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Data Fusion for aerodynamic model estimation using a bayesian framework applied to machine learning surrogates

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Required Education : Masters degree in fluid mechanics or applied mathematics
Start date : 1 October 2019
Mission duration : 3 years


Data Fusion is the process of aggregating information from multiple sources to produce a higher quality estimate of the actual value of interest [1]. The resulting value must be more accurate than any of the single sources alone, and robust to spurious input from erroneous sources. Additionally, the process should produce an estimate of the uncertainty of the output value, and this uncertainty should be lowered compared to that of the initial inputs.

In aerospace applications, such as the aircraft aerodynamic behavior determination, sources of input data include various experimental sensor data, as well as computational physics results. The engineering objective in this case is to produce the best estimate of the forces, moments and pressure loads on the complete flight envelope to assess the handling qualities, the loads and the performances of the aircraft. A first version of the aerodynamic model is built during the design phase, and is adjusted with some specific flight test measurements.

External aerodynamics rely on computational fluid dynamics (CFD) solvers, which typically have a high spatial resolution but are not trustworthy in some extreme cases where complex physical phenomena occur; and several sources of experimental wind tunnel data, including both in-situ pressure and velocity sensors, as well as more advanced remote sensing techniques such as pressure sensitive paint (PSP) observations. Each of these sources has its specifics in terms of resolution and reliability, and fusing them to produce the overall model of the wing design is crucial for later stages of conception, such as structural design to support the mechanical loads. Moreover, the standard CFD and wind tunnel tests inputs are often completed with other data from flight tests or previous design status of the aircraft.

The data fusion problem relates directly to the domain of data assimilation (DA) [2], which makes use of a bayesian framework to assess the maximum likelihood estimate of a value and the associated uncertainty from two or more sources of uncertain data. One core issue in DA is the estimation of the uncertainty associated with each input, and in the context of aerospace applications it is at the root of the engineering knowledge on a given case. Additionally, some specific challenges are associated:

  • Large amounts of data including numerous defects,
  • Different types of data (surface pressures vs integrated aerodynamic forces and moments for instance),
  • Different geometrical shapes related to flexibility effects,
  • Sparse tested points

This fine grained knowledge of the data must be encoded in the data fusion process to get a final exhaustive model, covering the complete aircraft flight envelope.

While the problem of fusing two uncertain data estimates of a given value is well known, the specific challenge in this case arises from the dimensionality of the problem. Indeed, in order to advance the design process and achieve high performing designs, the optimal output shape for the aerodynamic loads should be a full 3D surface of the pressure loads on the entire wing skin, well discretized in space, and available at any point in the aircraft operating range. This type of response function is classically described using surrogate models [3], but these typically cannot handle such high dimensional outputs. Linear dimensionality reduction techniques such as proper orthogonal decomposition have been historically successful in representing turbulent flows [4]. However, pressure distributions on wings have different characteristics, including sharp discontinuities in the regions of shock and of technological details of the aircraft. These are very hard to capture using linear dimensionality reduction techniques.

High dimensional non-linear reduction however is one of the topics that deep feedforward neural networks (a.k.a. Deep Learning, DL) [5] have shown exceptional performance in recent years, e.g. the specific case of autoencoders [6]. These end-to-end techniques enable to replace a surrogate + dimensionality reduction approach with a single model that performs the full input-to-output training.

Recent works ([7] & [8]) have also been able to apply the Bayesian approach with deep neural networks, showing promising technique to propagate uncertainties through deep nets.

Ph.D. Expected Work

In this Ph.D., the data fusion of wing pressure distribution data will be performed, with the objective of achieving a high-dimensional output with maximum accuracy and uncertainty quantification, from various input sources (CFD, wind tunnel tests, flight tests…). To this end, DA techniques will be investigated and adapted to the case at hand. Additionally, starting from simple surrogate modeling techniques and output linear dimensionality reduction, the candidate will then explore the possibilities offered by recent advancements in DL techniques to replace this approach in an end-to-end manner. The accuracy, as well as the uncertainty quantification of both these approaches will be assessed. The final result will be a methodology to systematically evaluate and select the best approach for data-fusion with the highest accuracy and lowest uncertainty in each engineering configuration. This resulting data fusion methodology will support the development of future Airbus aircraft, from early design phases to flight test analysis and identification.


[1] Boström, H., Andler, S. F., Brohede, M., Johansson, R., Karlsson, A., Van Laere, J., … & Ziemke, T. (2007). On the definition of information fusion as a field of research.

[2] Evensen, G. (2009). Data assimilation: the ensemble Kalman filter. Springer Science & Business Media.

[3] Forrester, A., Sobester, A., & Keane, A. (2008). Engineering design via surrogate modelling: a practical guide. John Wiley & Sons.

[4] Berkooz, G., Holmes, P., & Lumley, J. L. (1993). The proper orthogonal decomposition in the analysis of turbulent flows. Annual review of fluid mechanics, 25(1), 539-575.

[5] Goodfellow, I., Bengio, Y., & Courville, A. (2016). Deep learning. MIT press.


This Ph.D. will receive a CIFRE funding from Airbus. Work will be performed between Airbus (Toulouse) and the CERFACS laboratory (also in Toulouse). Applicants can manifest their interest directly to the Ph.D. advisors, but the recruitement process will ultimately be performed directly by Airbus through its HR services.


AIRBUS: X. Bertrand (xavier.bertrand@airbus.com), F. Tost

CERFACS: C. Lapeyre (lapeyre@cerfacs.fr), A. Misdariis, T. Poinsot