CEAS Aeronautical Journal

, Volume 6, Issue 1, pp 121–136

POD approach for unsteady aerodynamic model updating

Original Paper


A method for aerodynamic model updating is proposed in this paper. The approach is based upon a correction of the eigenvalues of the reduced-order unsteady aerodynamic matrix through an optimization with objective function defined through the difference in the generalized aerodynamic forces or on the aeroelastic poles. The high-fidelity model in reduced-order form is obtained by the proper orthogonal decomposition (POD) technique applied to the computational fluid dynamics Euler-based formulation. Many of the methods that have been developed in the past years for simpler aeroelastic models that use, for example, doublet-lattice method aerodynamics, can be adopted for this purpose as well. However, this model is not able to capture shocks and flow separation in transonic flow. The proposed approach performs the updating of the aerodynamic model by imposing the minimization of a global error between target aerodynamic performances, namely experimental performances, and an aerodynamic model in reduced-order form via POD approach. After a general presentation of the application of the POD method to the linearized Euler equations, the optimization strategy is presented. First, a simple test on a 2D wing section with theoretical biased data is performed, and then, the performances of different optimization strategies are tested on a 3D model updated by wind tunnel data.


Aeroelasticity POD Reduced-order model Unsteady aerodynamic updating WT test data 

List of symbols


Computational domain volume

\(\bar {W}\)

Mean instantaneous field




Normal to the cell face


Velocity in the cell face

f, g, h

Flux component vector


Proper orthogonal mode


Flow field


Vector of the components of the disturbance field in the POD base


Structural modes


Displacement field


Generalized coordinates


Generalized aerodynamic force


Stiffness matrix


Mass matrix


Damping matrix


The instantaneous position of the grid nodes

a0, a1

Fluid system matrix

b0, b1

Coupling vector


Reduced-order aerodynamic matrix


Right eigenvector


Aeroelastic poles


Complex aerodynamic poles


Design variable for real part


Design variable for complex part


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Copyright information

© Deutsches Zentrum für Luft- und Raumfahrt e.V. 2014

Authors and Affiliations

  1. 1.Loads and Aeroelasticity DepartmentAirbusToulouseFrance
  2. 2.Mechanical and Aerospace Engineering Department“La Sapienza” University of RomeRomeItaly
  3. 3.Structural Mechanics and Coupled System LaboratoryConservatoire National des Arts et MétiersParisFrance

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