 273–284. doi:https://doi.org/10.1007/s00158-012-0763-y 1615-147X
[18] , “pyOpt: A Python-Based Object-Oriented Framework for Nonlinear Constrained Optimization,” Structural and Multidisciplinary Optimization, Vol. 45, No. 1, Jan. 2012, pp. 101–118. doi:https://doi.org/10.1007/s00158-011-0666-3 1615-147X
[19] , “Review and Unification of Methods for Computing Derivatives of Multidisciplinary Computational Models,” AIAA Journal, Vol. 51, No. 11, 2013, pp. 2582–2599. doi:https://doi.org/10.2514/1.J052184 AIAJAH 0001-1452
[20] , “Aerodynamic Design via Control Theory,” Journal of Scientific Computing, Vol. 3, No. 3, 1988, pp. 233–260. doi:https://doi.org/10.1007/BF01061285 JSCOEB 0885-7474
[21] , “Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers, Part 1,” Journal of Aircraft, Vol. 36, No. 1, 1999, pp. 51–60. doi:https://doi.org/10.2514/2.2413 JAIRAM 0021-8669
[22] , “Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers, Part 2,” Journal of Aircraft, Vol. 36, No. 1, 1999, pp. 61–74. doi:https://doi.org/10.2514/2.2414 JAIRAM 0021-8669
[23] , “Aerodynamic Shape Optimization of a Blended-Wing-Body Aircraft,” 51st AIAA Aerospace Sciences Meeting, AIAA Paper 2013-0283, Jan. 2013.
[24] , “A Coupled-Adjoint Sensitivity Analysis Method for High-Fidelity Aero-Structural Design,” Optimization and Engineering, Vol. 6, No. 1, 2005, pp. 33–62. doi:https://doi.org/10.1023/B:OPTE.0000048536.47956.62 OEPNBR 1389-4420
[25] , “A Scalable Parallel Approach for High-Fidelity Steady-State Aeroelastic Analysis and Derivative Computations,” AIAA Journal (to be published). doi:https://doi.org/10.2514/1.J052255 AIAJAH 0001-1452
[26] , “SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization,” SIAM Journal on Optimization, Vol. 12, No. 4, 2002, pp. 979–1006. doi:https://doi.org/10.1137/S1052623499350013 SJOPE8 1095-7189
[27] , “Large-Scale MDO of a Small Satellite Using a Novel Framework for the Solution of Coupled Systems and their Derivatives,” 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, AIAA Paper 2013-1599, April 2013.
[28] , “The Complex-Step Derivative Approximation,” ACM Transactions on Mathematical Software, Vol. 29, No. 3, 2003, pp. 245–262. doi:https://doi.org/10.1145/838250.838251 ACMSCU 0098-3500
[29] , “Systematic Control Design by Optimizing a Vector Performance Index,” Proceedings of the International Federation of Active Controls Symposium on Computer-Aided Design of Control Systems, Zurich, Switzerland, 1979, pp. 113–117.
[30] , “An Adaptive Approach to Constraint Aggregation Using Adjoint Sensitivity Analysis,” Structural and Multidisciplinary Optimization, Vol. 34, No. 1, 2007, pp. 61–73. doi:https://doi.org/10.1007/s00158-006-0061-7 1615-147X
[31] , “Multi-Point High-Fidelity Aerostructural Optimization of a Transport Aircraft Configuration,” Journal of Aircraft, Vol. 51, No. 1, 2014, pp. 144–160. doi:https://doi.org/10.2514/1.C032150 JAIRAM 0021-8669
[32] , “A Comparison of Metallic and Composite Aircraft Wings Using Aerostructural Design Optimization,” 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA Paper 2012-5475, Sept. 2012.
[33] , “Simulation of I-V Characteristics of a PV Module with Shaded PV Cells,” Solar Energy Materials & Solar Cells, Vol. 75, Nos. 3–4, 2003, pp. 613–621. doi:https://doi.org/10.1016/S0927-0248(02)00134-4 0927-0248
[34] , Space Mission Analysis and Design, Kluwer Academic, Norwell, MA, Jan. 1991, pp. 550–558.
[35] , “Simultaneous Analysis and Design,” AIAA Journal, Vol. 23, No. 7, 1985, pp. 1099–1103. doi:https://doi.org/10.2514/3.9043 AIAJAH 0001-1452
[36] , “SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization,” SIAM Review, Vol. 47, No. 1, 2005, pp. 99–131. doi:https://doi.org/10.1137/S0036144504446096 SIREAD 0036-1445
[37] , “Standard Platform for Benchmarking Multidisciplinary Design Analysis and Optimization Architectures,” AIAA Journal, Vol. 51, No. 10, 2013, pp. 2380–2394. doi:https://doi.org/10.2514/1.J052160 AIAJAH 0001-1452