## 2 Research Methods
### Assessment Basics  
ISO 2631-1 and EN 12299 [31; 32] standards are available for evaluating ride comfort for rail vehicle passengers. However, they have some differences in their approach. ISO standards are globally recognized and widely used across industries. EN 12299, despite being younger than ISO 2631-1, has gained significant popularity due to its focus on ride comfort for rail passengers and its statistical method that provides a more precise evaluation of vibration levels. ISO 2631-1's sensitive vertical and lateral vibration ranges are 4-12 Hz and 0.6-2 Hz, respectively. On the EN 12299, the sensitive ranges are 4-16.5 Hz for vertical vibration and 0.6-2 Hz for lateral vibration. Applicable frequency ranges are 0.5-80 Hz for ISO 2631-1 and 0.4-100 Hz for EN 12299. One significant difference between the two standards is that EN 12299 does not take into account vibration dose value (VDV) metrics. VDV is a measure of the cumulative exposure to vibration over a certain period, which can be important for assessing long-term effects on passengers' comfort and health. While there is no universal consensus on the impact of exposure time on riding comfort for shorter periods, everyday experience shows that more prolonged exposure to a harmful factor is more significant than shorter ones. VDV is also said to be a preferred measurement for exposure to jolts, shocks, and intermittent vibration because it is sensitive to peaks in acceleration levels. In the presented paper, the aVDV metric is the same as the metric used in [PERSON] psychophysical model, used for comparison purposes; therefore, it seemed convenient to consider this measure. According to the ISO 2631-1 document, the RMS acceleration value was calculated from the following formula:  
\[a_{w}=[\ \frac{1}{T}\int_{0}^{T}a_{w}^{2}(t)\ dt\ ]^{0.5}\ \left(\text{ms}^{-2} \right), \tag{1}\]  
where \(a_{w}(t)\) is the acceleration weighted as a function of time and \(T\) is the measurement time(s). If the crest factor given by Formula (2) exceeded the value of 9, then the vibration dose was analyzed. \[Crest=\frac{ZP}{RMS} \tag{2}\]  
where \(ZP\) is the peak acceleration value of \(a_{w}(t)\). The amount of vibration dose \(VDV\) is assessed according to the following relationship (3):  
\[VDV=[\ \int_{0}^{T}a_{w}^{4}(t)dt\ ]^{0.25}\left(\text{ms}^{-1.75}\right) \tag{3}\]  
where \(T\) is the measurement duration. \(VDV\) is a coefficient for which the maximum values affecting the riding comfort of passengers have not yet been unanimously determined. The directive of the European Parliament specifying vibration exposure limits for employees in an eight-hour working period [33] is calculated according to Formula (4):  
\[VDV(\delta)=VDV\cdot[\frac{T_{e}}{T_{m}}]^{0.25}\left(\text{ms}^{-1.75}\right) \tag{4}\]  
where \(VDV(\delta)\) is the daily exposure (8 h), \(VDV\) is the frequency-weighted vibration dose, \(T_{e}\) is the exposure period (8 h), and \(T_{m}\) is the \(VDV\) measurement period (15 min). \(VDV(\delta)\) evaluates the effects of vibration from an occupational health perspective and is not informative for comfort assessment (compulsory for employers/workers according to EU Directive 89/391/EEC, Table 2). It is given for comparison purposes. In the case of noise, coefficients were used, such as the equivalent sound pressure level corrected by the A filter [30; 34], used for tests carried out at a standstill or while driving at a constant speed (or during acceleration/braking), described by Equation (5):  
\[L_{pAge,T}=10\ \text{log}_{10}\left(\ \frac{1}{T}\int_{0}^{T}\frac{\left[p_{a}(t) \right]^{2}}{p_{0}{}^{2}}dt\right)=20\ \text{log}_{10}\bigg{(}\ \frac{1}{T}\int_{0}^{T}\frac{p_{a}(t)}{p_{0}}dt\bigg{)}( \text{dB}) \tag{5}\]  
where \(T\) is the measurement time (s), \(p_{a}(t)\) is the RMS sound pressure value with A filter (Pa), and \(p_{0}\) is the reference sound pressure level (\(p_{0}=20\) uPa).