Flexible Aircraft - Revision history

Schuetz2 at 05:30, 17 June 2025

2025-06-17T05:30:36Z

← Older revision		Revision as of 05:30, 17 June 2025
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	** H : transfer function matrix evaluation at different output measurements points of the aircraft (complex <math>92 \times 1 \times 421</math> matrix).		** H : transfer function matrix evaluation at different output measurements points of the aircraft (complex <math>92 \times 1 \times 421</math> matrix).

	* The <tt>dataONERA_FlexibleAircraft_withMOR.mat</tt> data file, with 3 ROMs obtained with the [https://~~morwiki~~.~~mpi-magdeburg.mpg.de~~/morwiki/~~index.php/MORE~~ '''MOR toolbox'''] using the Loewner method		* The <tt>dataONERA_FlexibleAircraft_withMOR.mat</tt> data file, with 3 ROMs obtained with the [https://modelreduction.org/morwiki/MOR_Toolbox '''MOR toolbox'''] using the Loewner method
	** Hr1 : linear rational ROMs with varying dimensions (state-space models in Matlab form).		** Hr1 : linear rational ROMs with varying dimensions (state-space models in Matlab form).
	** Hr2 : linear rational ROMs with varying dimensions, with stability post enforcement and input/output normalisation to catch all transfer whatever the amplitude (state-space models in Matlab form).		** Hr2 : linear rational ROMs with varying dimensions, with stability post enforcement and input/output normalisation to catch all transfer whatever the amplitude (state-space models in Matlab form).

Poussotvassal: /* Considered data */

2021-06-04T10:08:01Z

Considered data

← Older revision		Revision as of 10:08, 4 June 2021
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	\{\omega_i,H_i^{n_y\times n_u}\}_{i=1}^N,		\{\omega_i,H_i^{n_y\times n_u}\}_{i=1}^N,
	</math>		</math>
	where <math>H_i\in\mathbb C^{n_y\times n_u}</math> represents the transfer from <math>n_u=1</math> input signal (gust disturbance) to <math>n_y=92</math> measurement outputs (accelerations and moments at different coordinates of a flexible aircraft wings and tail ), evaluated at varying frequencies <math>\omega_i\in\mathbb R</math> [rad/s], for <math>i=1,\dots,N=421</math>.		where <math>H_i\in\mathbb C^{n_y\times n_u}</math> represents the transfer from <math>n_u=1</math> input signal (gust disturbance) to <math>n_y=92</math> measurement outputs (accelerations and moments at different coordinates of a flexible aircraft wings and tail), evaluated at varying frequencies <math>\omega_i\in\mathbb R</math> [rad/s], for <math>i=1,\dots,N=421</math>.
	Specifically, the frequencies are between 0.1Hz until 42.1Hz in steps of 0.1Hz.		Specifically, the frequencies are between 0.1Hz until 42.1Hz in steps of 0.1Hz.

Himpe: Reviewed and revised.

2021-03-16T19:31:20Z

Reviewed and revised.

← Older revision		Revision as of 19:31, 16 March 2021
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	~~{{preliminary}} <!-- Do not remove -->~~

	[[Category:benchmark]]		[[Category:benchmark]]
	[[Category:ODE]]		[[Category:ODE]]
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	===Motivation===		===Motivation===

	<figure id="fig:flexibleAC">[[File:Flexible1.png\|450px\|thumb\|right\|<caption>~~View~~ of the aerostructure of the flexible aircraft.</caption>]]</figure>		<figure id="fig:flexibleAC">[[File:Flexible1.png\|450px\|thumb\|right\|<caption>The steady pressure coefficient distribution <math>C_p</math> of the aerostructure of the flexible aircraft.</caption>]]</figure>

	Flexible aircraft models are very challenging in civil aeronautics due to their ~~lighter~~ structure. Models are largely used by engineers to optimize and analyze critical phenomena in the pre-design phase. Such models can be used to monitor some dimensioning critical stress of the aircraft in response to discrete and continuous gust situations.		Flexible aircraft models are very challenging in civil aeronautics due to their light-weight structure.
			Models are largely used by engineers to optimize and analyze critical phenomena in the pre-design phase.
			Such models can be used to monitor some dimensioning critical stress of the aircraft in response to discrete and continuous gust situations.

