In this paper variable fidelity analyses are investigated. Moreover different kind of approximations to be used in a wide multidisciplinary design environment for aircraft design are built. In order to obtain the surrogate models used in the main design process, a proper framework is built by different design of experiments techniques for process and variables management. Approximated models for the estimation of aerodynamic coefficients are evaluated on design spaces of different dimensions and considering different set of variables (i.e. geometric parameters and flight conditions). They are mainly based on the hybrid combination of Vortex Lattice Method (VLM) models 
representing the basic low fidelity analysis) and 3D finite volume Computational Fluid Dynamics models (representing the basic high fidelity analysis). Different strategies for the evaluation of the surrogate model are considered and an original methodology for the model construction is here presented

Maggiore, Paolo

Mainini, Laura

Tosetti, Marco

English

PORTO Publications Open Repository TOrino

4TH EUROPEAN CONFERENCE FOR AEROSPACE SCIENCES (EUCASS) 
Copyright  2011 by First Author and Second Author. Published by the EUCASS association with permission. 
Approximated models for aerodynamics coefficients 
estimation in a multidisciplinary design environment  
 
L. Mainini* , A. Caimano**, M. Tosetti**, P. Maggiore*** 
*Ph.D. Student. Aerospace Engineering Department, Politecnico di Torino  
Corso Duca degli Abruzzi, 24, 10129 TORINO 
** Research Assistant. Aerospace Engineering Department, Politecnico di Torino  
Corso Duca degli Abruzzi, 24, 10129 TORINO 
***Associate Professor. Aerospace Engineering Department, Politecnico di Torino  
Corso Duca degli Abruzzi, 24, 10129 TORINO 
 
 
It is known how the aerospace engineering is characterized by great complexity. This is related to the 
fact that it deals with large-scale systems and that the involved issues are numerous, different in nature 
and often not independent. Also for aircraft industries, some design requirements are more and more 
demanding. 
On the one hand the need to maintain competitiveness in terms of design quality and reduction of time 
to market (which can be translated into a physiological reduction in design time). On the other hand 
the need to reduce development and production costs is reflected in the will to develop an optimal 
design since the early (preliminary) stages in order to reduce the entity and amount of changes 
(typically cumbersome and expensive) done in further design phases. 
A good response to these demands is the use of tools and methodologies that go under the name of 
Concurrent Engineering (CE) and Multidisciplinary Analysis (MDA)[1]. The need to reduce the time 
for design process is also strictly related to a containment of computational burden. It is therefore 
necessary to find methods of analysis that allow a significant reduction of both running time and 
computing resources used. In engineering literature there are several methods to address this problems. 
They are multi-fidelity modeling approaches and approximations of analysis process. 
The multi-fidelity approach involves the use of analysis models characterized by different levels of 
fidelity [2, 3]. In this framework typical high fidelity models are implementations of methods that 
allow a very accurate analysis (i.e. for aerodynamic analysis, 3D finite volume Computational Fluid 
Dynamics (CFD) model with very refined discretization and physics description). On the other hand 
low fidelity models families are various: implementation of the same high fidelity approach, but with a 
rougher description or discretization of the problem, implementation of simplified physics models and 
approximations by the use of surrogate modeling approaches. 
The first two options go under the name of hierarchical surrogate modeling [4]. Alexandrov and Lewis 
widely deals with this kind of methodologies and their performances [5].  
Speaking about surrogate modeling, different kind of methodologies can be found. In particular it is 
possible to distinguish between two families of surrogates. The first is the group of data fit models [6, 
7]; they are generated via interpolation of data related to simulations at given sets of design points; the 
most known data fit techniques are response surface models [8] and Kriging models [9]. The second 
family gathers reduced order models that are typically based on the reduction of the state dimension 
[10]; Proper Orthogonal Decomposition (POD) techniques are widely used examples of these methods 
[11, 12]. 
In this paper variable fidelity analyses are investigated. Moreover we will build different kind of 
approximations to be used in a wide multidisciplinary design environment for aircraft design. 
Speaking about the matter in hand, in order to obtain the surrogate models to be used in the main 
design process, a proper framework is built using the I-sight environment for process and variables 
management. Approximated models for the estimation of aerodynamic coefficients are evaluated on 
design spaces of different dimensions and considering different set of variables (i.e. geometric 
parameters and flight conditions). They are mainly based on the hybrid combination of Vortex Lattice 
Method (VLM) models (representing basic low fidelity analysis) and 3D finite volume Computational 
Fluid Dynamics models (representing basic high fidelity analysis tool). Different strategies for the 
evaluation of the surrogate model are considered and compared. 
 
