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Communication Dans Un Congrès Année : 2023

Formulation of a high-dimensional optimization problem combined with probabilistic learning in a turbomachinery detuning context

Résumé

This research concerns the improvement of the vibratory performances of turbomachines. In such a context, the detuning optimization is a good strategy for inhibating the amplifications induced by the unavoidable random blade mistuning of bladed-disks. In a green aviation context for which fan blade design yields larger blades made up of lighter materials, large displacements amplitudes occur requiring to include in the stochastic modeling the nonlinear geometrical effects. The detuning is defined by using alternating patterns of several different sector types. It is thus characterized by a discrete valued-vector whose size is the number of blades and for which each component belongs to the same subset of natural integers. The major difficulty is directly related to the dimension of the set of all possible detuning configurations that exponentially increases with the number of blades. Such a detuning optimization requires to solve an high-dimensional combinatorial optimization problem for which the cost function is evaluated from a nonlinear stochastic reduced computational model (viewed as an High-Fidelity Computational Model (HFCM)), that has previously been constructed [1]. The main idea is then to use an available full data basis [2] involving a set of 352 detuning configurations issued from a 12 blades structure with 2 different types of blades. As a consequence, the configurations allowing for reducing the mistuning amplifications are known and it happens that nearly a dozen can be considered as improving ones. A first difficulty concerns the definition of the cost function since we are interested in the extreme values of random outputs that are related to the largest resonance of the most unfavourable blade. A second difficulty is that the cost function can only be computed in practical situations at a limited number of points, due to the curse of dimensionality. Therefore, probabilistic learning strategies have to be considered. This means that only a small data training set, issued from the HFCM and which does not a priori include any optima, is available. The main idea is then to construct a continuous approximation of this cost function, based on the use of the probabilistic learning PLoM tool [3], and that will be used in the learning step. Several difficulties inherent to the definition of the cost function (weak contrast and numerous local minima) require to reformulate the definition of the optimum. A numerical validation using the available full data basis is then performed in order to test the capability of the proposed methodology. [1] A. Picou, E. Capiez-Lernout, C. Soize, M. Mbaye, Robust dynamic analysis of detuned-mistuned rotating bladed disks with geometric nonlinearities, Computational Mechanics, 65(3), 711–730, (2020). [2] E. Capiez-Lernout, C. Soize, Nonlinear stochastic dynamics of detuned bladed-disks with uncertain mistuning and detuning optimization using a probabilistic machine learning tool, International Journal of Non-Linear Mechanics, Elsevier, 2022, 143, pp.104023, (2022). [3] C. Soize, R. Ghanem, Probabilistic learning on manifolds (PLoM) with partition, International Journal for Numerical Methods in Engineering, doi: 10.1002/nme.6856, 123(1), 268-290 (2022).
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Dates et versions

hal-04129008 , version 1 (15-06-2023)

Identifiants

  • HAL Id : hal-04129008 , version 1

Citer

Evangéline Capiez-Lernout, Christian Soize. Formulation of a high-dimensional optimization problem combined with probabilistic learning in a turbomachinery detuning context. 5th International Conference on Uncertainty Quantification in Computational Sciences and Engineering, UNCECOMP 2023, Jun 2023, Athens, Greece. ⟨hal-04129008⟩
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