Abstract
This chapter presents the design of a space mission at a preliminary stage, when uncertainties are high. At this particular stage, an insufficient consideration for uncertainty could lead to a wrong decision on the feasibility of the mission. Contrary to the traditional margin approach, the methodology presented here explicitly introduces uncertainties in the design process. The overall system design is then optimised, minimising the impact of uncertainties on the optimal value of the design criteria. Evidence Theory, used as the framework to model uncertainties, is presented in details. Although its use in the design process would greatly improve the quality of the design, it increases significantly the computational cost of any multidisciplinary optimisation. Therefore, two approaches to tackle an Optimisation Problem Under Uncertainties are proposed: (a) a direct solution through a multi-objective optimisation algorithm and (b) an indirect solution through a clustering algorithm. Both methods are presented, highlighting the techniques used to reduce the computational time. It will be shown in particular that the indirect method is an attractive alternative when the complexity of the problem increases.
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References
Agarwal, H., Renaud, J.E., Preston, E.L.: Trust region managed reliability based design optimization using evidence theory. In: Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, vol. 5, pp. 3449–3463 (2003)
Agarwal, H., Renaud, J.E., Preston, E.L., Padmanabhan, D.: Uncertainty quantification using evidence theory in multidisciplinary design optimization. Reliability Engineering and System Safety 85(1-3), 281–294 (2004)
Bae, H.R., Grandhi, R.V., Canfield, R.A.: Uncertainty quantification of structural response using evidence theory. In: Collection of Technical Papers - AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, vol. 4, pp. 2135–2145 (2002)
Bauer, M.: Approximation algorithms and decision making in the dempster-shafer theory of evidence - an empirical study. International Journal of Approximate Reasoning 17( 2-3), 217–237 (1997)
Bunday, B.D.: Basic Linear programming. Hodder Arnold (1984)
Dantzig, G.B.: Linear Programming and Extensions. Princeton University Press, Princeton (1965)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: Nsga-ii. IEEE Transactions on Evolutionary Computation 6( 2), 182–197 (2002)
Dempster, A.P.: New methods for reasoning towards posterior distributions based on sample data. The Annals of Mathematical Statistics 37(2), 355–374 (1966)
Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. Ann. Math. Statist. 38, 325–339 (1967)
Du, X., Wang, Y., Chen, W.: Methods for robust multidisciplinary design. In: AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference and Exhibit, 41st, Atlanta, GA, no. 1785 in AIAA 2000 (2000)
Dubois, D., Prade, H.: Fuzzy sets, probability and measurement. European Journal of Operational Research 40(2), 135–154 (1989)
Ferson, S., Nelsen, R.B., Hajagos, J., Berleant, D.J., Zhang, J., Tucker, W.T., Ginzburg, L.R., Oberkampf, W.L.: Dependence in probabilistic modeling, dempster-shafer theory, and probability bounds analysis. Tech. Rep. SAND2004-3072, Sandia National Laboratories (2004)
Hayes, B.: A lucid intervals. American Scientist 91(6), 484–488 (2003)
Helton, J.C.: Uncertainty and sensitivity analysis in the presence of stochastic and subjective uncertainty. Journal of Statistical Computation and Simulation 57, 3–76 (1997)
Helton, J.C., Johnson, J., Oberkampf, W.L., Storlie, C.: A sampling-based computational strategy for the representation of epistemic uncertainty in model predictions with evidence theory. Computer Methods in Applied Mechanics and Engineering 196(37-40 SPEC ISS), 3980–3998 (2007)
Hoffman, F.O., Hammonds, J.S.: Propagation of uncertainty in risk assessments: The need to distinguish between uncertainty due to lack of knowledge and uncertainty due to variability. Risk Analysis 14(5), 707–712 (1994)
Kemble, S.: Interplanetary Mission Analysis and Design. Springer Praxis Books, Heidelberg (2006)
Klir, G.J., Smith, R.M.: On measuring uncertainty and uncertainty-based information: Recent developments. Annals of Mathematics and Artificial Intelligence 32(1-4), 5–33 (2001)
Kreinovich, V., Xiang, G., Starks, S.A., Longpré, L., Ceberio, M., Araiza, R., Beck, J., Kandathi, R., Nayak, A., Torres, R., Hajagos, J.G.: Towards combining probabilistic and interval uncertainty in engineering calculations: Algorithms for computing statistics under interval uncertainty, and their computational complexity. Reliable Computing 12, 471–501 (2006)
Limbourg, P.: Multi-objective optimization of problems with epistemic uncertainty. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 413–427. Springer, Heidelberg (2005)
Lophaven, S.N., Nielsen, H.B., Sondergaard, J.: DACE: a MatLab kriging toolbox. Tech. Rep. IMM-TR-2002-12, Technical University of Denmark (2002)
Neumaier, A.: Clouds, fuzzy sets, and probability intervals. Reliable Computing 10(4), 249–272 (2004)
Oberkampf, W., Helton, J.C.: Investigation of evidence theory for engineering applications. In: 4th Non-Deterministic Approaches Forum, AIAA, vol. 1569 (2002)
Pate-Cornell, M.E.: Uncertainties in risk analysis: Six levels of treatment. Reliability Engineering and System Safety 54, 95–111 (1996)
Shafer, G.: A Mathematical Theory of Evidence. Princeton University Press, Princeton (1976)
Smarandache, F., Dezert, J.: An introduction to the DSm theory for the combination of paradoxical, uncertain and imprecise sources of information. In: 13th International Congress of Cybernetics and Systems (2005)
Tessem, B.: Approximations for efficient computation in the theory of evidence. Artif. Intell. 61(2), 315–329 (1993)
Vasile, M.: Robust mission design through evidence theory and multiagent collaborative search. Annals of the New York Academy of Sciences 1065, 152–173 (2005)
Zadeh, L.A.: Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 100(suppl. 1), 9–34 (1999)
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Vasile, M., Croisard, N. (2010). Robust Preliminary Space Mission Design under Uncertainty. In: Tenne, Y., Goh, CK. (eds) Computational Intelligence in Expensive Optimization Problems. Adaptation Learning and Optimization, vol 2. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-10701-6_21
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