	Computing responses to discrete gusts are ~~sizing~~ steps when designing and optimizing a new aircraft structure and geometry. ~~Indeed~~, this is part of the imposed clearance certifications requested by the flight authorities. During the aircraft preliminary design phase, this clearance is done by intensive simulations. However, due to the involved model's complexity, these latter are time-consuming and imply an important computational burden. Moreover, these simulations are involved at different steps of the aircraft optimization process, by aeroelastic, flight and control engineers.		Computing responses to discrete gusts are expensive steps when designing and optimizing a new aircraft structure and geometry.
			In fact, this is part of the imposed clearance certifications requested by the flight authorities.
			During the aircraft preliminary design phase, this clearance is done by intensive simulations.
			However, due to the involved model's complexity, these latter are time-consuming and imply an important computational burden.
			Moreover, these simulations are involved at different steps of the aircraft optimization process, by aeroelastic, flight and control engineers.

	In <ref name=PousstVassal2018>C. Poussot-Vassal, D. Quero, and P. Vuillemin, "<span class="plainlinks">[https://doi.org/10.1016/j.ifacol.2018.03.094 Data-driven approximation of a high fidelity gust-oriented flexible aircraft dynamical model]</span>", in Proceedings of the 9th Vienna International Conference on Mathematical Modelling (MATHMOD), Vienna, Austria, 2018, pp 559--564.</ref>, a systematic way to fasten the gust simulation step and simplify the analysis by mean of data-driven model approximation in the Loewner framework is proposed, as well as a description of this model.		In <ref name=PousstVassal2018>C. Poussot-Vassal, D. Quero, and P. Vuillemin, "<span class="plainlinks">[https://doi.org/10.1016/j.ifacol.2018.03.094 Data-driven approximation of a high fidelity gust-oriented flexible aircraft dynamical model]</span>", in Proceedings of the 9th Vienna International Conference on Mathematical Modelling (MATHMOD), Vienna, Austria, 2018, pp 559--564.</ref>, a systematic way to fasten the gust simulation step and simplify the analysis by mean of data-driven model approximation in the Loewner framework is proposed, as well as a description of this model.
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	This benchmark contains a set of frequency-domain input-output data computed from a high fidelity simulator, and given as the couple		This benchmark contains a set of frequency-domain input-output data computed from a high fidelity simulator, and given as the couple
	:<math>		:<math>
	\{\omega_i,~~\Phi_i~~^{n_y\times n_u}\}_{i=1}^N,		\{\omega_i,H_i^{n_y\times n_u}\}_{i=1}^N,
	</math>		</math>
	where <math>~~\Phi_i~~\in\mathbb C^{n_y\times n_u}</math> represents the transfer from <math>n_u=1</math> input signal (gust disturbance) to <math>n_y=92</math> measurement outputs (accelerations and moments at different coordinates of a flexible aircraft wings and tail ), evaluated at varying frequencies <math>\omega_i\in\mathbb R</math> [rad/s], for <math>i=1,\dots,N=421</math>.		where <math>H_i\in\mathbb C^{n_y\times n_u}</math> represents the transfer from <math>n_u=1</math> input signal (gust disturbance) to <math>n_y=92</math> measurement outputs (accelerations and moments at different coordinates of a flexible aircraft wings and tail ), evaluated at varying frequencies <math>\omega_i\in\mathbb R</math> [rad/s], for <math>i=1,\dots,N=421</math>.
			Specifically, the frequencies are between 0.1Hz until 42.1Hz in steps of 0.1Hz.

	==Origin==		==Origin==
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	===Objective===		===Objective===

	Find a (linear) stable reduced order model that well ~~reconstitutes~~ the data.		Find a (linear) stable reduced order model that well approximates the data.

