Skip to main content
SpringerLink
Log in

Evidence-Based Robust Optimization of Pulsed Laser Orbital Debris Removal Under Epistemic Uncertainty

  • Chapter
  • First Online:
Modeling and Optimization in Space Engineering

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 144))

Abstract

An evidence-based robust optimization method for pulsed laser orbital debris removal (LODR) is presented. Epistemic type uncertainties due to limited knowledge are considered. The objective of the design optimization is set to minimize the debris lifetime while at the same time maximizing the corresponding belief value. The Dempster–Shafer theory of evidence (DST), which merges interval-based and probabilistic uncertainty modeling, is used to model and compute the uncertainty impacts. A Kriging based surrogate is used to reduce the cost due to the expensive numerical life prediction model. Effectiveness of the proposed method is illustrated by a set of benchmark problems. Based on the method, a numerical simulation of the removal of Iridium 33 with pulsed lasers is presented, and the most robust solutions with minimum lifetime under uncertainty are identified using the proposed method.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 129.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Program code of POD-MOO and experimental simulations of the bi-objective and three objective benchmarks are available at https://sites.google.com/site/adloptimization/moo-with-principle-component-analysis.

  2. 2.

    Part of program code of the robust POD-MOO and numerical simulation of LODR are available at https://sites.google.com/site/adloptimization.

References

  1. Agarwal, H., Renaud, J.E., Preston, E.L., Padmanabhan, D.: Uncertainty quantification using evidence theory in multidisciplinary design optimization. Reliab. Eng. Syst. Saf. 85(1), 281–294 (2004)

    Article  Google Scholar 

  2. Asafuddoula, M., Ray, T., Sarker, R.: A decomposition-based evolutionary algorithm for many objective optimization. IEEE Trans. Evol. Comput. 19(3), 445–460 (2015)

    Article  Google Scholar 

  3. Auer, E., Luther, W., Rebner, G., Limbourg, P.: A verified Matlab toolbox for the Dempster-Shafer theory. In: Workshop on the Theory of Belief Functions (2010)

    Google Scholar 

  4. Balakrishnan, N.: Continuous Multivariate Distributions. Wiley, London (2006)

    Google Scholar 

  5. Couckuyt, I., Dhaene, T., Demeester, P.: ooDACE toolbox: a flexible object-oriented Kriging implementation. J. Mach. Learn. Res. 15, 3183–3186 (2014)

    Google Scholar 

  6. Croisard, N., Vasile, M., Kemble, S., Radice, G.: Preliminary space mission design under uncertainty. Acta Astronaut. 66(5), 654–664 (2010)

    Article  Google Scholar 

  7. Deb, K.: Multi-objective optimization. In: Search Methodologies, pp. 403–449. Springer, Berlin (2014)

    Google Scholar 

  8. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)

    Article  Google Scholar 

  9. Forrester, A., Keane, A., et al.: Engineering Design via Surrogate Modelling: A Practical Guide. Wiley, London (2008)

    Book  Google Scholar 

  10. Hou, L., Pirzada, A., Cai, Y., Ma, H.: Robust design optimization using integrated evidence computationłwith application to orbital debris removal. In: 2015 IEEE Congress on Evolutionary Computation (CEC), pp. 3263–3270. IEEE, Piscataway (2015)

    Google Scholar 

  11. Hou, L., Tan, W., Ma, H.: Multi-fidelity design optimization under epistemic uncertainty. In: 2016 IEEE Congress on Evolutionary Computation (CEC), pp. 4452–4459. IEEE, Piscataway (2016)

    Google Scholar 

  12. Kelso, T., et al.: Analysis of the iridium 33-cosmos 2251 collision. Adv. Astronaut. Sci. 135(2), 1099–1112 (2009)

    Google Scholar 

  13. Liedahl, D., Rubenchik, A., Libby, S.B., Nikolaev, S., Phipps, C.R.: Pulsed laser interactions with space debris: target shape effects. Adv. Space Res. 52(5), 895–915 (2013)

    Article  Google Scholar 

  14. Mason, J., Stupl, J., Marshall, W., Levit, C.: Orbital debris–debris collision avoidance. Adv. Space Res. 48(10), 1643–1655 (2011)

