Probabilistic learning on manifolds for liner impedance for design optimisation
Résumé
We address the problem of noise reduction for Ultra High By Pass Ratio (UHBR) engines. This is to be done for low frequency tonal noises by means of tailored acoustic liners. In order to avoid the prohibitively high computational and experimental costs for the design optimisation of these liners, recent advances made in probabilistic machine learning and AI are used for constructing meta-models of liner acoustic impedances.
Probabilistic learning on Manifolds (PLoM) [1] is a machine-learning tool that allows a learned set to be generated from a given training set whose points are realisations of a non-Gaussian random vector whose support of its probability distribution is concentrated in a subset (a manifold). This approach preserves the concentration of the probability measure for the learned set. This approach has been developed for the case of small data in the training set as opposed to big data that are usually used for deep learning of ANN. We use this probabilistic learning tool for constructing a probabilistic meta-model of a liner acoustic impedance for which a training set has been constructed with a computational model. Conditional statistics of the real and imaginary parts of the frequency dependent impedance are estimated, which allow a digital twin of the liner to be created. This digital twin is robust and has been validated though conditional statistics and measure of concentration. This surrogate model can be further improved upon by addition of physics-based impedance data from experimental and/or finite elements calculations through data fusion techniques.
References:
[1] C. Soize, R. Ghanem. “Probabilistic learning on manifolds (PLoM) with partition”. In: International Journal for Numerical Methods in Engineering 123 (2022) pp. 268-290. DOI: https://doi.org/10.1002/nme.6856.