Aerodynamic shape optimization for minimum robust drag and lift reliability constraint
A methodology for shape optimization of aerodynamic bodies under uncertainties is presented. Flow-related and geometrical uncertainties are considered and quantified by probability distribution functions. The optimal shape is computed by minimizing a robust estimate of the drag coefficient subject t...
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| Published in | Aerospace science and technology Vol. 55; pp. 24 - 33 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier Masson SAS
01.08.2016
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1270-9638 1626-3219 |
| DOI | 10.1016/j.ast.2016.05.005 |
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| Abstract | A methodology for shape optimization of aerodynamic bodies under uncertainties is presented. Flow-related and geometrical uncertainties are considered and quantified by probability distribution functions. The optimal shape is computed by minimizing a robust estimate of the drag coefficient subject to reliability constraint for the lift coefficient. The robust drag is formulated as a weighted sum of the mean and the standard deviation of the drag coefficient over the space of uncertain parameters. The mean and standard deviation of the drag coefficient are computed using sparse grid techniques. The lift reliability, defined by the probability the lift coefficient is lower than a reference value, is computed using First Order Reliability Method (FORM). A gradient-based optimization algorithm is used to obtain the optimal shape. The sensitivity derivatives of robust drag measure and the lift reliability with respect to the shape controlling and flow related design parameters as well as the uncertain parameters are computed using the adjoint problem for the flow. The methodology is applied to pure aerodynamic shape optimization, comparing optimal designs that arise from the formulation to optimal designs that correspond to special cases, including the case of no uncertainties. A 2D airfoil case is designed based on the Euler equations under uncertain Mach number and angle of attack and geometric variability. |
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| AbstractList | A methodology for shape optimization of aerodynamic bodies under uncertainties is presented. Flow-related and geometrical uncertainties are considered and quantified by probability distribution functions. The optimal shape is computed by minimizing a robust estimate of the drag coefficient subject to reliability constraint for the lift coefficient. The robust drag is formulated as a weighted sum of the mean and the standard deviation of the drag coefficient over the space of uncertain parameters. The mean and standard deviation of the drag coefficient are computed using sparse grid techniques. The lift reliability, defined by the probability the lift coefficient is lower than a reference value, is computed using First Order Reliability Method (FORM). A gradient-based optimization algorithm is used to obtain the optimal shape. The sensitivity derivatives of robust drag measure and the lift reliability with respect to the shape controlling and flow related design parameters as well as the uncertain parameters are computed using the adjoint problem for the flow. The methodology is applied to pure aerodynamic shape optimization, comparing optimal designs that arise from the formulation to optimal designs that correspond to special cases, including the case of no uncertainties. A 2D airfoil case is designed based on the Euler equations under uncertain Mach number and angle of attack and geometric variability. |
| Author | Papadimitriou, Dimitrios I. Papadimitriou, Costas |
| Author_xml | – sequence: 1 givenname: Dimitrios I. surname: Papadimitriou fullname: Papadimitriou, Dimitrios I. email: dpapadim@uth.gr – sequence: 2 givenname: Costas surname: Papadimitriou fullname: Papadimitriou, Costas email: costasp@uth.gr |
