# A Feasibility Study of the Drive-By Method for Damage Detection in Railway Bridges
## 4 Simulation Results
### Best Sensor Positioning  
The quasi-static algorithm for damage identification was run for vertical accelerations of the first and fourth bogies and vertical accelerations of their leading wheelsets, for all speeds, damage levels, damage locations, bridge models, and train types. A damage localization error index (DLE) is introduced to quantify the accuracy of damage localization that is achievable with sensors installed in different positions on the train. This index averages the differences between the predicted damage location and the actual position of the \"damaged\" finite element for all the results from every bridge model, every damage level, and every considered speed. DLE is defined in the following equation:  
\[DLE=\ \frac{\sum\left|x_{predicted}-\frac{x_{begin}+x_{end}}{2}\right|}{n}.100 \left[\%\right] \tag{3}\]  
in which \(x_{begin}\) and \(x_{end}\) are the starting and ending positions of the defective finite element, and \(n\) is the number of simulation cases (i.e., \(n=64\), having four bridge models, four damage levels, and four speeds). Tables 5 and 6 report the DLE results for all the measuring point considered, for the damage at midspan and at a quarter of the span. In the case of measuring points on bogie number 1 and 4, the label \"central\" indicates the position of the bogie center of gravity, whereas \"Mp1\" and \"Mp3\" are the measuring points numbered 1 and 3 in Figure 9. As for the wheelset, the label \"wheelset 1b1\" refers to the leading wheelset of the first bogie, whereas the label \"wheelset 1b4\" refers to the leading wheelset of the fourth bogie. The results in Table 5 correspond to the CSA train, and those of Table 6 to the TSR train. The measuring point that yields the smallest DLE value can be considered as the optimal measuring point location. Indications given by the two train types are consistent with the fact that a sensor placed at the front of the train can better identify the damage location, when compared to sensors that are placed in the middle of the train. The DLE indices corresponding to the column 'Bogie 1' are indeed always lower than the corresponding values in 'Bogie 4', as well as the DLE values in column 'Wheelset 1b1' are always lower than the corresponding values in 'Wheelset 1b4'. The optimal measuring point should therefore be found on the first bogie or on its corresponding wheelsets, and the next appraisals in this paper will neglect the results from bogie 4 and its wheelset. This result is remarkably different from the one that is obtained in resonant bridges, in which the trailing bogies give stronger indications for the presence of a defect, with the signal amplitude becoming higher and higher during the train passage [7]. In the case here investigated, in which the algorithm seeks for alteration in the quasi-static response, differences in accelerations generated by a defect can be identified more precisely on the leading bogie, since it interacts with an unperturbed bridge. To evaluate the best sensor placement between the bogie and the axlebox, column 'Bogie 1' is compared to column 'Wheelset 1b1'. The lowest value for the DLE index can be found in the column 'Bogie 1' in most of the cases, so that the sensor placement on the bogie must be preferred. Another reason supports this choice: thanks to the filtering action from the primary suspension, in the higher frequency range, the acceleration levels potentially measured on the bogie frame are much lower than on the axleboxes. Therefore, a more sensitive accelerometer with lower full-scale can be fitted on the bogie, without saturation. This is fundamental in applications such the one considered here, in which the differences to be discerned in the accelerations are very small. Finally, DLE indices are smaller for the CSA train type for each measuring point location on the first bogie.