# Measurements of Human Perception of Train Vibration  
[PERSON]  
1 Faculty of Civil Engineering, Cracow University of Technology, 31-155 Krakow, Poland; [EMAIL_ADDRESS] (F.P. ); [EMAIL_ADDRESS] (T.T. )1  
[PERSON]  
2 Faculty of Civil Engineering, Cracow University of Technology, 31-155 Krakow, Poland; [EMAIL_ADDRESS] (F.P. ); [EMAIL_ADDRESS] (T.T. )1  
[PERSON]  
3 Faculty of Civil Engineering, Cracow University of Technology, 31-155 Krakow, Poland; [EMAIL_ADDRESS] (F.P. ); [EMAIL_ADDRESS] (T.T. )1  
Footnote 1: [[https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci)]([https://www.mdpi.com/journal/applsci](https://www.mdpi.com/journal/applsci))  
Footnote 2: [[https://www.mdpi.com/journals/pdf/10.3390/appl/10](https://www.mdpi.com/journals/pdf/10.3390/appl/10)]([https://www.mdpi.com/journals/pdf/10.3390/appl/10](https://www.mdpi.com/journals/pdf/10.3390/appl/10)). vibration remain unclear. Individuals exhibit heightened sensitivity to unexpected low-frequency vibrations, emphasizing the importance of incorporating vibrational comfort as a fundamental criterion in building design [9; 10]. While some authors establish connections between height, gender, or age and vibration perception [9; 10], others do not [11], contributing to the non-deterministic nature of research on human vibration perception. Another crucial aspect is the active versus passive perception of vibrations. Active perception arises when vibrations are directly transmitted to the body from the vibration source, common among operators of construction machinery or vehicle drivers and passengers [12; 13]; passive perception, on the other hand, occurs when vibrations are transmitted from the source to the human body through a medium, typically the ground. This situation predominantly occurs in buildings where vibrations are transmitted from transport sources [14; 15]. This article specifically delves into the passive perception of vibration within a building induced by the passage of trains. In such scenarios, according to [16], three evaluation methods are employed: the root mean squared method (RMS); vibration dose value (VDV); and maximum transient vibration value (MTVV). The RMS method, as referred to in [16], is considered the basic method suitable for vibrations exhibiting a low crest factor. The crest factor, defined as the modulus of the ratio between the maximum instantaneous peak value of the frequency-weighted acceleration signal and its RMS value, plays a crucial role in this evaluation:  
\[\mathrm{CF}=\frac{|\mathrm{a}_{\mathrm{w}}|_{\mathrm{PEAK}}}{\mathrm{a}_{ \mathrm{wRMS}}}. \tag{1}\]  
The RMS method averages acceleration values in the time duration:  
\[\mathrm{a}_{\mathrm{w}}=\left[\frac{1}{\mathrm{T}}\int_{0}^{\mathrm{T}} \mathrm{a}_{\mathrm{w}}^{2}(\mathrm{t})\mathrm{d}t\right]^{\frac{1}{2}}, \tag{2}\]  
where \(a_{\mathrm{w}}(t)\) is the weighted acceleration as a function of time [m/s\({}^{2}\)], and \(T\) is the duration of measurement [s]. The MTVV method also averages acceleration values but is more sensitive to occasional shocks and transient vibration, using a short integration time constant:  
\[\mathrm{a}_{\mathrm{w}}=\left[\frac{1}{\mathrm{T}}\int_{t_{0}-\tau}^{t_{0}} \mathrm{a}_{\mathrm{w}}^{2}(\mathrm{t})\mathrm{d}t\right]^{\frac{1}{2}}, \tag{3a}\]  
\[\mathrm{MTVV}=\mathrm{max}[\mathrm{a}_{\mathrm{w}}(\mathrm{t})], \tag{3b}\]  
where \(\tau\) is the integration time (for running averaging, it is recommended to use \(\tau=1\) s), and \(t_{0}\) is the time of observation (instantaneous time). The VDV method is best for peaks in recorded signals because it uses the fourth power instead of the second power, as is used in RMS and MTVV:  
\[\mathrm{VDV}=\left[\int_{0}^{\mathrm{T}}\mathrm{a}_{\mathrm{w}}^{4}(\mathrm{ t})\mathrm{d}t\right]. \tag{4}\]  
Considering the passive perception of vibration in buildings, there are five diagnosis situations in which vibrations are investigated (comp. Table 1). Diagnosis represents the simplest scenario, necessitating only measurements.