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| Cites_doi | 10.1007/s00158-014-1160-5 10.1007/s11831-008-9025-y 10.1016/j.ress.2010.09.013 10.2514/1.J052940 10.1088/1742-6596/318/4/042032 10.1002/nme.4438 10.1007/s00158-002-0212-4 10.1017/S0962492904000182 10.2514/1.C031693 10.1016/0021-9991(81)90128-5 10.1023/A:1019129717644 10.1061/(ASCE)0733-9399(1997)123:12(1219) 10.1115/1.1446068 10.1016/j.strusafe.2013.02.003 10.1007/s00158-004-0384-1 10.1016/j.finel.2004.06.002 10.1016/j.ast.2004.07.006 10.1016/0167-4730(94)90039-6 10.1016/j.compfluid.2005.11.006 10.1016/S0045-7949(03)00008-7 10.1016/j.probengmech.2007.12.011 10.1002/nme.1620240207 10.1007/s00158-010-0516-8 10.1061/(ASCE)0733-9399(2004)130:3(303) 10.2514/1.J053535 10.1016/j.compfluid.2015.07.019 10.1002/fld.885 10.2514/2.1881 10.1016/j.compfluid.2010.12.007 10.1016/j.cma.2009.08.016 10.1016/j.compfluid.2010.01.007 10.1007/s00158-006-0039-5 10.1063/1.4757266 10.1016/j.jcp.2013.10.027 10.2514/1.J050448 10.1016/j.cma.2008.01.003 10.1002/fld.2604 10.2514/1.37955 10.1007/s00158-003-0322-7 10.1002/fld.3677 10.1007/s11081-006-9974-7 10.2514/1.23658 |
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| References | Der Kiureghian (br0090) 2005 Zingg, Elias (br0510) 2006; 44 Jensen, Valdebenito, Schueller, Kusanovic (br0190) 2009; 198 Ghanem, Spanos (br0150) 2003 Papadimitriou, Beck, Katafygiotis (br0360) 1997; 123 Au (br0030) 2004; 130 Jalalpour, Guest, Igusa (br0170) 2013; 43 Edeling, Cinnella, Dwight, Bijl (br0120) 2014; 258 Carrier, Destarac, Dumont, Meheut, Din, Peter, Khelil, Brezillon, Pestana (br0060) 2014; vol. 10 Lyu, Kenway, Paige, Martins (br0260) 2013 Mogami, Nishiwaki, Izui, Yoshimura, Kogiso (br0300) 2006; 32 Müller, Cusdin (br0310) 2005; 47 Papadimitriou, Giannakoglou (br0380) 2008; 15 Taflanidis, Beck (br0490) 2008; 23 Putko, Taylor, Newman, Green (br0420) 2002; 124 Wang, Hirsch, Liu, Kang, Lacor (br0500) 2013; 94 Kharmanda, Olhoff, Mohamed, Lemaire (br0210) 2004; 26 Schulz, Schillings (br0460) 2009; 47 Schillings, Schmidt, Schulz (br0450) 2011; 46 Padulo, Campobasso, Guenov (br0350) 2011; 49 Davis, Rabinowitz (br0080) 2007 Ditlevsen, Madsen (br0100) 1996; vol. 178 Padula, Gumbert, Li (br0340) 2006; 7 Maute, Frangopol (br0280) 2003; 81 Li, Huyse, Padula (br0230) 2002; 24 Papoutsis-Kiachagias, Papadimitriou, Giannakoglou (br0410) 2012; 69 Bungartz, Griebel (br0050) 2004; 13 Papadimitriou, Papadimitriou (br0400) 2015; 120 Oliver, Moser (br0330) 2011; 318 Papadimitriou, Giannakoglou (br0370) 2007; 36 Smolyak (br0470) 1963; 4 Gerstner, Griebel (br0140) 1998; 18 Martinelli, Duvigneau (br0270) 2010; 39 Roe (br0440) 1981; 43 Liem, Kenway, Martins (br0240) 2014; 53 Cheung, Oliver, Prudencio, Prudhomme, Moser (br0070) 2011; 96 Nikbay, Kuru (br0320) 2013; 50 LeDoux, Vassberg, Young, Fugal, Kamenetskiy, Huffman, Melvin, Smith (br0220) 2015; 53 Reuther, Jameson, Farmer, Martinelli, Saunders (br0430) 1996; vol. 96 Lorentz (br0250) 1986 Brezillon, Gauger (br0040) 2004; 8 Svanberg (br0480) 1987; 24 Jensen, Valdebenito, Schueller (br0180) 2008; 198 Angelikopoulos, Papadimitriou, Koumoutsakos (br0020) 2012; 137 Huyse, Padula, Lewis, Li (br0160) 2002; 40 Medina, Taflanidis (br0290) 2015; 51 Allen, Maute (br0010) 2004; 27 Dribusch, Missoum, Beran (br0110) 2010; 42 Jung, Cho (br0200) 2004; 41 Enevoldsen, Sørensen (br0130) 1994; 15 Papadimitriou, Giannakoglou (br0390) 2013; 71 Medina (10.1016/j.ast.2016.05.005_br0290) 2015; 51 Angelikopoulos (10.1016/j.ast.2016.05.005_br0020) 2012; 137 Taflanidis (10.1016/j.ast.2016.05.005_br0490) 2008; 23 Liem (10.1016/j.ast.2016.05.005_br0240) 2014; 53 Reuther (10.1016/j.ast.2016.05.005_br0430) 1996; vol. 96 Zingg (10.1016/j.ast.2016.05.005_br0510) 2006; 44 Davis (10.1016/j.ast.2016.05.005_br0080) 2007 Jung (10.1016/j.ast.2016.05.005_br0200) 2004; 41 Carrier (10.1016/j.ast.2016.05.005_br0060) 2014; vol. 10 Papoutsis-Kiachagias (10.1016/j.ast.2016.05.005_br0410) 2012; 69 