SESSION NUMBER & NAME 
 2
 
References 
[1] Alexandrov, N., Lewis, R. M. 2002. Analytical and computational aspects of collaborative optimization for 
multidisciplinary design. AIAA Journal. 40(2):301-309. 
[2] Alexandrov, N., Lewis, R., Lewis, M., Gumbert, C., Green, L., Newman, P., 1999. Optimization with variable-
fidelity models applied to wing design. Technical Report CR 209826, NASA. 
[3] Alexandrov, N., Lewis, R., Lewis, M., Gumbert, C., Green, L., and Newman, P. 2001. Approximation and 
model management in aerodynamic optimization with variable-fidelity models. AIAA Journal. 38(6):1093-
1101. 
[4] Robinson, T., Eldred, M., Willcox, K., and Haimes, R. 2006. Strategies for multi-fidelity optimization with 
variable dimensional hierarchical models., In: 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural 
Dynamics, and Materials Conference. AIAA-2006-1819. 
[5] Alexandrov, N., Lewis, R. M. 2000. First-order frameworks for managing models in engineering optimization. 
In: 1st Int. Workshop on Surrogate Modelling and Space Mapping for Eng Opt. 
[6] Venter, G., Haftka, R., and Starnes, J. 1998. Construction of response surface approximations for design 
optimization. AIAA Journal. 36(12):2242-2249. 
[7] Eldred, M., Giunta, A., and Collis, S. 2004. Second-order corrections for surrogate based optimization with 
model hierarchies. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. AIAA 2004-
4457. 
[8] Simpson, T., Peplinski, J., Koch, P., and Allen, J. 2001. Metamodels for computer based engineering design: 
Survey and recommendations. Engineering with Computers. 17:129-150. 
[9] Sacks, J., Welch, W., Mitchell, T., and Wynn, H. 1989. Design and analysis of computer experiments. 
Statistical Scienc. 4(4):409-435. 
[10] Antoulas, A.C. 2005. Approximation of Large-Scale Dynamical Systems. Book Series: Advances in Design and 
Control, DC 06, 479 pages, SIAM, Philadelphia. 
[11] Willcox, K., Peraire, J. 2002. Balanced model reduction via the proper orthogonal decomposition. AIAA 
Journal. 40(11):2323-2330. 
[12] Bui-Thanh, T., Damodaran, M., Willcox, K. 2003. Proper orthogonal decomposition extensions for 
parametricapplications in transonic aerodynamics. In: 21th AIAA Applied Aerodynamics Conference. AIAA 
2003-4213. 
 
 
 


Analytical and computational aspects of collaborative optimization for multidisciplinary design.

Approximation and model management in aerodynamic optimization with variable-fidelity models.

Approximation of Large-Scale Dynamical Systems.

Balanced model reduction via the proper orthogonal decomposition.

Construction of response surface approximations for design optimization.

Design and analysis of computer experiments.

First-order frameworks for managing models in engineering optimization. In: 1st Int. Workshop on Surrogate Modelling and Space Mapping for Eng Opt.

Metamodels for computer based engineering design: Survey and recommendations. Engineering with Computers.

Optimization with variablefidelity models applied to wing design.

Proper orthogonal decomposition extensions for parametricapplications in transonic aerodynamics.

Second-order corrections for surrogate based optimization with model hierarchies. In:

Strategies for multi-fidelity optimization with variable dimensional hierarchical models., In:

Approximated models for aerodynamic coefficients estimation in a multidisciplinary design environment

MAININI, LAURA

TOSETTI, MARCO

MAGGIORE, Paolo

PORTO@iris (Publications Open Repository TOrino - Politecnico di Torino)

