# Validation of the Developed Psychoacoustic Model for Sound Quality Valuation of Washing Machines
## 2 Materials and Methods
### Description and Analysis of Developed Psychaocustic Model  
Five models of automatic washing machines in three operation modes were selected for sound quality assessment. The psychoacoustic metrics of the automatic washing machines were specified by processing audio signals recorded through the binaural measurement method. The values measured for the psychoacoustic metrics, in particular operating cycles, are presented in Figure 2. Psychaocustic parameters are measured in different units; the graphs show the normalized values. We transpose the values of individual parameters into the standardized form. As all evaluated psychoacoustic parameters are measured in different units, it was important to standardize the measured values (mathematical-statistical transformation of the measured values into standard scores) so that all parameters have comparable ranges. The normalization of z-scores (standardization) is calculated as follows:  
* while maximizing the indicator: \[n_{ij}=\frac{x_{ij}-\overline{x}_{j}}{s_{j}}\] (1)
* while minimizing the indicator: \[n_{ij}=\frac{\overline{x}_{j}-x_{ij}}{s_{j}}\] (2)  
where: \(x_{ij}\)--value of the \(j\)-th indicator of the \(i\)-th object; \(\overline{x}_{j}\)--average value of the \(j\)-th indicator; \(s_{j}\)--standard deviation of the \(j\)-th indicator; \(n_{ij}\)--standard value of the \(i\)-th object for the \(j\)-th indicator. The questionnaire survey for sound quality assessment with 81 respondents was carried out and evaluated. The results of the jury study, along with the average point scores for individual washing machines in three operation modes, are shown in Table 3.  
Our contribution was to determine the weights of psychoacoustic parameters by correlating the objective and subjective evaluations of the washing machine properties (based on the values of psychoacoustic parameters and the number of questionnaire scores) through the Weighted Sum Method. To determine the weights of individual indicators, we used the correlation coefficients. Correlation coefficients and multicriteria analysis were used to analyze the relationship between objective measurements and the questionnaire survey. Correlation coefficients (the Pearson correlation coefficient) are used in statistics to measure the strength of a relationship between two variables. Correlation coefficient formulas are used to find the strength of a relationship between data; the Pearson correlation coefficient will not give you any information about the slope of the line, it only tells you whether there is a relationship. It turns out that r will always be between \(-1\) and \(+1\). A correlation coefficient of 1 means  
Figure 2: Psychoacoustic parameters—normalized values. \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Washing Machine**} & \multicolumn{3}{c}{**Average Point Score**} \\ \cline{2-4}  & **FILL** & **WASH** & **SPIN** \\ \hline Machine–1 & 5.60 & 8.77 & 5.60 \\ Machine–2 & 6.36 & 6.28 & 6.36 \\ Machine–3 & 6.98 & 5.41 & 6.98 \\ Machine–4 & 5.90 & 8.06 & 5.90 \\ Machine–2 & 6.60 & 7.04 & 6.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Average point score according to jury study [12]. that for every positive increase in one variable, there is a positive increase in the other. The zero result indicates no relationship. The value of the Pearson correlation coefficient between psychoacoustic parameters and the number of scores of the questionnaire is in Table 4 for each cycle (FILL, WASH, SPIN). The values of correlation coefficients are calculated as follows:  
\[r_{xy}=\frac{cov(x,y)}{\sqrt{Var(x)\cdot Var(y)}} \tag{3}\]  
where: _cov(x,y)_--covariance between \(x\) and \(y\); _Var(x)_--variance of variable \(x\); _Var(y)_--variance of variable \(y\).