Edeling (10.1016/j.ast.2016.05.005_br0120) 2014; 258 Müller (10.1016/j.ast.2016.05.005_br0310) 2005; 47 Putko (10.1016/j.ast.2016.05.005_br0420) 2002; 124 Ghanem (10.1016/j.ast.2016.05.005_br0150) 2003 Papadimitriou (10.1016/j.ast.2016.05.005_br0370) 2007; 36 Jalalpour (10.1016/j.ast.2016.05.005_br0170) 2013; 43 LeDoux (10.1016/j.ast.2016.05.005_br0220) 2015; 53 Schillings (10.1016/j.ast.2016.05.005_br0450) 2011; 46 Svanberg (10.1016/j.ast.2016.05.005_br0480) 1987; 24 Brezillon (10.1016/j.ast.2016.05.005_br0040) 2004; 8 Dribusch (10.1016/j.ast.2016.05.005_br0110) 2010; 42 Ditlevsen (10.1016/j.ast.2016.05.005_br0100) 1996; vol. 178 Oliver (10.1016/j.ast.2016.05.005_br0330) 2011; 318 Jensen (10.1016/j.ast.2016.05.005_br0190) 2009; 198 Cheung (10.1016/j.ast.2016.05.005_br0070) 2011; 96 Wang (10.1016/j.ast.2016.05.005_br0500) 2013; 94 Padula (10.1016/j.ast.2016.05.005_br0340) 2006; 7 Papadimitriou (10.1016/j.ast.2016.05.005_br0380) 2008; 15 Roe (10.1016/j.ast.2016.05.005_br0440) 1981; 43 Allen (10.1016/j.ast.2016.05.005_br0010) 2004; 27 Schulz (10.1016/j.ast.2016.05.005_br0460) 2009; 47 Lorentz (10.1016/j.ast.2016.05.005_br0250) 1986 Mogami (10.1016/j.ast.2016.05.005_br0300) 2006; 32 Padulo (10.1016/j.ast.2016.05.005_br0350) 2011; 49 Smolyak (10.1016/j.ast.2016.05.005_br0470) 1963; 4 Huyse (10.1016/j.ast.2016.05.005_br0160) 2002; 40 Kharmanda (10.1016/j.ast.2016.05.005_br0210) 2004; 26 Au (10.1016/j.ast.2016.05.005_br0030) 2004; 130 Papadimitriou (10.1016/j.ast.2016.05.005_br0400) 2015; 120 Jensen (10.1016/j.ast.2016.05.005_br0180) 2008; 198 Li (10.1016/j.ast.2016.05.005_br0230) 2002; 24 Bungartz (10.1016/j.ast.2016.05.005_br0050) 2004; 13 Maute (10.1016/j.ast.2016.05.005_br0280) 2003; 81 Papadimitriou (10.1016/j.ast.2016.05.005_br0360) 1997; 123 Der Kiureghian (10.1016/j.ast.2016.05.005_br0090) 2005 Nikbay (10.1016/j.ast.2016.05.005_br0320) 2013; 50 Enevoldsen (10.1016/j.ast.2016.05.005_br0130) 1994; 15 Papadimitriou (10.1016/j.ast.2016.05.005_br0390) 2013; 71 Gerstner (10.1016/j.ast.2016.05.005_br0140) 1998; 18 Lyu (10.1016/j.ast.2016.05.005_br0260) 2013 Martinelli (10.1016/j.ast.2016.05.005_br0270) 2010; 39 |
| References_xml | – volume: 15 start-page: 169 year: 1994 end-page: 196 ident: br0130 article-title: Reliability-based optimization in structural engineering publication-title: Struct. Saf. – volume: 50 start-page: 708 year: 2013 end-page: 715 ident: br0320 article-title: Reliability based multidisciplinary optimization of aeroelastic systems with structural and aerodynamic uncertainties publication-title: J. Aircr. – volume: 120 start-page: 82 year: 2015 end-page: 97 ident: br0400 article-title: Bayesian uncertainty quantification of turbulence models based on high-order adjoint publication-title: Comput. Fluids – volume: 15 start-page: 447 year: 2008 end-page: 488 ident: br0380 article-title: Aerodynamic shape optimization using first and second order adjoint and direct approaches publication-title: Arch. Comput. Methods Eng. – volume: 47 start-page: 939 year: 2005 end-page: 945 ident: br0310 article-title: On the performance of discrete adjoint CFD codes using automatic differentiation publication-title: Int. J. Numer. Methods Fluids – volume: 41 start-page: 311 year: 2004 end-page: 331 ident: br0200 article-title: Reliability-based topology optimization of geometrically nonlinear structures with loading and material uncertainties publication-title: Finite Elem. Anal. Des. – volume: 69 start-page: 691 year: 2012 end-page: 709 ident: br0410 article-title: Robust design in aerodynamics using third-order sensitivity analysis based on discrete adjoint. Application to quasi-1D flows publication-title: Int. J. Numer. Methods Fluids – volume: 43 start-page: 41 year: 2013 end-page: 49 ident: br0170 article-title: Reliability-based topology optimization of trusses with stochastic stiffness publication-title: Struct. Saf. – volume: 71 start-page: 652 year: 2013 end-page: 670 ident: br0390 article-title: