# Modernization of Heavy Loaded Tram Radial Effect on Noise and Vibration
## 3 Noise and Vibration Effects of Modernisation
### Experimental Measurement on Stur Street
#### 3.1.1 Objectives of Experimental Measurements  
The first objective of the experimental measurements was to determine the current noise situation by measuring the noise in the location and defining its levels from the passage of individual tram sets. The measuring points were determined objectively regarding the monitored surrounding buildings.  
For each measurement, especially the level parameters as defined in the following apply: \(L_{\textit{Aeq}}\)--A-weighted continuous sound level for continuous sound signals; \(L_{\textit{AFmax}}\)--maximum sound pressure level during the measurement interval.  
The time-averaged sound pressure level (equivalent continuous sound pressure level) is obtained using (1).  
\[L_{\textit{eq}}=10\log\frac{\frac{1}{T}\int_{0}^{T}p(t)^{2}dt}{p_{0}^{2}} \tag{1}\]  
where  
\(L_{\textit{eq}}\)--the time-averaged sound pressure level (equivalent continuous sound pressure level) in dB;  
\(p(t)\)--the sound pressure in Pa;  
\(p_{0}\)--the reference sound pressure;  
\(T\)--the averaging time in s\({}^{3}\)  
The second objective was to measure vibrations in the vicinity of the foundation structures of a residential building in a given urban and geological location. Specifically, the following quantities were surveyed:  
* vibration levels on the foundation structure of building no. 20 (Police of the Slovak Republic), and the results were evaluated by methods of statistical analysis;
* frequency characteristics of vibration amplitudes at point **B1V** on the selected building (to determine the frequency spectrum of the vibration of the subsoil generated by the tram passage--application of spectral analysis);
* vibration time histories in (t), recorded by a set of accelerometers in the vertical direction z and horizontal direction y perpendicular to the axis of the tramway (sensors marked **B1 Vz**, **B1 Vy**).  
Measurement functions \(v_{rms}\) and \(v_{max}\) are a means of expressing vibration in absolute value on the basis of measured waveforms. The root mean square value of the instantaneous values over a period of time refers to the power of the wave. The \(v_{rms}\) value of the velocity is one of the important factors for diagnosis. This value of the vibration velocity is obtained by using (2).  
\[v_{rms}=\frac{1}{T}\int_{t_{1}}^{t_{2}}v(t)^{2}dt \tag{2}\]  
where  
\(v_{rms}\)--root mean square value of the instantaneous values over a period of time;  
\(v(t)\)--the vibration speed;  
\(T\)--the averaging time.  
Peak amplitude \(v_{PEAK}\) is a peak value in a certain time duration. It is used to measure shocks or waves which are rather stable (3).  
\[v_{PEAK}=max|v(t)| \tag{3}\]The following mathematical Formula (4) is used to calculate the PSD (power spectral density) of the vibration velocity. It is a standard equation based on the Fourier transform.  
\[G_{xx}=\left|\int_{0}^{\infty}v_{(t)}e^{-i2\pi ft}dt\right|^{2} \tag{4}\]  
Since the processing of the results deals with digital data, all the above formulas are used in discrete form. That is, integrals are converted into sums and continuous functions into data sets in time samples with sampling frequency.