A statistical approach to violin evaluation

Comparing violins requires competence and involves both subjective and objective evaluations. In this manuscript, vibration tests were performed on a set of 25 violins, both historical and new. The resulting bridge admittances were modeled in the low and mid-frequency ranges through a set of objective features. Once projected into the new representation, the bridge admittances of three historical violins made by Stradivari and a famous reproduction revealed high similarity. PCA highlighted the importance of signature mode frequencies, bridge hill behavior, and signature mode amplitudes in distinguishing different violins

A neural network-based method for spruce tonewood characterization

The acoustical properties of wood are primarily a function of its elastic properties. Numerical and analytical methods for wood material characterization are available, although they are either computationally demanding or not always valid. Therefore, an affordable and practical method with sufficient accuracy is missing. In this article, we present a neural network-based method to estimate the elastic properties of spruce thin plates. The method works by encoding information of both the eigenfrequencies and eigenmodes of the system and using a neural network to find the best possible material parameters that reproduce the frequency response function. Our results show that data-driven techniques can speed up classic finite element model updating by several orders of magnitude and work as a proof of concept for a general neural network-based tool for the workshop. © 2023 Acoustical Society of America

The impact of alkaline treatments on elasticity in spruce tonewood

It is commonly believed that violins sound differently when finished. However, if the role of varnishes on the vibrational properties of these musical instruments is well-established, how the first components of the complete wood finish impact on the final result is still unclear. According to tradition, the priming process consists of two distinct stages, called pre-treatment and sizing. The literature reports some recipes used by old Cremonese luthiers as primers, mainly based on alkaline aqueous solutions and protein-based glues. In this manuscript, we analyze the impact of these treatments on the mechanical properties of the material. The combination of two pre-treatments and three sizes is considered on nine different plates. We compare the vibrational properties before and after the application and assess the effects of the different primers, also supported by finite element modeling. The main outcome is that the combination of particular treatments on the violin surface before varnishing leads to changes not only to the wood appearance, but also to its vibrational properties. Indeed pre-treatments, often considered negligible in terms of vibrational changes, enhance the penetration of the size into the wood structure and strengthen the impact of the latter on the final rigidity of the material along the longitudinal and radial directions

Prediction of Missing Frequency Response Functions Through Deep Image Prior

Vibration analysis is crucial when designing and monitoring resonant structures. The characterization of vibrational properties in mechanical systems, e.g. machinery or musical instruments, can indeed detect noise sources and damages. Several methods can retrieve these parameters starting from a set of measurements. The level of detail in the estimate mostly depends on the amount and distribution of points acquired over space. A potential issue for these techniques consists in the presence of regions over the object where sensors cannot be attached. In this case, an interpolation scheme with a suitable prior of the data model should be devised. We propose here to predict the missing vibrational data within the framework of image inpainting and apply a fully data-driven method based on Deep Image Prior, which allows to capture the prior inside data without the need of a dataset. The performance is assessed in the case of violin top plates. The proposed method proved to better predict data, in particular resonances, for points close to the boundary, whereas a baseline based on Thin Plate Splines fails, due to the reduced number of available samples

Beamformer-based estimation of longitudinal wave speed in tonewood

Mechanical properties of the wood have great impact on the design of musical instruments. As a matter of fact, luthiers accurately select tonewoods according to some desired elastic features. Typically, their choices are based on the longitudinal wave speed. In order to avoid direct parameter estimation techniques which can bring wood specimens to rupture, either empirical rules of thumb or expensive equipment with high sampling frequency are customarily employed. In this paper we propose a methodology for speed estimation starting from impulse responses acquired by accelerometers placed at the block edges. The technique relies on the definition of the Delay And Sum (DAS) beamformer, where instead of steering the beamformer to different Directions of Arrival (DOAs), we evaluate the filter output varying the wave speed. The proposed method is non-invasive, low-cost and it requires only basic expertise on hammer testing. We assessed the accuracy of the estimation using both simulated signals and measures on actual tonewoods. We compared the resulting performance with that of another state-of-the-art technique working at the same sampling frequency and with the same setup. Results show the effectiveness of the beamformer also in the case of low sampling frequency and high speeds

Near-field acoustic holography analysis with convolutional neural networks

Near-field Acoustic Holography (NAH) enables the contactless analysis of the vibrational field on plates and shells from the acoustic data captured in proximity of the vibrating object. In this paper, we propose a data-driven approach to NAH by using a Convolutional Neural Network (CNN) that predicts the vibrational field on the object from the acoustic pressure field captured by a microphone array deployed in its proximity. We have conducted an extensive simulation campaign on rectangular plates of different dimensions, boundary conditions and mechanical properties. This dataset has been generated using Finite Element Method simulation for predicting both vibrational and acoustic pressure fields. The performance of the proposed data-driven NAH method is assessed by comparing the estimated vibrational field with the ground truth. Moreover, we offer an analysis of the robustness of the estimate against noisy input data

Interpolation of irregularly sampled frequency response functions using convolutional neural networks

In the field of structural mechanics, classical methods for the vibrational characterization of objects exploit the inherent redundancy of a relevant amount of measurements acquired over regular sampling grids. However, there are cases in which parts of the objects under analysis are not accessible with sensors, leading to irregular sampling grids characterized by holes. Recent works have proved the benefits of adding prior knowledge in these scenarios, either through the definition of a suitable decomposition or using Finite Element modelling. In this paper we propose to use Convolutional Autoencoders (CA) for Frequency Response Function (FRF) interpolation from grids with different subsampling schemes. CA learn a compressed representation from a dataset of FRFs synthetized through Finite Element Analysis. Experiments with numerical and experimental data show the effectiveness of the model with a different amount of missing data and its ability to predict real FRFs characterized by different damping and sampling frequency

On the prediction of the frequency response of a wooden plate from its mechanical parameters

Inspired by deep learning applications in structural mechanics, we focus on how to train two predictors to model the relation between the vibrational response of a prescribed point of a wooden plate and its material properties. In particular, the eigenfrequencies of the plate are estimated via multilinear regression, whereas their amplitude is predicted by a feedforward neural network. We show that labeling the train set by mode numbers instead of by the order of appearance of the eigenfrequencies greatly improves the accuracy of the regression and that the coefficients of the multilinear regressor allow the definition of a linear relation between the first eigenfrequencies of the plate and its material properties

Feature-based representation for violin bridge admittances

Frequency Response Functions (FRFs) are one of the cornerstones of musical acoustic experimental research. They describe the way in which musical instruments vibrate in a wide range of frequencies and are used to predict and understand the acoustic differences between them. In the specific case of stringed musical instruments such as violins, FRFs evaluated at the bridge are known to capture the overall body vibration. These indicators, also called bridge admittances, are widely used in the literature for comparative analyses. However, due to their complex structure they are rather difficult to quantitatively compare and study. In this manuscript we present a way to quantify differences between FRFs, in particular violin bridge admittances, that separates the effects in frequency, amplitude and quality factor of the first resonance peaks characterizing the responses. This approach allows us to define a distance between FRFs and clusterise measurements according to this distance. We use two case studies, one based on Finite Element Analysis and another exploiting measurements on real violins, to prove the effectiveness of such representation. In particular, for simulated bridge admittances the proposed distance is able to highlight the different impact of consecutive simulation 'steps' on specific vibrational properties and, for real violins, gives a first insight on similar styles of making, as well as opposite ones