Third-order sensitivity analysis for robust aerodynamic design using continuous adjoint publication-title: Int. J. Numer. Methods Fluids – year: 1986 ident: br0250 article-title: Bernstein Polynomials – start-page: 1 year: 2013 end-page: 24 ident: br0260 article-title: Automatic differentiation adjoint of the Reynolds-averaged Navier–Stokes equations with a turbulence model publication-title: 21st AIAA Computational Fluid Dynamics Conference – volume: 26 start-page: 295 year: 2004 end-page: 307 ident: br0210 article-title: Reliability-based topology optimization publication-title: Struct. Multidiscip. Optim. – volume: 44 start-page: 2787 year: 2006 end-page: 2792 ident: br0510 article-title: Aerodynamic optimization under a range of operating conditions publication-title: AIAA J. – volume: 49 start-page: 530 year: 2011 end-page: 543 ident: br0350 article-title: Novel uncertainty propagation method for robust aerodynamic design publication-title: AIAA J. – volume: 18 start-page: 209 year: 1998 end-page: 232 ident: br0140 article-title: Numerical integration using sparse grids publication-title: Numer. Algorithms – volume: 53 start-page: 1910 year: 2015 end-page: 1935 ident: br0220 article-title: Study based on the AIAA aerodynamic design optimization discussion group test cases publication-title: AIAA J. – volume: 13 start-page: 147 year: 2004 end-page: 269 ident: br0050 article-title: Sparse grids publication-title: Acta Numer. – volume: 94 start-page: 111 year: 2013 end-page: 127 ident: br0500 article-title: Uncertainty-based robust aerodynamic optimization of rotor blades publication-title: Int. J. Numer. Methods Eng. – volume: 198 start-page: 3915 year: 2009 end-page: 3924 ident: br0190 article-title: Reliability-based optimization of stochastic systems using line search publication-title: Comput. Methods Appl. Mech. Eng. – volume: 32 start-page: 299 year: 2006 end-page: 311 ident: br0300 article-title: Reliability-based structural optimization of frame structures for multiple failure criteria using topology optimization techniques publication-title: Struct. Multidiscip. Optim. – volume: 123 start-page: 1219 year: 1997 end-page: 1229 ident: br0360 article-title: Asymptotic expansions for reliability and moments of uncertain systems publication-title: J. Eng. Mech. – volume: 47 start-page: 646 year: 2009 end-page: 654 ident: br0460 article-title: Problem formulations and treatment of uncertainties in aerodynamic design publication-title: AIAA J. – volume: 7 start-page: 317 year: 2006 end-page: 328 ident: br0340 article-title: Aerospace applications of optimization under uncertainty publication-title: Optim. Eng. – volume: 46 start-page: 78 year: 2011 end-page: 87 ident: br0450 article-title: Efficient shape optimization for certain and uncertain aerodynamic design publication-title: Comput. Fluids – volume: vol. 96 year: 1996 ident: br0430 article-title: Aerodynamic Shape Optimization of Complex Aircraft Configurations via an Adjoint Formulation – volume: vol. 178 year: 1996 ident: br0100 article-title: Structural Reliability Methods – volume: 43 start-page: 357 year: 1981 end-page: 372 ident: br0440 article-title: Approximate Riemann solvers, parameter vectors, and difference schemes publication-title: J. Comput. Phys. – volume: 137 year: 2012 ident: br0020 article-title: Bayesian uncertainty quantification and propagation in molecular dynamics simulations: a high performance computing framework publication-title: J. Chem. Phys. – volume: vol. 10 year: 2014 ident: br0060 article-title: Gradient-based aerodynamic optimization with the elsA software publication-title: 52nd Aerospace Sciences Meeting – volume: 198 start-page: 72 year: 2008 end-page: 87 ident: br0180 article-title: An efficient reliability-based optimization scheme for uncertain linear systems subject to general Gaussian excitation publication-title: Comput. Methods Appl. Mech. Eng. – volume: 27 start-page: 228 year: 2004 end-page: 