Figure 4. IMU platform placed inside the case.
4. Test Results and Discussion
As already specified in the previous paragraph, a total amount of 14 measures were conducted on each section. All the analyses were conducted by means of MatlabTM software.
In order to verify the speed rate of the train at the different measured passages along a single section, signal similarities analysis was performed using cross-correlation function in MatlabTM (i.e. corrcoef). Such analysis was performed on the overall signal collected along each whole section. In this way, it was also possible to identify which measures should not be considered in the repeatability study of RMS accelerations. Taking into account all the 14 measurements, the correlation coefficients (a value of 1 means perfect matching) were calculated in matrix form (14x14). An example of the results obtained can be seen in Table 6, where correlation coefficients calculated for section 04 direction EW are reported. As can be noted all values are greater than 0.92. The correspondent speed signals are depicted in Figure 5 where it is possible to verify the good repeatability of the speed rate at the various passages, except for local and occasional differences due to braking and acceleration actions far from mean values, such as the minimum speed values recorded at around 28 seconds for a couple of passages and depicted in Figure 5.
Table 6. Correlation coefficients for section 04 direction EW.
Measure Number
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
|
10
|
11
|
12
|
13
|
14
|
1
|
1.00
|
0.99
|
0.97
|
0.95
|
0.98
|
0.98
|
0.96
|
0.99
|
0.99
|
0.99
|
0.99
|
0.99
|
0.98
|
0.98
|
2
|
0.99
|
1.00
|
0.98
|
0.97
|
0.97
|
0.97
|
0.97
|
0.98
|
0.97
|
0.98
|
0.98
|
0.98
|
0.98
|
0.97
|
3
|
0.97
|
0.98
|
1.00
|
0.98
|
0.94
|
0.94
|
0.97
|
0.97
|
0.96
|
0.98
|
0.98
|
0.96
|
0.98
|
0.95
|
4
|
0.95
|
0.97
|
0.98
|
1.00
|
0.92
|
0.92
|
0.98
|
0.96
|
0.94
|
0.96
|
0.97
|
0.95
|
0.96
|
0.93
|
5
|
0.98
|
0.97
|
0.94
|
0.92
|
1.00
|
0.98
|
0.93
|
0.98
|
0.99
|
0.97
|
0.97
|
0.99
|
0.97
|
0.99
|
6
|
0.98
|
0.97
|
0.94
|
0.92
|
0.98
|
1.00
|
0.92
|
0.98
|
0.98
|
0.97
|
0.97
|
0.99
|
0.97
|
0.98
|
7
|
0.96
|
0.97
|
0.97
|
0.98
|
0.93
|
0.92
|
1.00
|
0.96
|
0.94
|
0.97
|
0.97
|
0.95
|
0.96
|
0.94
|
8
|
0.99
|
0.98
|
0.97
|
0.96
|
0.98
|
0.98
|
0.96
|
1.00
|
0.99
|
0.98
|
0.99
|
0.99
|
0.98
|
0.98
|
9
|
0.99
|
0.97
|
0.96
|
0.94
|
0.99
|
0.98
|
0.94
|
0.99
|
1.00
|
0.98
|
0.98
|
0.99
|
0.97
|
0.99
|
10
|
0.99
|
0.98
|
0.98
|
0.96
|
0.97
|
0.97
|
0.97
|
0.98
|
0.98
|
1.00
|
0.99
|
0.98
|
0.98
|
0.97
|
11
|
0.99
|
0.98
|
0.98
|
0.97
|
0.97
|
0.97
|
0.97
|
0.99
|
0.98
|
0.99
|
1.00
|
0.98
|
0.98
|
0.98
|
12
|
0.99
|
0.98
|
0.96
|
0.95
|
0.99
|
0.99
|
0.95
|
0.99
|
0.99
|
0.98
|
0.98
|
1.00
|
0.98
|
0.99
|
13
|
0.98
|
0.98
|
0.98
|
0.96
|
0.97
|
0.97
|
0.96
|
0.98
|
0.97
|
0.98
|
0.98
|
0.98
|
1.00
|
0.97
|
14
|
0.98
|
0.97
|
0.95
|
0.93
|
0.99
|
0.98
|
0.94
|
0.98
|
0.99
|
0.97
|
0.98
|
0.99
|
0.97
|
1.00
|
Figure 5. Measured speed rates along section 04 direction EW for all the 14 different runs.
A summary of the results obtained for all sections taken into account is reported in Table 7, where the number of passages considered as acceptable for each section is also specified. The criterion to decide which sets of measurements were considered acceptable or not, concerns GPS signal quality and acceleration measures check. In particular, for GPS signal the minimum number of satellites during each measurement had to be of 4 and the dilution of precision (DOP), both horizontal (HDOP) and vertical (VDOP), had to be lower than 5, which corresponds to a good rating [40, 41]. In addition, a couple of measures where external problems affected the trains regular movement were discarded. As can be seen in Table 7, the number of measures for each section is at least equal to 11.
In certain cases, pretty low values of the correlation coefficient were found (< 0.8), which depend on train operations variability (braking and acceleration actions) during the different measurements. In addition, in correspondence of the single measure for which these lower values of the correlation coefficient were calculated, the HDOP and VDOP values were found to be greater than 3 (maximum value 3.9).
Table 7. Statistical analysis of correlation coefficients for all sections.
|
Direction WE
|
Direction EW
|
|
Max
|
Min
|
Mean
|
N. Measures
|
Max
|
Min
|
Mean
|
N. Measures
|
1
|
0.99
|
0.89
|
0.96
|
13
|
0.99
|
0.90
|
0.97
|
13
|
2
|
0.99
|
0.87
|
0.94
|
11
|
0.98
|
0.59
|
0.87
|
11
|
3
|
0.99
|
0.88
|
0.96
|
13
|
0.99
|
0.77
|
0.95
|
12
|
4
|
0.99
|
0.80
|
0.92
|
13
|
0.99
|
0.92
|
0.97
|
14
|
5
|
0.99
|
0.70
|
0.91
|
12
|
0.99
|
0.87
|
0.94
|
12
|
6
|
0.99
|
0.83
|
0.94
|
13
|
0.99
|
0.89
|
0.95
|
14
|
7
|
0.97
|
0.62
|
0.84
|
11
|
0.99
|
0.88
|
0.97
|
11
|
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