	==Citation==		==Citation==

Himpe: Minor Fixes.

2021-02-01T11:42:13Z

Minor Fixes.

← Older revision		Revision as of 11:42, 1 February 2021
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	Computing responses to discrete gusts are sizing steps when designing and optimizing a new aircraft structure and geometry. Indeed, this is part of the imposed clearance certifications requested by the flight authorities. During the aircraft preliminary design phase, this clearance is done by intensive simulations. However, due to the involved model's complexity, these latter are time-consuming and imply an important computational burden. Moreover, these simulations are involved at different steps of the aircraft optimization process, by aeroelastic, flight and control engineers.		Computing responses to discrete gusts are sizing steps when designing and optimizing a new aircraft structure and geometry. Indeed, this is part of the imposed clearance certifications requested by the flight authorities. During the aircraft preliminary design phase, this clearance is done by intensive simulations. However, due to the involved model's complexity, these latter are time-consuming and imply an important computational burden. Moreover, these simulations are involved at different steps of the aircraft optimization process, by aeroelastic, flight and control engineers.

	In <ref name=PousstVassal2018>C. Poussot-Vassal, D. Quero, and P. Vuillemin, "Data-driven approximation of a high fidelity gust-oriented flexible aircraft dynamical model", in Proceedings of the 9th Vienna International Conference on Mathematical Modelling (MATHMOD), Vienna, Austria, 2018, pp 559-564~~, DOI: https://doi.org/10.1016/j.ifacol.2018.03.094~~.</ref>, a systematic way to fasten the gust simulation step and simplify the analysis by mean of data-driven model approximation in the Loewner framework is proposed, as well as a description of this model.		In <ref name=PousstVassal2018>C. Poussot-Vassal, D. Quero, and P. Vuillemin, "<span class="plainlinks">[https://doi.org/10.1016/j.ifacol.2018.03.094 Data-driven approximation of a high fidelity gust-oriented flexible aircraft dynamical model]</span>", in Proceedings of the 9th Vienna International Conference on Mathematical Modelling (MATHMOD), Vienna, Austria, 2018, pp 559--564.</ref>, a systematic way to fasten the gust simulation step and simplify the analysis by mean of data-driven model approximation in the Loewner framework is proposed, as well as a description of this model.

	===Considered data===		===Considered data===
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	where <math>\Phi_i\in\mathbb C^{n_y\times n_u}</math> represents the transfer from <math>n_u=1</math> input signal (gust disturbance) to <math>n_y=92</math> measurement outputs (accelerations and moments at different coordinates of a flexible aircraft wings and tail ), evaluated at varying frequencies <math>\omega_i\in\mathbb R</math> [rad/s], for <math>i=1,\dots,N=421</math>.		where <math>\Phi_i\in\mathbb C^{n_y\times n_u}</math> represents the transfer from <math>n_u=1</math> input signal (gust disturbance) to <math>n_y=92</math> measurement outputs (accelerations and moments at different coordinates of a flexible aircraft wings and tail ), evaluated at varying frequencies <math>\omega_i\in\mathbb R</math> [rad/s], for <math>i=1,\dots,N=421</math>.

	===Origin===		==Origin==

	Collaboration between [https://www.onera.fr ONERA] and [https://www.onera.fr DLR]. The data from the high fidelity simulator have been generated by D. Quero (DLR), and the treatment performed jointly with P. Vuillemin, D. Quero and C. Poussot-Vassal.		Collaboration between [https://www.onera.fr ONERA] and [https://www.onera.fr DLR]. The data from the high fidelity simulator have been generated by D. Quero (DLR), and the treatment performed jointly with P. Vuillemin, D. Quero and C. Poussot-Vassal.
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	===Description===		===Description===

	The [[:File:FlexibleAircraft.zip\|FlexibleAircraft.zip]] (1.~~4Mo~~) repository contains three files:		The [[:File:FlexibleAircraft.zip\|FlexibleAircraft.zip]] (1.4MB) repository contains three files:

