# Development and Testing of a Railway Bridge Weigh-in-Motion System
## 4 Results and Discussion  
Figure 9 summarises the initial results for all four pre-weighed trains in a spider chart. The solid black line represents the error in GVW estimated using the RB-WIM algorithm applied to the 35 locomotives/individual carriages. The dashed grey line represents the relative velocity of individual carriages, calculated as the ratio of the individual carriage velocity to the average velocity of the entire train, as described in Section 2.1. While the train speed can be assumed to be constant at any point in time, it varies through time. The speed limit on the bridge was 20 km/h. It appears that this was not adhered to precisely by the drivers, but its presence resulted in significant braking and acceleration as the trains crossed. Figure 9: Error in gross vehicle weight (GVW) of carriages and relative velocity of individual carriages: Trains 1–4. It can be seen that the carriage accuracy for Train 2 represents the best match with maximum weight error of 2% and standard deviation of 0.64%. The maximum error in GVW estimation occurs in Train 4 with an error of up to 28%. The obvious reason for this error is the assumption of constant velocity for all carriages in an event where it is varying quite significantly about the mean. The assumption of constant velocity is reasonable on roads, as trucks typically cross a short-span bridge in one or two seconds, but trains are too long for such an assumption. The speed variation was more pronounced for longer trains, some of which exceeded 500 m in length. As the variation in measured speed in the worst case (Train 4) surpassed 25% (negative error), the assumption of constant velocity clearly was not appropriate and had to be addressed. Figure 10 shows the correlation between the error in carriage GVW and the relative velocity for all carriages of all four trains. It can be seen that Trains 3 and 4 in particular show strong linear correlations between GVW error and relative velocity with correlation coefficients of 0.99 and 0.96, respectively. To address this issue, the constant velocity of the whole train was replaced with different velocities for individual carriages. The additional step in the modified algorithm consists of determining the sections of the SMP signals where a locomotive/carriage is on the bridge (as isolated as possible), calculating the correlations for only those parts of the signals and assigning the resulting speeds to the locomotive/carriage in question. Figure 11 displays the errors in the predicted carriage gross weights for each train when considering (i) the average velocity of the train obtained from the entire train crossing (solid black line curves as shown in Figure 9) and (ii) variable velocities calculated for each carriage (dashed grey line). There are clear improvements in accuracy for all four trains. The improvements are less pronounced for Trains 2 and 3 but the accuracy for these was already good, and it is significant that where there were some larger errors in Train 3 (Carriages 37-39), these were greatly reduced. The improvements in Train 4 were quite pronounced although some errors persisted at Carriages 1, 3, and 4. This may  
Figure 10: Correlation between carriage GVW error and relative velocity of carriages. be explained by the occurrence of heavy rain just before the crossing of this train and insufficient protection of the strain gauges (due to the short testing campaign), which resulted in a noisy speed measurement signal (the shaded area in Figure 12) and, consequently, unreliable velocity measurements for these carriages. Such errors can easily be avoided in the future by protecting the sensors against environmental effects. Figure 13 summarises the results obtained with the original RB-WIM algorithm and those obtained using the revised algorithm for all four reference trains (calibration trains). It can be seen from this figure that the mean error in GVW was considerably reduced by the revised algorithm. For Train 4 in particular, the maximum error was reduced from 28.19 to 10.17%.