DyMAD highlights

DyMAD Research - Dynamical Model Approximation Driven Research

Some graphical illustrations of the importance of model approximation, reduction and applied mathematics in different domains.
The methods I develop are embedded within the MDSPACK library.
This latter allows to treat real-life physics and engineering-driven problems going from aircraft, fluids to pollutants.

flop comparison. Cascaded n-D Loewner best and worst combination are respectively materialized by red and yellow dots. An upper bound of the best and worst combination is given with the red and yellow lines. The average complexity is materialized by the dash-dotted black line. Full n-D Loewner is O(N^3) (blue dashed). Comparison with O(N^2) and O(N log(N )) references are shown in dash-dotted and solid blue lines.

The Loewner framework for parametric systems: Taming the curse of dimensionality
(May 2024)

First, we propose a generalized realization form for rational functions in n-variables (for any n), which are described in the Lagrange basis. Secondly, we show that the corresponding n-dimensional Loewner matrix is the solution of a cascaded Sylvester equation set. Finally, we demonstrate that the barycentric coefficients can be obtained using a sequence of 1-dimensional Loewner matrices instead of the large-scale n-dimensional one, drastically reducing the computational effort.

Reference
A. C. Antoulas, I. V. Gosea and C. Poussot-Vassal, "The Loewner framework for parametric systems: Taming the curse of dimensionality", submitted
>> available as arXiv
>> additional material 

Riemann zeta function zeros and prime counting function approximation
(January 2021)

The realisation landmark of Mayo and Antoulas, through the lens of the modified Loewner framework is used to approximate the non-trivial zeros of the famous Riemann zeta function. 

These approximated zeros are then used to approximate the Riemann prime counting function, as illustrated in the right frame.

Reference
C. Poussot-Vassal, I.V. Gosea, P. Vuillemin and A.C. Antoulas "Loewner framework for Riemann zeta function non-trivial zeros and prime counting function approximation", in preparation.

Comparison of the prime counting function (thin red) with the Riemann formulae including non-trivial zeros approximated by the Loewner approach (solid blue). As the number of non-trivial (harmonics) zeros increases, the step shape is revealed.

Horizontal cross section of pollutants concentration from four sources (red stars) with an eastward wind. Original data from complex simulator LES (left), nonlinear ROM (center) and relative error in percentage (right). The LES solution runs in 5800h on a cluster while the ROM in seconds over a standard laptop.


Non-intrusive nonlinear reduced order modelling of a pollutant dispersion
(December 2020)

The non-intrusive MII for mixed interpolatory and inference procedure aims at constructing a nonlinear reduced order model (ROM) from time-domain input-output data issued from any complex simulator or measurements.

The proposed process allows  to construct a nonlinear ROM that accurately reproduce the complex simulation and that can be used for prediction, analysis. This ROM is a dynamical model of an appropriate structure.

The procedure is applied on a pollutant plume dispersion use case, simulated using Large Eddy Simulation (LES). 

Reference
C. Poussot-Vassal, T. Sabatier, C. Sarrat and P. Vuillemin, "Mixed interpolatory and inference non-intrusive reduced order modeling with application to pollutants dispersion", submitted (initial version on arXiv).

Data-driven control of a pulsed fluidic actuator
(February 2020)

Illustration of the data-driven control design, applied on a pulsed fluidic actuator (PFA). PFA are typical on/off actuators that blow air in order to modify the pressure in a flow setup. They are typically used to control fluidic phenomena. The design is done using the Loewner-Data Driven Control (L-DDC) rationale.

Video
Video illustrating the closed-loop performances obtained on the experimental setup of the controlled PFA. This loop can be considered as the inner-loop of a future flow control setup. Sound is the noise of the blowed on/off air :)

Reference
C. Poussot-Vassal, P. Kergus, F. Kerhervé and D. Sipp "Interpolatory-based data-driven pulsed fluidic actuator control design and experimental validation", submitted  (initial version on arXiv).

Top: Illustration of the considered closed-loop (the photo is the top view of the PFA). Bottom: performance in signal tracking obtained on the experimental tech bench.

Open cavity geometry. The flow U goes from left to right. The actuator is a blowing one modifying the pressure located on B (yellow) and the sensor measure the pressure variation is on C. The feedback loops C to B (see video).

Model reduction and control of fluid phenomena
(June 2017)

Model reduction and control of a complex fluid phenomena (here the oscillator open cavity geometry). This has been done by data-driven model approximation done with the MOR Toolbox and an unconventional iteratively designed controller.

Video
Illustration of the feedback controller performance in attenuating the fluid oscillations. Top : with control; bottom : without control.

Reference
C. Poussot-Vassal, C. Leclercq and D. Sipp, "Structured linear fractional parametric controller Hinf design and its applications" (initial version on arXiv), in Proceedings of the European Control Conference (ECC), Limassol, Cyprus, June, 2018, pp. 2629-2634.

C. Poussot-Vassal and D. Sipp, "Parametric reduced order dynamical model construction of a fluid flow control problem", in Proceedings of the Workshop on Linear Parameter Varying Systems (LPVS), Grenoble, France, October, 2015, pp. 133-138.

Vibration control demonstrator applied on a Dassault-Aviation Business jet
>> Ground vibration tests (September 2015)
>> Flight tests (September 2017)

The vibration attenuation achieved on a Dassaut-Aviation Business Jet Falcon 7X has been done. To this aim, 

(i) the MOR Toolbox has been extensively used to approximate the faithful but very complex dynamical models of Dassault-Aviation (obtained from finite elements methods), and 

(ii) a structured H-infinity controller (hinfstruct) has been designed to attenuate the vibration over a frequency-limited range.

Video
The video shows the effect of the feedback control design to attenuate the vibrations at  the pilot cabin level. 

Video (interview)
The interview deals with the importance of vibration and load control in small aircrafts.

References
C. Poussot-Vassal, C. Roos, P. Vuillemin, O. Cantinaud and J-P. Lacoste, "Chapter 11: Control-oriented Aeroelastic BizJet Low-order LFT modeling", Control-oriented modelling and identification: theory and practice (ISBN: 978-1-84919-614-7), M. Lovera Eds. January, 2015, IET - Control Engineering Series 80 (Hardcover).

C. Meyer, G. Broux, J. Prodigue, O. Cantinaud and C. Poussot-Vassal, "Demonstration of innovative vibration control on a Falcon Business Jet", in Proceedings of the International Forum on Aeroelasticity and Structural Dynamics (IFASD), Como, Italy, June, 2017.

Falcon 7X s/n 001 during ground vibration test (Dassault-Aviation colleagues and me)

Experimental set-up in the ONERA S3Ch WT: aeroelastic airofoil (foreground) and gust generator (background)

Active gust load alleviation on an Aeroelastic model
(May 2015) 

This press article spots the results obtained in Onera wind tunnel facility for both trans- and sub-sonic configurations to attenuate gust load, thanks to 

(i) an advanced frequency-domain identification procedure based on data-driven model approximation performed with the MOR Toolbox 

(ii) followed by an active closed-loop control done in the structured H-infinity (hinfstruct) framework.

Video
Illustration of the loads attenuation of when the feedback control loop is activated (at 19 seconds). The video is shot in high speed.

>> see more here <<