	* The <tt>dataONERA_FlexibleAircraft.mat</tt> data file, with		* The <tt>dataONERA_FlexibleAircraft.mat</tt> data file, with
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	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	::The MORwiki Community, '''Flexible Aircraft'''. MORwiki - Model Order Reduction Wiki, 2018. https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Flexible_Aircraft		::The MORwiki Community, '''Flexible Aircraft'''. MORwiki - Model Order Reduction Wiki, 2018. https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Flexible_Aircraft

			* For the background on the benchmark:

	@inproceedings{PoussotMATHMOD:2018,		@inproceedings{PoussotMATHMOD:2018,
	author = {C. Poussot-Vassal and D. Quero and P. Vuillemin},		author = {C. Poussot-Vassal and D. Quero and P. Vuillemin},
	title = {Data-driven approximation of a high fidelity gust-oriented flexible aircraft dynamical model},		title = {Data-driven approximation of a high fidelity gust-oriented flexible aircraft dynamical model},
	booktitle = {~~Proceedings of the~~ IFAC Mathematical Modelling},		booktitle = {IFAC PaperOnLine (9th Vienna International Conference on Mathematical Modelling)},
	~~address = {Vienna, Austria},~~		volume = {51},
	~~month~~ = {~~February~~},
	year = {2018},		year = {2018},
	pages = {559-564},		pages = {559--564},
			doi = {10.1016/j.ifacol.2018.03.094}
	}		}

Poussotvassal: /* Data */

2021-01-28T15:56:29Z

Data

← Older revision		Revision as of 15:56, 28 January 2021
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	==Data==		==Data==

			===Description===

	The [[:File:FlexibleAircraft.zip\|FlexibleAircraft.zip]] (1.4Mo) repository contains three files:		The [[:File:FlexibleAircraft.zip\|FlexibleAircraft.zip]] (1.4Mo) repository contains three files:
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	* 45--88: the local aerodynamic pitch moment on the aerodynamic strips.		* 45--88: the local aerodynamic pitch moment on the aerodynamic strips.
	* 89--92: the four generalized coordinates derivative (heave and pitch derivatives) and the first two flexible modes.		* 89--92: the four generalized coordinates derivative (heave and pitch derivatives) and the first two flexible modes.


			===Objective===

			Find a (linear) stable reduced order model that well reconstitutes the data.

	==Citation==		==Citation==

Poussotvassal: /* Data */

2021-01-28T15:31:45Z

Data

← Older revision		Revision as of 15:31, 28 January 2021
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	* The <tt>dataONERA_FlexibleAircraft_withMOR.mat</tt> data file, with 3 ROMs obtained with the [https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/MORE '''MOR toolbox'''] using the Loewner method		* The <tt>dataONERA_FlexibleAircraft_withMOR.mat</tt> data file, with 3 ROMs obtained with the [https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/MORE '''MOR toolbox'''] using the Loewner method
	** Hr1 : linear rational ~~ROM~~ with varying dimensions (state-space models in Matlab form ~~<math>n_y \times n_u</math>~~).		** Hr1 : linear rational ROMs with varying dimensions (state-space models in Matlab form).
	** Hr2 : linear rational ~~ROM~~ with varying dimensions, with stability post enforcement and input/output normalisation to catch all transfer whatever the amplitude (state-space models in Matlab form ~~<math>n_y \times n_u</math>~~).		** Hr2 : linear rational ROMs with varying dimensions, with stability post enforcement and input/output normalisation to catch all transfer whatever the amplitude (state-space models in Matlab form).

	* The <tt>startONERA_FlexibleAircraft.m</tt> script file, used to loads and plots the data for illustration.		* The <tt>startONERA_FlexibleAircraft.m</tt> script file, used to loads and plots the data for illustration.