242 ident: br0010 article-title: Reliability-based design optimization of aeroelastic structures publication-title: Struct. Multidiscip. Optim. – volume: 39 start-page: 953 year: 2010 end-page: 964 ident: br0270 article-title: On the use of second-order derivatives and metamodel-based Monte-Carlo for uncertainty estimation in aerodynamics publication-title: Comput. Fluids – year: 2007 ident: br0080 article-title: Methods of Numerical Integration – volume: 53 start-page: 104 year: 2014 end-page: 122 ident: br0240 article-title: Multimission aircraft fuel-burn minimization via multipoint aerostructural optimization publication-title: AIAA J. – volume: 130 start-page: 303 year: 2004 end-page: 311 ident: br0030 article-title: Probabilistic failure analysis by importance sampling Markov chain simulation publication-title: J. Eng. Mech. – volume: 42 start-page: 693 year: 2010 end-page: 705 ident: br0110 article-title: A multifidelity approach for the construction of explicit decision boundaries: application to aeroelasticity publication-title: Struct. Multidiscip. Optim. – year: 2005 ident: br0090 article-title: First- and second-order reliability methods publication-title: Engineering Design Reliability Handbook – volume: 40 start-page: 1764 year: 2002 end-page: 1772 ident: br0160 article-title: Probabilistic approach to free-form airfoil shape optimization under uncertainty publication-title: AIAA J. – volume: 24 start-page: 38 year: 2002 end-page: 50 ident: br0230 article-title: Robust airfoil optimization to achieve drag reduction over a range of Mach numbers publication-title: Struct. Multidiscip. Optim. – volume: 124 start-page: 60 year: 2002 end-page: 69 ident: br0420 article-title: Approach for input uncertainty propagation and robust design in CFD using sensitivity derivatives publication-title: J. Fluids Eng. – volume: 81 start-page: 813 year: 2003 end-page: 824 ident: br0280 article-title: Reliability-based design of MEMS mechanisms by topology optimization publication-title: Comput. Struct. – volume: 23 start-page: 324 year: 2008 end-page: 338 ident: br0490 article-title: Stochastic subset optimization for optimal reliability problems publication-title: Probab. Eng. Mech. – volume: 4 start-page: 123 year: 1963 ident: br0470 article-title: Quadrature and interpolation formulas for tensor products of certain classes of functions publication-title: Dokl. Akad. Nauk SSSR – year: 2003 ident: br0150 article-title: Stochastic Finite Elements: A Spectral Approach – volume: 36 start-page: 325 year: 2007 end-page: 341 ident: br0370 article-title: A continuous adjoint method with objective function derivatives based on boundary integrals, for inviscid and viscous flows publication-title: Comput. Fluids – volume: 8 start-page: 715 year: 2004 end-page: 727 ident: br0040 article-title: 2d and 3d aerodynamic shape optimisation using the adjoint approach publication-title: Aerosp. Sci. Technol. – volume: 96 start-page: 1137 year: 2011 end-page: 1149 ident: br0070 article-title: Bayesian uncertainty analysis with applications to turbulence modeling publication-title: Reliab. Eng. Syst. Saf. – volume: 258 start-page: 73 year: 2014 end-page: 94 ident: br0120 article-title: Bayesian estimates of parameter variability in the k– publication-title: J. Comput. Phys. – volume: 24 start-page: 359 year: 1987 end-page: 373 ident: br0480 article-title: The method of moving asymptotes – a new method for structural optimization publication-title: Int. J. Numer. Methods Eng. – volume: 318 year: 2011 ident: br0330 article-title: Bayesian uncertainty quantification applied to RANS turbulence models publication-title: J. Phys. Conf. Ser. – volume: 51 start-page: 813 year: 2015 end-page: 834 ident: br0290 article-title: Probabilistic measures for assessing appropriateness of robust design optimization solutions publication-title: Struct. Multidiscip. Optim. – volume: 51 start-page: 813 issue: 4 year: 2015 ident: 10.1016/j.ast.2016.05.005_br0290 