Abstract
Space launcher complexity arises, on the one hand, from the coupling between several subsystems such as stages or boosters and other embedded systems, and on the other hand, from the physical phenomena endured during the flight. Optimal trajectory assessment is a key discipline since it is one of the cornerstones of the mission success. However, during the real flight, uncertainties can affect the different flight phases at different levels and be combined to lead to a failure state of the space vehicle trajectory. After their propelled phase, the different stages reach successively their separation altitudes and may fall back into the ocean. Such a dynamic phase is of major importance in terms of launcher safety since the consequence of a mistake in the prediction of the fallout zone can be dramatic in terms of human security and environmental impact. For that reason, the handling of uncertainties plays a crucial role in the comprehension and prediction of the global system behavior. Consequently, it is of major concern to take them into account during the reliability analysis. In this book chapter, two new sensitivity analysis techniques are considered to characterize the system uncertainties and optimize its reliability.
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References
Beer, M., Ferson, S., Kreinovich, V.: Imprecise probabilities in engineering structures. Mech. Syst. Signal Process. 37, 4–29 (2013)
Bilal, N.: Implementation of Sobol’s method of global sensitivity analysis to a compressor simulation model. In: Proc. of the 22nd International Compressor Engineering Conference, Purdue (2014)
Borgonovo, E.: Measuring uncertainty importance: investigation and comparison of alternative approaches. Risk Anal. 26(5), 1349–1361 (2006)
Borgonovo, E.: A new uncertainty importance measure. Reliab. Eng. Syst. Saf. 92(6), 771–784 (2007)
Borgonovo, E., Plischke, E.: Sensitivity analysis: a review of recent advances. Eur. J. Oper. Res. 248(3), 869–887 (2016)
Botev, Z.I., Grotowski, J.F., Kroese, D.P.: Kernel density estimation via diffusion. Ann. Stat. 38(5), 2916–2957 (2010)
Bourinet, J.M.: Rare-event probability estimation with adaptive support vector regression surrogates. Reliab. Eng. Syst. Saf. 150, 210–221 (2016)
Bourinet, J.M.: FORM sensitivities to distribution parameters with the Nataf transformation. In: Gardoni, P. (ed.) Risk and Reliability Analysis: Theory and Applications. In Honor of Prof. Armen Der Kiureghian, Springer Series in Reliability Engineering, pp. 277–302. Springer International Publishing, Cham (2017)
Bucklew, J.A.: Introduction to Rare Event Simulation. Springer, New York (2004)
Chabridon, V., Balesdent, M., Bourinet, J.M., Morio, J., Gayton, N.: Evaluation of failure probability under parameter epistemic uncertainty: application to aerospace system reliability assessment. Aerosp. Sci. Technol. 69, 526–537 (2017)
Chabridon, V., Balesdent, M., Bourinet, J.M., Morio, J., Gayton, N.: Reliability-based sensitivity analysis of aerospace systems under distribution parameter uncertainty using an augmented approach. In: Proc. of the 12th International Conference on Structural Safety and Reliability (ICOSSAR’17), Vienna (2017)
Chabridon, V., Balesdent, M., Bourinet, J.M., Morio, J., Gayton, N.: Reliability-based sensitivity estimators of rare event probability in the presence of distribution parameter uncertainty. Reliab. Eng. Syst. Saf. 178, 164–178 (2018)
Der Kiureghian, A.: Measures of structural safety under imperfect states of knowledge. J. Struct. Eng. ASCE 115(5), 1119–1140 (1989)
Der Kiureghian, A.: Analysis of structural reliability under parameter uncertainties. Probab. Eng. Mech. 23(4), 351–358 (2008)
Der Kiureghian, A., Dakessian, T.: Multiple design points in first and second-order reliability. Struct. Saf. 20, 37–49 (1998)
Derennes, P., Morio, J., Simatos, F.: A nonparametric importance sampling estimator for moment independent importance measures. Reliab. Eng. Syst. Saf. (2018). https://doi.org/10.1016/j.ress.2018.02.009
Devroye, L., Gyorfi, L.: Nonparametric Density Estimation: The L1 View. Wiley, New York (1985)
Ditlevsen, O.: Generalized second moment reliability index. J. Struct. Mech. 7(4), 435–451 (1979)
Ditlevsen, O., Madsen, H.O.: Structural Reliability Methods, Internet ed. 2.3.7. Technical University of Denmark, Lyngby (2007)
Dubourg, V.: Adaptive surrogate models for reliability analysis and reliability-based design optimization. Ph.D. thesis, Université Blaise Pascal – Clermont II (2011)
