Data-Driven Aeroacoustic Modelling: Trailing-Edge Noise

Broadband noise emitted at the trailing edge of an airfoil represents a significant contribu- tion to the noise emission in rotors, wind turbine and fan blades, in low Mach number flows. High-fidelity calculations are out of the scope when fast parametric calculations are needed. In these cases it is necessary to resort to analytical models and the most popular one is the model proposed by Amiet. In the model, the knowledge of the wall pressure spectrum allows to define an equivalent point source located at the trailing edge. The description of the turbulent wall pressure spectrum is of major importance for the correct noise prediction. Proposed empirical laws of wall pressure spectra in presence of adverse pressure gradients are limited to cases which are not too far from the test cases employed for their calibration. Recently, the development of machine learning techniques make it possible to analyze large amounts of experimental data in order to automatically extract modeling knowledge. However measurements of pressure fluctuations near a trailing edge are difficult. An alternative solution is to measure the far-field trailing-edge noise at each condition. The measures are comparatively simpler and contain all the information about the source. In this work a deep learning algorithm, based on a standard feed-forward Artificial Neural Network (ANN) and a Random Forest (RF) algorithm are applied to far-field directivity data sets. The motivation of the present work is to evaluate the prediction ability of the ANN and RF models. The proposed approach allows to build a general model which can potentially be trained on experimental data and so it is not limited by the simplifying assumptions required by analytical models or empirical wall pressure spectrum. The prediction capabilities of ANN and RF are investigated by considering data not included in the training database. The potential of RF regression for the evaluation of the prediction uncertainty is also addressed. The proposed models are based on a splitting in sub models: the ANN or the RF algorithm is used to describe the noise directivity while a polynomial model is introduced for the prediction of the emitted acoustic power. This splitting, which improves significantly the training performance, can be seen as a possible way to introduce a physical constraint to the machine learning model which is forced to satisfy a constraint on the emitted power. The proposed procedure is tested on an artificial database generated by the Amiet model. However, it can be directly applied to experimental data or high-fidelity calculations.