article-title: Probabilistic measures for assessing appropriateness of robust design optimization solutions publication-title: Struct. Multidiscip. Optim. doi: 10.1007/s00158-014-1160-5 – volume: 15 start-page: 447 issue: 4 year: 2008 ident: 10.1016/j.ast.2016.05.005_br0380 article-title: Aerodynamic shape optimization using first and second order adjoint and direct approaches publication-title: Arch. Comput. Methods Eng. doi: 10.1007/s11831-008-9025-y – volume: 96 start-page: 1137 issue: 9 year: 2011 ident: 10.1016/j.ast.2016.05.005_br0070 article-title: Bayesian uncertainty analysis with applications to turbulence modeling publication-title: Reliab. Eng. Syst. Saf. doi: 10.1016/j.ress.2010.09.013 – volume: 53 start-page: 104 issue: 1 year: 2014 ident: 10.1016/j.ast.2016.05.005_br0240 article-title: Multimission aircraft fuel-burn minimization via multipoint aerostructural optimization publication-title: AIAA J. doi: 10.2514/1.J052940 – volume: 318 year: 2011 ident: 10.1016/j.ast.2016.05.005_br0330 article-title: Bayesian uncertainty quantification applied to RANS turbulence models publication-title: J. Phys. Conf. Ser. doi: 10.1088/1742-6596/318/4/042032 – volume: 94 start-page: 111 issue: 2 year: 2013 ident: 10.1016/j.ast.2016.05.005_br0500 article-title: Uncertainty-based robust aerodynamic optimization of rotor blades publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.4438 – year: 2007 ident: 10.1016/j.ast.2016.05.005_br0080 – volume: 24 start-page: 38 issue: 1 year: 2002 ident: 10.1016/j.ast.2016.05.005_br0230 article-title: Robust airfoil optimization to achieve drag reduction over a range of Mach numbers publication-title: Struct. Multidiscip. Optim. doi: 10.1007/s00158-002-0212-4 – volume: 13 start-page: 147 year: 2004 ident: 10.1016/j.ast.2016.05.005_br0050 article-title: Sparse grids publication-title: Acta Numer. doi: 10.1017/S0962492904000182 – volume: 50 start-page: 708 issue: 3 year: 2013 ident: 10.1016/j.ast.2016.05.005_br0320 article-title: Reliability based multidisciplinary optimization of aeroelastic systems with structural and aerodynamic uncertainties publication-title: J. Aircr. doi: 10.2514/1.C031693 – volume: 43 start-page: 357 issue: 2 year: 1981 ident: 10.1016/j.ast.2016.05.005_br0440 article-title: Approximate Riemann solvers, parameter vectors, and difference schemes publication-title: J. Comput. Phys. doi: 10.1016/0021-9991(81)90128-5 – volume: 18 start-page: 209 issue: 3–4 year: 1998 ident: 10.1016/j.ast.2016.05.005_br0140 article-title: Numerical integration using sparse grids publication-title: Numer. Algorithms doi: 10.1023/A:1019129717644 – volume: 123 start-page: 1219 issue: 12 year: 1997 ident: 10.1016/j.ast.2016.05.005_br0360 article-title: Asymptotic expansions for reliability and moments of uncertain systems publication-title: J. Eng. Mech. doi: 10.1061/(ASCE)0733-9399(1997)123:12(1219) – volume: vol. 10 year: 2014 ident: 10.1016/j.ast.2016.05.005_br0060 article-title: Gradient-based aerodynamic optimization with the elsA software – volume: 124 start-page: 60 issue: 1 year: 2002 ident: 10.1016/j.ast.2016.05.005_br0420 article-title: Approach for input uncertainty propagation and robust design in CFD using sensitivity derivatives publication-title: J. Fluids Eng. doi: 10.1115/1.1446068 – volume: 43 start-page: 41 year: 2013 ident: 10.1016/j.ast.2016.05.005_br0170 article-title: Reliability-based topology optimization of trusses with stochastic stiffness publication-title: Struct. Saf. doi: 10.1016/j.strusafe.2013.02.003 – volume: 27 start-page: 228 issue: 4 year: 2004 ident: 10.1016/j.ast.2016.05.005_br0010 article-title: Reliability-based design optimization of aeroelastic structures publication-title: Struct. Multidiscip. Optim. doi: 10.1007/s00158-004-0384-1 – volume: 41 start-page: 311 issue: 3 year: 2004 ident: 10.1016/j.ast.2016.05.005_br0200 article-title: Reliability-based topology optimization of geometrically nonlinear structures