Poussotvassal: /* Origin */

2021-01-28T15:25:43Z

Origin

← Older revision		Revision as of 15:25, 28 January 2021
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	===Origin===		===Origin===

	Collaboration between [https://www.onera.fr ONERA] and [https://www.onera.fr DLR]. The data from the high fidelity simulator have been generated by D. Quero (DLR), and the treatment performed jointly with P. Vuillemin, D. Quero and C. Poussot-Vassal		Collaboration between [https://www.onera.fr ONERA] and [https://www.onera.fr DLR]. The data from the high fidelity simulator have been generated by D. Quero (DLR), and the treatment performed jointly with P. Vuillemin, D. Quero and C. Poussot-Vassal.

	==Data==		==Data==

Poussotvassal at 13:45, 28 January 2021

2021-01-28T13:45:35Z

← Older revision		Revision as of 13:45, 28 January 2021
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	where <math>\Phi_i\in\mathbb C^{n_y\times n_u}</math> represents the transfer from <math>n_u=1</math> input signal (gust disturbance) to <math>n_y=92</math> measurement outputs (accelerations and moments at different coordinates of a flexible aircraft wings and tail ), evaluated at varying frequencies <math>\omega_i\in\mathbb R</math> [rad/s], for <math>i=1,\dots,N=421</math>.		where <math>\Phi_i\in\mathbb C^{n_y\times n_u}</math> represents the transfer from <math>n_u=1</math> input signal (gust disturbance) to <math>n_y=92</math> measurement outputs (accelerations and moments at different coordinates of a flexible aircraft wings and tail ), evaluated at varying frequencies <math>\omega_i\in\mathbb R</math> [rad/s], for <math>i=1,\dots,N=421</math>.

	==Origin==		===Origin===

	Collaboration between [https://www.onera.fr ONERA] and [https://www.onera.fr DLR]. The data from the high fidelity simulator have been generated by D. Quero (DLR), and the treatment performed jointly with P. Vuillemin, D. Quero and C. Poussot-Vassal		Collaboration between [https://www.onera.fr ONERA] and [https://www.onera.fr DLR]. The data from the high fidelity simulator have been generated by D. Quero (DLR), and the treatment performed jointly with P. Vuillemin, D. Quero and C. Poussot-Vassal

Poussotvassal: /* Motivation */

2021-01-28T13:42:57Z

Motivation

← Older revision		Revision as of 13:42, 28 January 2021
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	In <ref name=PousstVassal2018>C. Poussot-Vassal, D. Quero, and P. Vuillemin, "Data-driven approximation of a high fidelity gust-oriented flexible aircraft dynamical model", in Proceedings of the 9th Vienna International Conference on Mathematical Modelling (MATHMOD), Vienna, Austria, 2018, pp 559-564, DOI: https://doi.org/10.1016/j.ifacol.2018.03.094.</ref>, a systematic way to fasten the gust simulation step and simplify the analysis by mean of data-driven model approximation in the Loewner framework is proposed, as well as a description of this model.		In <ref name=PousstVassal2018>C. Poussot-Vassal, D. Quero, and P. Vuillemin, "Data-driven approximation of a high fidelity gust-oriented flexible aircraft dynamical model", in Proceedings of the 9th Vienna International Conference on Mathematical Modelling (MATHMOD), Vienna, Austria, 2018, pp 559-564, DOI: https://doi.org/10.1016/j.ifacol.2018.03.094.</ref>, a systematic way to fasten the gust simulation step and simplify the analysis by mean of data-driven model approximation in the Loewner framework is proposed, as well as a description of this model.


	===Considered data===		===Considered data===

Poussotvassal: /* Citation */

2021-01-28T13:42:43Z

Citation

← Older revision		Revision as of 13:42, 28 January 2021
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	* For the benchmark itself and its data:		* For the benchmark itself and its data:
	::The MORwiki Community, '''Flexible ~~AIrcraft~~'''. MORwiki - Model Order Reduction Wiki, 2018. https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Flexible_Aircraft		::The MORwiki Community, '''Flexible Aircraft'''. MORwiki - Model Order Reduction Wiki, 2018. https://morwiki.mpi-magdeburg.mpg.de/morwiki/index.php/Flexible_Aircraft

	@inproceedings{PoussotMATHMOD:2018,		@inproceedings{PoussotMATHMOD:2018,