A robust optimization methodology for preliminary aircraft design

This article focuses on a robust optimization of an aircraft preliminary design under operational constraints. According to engineers' know-how, the aircraft preliminary design problem can be modelled as an uncertain optimization problem whose objective (the cost or the fuel consumption) is almost affine, and whose constraints are convex. It is shown that this uncertain optimization problem can be approximated in a conservative manner by an uncertain linear optimization program, which enables the use of the techniques of robust linear programming of Ben-Tal, El Ghaoui, and Nemirovski [Robust Optimization, Princeton University Press, 2009]. This methodology is then applied to two real cases of aircraft design and numerical results are presented.

[1]  Xiaoping Du,et al.  The use of metamodeling techniques for optimization under uncertainty , 2001 .

[2]  Tae Won Lee,et al.  A Reliability-Based Optimal Design Using Advanced First Order Second Moment Method , 1987 .

[3]  Max Henrion,et al.  Uncertainty: A Guide to Dealing with Uncertainty in Quantitative Risk and Policy Analysis , 1990 .

[4]  A. L. Tits,et al.  User's Guide for FSQP Version 3.0c: A FORTRAN Code for Solving Constrained Nonlinear (Minimax) Optimization Problems, Generating Iterates Satisfying All Inequality and Linear Constraints , 1992 .

[5]  Mattia Padulo,et al.  A MinMax Framework for Robust Design Optimization , 2013 .

[6]  Charles Annis,et al.  Statistical Distributions in Engineering , 2001, Technometrics.

[7]  Narendra Karmarkar,et al.  A new polynomial-time algorithm for linear programming , 1984, Comb..

[8]  Marin D. Guenov,et al.  Comparative Analysis of Uncertainty Propagation Methods for Robust Engineering Design , 2007 .

[9]  Marin D. Guenov,et al.  Novel Uncertainty Propagation Method for Robust Aerodynamic Design , 2011 .

[10]  J. Frédéric Bonnans,et al.  Numerical Optimization: Theoretical and Practical Aspects (Universitext) , 2006 .

[11]  Cécile Badufle.  Définition conceptuelle d'avions : vers une optimisation multiobjet, robuste et incertaine , 2007 .

[12]  Arkadi Nemirovski,et al.  Lectures on modern convex optimization - analysis, algorithms, and engineering applications , 2001, MPS-SIAM series on optimization.

[13]  Praveen Chandrashekarappa,et al.  Uncertainty Quantification for Robust Design , 2013 .

[14]  Joël Clément.  Optimisation multidisciplinaire : étude théorique et application à la conception des avions en phase d'avant projet , 2009 .

[15]  Aude Rondepierre,et al.  Chance constrained business case of a three-engines hybrid aircraft , 2013 .

[16]  Bernhard Sendhoff,et al.  Robust Optimization - A Comprehensive Survey , 2007 .

[17]  M. Wendt,et al.  Nonlinear Chance-Constrained Process Optimization under Uncertainty , 2002 .

[18]  Jean Charles Gilbert,et al.  Numerical Optimization: Theoretical and Practical Aspects , 2003 .

[19]  Laure Jaeger.  Optimisation multidisciplinaire sous incertitude en phase conceptuelle avion , 2013 .

[20]  Terje Aven,et al.  Models and model uncertainty in the context of risk analysis , 2003, Reliab. Eng. Syst. Saf..

[21]  M. Tichý.  First-order third-moment reliability method , 1994 .

[22]  Jung-Keun Lee,et al.  EURACHEM/CITAC Guide: Quantifying Uncertainty in Analytical Measurement, Ellison, S.L.R., Rosslein, M., and Williams, A., Eds., 2nd ed.; translated under the title Rukovodstvo EVRAKhIM/SITAK: Kolichestvennoe opisanie neopredelennosti v analiticheskikh izmereniyakh, Konopel'ko, L.A., Ed., St. Petersb , 2003 .

[23]  Genichi Taguchi,et al.  Performance analysis design , 1978 .

[24]  Pu Li,et al.  Advances and applications of chance-constrained approaches to systems optimisation under uncertainty , 2013, Int. J. Syst. Sci..

[25]  René Henrion,et al.  Some remarks on value-at-risk optimization , 2006 .

[26]  Karl Pearson,et al.  METHOD OF MOMENTS AND METHOD OF MAXIMUM LIKELIHOOD , 1936 .

[27]  Jean-Philippe Vial,et al.  Robust Optimization , 2021, ICORES.