Homma, T., Saltelli, A.: Importance measures in global sensitivity analysis of nonlinear models. Reliab. Eng. Syst. Saf. 52(1), 1–17 (1996)
Hoogendoorn, R., Mooij, E., Geul, J.: Uncertainty propagation for statistical impact prediction of space debris. Adv. Space Res. 61(1), 167–181 (2018)
Hurtado, J.E.: Structural Reliability: Statistical Learning Perspectives. Lecture Notes in Applied and Computational Mechanics. Springer, Berlin (2004)
Iooss, B., Lemaître, P.: A review on global sensitivity analysis methods. In: Dellino, G., Meloni, C. (eds.) Uncertainty Management in Simulation-Optimization of Complex Systems: Algorithms and Applications, chap. 5, pp. 101–122. Springer, Boston (2015)
Iooss, B., Lemaître, P.: A review on global sensitivity analysis methods. In: Uncertainty Management in Simulation-Optimization of Complex Systems, pp. 101–122. Springer, Berlin (2015)
Lebrun, R., Dutfoy, A.: Do Rosenblatt and Nataf isoprobabilistic transformations really differ? Probab. Eng. Mech. 24, 577–584 (2009)
Lemaire, M.: Structural Reliability. ISTE Ltd, London; Wiley, Hoboken (2009)
Lemaître, P., Sergienko, E., Arnaud, A., Bousquet, N., Gamboa, F., Iooss, B.: Density modification-based reliability sensitivity analysis. J. Stat. Comput. Simul. 85(6), 1200–1223 (2015)
Limbourg, P., De Rocquigny, E., Andrianov, G.: Accelerated uncertainty propagation in two-level probabilistic studies under monotony. Reliab. Eng. Syst. Saf. 95, 998–1010 (2010)
Millwater, H.R.: Universal properties of kernel functions for probabilistic sensitivity analysis. Probab. Eng. Mech. 24, 89–99 (2009)
Morio, J., Balesdent, M.: Estimation of Rare Event Probabilities in Complex Aerospace and Other Systems: A Practical Approach. Woodhead Publishing, Elsevier, Cambridge (2015)
Pasanisi, A., De Rocquigny, E., Bousquet, N., Parent, E.: Some useful features of the Bayesian setting while dealing with uncertainties in industrial practice. In: Proc. of the 19th European Safety and Reliability Conference (ESREL), Prague (2009)
Pasanisi, A., Keller, M., Parent, E.: Estimation of a quantity of interest in uncertainty analysis: some help from Bayesian decision theory. Reliab. Eng. Syst. Saf. 100, 93–101 (2012)
Ridolfi, G., Mooij, E.: Regression-Based Sensitivity Analysis and Robust Design, pp. 303–336. Springer International Publishing, Cham (2016)
Ronse, A., Mooij, E.: Statistical impact prediction of decaying objects. J. Spacecr. Rocket. 51(6), 1797–1810 (2014)
Rosenblatt, M.: Remarks on a multivariate transformation. Ann. Math. Stat. 23(3), 470–472 (1952)
Rubino, G., Tuffin, B.: Rare Event Simulation Using Monte Carlo Methods. Wiley, New York (2009)
Rubinstein, R.Y., Kroese, D.P.: Simulation and the Monte Carlo Method, 2nd edn. Wiley, New York (2008)
Sankararaman, S., Mahadevan, S.: Integration of model verification, validation, and calibration for uncertainty quantification in engineering systems. Reliab. Eng. Syst. Saf. 138, 194–209 (2014)
Sobol, I.M.: Sensitivity estimates for nonlinear mathematical models. Math. Model. Comput. Experiments 1(4), 407–414 (1993)
Sobol, I.M.: A Primer for the Monte Carlo Method. CRC Press, Boca Raton (1994)
Soize, C.: Uncertainty Quantification: An Accelerated Course with Advanced Applications in Computational Engineering. Interdisciplinary Applied Mathematics. Springer International Publishing, Cham (2017)
Sudret, B.: Uncertainty propagation and sensitivity analysis in mechanical models – Contributions to structural reliability and stochastic spectral methods. Habilitation à Diriger des Recherches, Université Blaise Pascal – Clermont II (2007)
Tokdar, S.T., Kass, R.E.: Importance sampling: a review. Wiley Interdiscip. Rev. Comput. Stat. 2(1), 54–60 (2009)
Zhang, P.: Nonparametric importance sampling. J. Am. Stat. Assoc. 91(435), 1245–1253 (1996)
Acknowledgements
The first and second author contributed equally to this work. The first two authors are currently enrolled in a PhD program, respectively, funded by Université Toulouse III—Paul Sabatier and co-funded by ONERA—The French Aerospace Lab and SIGMA Clermont. Their financial supports are gratefully acknowledged. The authors would like to thank Dr. Loïc Brevault (Research scientist at ONERA—The French Aerospace Lab) for having provided the launch vehicle fallout zone estimation code.
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Derennes, P. et al. (2019). Nonparametric Importance Sampling Techniques for Sensitivity Analysis and Reliability Assessment of a Launcher Stage Fallout. 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_3
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