DOI: 10.21950/z0bei4
title: Acoustic Cavity Spectra for Classifying Salt Concentrations

description: &lt;p&gt;We present and validate an audible-band, resonant-cavity acoustic system that operates both as a sensor and as an automatic classifier for the nondestructive analysis of aqueous solutions, enabling the discrimination of solute concentrations using small liquid volumes.&lt;/p&gt; 
&lt;p&gt;Frequency spectra computed from impact recordings on a glass resonator were used to construct ten datasets spanning two salts (MgCl2 and KCl), four concentrations (0.001, 0.01, 0.1, and 1\,M), for a total of 1918 normalized spectra represented by 511 features.&lt;/p&gt;
&lt;p&gt;We evaluate three supervised learning approaches coupled with feature selection to reduce dimensionality: Random Forest (RF), linear-kernel Support Vector Machine (SVM) and a hybrid Genetic Algorithm with Extreme Learning Machine (GA+ELM) as fitness function tailored to select frequency bands.&lt;/p&gt; 
&lt;p&gt;Across all datasets, every method exceeds 99\% accuracy on held-out validation sets; SVM attains the highest accuracy among the three strategies in the binary and 4-class settings, whereas GA+ELM yields the top scores in the 9-class setting, highlighting the value of band-oriented selection as spectral overlap increases. 
RF consistently ranks last both in accuracy and in the compactness of the selected frequency regions across the audible spectrum.&lt;/p&gt; 
&lt;p&gt;For SVM and GA+ELM, the feature reduction surpasses 92\%, evidencing a high signal-information ratio.&lt;/p&gt;
&lt;p&gt;Analysis of the selected bands reveals clear algorithmic profiles: RF tends to disperse selections; SVM concentrates on mid-to-high bands; and GA+ELM emphasizes a few contiguous intervals that are amenable to physical interpretation and to the design of bespoke sensing front-ends.&lt;/p&gt; 
&lt;p&gt;These results indicate a practical route to rapid, low-cost, and interpretable acoustic characterization of aqueous solutions.&lt;/p&gt;
&lt;p&gt;A large number of frequency spectra were generated from each audio signal recorded during the impact of the pendulum on the surface of the resonant vessel for all experiments conducted on the nine aqueous solutions. 
The frequency spectra were computed using the Fast Fourier Transform (FFT) implemented in Audacity 3.7.4. 
A 1024-point Hann window was selected for the FFT computation (sampling rate of fs = 44.1 kHz used during acoustic acquisition).
All measurements were acquired in a single session under identical temperature and humidity conditions using the same acquisition procedure and geometry.&lt;/p&gt; 

&lt;p&gt;To compensate for small variations between individual measurements, the spectra were averaged over groups of 3 and 5 consecutive impacts. 
This averaging procedure reduces noise and enhances the reliability of the spectral data. 
For each aqueous solution, at least 80 spectra averaged over 3 impacts and 150 spectra averaged over 5 impacts were obtained. 
Spectra exhibiting interference or excessive noise were discarded, resulting in a final total of 1918 valid spectra with broadband SNR&gt;20 dB.&lt;/p&gt;

&lt;p&gt;Following this processing stage, several datasets were constructed to perform the automatic classification of the aqueous solutions using Machine Learning algorithms. 
Five classification tasks were defined according to the number of classes involved (2, 4, or 9) and the number of averaged impacts (3 or 5), resulting in ten different datasets, labeled Id = 1 to Id = 10.
Datasets with an odd identifier correspond to spectra averaged over 3 consecutive impacts, whereas those with an even identifier contain spectra averaged over 5 consecutive impacts. 
Datasets Id = 1 and Id = 2 comprise all spectra from the nine aqueous solutions (complete set of 1918 spectra obtained in the experiments). 
Datasets Id = 3 through Id = 6 correspond to binary classification tasks, containing spectra from two classes: pure water and the lowest concentration (0.001 M) of each salt. 
Finally, datasets Id = 7 through Id = 10 contain spectra from four classes, corresponding to the four concentrations of a single salt.&lt;/p&gt;
description: Methodology
A large number of frequency spectra were generated from each audio signal recorded during the impact of the pendulum on the surface of the resonant vessel for all experiments conducted on the nine aqueous solutions. 
The frequency spectra were computed using the Fast Fourier Transform (FFT) implemented in Audacity 3.7.4. 
A 1024-point Hann window was selected for the FFT computation (sampling rate of fs = 44.1 kHz used during acoustic acquisition).
All measurements were acquired in a single session under identical temperature and humidity conditions using the same acquisition procedure and geometry.