with loading and material uncertainties publication-title: Finite Elem. Anal. Des. doi: 10.1016/j.finel.2004.06.002 – volume: 8 start-page: 715 issue: 8 year: 2004 ident: 10.1016/j.ast.2016.05.005_br0040 article-title: 2d and 3d aerodynamic shape optimisation using the adjoint approach publication-title: Aerosp. Sci. Technol. doi: 10.1016/j.ast.2004.07.006 – volume: 15 start-page: 169 issue: 3 year: 1994 ident: 10.1016/j.ast.2016.05.005_br0130 article-title: Reliability-based optimization in structural engineering publication-title: Struct. Saf. doi: 10.1016/0167-4730(94)90039-6 – volume: 36 start-page: 325 issue: 2 year: 2007 ident: 10.1016/j.ast.2016.05.005_br0370 article-title: A continuous adjoint method with objective function derivatives based on boundary integrals, for inviscid and viscous flows publication-title: Comput. Fluids doi: 10.1016/j.compfluid.2005.11.006 – volume: 81 start-page: 813 issue: 8 year: 2003 ident: 10.1016/j.ast.2016.05.005_br0280 article-title: Reliability-based design of MEMS mechanisms by topology optimization publication-title: Comput. Struct. doi: 10.1016/S0045-7949(03)00008-7 – year: 2005 ident: 10.1016/j.ast.2016.05.005_br0090 article-title: First- and second-order reliability methods – volume: 23 start-page: 324 issue: 2 year: 2008 ident: 10.1016/j.ast.2016.05.005_br0490 article-title: Stochastic subset optimization for optimal reliability problems publication-title: Probab. Eng. Mech. doi: 10.1016/j.probengmech.2007.12.011 – volume: 24 start-page: 359 issue: 2 year: 1987 ident: 10.1016/j.ast.2016.05.005_br0480 article-title: The method of moving asymptotes – a new method for structural optimization publication-title: Int. J. Numer. Methods Eng. doi: 10.1002/nme.1620240207 – year: 2003 ident: 10.1016/j.ast.2016.05.005_br0150 – volume: 42 start-page: 693 issue: 5 year: 2010 ident: 10.1016/j.ast.2016.05.005_br0110 article-title: A multifidelity approach for the construction of explicit decision boundaries: application to aeroelasticity publication-title: Struct. Multidiscip. Optim. doi: 10.1007/s00158-010-0516-8 – volume: 130 start-page: 303 issue: 3 year: 2004 ident: 10.1016/j.ast.2016.05.005_br0030 article-title: Probabilistic failure analysis by importance sampling Markov chain simulation publication-title: J. Eng. Mech. doi: 10.1061/(ASCE)0733-9399(2004)130:3(303) – volume: 53 start-page: 1910 issue: 7 year: 2015 ident: 10.1016/j.ast.2016.05.005_br0220 article-title: Study based on the AIAA aerodynamic design optimization discussion group test cases publication-title: AIAA J. doi: 10.2514/1.J053535 – volume: 120 start-page: 82 year: 2015 ident: 10.1016/j.ast.2016.05.005_br0400 article-title: Bayesian uncertainty quantification of turbulence models based on high-order adjoint publication-title: Comput. Fluids doi: 10.1016/j.compfluid.2015.07.019 – volume: 47 start-page: 939 issue: 8–9 year: 2005 ident: 10.1016/j.ast.2016.05.005_br0310 article-title: On the performance of discrete adjoint CFD codes using automatic differentiation publication-title: Int. J. Numer. Methods Fluids doi: 10.1002/fld.885 – volume: 40 start-page: 1764 issue: 9 year: 2002 ident: 10.1016/j.ast.2016.05.005_br0160 article-title: Probabilistic approach to free-form airfoil shape optimization under uncertainty publication-title: AIAA J. doi: 10.2514/2.1881 – volume: 46 start-page: 78 issue: 1 year: 2011 ident: 10.1016/j.ast.2016.05.005_br0450 article-title: Efficient shape optimization for certain and uncertain aerodynamic design publication-title: Comput. Fluids doi: 10.1016/j.compfluid.2010.12.007 – volume: vol. 178 year: 1996 ident: 10.1016/j.ast.2016.05.005_br0100 – volume: 198 start-page: 3915 issue: 49 year: 2009 ident: 10.1016/j.ast.2016.05.005_br0190 article-title: Reliability-based optimization of stochastic systems using line search publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2009.08.016 – volume: 39 start-page: 953 issue: 6 year: 2010 ident: 10.1016/j.ast.2016.05.005_br0270 