## 3 Results and Discussion
### Braking Phase--Noise
The value \(R_{ij}(x,\,y)=0\) is the most unfavorable; it means that a given indicator \(\overline{S}_{ij}\) has taken the maximum value (in the case of the vibration and noise level measures used, the higher the value of a given indicator, the greater the vibration and noise level). The final assessment compares the \(F_{i}\) values, which are the average value of all relative measures \(R_{ij}(x,\,y)\). The higher the value of this indicator, the lower the overall nuisance and the better the comfort (a higher value means that the values of individual indicators are further from the unfavorable values). \[\overline{S}_{ij}=\frac{1}{n}\sum_{k=1}^{n}s_{ijk}\ ;\ \ S_{ijk}=\{s_{ij1}\ldots s_{ jn}\} \tag{15}\]  
\[A_{ij}^{max}=max\{\overline{S}_{ij}\ :\ j=1\ldots m\} \tag{16}\]  
\[\psi_{s}=k_{s}\varphi_{s}^{n_{s}}\,, \tag{8}\]0  
\[\psi_{s}=k_{s}\varphi_{s}^{n_{s}}\,, \tag{8}\]1  
It is interesting to note the consistency of the results between the individual vibration and noise measurements (international standards) and the combined vibroacoustic measurement (\(F_{c}\), [PERSON]'s metrics), as presented in the paper. There appears to be a general agreement between the two sets of results, with train D being the most comfortable according to individual and combined metrics while train A was the least comfortable for both metrics. However, it should be noted that the production dates of each train type vary significantly: A-train-type production started in 1976, and D-train-type production started in 2012; hence, there is a vast technological gap between their constructions, and they can be considered extreme cases. On the other hand, according to individual metrics, train B, produced in 1997, subsequently reached the second lowest noise level (\(L_{Aeq}\)) and third lowest vibration level (VDV and RMS). Train E reached the fourth lowest noise level (\(L_{Aeq}\)), first lowest RMS level, and second lowest VDV level. It would not be obvious to rank these trains based solely on their performance in the international standards until we use combined metrics. However, the combined metric might not always lead to significant variations from what one would expect based on the individual measurements alone due to the strong physical correlation between vibration and noise. They are closely related phenomena in rail transport, as they often have common sources and can interact. In the presented case of noise and vibration measurements, a statistically significant relationship (\(p\)-value = 0.018, alpha = 0.05) can be observed between the equivalent noise level and vibration dose (Figure 5a) with a moderate positive linear relationship (Pearson correlation coefficient PCC = 0.43). Compared to VDV, \(L_{Aeq}\) is less sensitive to peaks and more focused on overall energy, whereas VDV emphasizes high-intensity peaks due to its fourth power integration. RMS provides an average power measure and is less sensitive to peaks than both VDV and \(L_{Aeq}\), focusing on the effective value of the signal. Each metric is designed to capture cumulative effects in their respective domains, with varying sensitivities to fluctuations and peaks in the data. The cross-correlation between the signals is very low in the range of measured frequencies (sampling rate 2000 Hz for vibration and 48 kHz for noise). At the same time, a high correlation was observed between the vibration acceleration signals themselves, regardless of the measurement location and wagon type, and a low correlation between the acoustic signals themselves (Table 5).