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In this manuscript, we describe a novel methodology for nearfield acoustic holography (NAH). The proposed technique is based on convolutional neural networks, with autoencoder architecture, to reconstruct the pressure and velocity fields on the surface of the vibrating structure using the sampled pressure soundfield on the holographic plane as input. The loss function used for training the network is based on a combination of two components. The first component is the error in the reconstructed velocity. The second component is the error between the sound pressure on the holographic plane and its estimate obtained from forward propagating the pressure and velocity fields on the structure through the Kirchhoff–Helmholtz integral; thus, bringing some knowledge about the physics of the process under study into the estimation algorithm. Due to the explicit presence of the Kirchhoff–Helmholtz integral in the loss function, we name the proposed technique the Kirchhoff–Helmholtz-based convolutional neural network, KHCNN. KHCNN has been tested on two large datasets of rectangular plates and violin shells. Results show that it attains very good accuracy, with a gain in the NMSE of the estimated velocity field that can top 10 dB, with respect to state-of-the-art techniques. The same trend is observed if the normalized cross correlation is used as a metric.

Near-field Acoustic Holography (NAH) is a wellknown problem aimed at estimating the vibrational velocity field of a structure by means of acoustic measurements. In this paper, we propose a NAH technique based on Convolutional Neural Network (CNN). The devised CNN predicts the vibrational field on the surface of arbitrary shaped plates (violin plates) with orthotropic material properties from a limited number of measurements. In particular, the architecture, named super resolution CNN (SRCNN), is able to estimate the vibrational field with a higher spatial resolution compared to the input pressure. The pressure and velocity datasets have been generated through Finite Element Method simulations. We validate the proposed method by comparing the estimates with the synthesized ground truth and with a state-of-the-art technique. Moreover, we evaluate the robustness of the devised network against noisy input data.

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