Monday  |  Salon 14  |  04:40 PM–05:00 PM

#18334–Stochastic Dynamics and Surrogate Modeling for Nonlinear Aerospace Nozzle Systems with Partial Observations

This research addresses a computational implementation of a methodology aimed at identifying a statistical surrogate model using a small incomplete target dataset [1]. The structure is an engine nozzle, made of an elastic homogenized material and that is subjected to an internal stochastic pressure jet. It is assumed to undergo large displacements. A limited target dataset consisting of a subset of normal displacements located at the nozzle exit, is assumed to be available.

A nonlinear stochastic computational model (SCM) of the nozzle dynamics is developed [2], where controlled parameters represent the spectral properties of the stochastic load, while uncontrolled parameters describe the anisotropic properties of the material. Due to the complexity of such a highly nonlinear SCM, significant computational resources are required to obtain one response for a given set of parameters.

Initially, the nonlinear SCM is used with given control parameters, without uncontrolled parameters and with stiffened elastic moduli, in order to get the quantities of interest (QoI) corresponding to the small incomplete target dataset. The parameterized nonlinear SCM is also employed with random values of both controlled and uncontrolled parameters to construct a small training dataset. This latter one describes the realizations of the controlled parameters, the corresponding random responses at the nozzle exit, and the corresponding QoI related to the target.

The PLoM algorithm, based on a purely probabilistic approach [3], is used and adapted to the constraint of an existing incomplete target dataset [1] in order to develop a surrogate computational model. The learning set consists of realizations of controlled parameters and their corresponding QoI. This surrogate computational model allows for updating the response, which is brought closer to the target response.

[1] C. Soize, R. Ghanem, Probabilistic-learning-based stochastic surrogate model from small incomplete datasets, Computer Methods in Applied Mechanics and Engineering, 418(A), 116798, 2024.

[2] E. Capiez-Lernout, O. Ezvan, C. Soize, Updating nonlinear stochastic dynamics of an uncertain nozzle model using probabilistic learning with partial observability and incomplete dataset, Journal of Computing and Information Science and Engineering, 24(6): 061006, 2024.

[3] C. Soize, R. Ghanem, Data-driven probability concentration and sampling on manifold,
Journal of Computational Physics, 321 242-258 (2016).

Evangéline Capiez-Lernout   Université Gustave Eiffel
Olivier Ezvan   Université Gustave Eiffel
Christian Soize   Université Gustave Eiffel