04 August 2020POLITECNICO DI TORINORepository ISTITUZIONALEApproximated models for aerodynamic coefficients estimation in a multidisciplinary design environment / Mainini L.;Tosetti M.; Maggiore P.. - ELETTRONICO. - (2011). ((Intervento presentato al convegno 4th European Conference forAerospace Sciences (EUCASS) 2011 tenutosi a Saint Petersburg (RUSSIA) nel 4-8 July 2011.OriginalApproximated models for aerodynamic coefficients estimation in a multidisciplinary design environmentPublisher:PublishedDOI:Terms of use:openAccessPublisher copyright(Article begins on next page)This article is made available under terms and conditions as specified in the  corresponding bibliographic description inthe repositoryAvailability:This version is available at: 11583/2429582 since:4TH EUROPEAN CONFERENCE FOR AEROSPACE SCIENCES (EUCASS) Copyright  2011 by First Author and Second Author. Published by the EUCASS association with permission. Approximated models for aerodynamics coefficients estimation in a multidisciplinary design environment   L. Mainini* , A. Caimano**, M. Tosetti**, P. Maggiore*** *Ph.D. Student. Aerospace Engineering Department, Politecnico di Torino  Corso Duca degli Abruzzi, 24, 10129 TORINO ** Research Assistant. Aerospace Engineering Department, Politecnico di Torino  Corso Duca degli Abruzzi, 24, 10129 TORINO ***Associate Professor. Aerospace Engineering Department, Politecnico di Torino  Corso Duca degli Abruzzi, 24, 10129 TORINO   It is known how the aerospace engineering is characterized by great complexity. This is related to the fact that it deals with large-scale systems and that the involved issues are numerous, different in nature and often not independent. Also for aircraft industries, some design requirements are more and more demanding. On the one hand the need to maintain competitiveness in terms of design quality and reduction of time to market (which can be translated into a physiological reduction in design time). On the other hand the need to reduce development and production costs is reflected in the will to develop an optimal design since the early (preliminary) stages in order to reduce the entity and amount of changes (typically cumbersome and expensive) done in further design phases. A good response to these demands is the use of tools and methodologies that go under the name of Concurrent Engineering (CE) and Multidisciplinary Analysis (MDA)[1]. The need to reduce the time for design process is also strictly related to a containment of computational burden. It is therefore necessary to find methods of analysis that allow a significant reduction of both running time and computing resources used. In engineering literature there are several methods to address this problems. They are multi-fidelity modeling approaches and approximations of analysis process. The multi-fidelity approach involves the use of analysis models characterized by different levels of fidelity [2, 3]. In this framework typical high fidelity models are implementations of methods that allow a very accurate analysis (i.e. for aerodynamic analysis, 3D finite volume Computational Fluid Dynamics (CFD) model with very refined discretization and physics description). On the other hand low fidelity models families are various: implementation of the same high fidelity approach, but with a rougher description or discretization of the problem, implementation of simplified physics models and approximations by the use of surrogate modeling approaches. The first two options go under the name of hierarchical surrogate modeling [4]. Alexandrov and Lewis widely deals with this kind of methodologies and their performances [5].  Speaking about surrogate modeling, different kind of methodologies can be found. In particular it is possible to distinguish between two families of surrogates. The first is the group of data fit models [6, 7]; they are generated via interpolation of data related to simulations at given sets of design points; the most known data fit techniques are response surface models [8] and Kriging models [9]. The second family gathers reduced order models that are typically based on the reduction of the state dimension [10]; Proper Orthogonal Decomposition (POD) techniques are widely used examples of these methods [11, 12]. In this paper variable fidelity analyses are investigated. Moreover we will build different kind of approximations to be used in a wide multidisciplinary design environment for aircraft design. Speaking about the matter in hand, in order to obtain the surrogate models to be used in the main design process, a proper framework is built using the I-sight environment for process and variables management. Approximated models for the estimation of aerodynamic coefficients are evaluated on design spaces of different dimensions and considering different set of variables (i.e. geometric parameters and flight conditions). They are mainly based on the hybrid combination of Vortex Lattice Method (VLM) models (representing basic low fidelity analysis) and 3D finite volume Computational Fluid Dynamics models (representing basic high fidelity analysis tool). Different strategies for the evaluation of the surrogate model are considered and compared.  SESSION NUMBER & NAME  2 References [1] Alexandrov, N., Lewis, R. M. 2002. Analytical and computational aspects of collaborative optimization for multidisciplinary design. AIAA Journal. 40(2):301-309. [2] Alexandrov, N., Lewis, R., Lewis, M., Gumbert, C., Green, L., Newman, P., 1999. Optimization with variable-fidelity models applied to wing design. Technical Report CR 209826, NASA. [3] Alexandrov, N., Lewis, R., Lewis, M., Gumbert, C., Green, L., and Newman, P. 2001. Approximation and model management in aerodynamic optimization with variable-fidelity models. AIAA Journal. 38(6):1093-1101. [4] Robinson, T., Eldred, M., Willcox, K., and Haimes, R. 2006. Strategies for multi-fidelity optimization with variable dimensional hierarchical models., In: 47th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference. AIAA-2006-1819. [5] Alexandrov, N., Lewis, R. M. 2000. First-order frameworks for managing models in engineering optimization. In: 1st Int. Workshop on Surrogate Modelling and Space Mapping for Eng Opt. [6] Venter, G., Haftka, R., and Starnes, J. 1998. Construction of response surface approximations for design optimization. AIAA Journal. 36(12):2242-2249. [7] Eldred, M., Giunta, A., and Collis, S. 2004. Second-order corrections for surrogate based optimization with model hierarchies. In: 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. AIAA 2004-4457. [8] Simpson, T., Peplinski, J., Koch, P., and Allen, J. 2001. Metamodels for computer based engineering design: Survey and recommendations. Engineering with Computers. 17:129-150. [9] Sacks, J., Welch, W., Mitchell, T., and Wynn, H. 1989. Design and analysis of computer experiments. Statistical Scienc. 4(4):409-435. [10] Antoulas, A.C. 2005. Approximation of Large-Scale Dynamical Systems. Book Series: Advances in Design and Control, DC 06, 479 pages, SIAM, Philadelphia. [11] Willcox, K., Peraire, J. 2002. Balanced model reduction via the proper orthogonal decomposition. AIAA Journal. 40(11):2323-2330. [12] Bui-Thanh, T., Damodaran, M., Willcox, K. 2003. Proper orthogonal decomposition extensions for parametricapplications in transonic aerodynamics. In: 21th AIAA Applied Aerodynamics Conference. AIAA 2003-4213.    

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Approximated models for aerodynamic coefficients estimation in a multidisciplinary design environment

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