article-title: On the use of second-order derivatives and metamodel-based Monte-Carlo for uncertainty estimation in aerodynamics publication-title: Comput. Fluids doi: 10.1016/j.compfluid.2010.01.007 – volume: 32 start-page: 299 issue: 4 year: 2006 ident: 10.1016/j.ast.2016.05.005_br0300 article-title: Reliability-based structural optimization of frame structures for multiple failure criteria using topology optimization techniques publication-title: Struct. Multidiscip. Optim. doi: 10.1007/s00158-006-0039-5 – year: 1986 ident: 10.1016/j.ast.2016.05.005_br0250 – volume: 4 start-page: 123 year: 1963 ident: 10.1016/j.ast.2016.05.005_br0470 article-title: Quadrature and interpolation formulas for tensor products of certain classes of functions publication-title: Dokl. Akad. Nauk SSSR – volume: 137 issue: 14 year: 2012 ident: 10.1016/j.ast.2016.05.005_br0020 article-title: Bayesian uncertainty quantification and propagation in molecular dynamics simulations: a high performance computing framework publication-title: J. Chem. Phys. doi: 10.1063/1.4757266 – start-page: 1 year: 2013 ident: 10.1016/j.ast.2016.05.005_br0260 article-title: Automatic differentiation adjoint of the Reynolds-averaged Navier–Stokes equations with a turbulence model – volume: 258 start-page: 73 year: 2014 ident: 10.1016/j.ast.2016.05.005_br0120 article-title: Bayesian estimates of parameter variability in the k–ε turbulence model publication-title: J. Comput. Phys. doi: 10.1016/j.jcp.2013.10.027 – volume: 49 start-page: 530 issue: 3 year: 2011 ident: 10.1016/j.ast.2016.05.005_br0350 article-title: Novel uncertainty propagation method for robust aerodynamic design publication-title: AIAA J. doi: 10.2514/1.J050448 – volume: 198 start-page: 72 issue: 1 year: 2008 ident: 10.1016/j.ast.2016.05.005_br0180 article-title: An efficient reliability-based optimization scheme for uncertain linear systems subject to general Gaussian excitation publication-title: Comput. Methods Appl. Mech. Eng. doi: 10.1016/j.cma.2008.01.003 – volume: 69 start-page: 691 issue: 3 year: 2012 ident: 10.1016/j.ast.2016.05.005_br0410 article-title: Robust design in aerodynamics using third-order sensitivity analysis based on discrete adjoint. Application to quasi-1D flows publication-title: Int. J. Numer. Methods Fluids doi: 10.1002/fld.2604 – volume: 47 start-page: 646 issue: 3 year: 2009 ident: 10.1016/j.ast.2016.05.005_br0460 article-title: Problem formulations and treatment of uncertainties in aerodynamic design publication-title: AIAA J. doi: 10.2514/1.37955 – volume: 26 start-page: 295 issue: 5 year: 2004 ident: 10.1016/j.ast.2016.05.005_br0210 article-title: Reliability-based topology optimization publication-title: Struct. Multidiscip. Optim. doi: 10.1007/s00158-003-0322-7 – volume: vol. 96 year: 1996 ident: 10.1016/j.ast.2016.05.005_br0430 – volume: 71 start-page: 652 issue: 5 year: 2013 ident: 10.1016/j.ast.2016.05.005_br0390 article-title: Third-order sensitivity analysis for robust aerodynamic design using continuous adjoint publication-title: Int. J. Numer. Methods Fluids doi: 10.1002/fld.3677 – volume: 7 start-page: 317 issue: 3 year: 2006 ident: 10.1016/j.ast.2016.05.005_br0340 article-title: Aerospace applications of optimization under uncertainty publication-title: Optim. Eng. doi: 10.1007/s11081-006-9974-7 – volume: 44 start-page: 2787 issue: 11 year: 2006 ident: 10.1016/j.ast.2016.05.005_br0510 article-title: Aerodynamic optimization under a range of operating conditions publication-title: AIAA J. doi: 10.2514/1.23658 |
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| SubjectTerms | Adjoint method Aerodynamic shape optimization Aerodynamics Computation Drag (hindrance) Drag coefficients FORM Lift Optimization Reliability Robustness Shape optimization Sparse grid quadrature Uncertainty |
| Title | Aerodynamic shape optimization for minimum robust drag and lift reliability constraint |
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