# Validation of the Developed Psychoacoustic Model for Sound Quality Valuation of Washing Machines
## 3 Results and Discussion
The results presented in Table 7 demonstrate a strong correlation between the subjective rating and the calculated value of the sound quality index. From the above results, it is clear that there was no agreement between the objective and subjective evaluations for the FILL operating mode. This is due to the fact that with Machine-\(I\) in FILL mode, there was a sound of a tonal nature that respondents perceived as disturbing. This tonal sound was also confirmed by the psychoacoustic parameter Tonality in objective measurement. This phenomenon of tonal sound was not captured in the development of the psychoacoustic model for evaluating the sound quality of washing machines. As a result, there were deviations in determining the ranking of washing machines, based on these methods. On \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Overall Order**} & \multicolumn{2}{c}{**FILL**} & \multicolumn{2}{c}{**WASH**} & \multicolumn{2}{c}{**SPIN**} \\ \cline{2-7}  & **Model \(S_{Qi}\)** & **Subject.** & **Model \(S_{Qi}\)** & **Subject.** & **Model \(S_{Qi}\)** & **Subject.** \\ \hline \multirow{3}{*}{1} & Machine–\(I\) & Machine–\(3\) & Machine–\(I\) & Machine–\(I\) & Machine–\(I\) & Machine–\(I\) & Machine–\(I\) \\  & (1.06) \(\star\) & (8.5) & (0.36) \(\star\) & (8.1) & (2.13) \(\star\) & (6.5) \\ \multirow{3}{*}{2} & Machine–\(3\) & Machine–\(2\) & Machine–\(3\) & Machine–\(3\) & Machine–\(3\) & Machine–\(3\) & Machine–\(3\) \\  & (1.13) & (6.5) & (0.53) & (7.8) & (2.21) & (5.7) \\ \multirow{3}{*}{3} & Machine–\(2\) & Machine–\(I\) & Machine–\(2\) & Machine–\(2\) & Machine–\(2\) & Machine–\(2\) \\  & (1.32) \(\star\) & (4.9) & (0.90) \(\star\) & (5.1) & (2.31) \(\star\) & (5.2) \\ \hline \hline \end{tabular}  
*—best achieved values: ***–worst achieved values.  
\end{table} 
Table 7: Established ranking of washing machines based on sound quality index and jury study results. the contrary, in the WASH and SPIN modes, the results showed the same agreement not only in the ranking of the washing machines but also in the comparison between objective and subjective evaluations. Machine-2 received the lowest number of points in the listening tests for all evaluated psychoacoustic parameters (FILL--4.9, WASH--5.1, SPIN--5.2). However, there is a great degree of variability in the washing performance of each washing machine, depending on the ongoing operating washing mode. To verify the agreement of the ranking in each operating mode, we used the Spearman coefficient, which can be calculated as follows:  
\[r_{s}=1-\frac{6}{n(n^{2}-1)}\sum_{i=1}^{n}(R_{i}-Q_{i})^{2} \tag{6}\]  
where: \(R\)--rank of the data \(x\); \(Q\)--rank of the data \(y\); \(n\)--file size. Values of Spearman's rank correlation coefficient are presented in Table 8. Values close to 0 indicate a weaker ordinal dependence between variables, while values close to 1 or \(-1\) indicate a tighter ordinal dependence (direct or indirect). Based on [PERSON]'s rank correlation coefficient, the ranking of the washing machines in the two operating modes (WASH, SPIN) is 100% consistent. In the FILL operating mode, the ranking match was not fully confirmed. The following (Figure 4) shows the overall process of evaluating the psychoacoustic properties of automatic washing machines based on the developed psychoacoustic model and the proposed validation process. For further investigation, we recommend using machine learning to adapt psychoacoustic models based on individual listener profiles. This would allow for personalized sound quality assessments that consider hearing acuity, preferences, and even psychological state, improving the accuracy of predictions in consumer products  
Deep learning integration combines human perceptual ratings with neural networks to predict sound quality metrics, such as loudness and sharpness, more accurately. Neural networks are increasingly integral to sound quality engineering, bridging the gap between objective measurements and human perception.