    Article  Google Scholar 

  15. Moon, T.K., Stirling, W.C.: Mathematical Methods and Algorithms for Signal Processing, vol. 1. Prentice Hall, New York (2000)

    Google Scholar 

  16. Phipps, C., Albrecht, G., Friedman, H., Gavel, D., George, E., Murray, J., Ho, C., Priedhorsky, W., Michaelis, M., Reilly, J.: Orion: Clearing near-earth space debris using a 20-kw, 530-nm, earth-based, repetitively pulsed laser. Laser Part. Beams 14(1), 1–44 (1996)

    Article  Google Scholar 

  17. Phipps, C.R., Baker, K.L., Libby, S.B., Liedahl, D.A., Olivier, S.S., Pleasance, L.D., Rubenchik, A., Trebes, J.E., George, E.V., Marcovici, B., et al.: Removing orbital debris with lasers. Adv. Space Res. 49(9), 1283–1300 (2012)

    Article  Google Scholar 

  18. Rebner, G., Auer, E., Luther, W.: A verified realization of a Dempster–Shafer based fault tree analysis. Computing 94(2), 313–324 (2012)

    Article  MathSciNet  Google Scholar 

  19. Roy, A.E.: Orbital Motion. CRC Press, West Palm Beach (2004)

    Book  Google Scholar 

  20. Schall, W.O.: Laser radiation for cleaning space debris from lower earth orbits. J. Spacecr. Rocket. 39(1), 81–91 (2002)

    Article  MathSciNet  Google Scholar 

  21. Vasile, M.: Robust mission design through evidence theory and multiagent collaborative search. Ann. N. Y. Acad. Sci. 1065(1), 152–173 (2005)

    Article  Google Scholar 

  22. Vasile, M.: A behavioral-based meta-heuristic for robust global trajectory optimization. In: IEEE Congress on Evolutionary Computation, CEC 2007, pp. 2056–2063. IEEE, Piscataway (2007)

    Google Scholar 

  23. Volkwein, S.: Proper Orthogonal Decomposition: Theory and Reduced-Order Modelling. Lecture Notes. vol. 4(4). University of Konstanz, Konstanz (2013)

    Google Scholar 

  24. Xiao, D., Fang, F., Buchan, A.G., Pain, C.C., Navon, I.M., Du, J., Hu, G.: Non-linear model reduction for the Navier–Stokes equations using residual DEIM method. J. Comput. Phys. 263, 1–18 (2014)

    Article  MathSciNet  Google Scholar 

  25. Xie, D., Xu, M., Dowell, E.H.: Proper orthogonal decomposition reduced-order model for nonlinear aeroelastic oscillations. AIAA J. 52(2), 229–241 (2014)

    Article  Google Scholar 

  26. Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)

    Article  Google Scholar 

  27. Zuiani, F., Vasile, M., Gibbings, A.: Evidence-based robust design of deflection actions for near earth objects. Celest. Mech. Dyn. Astron. 114, 107–136 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Xian Satellite Control Center, Xian, China

    Liqiang Hou

  2. Department of Mechanical and Aerospace Engineering, University of Strathclyde, Glasgow, UK

    Massimiliano Vasile

  3. School of Information and Communication Engineering, Beijing University of Posts and Telecommunications, Beijing, China

    Zhaohui Hou

Authors
  1. Liqiang Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Massimiliano Vasile
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhaohui Hou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Liqiang Hou .

Editor information

Editors and Affiliations

  1. Thales Alenia Space, Turin, Italy

    Giorgio Fasano

  2. Department of Industrial and Systems Engineering, Lehigh University , Bethlehem, PA, USA

    János D. Pintér

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Hou, L., Vasile, M., Hou, Z. (2019). Evidence-Based Robust Optimization of Pulsed Laser Orbital Debris Removal Under Epistemic Uncertainty. In: Fasano, G., Pintér, J. (eds) Modeling and Optimization in Space Engineering . Springer Optimization and Its Applications, vol 144. Springer, Cham. https://doi.org/10.1007/978-3-030-10501-3_7

Download citation

Publish with us

Policies and ethics

Search

Navigation