# Stochastic Inverse Problem with Noisy Simulator. Application to aeronautical model

Nabil Rachdi^{[1]}; Jean-Claude Fort^{[2]}; Thierry Klein^{[3]}

- [1] Institut de Mathématiques de Toulouse - EADS Innovation Works, 12 rue Pasteur, 92152 Suresnes
- [2] MAP5, Université Paris Descartes SPC, 45 rue des saints pères, 75006 Paris
- [3] Institut de Mathématiques de Toulouse, 118 route de Narbonne F-31062 Toulouse

Annales de la faculté des sciences de Toulouse Mathématiques (2012)

- Volume: 21, Issue: 3, page 593-622
- ISSN: 0240-2963

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topRachdi, Nabil, Fort, Jean-Claude, and Klein, Thierry. "Stochastic Inverse Problem with Noisy Simulator. Application to aeronautical model." Annales de la faculté des sciences de Toulouse Mathématiques 21.3 (2012): 593-622. <http://eudml.org/doc/251013>.

@article{Rachdi2012,

abstract = {Inverse problem is a current practice in engineering where the goal is to identify parameters from observed data through numerical models. These numerical models, also called Simulators, are built to represent the phenomenon making possible the inference. However, such representation can include some part of variability or commonly called uncertainty (see [4]), arising from some variables of the model. The phenomenon we study is the fuel mass needed to link two given countries with a commercial aircraft, where we only consider the Cruise phase.From a data base of fuel mass consumptions during the cruise phase, we aim at identifying the Specific Fuel Consumption ($SFC$) in a robust way, given the uncertainty of the cruise speed$V$ and the lift-to-drag ratio$F$.In this paper, we present an estimation procedure based on Maximum-Likelihood estimation, taking into account this uncertainty.},

affiliation = {Institut de Mathématiques de Toulouse - EADS Innovation Works, 12 rue Pasteur, 92152 Suresnes; MAP5, Université Paris Descartes SPC, 45 rue des saints pères, 75006 Paris; Institut de Mathématiques de Toulouse, 118 route de Narbonne F-31062 Toulouse},

author = {Rachdi, Nabil, Fort, Jean-Claude, Klein, Thierry},

journal = {Annales de la faculté des sciences de Toulouse Mathématiques},

keywords = {inverse problem; parameter identification from observed data; numerical models; maximum-likelihood estimation},

language = {eng},

month = {4},

number = {3},

pages = {593-622},

publisher = {Université Paul Sabatier, Toulouse},

title = {Stochastic Inverse Problem with Noisy Simulator. Application to aeronautical model},

url = {http://eudml.org/doc/251013},

volume = {21},

year = {2012},

}

TY - JOUR

AU - Rachdi, Nabil

AU - Fort, Jean-Claude

AU - Klein, Thierry

TI - Stochastic Inverse Problem with Noisy Simulator. Application to aeronautical model

JO - Annales de la faculté des sciences de Toulouse Mathématiques

DA - 2012/4//

PB - Université Paul Sabatier, Toulouse

VL - 21

IS - 3

SP - 593

EP - 622

AB - Inverse problem is a current practice in engineering where the goal is to identify parameters from observed data through numerical models. These numerical models, also called Simulators, are built to represent the phenomenon making possible the inference. However, such representation can include some part of variability or commonly called uncertainty (see [4]), arising from some variables of the model. The phenomenon we study is the fuel mass needed to link two given countries with a commercial aircraft, where we only consider the Cruise phase.From a data base of fuel mass consumptions during the cruise phase, we aim at identifying the Specific Fuel Consumption ($SFC$) in a robust way, given the uncertainty of the cruise speed$V$ and the lift-to-drag ratio$F$.In this paper, we present an estimation procedure based on Maximum-Likelihood estimation, taking into account this uncertainty.

LA - eng

KW - inverse problem; parameter identification from observed data; numerical models; maximum-likelihood estimation

UR - http://eudml.org/doc/251013

ER -

## References

top- Barbillon (P.).— Méthodes d’interpolation à noyaux pour l’approximation de fonctions type boîte noire coûteuses. Thèse de doctorat, Université de Paris-Sud (2010).
- Billingsley (P.).— Convergence of probability measures. Wiley New York (1968). Zbl0944.60003MR233396
- De Rocquigny (E.) and Cambier (S.).— Inverse probabilistic modelling of the sources of uncertainty: a non-parametric simulated-likelihood method with application to an industrial turbine vibration assessment. Inverse Problems in Science and Engineering, 17(7), p. 937-959 (2009). Zbl1202.74207
- de Rocquigny (E.), Devictor (N.) and Tarantola (S.) editors.— Uncertainty in industrial practice. John Wiley. Zbl1161.90001
- Kuhn (E.).— Estimation par maximum de vraisemblance dans des problèmes inverses non linéaires. Thèse de doctorat, Université de Paris-Sud (2003).
- Ledoux (N.).— The concentration of measure phenomenon. AMS (2001). Zbl0995.60002
- Rachdi (N.), Fort (J.C.) and Klein (T.).— Risk bounds for new M-estimation problems. http://hal.archives-ouvertes.fr/hal-00537236_v2/ (submitted) (2012).
- Talagrand (M.).— Sharper bounds for Gaussian and empirical processes. The Annals of Probability, 22(1), p. 28-76 (1994). Zbl0798.60051MR1258865
- van der Vaart (A.W.).— Asymptotic statistics. Cambridge University Press (2000). Zbl0910.62001
- van der Vaart (A.W.) and Wellner (J.A.).— Weak Convergence and Empirical Processes. Springer Series in Statistics (1996). Zbl0862.60002MR1385671
- Wiener (N.).— The homogeneous chaos. American Journal of Mathematics, 60(4), p. 897-936 (1938). Zbl0019.35406MR1507356

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