## 2 Multisensor Array Layout Scheme Based on the Spatial Distribution Characteristics of Rail Strain
### Layout Scheme of Multisensor Arrays along the Longitudinal Direction of Rail
#### 2.3.2 Comparison of Different Sensor Arrangement Plans  
The \"most unfavorable impact position\" is introduced to describe the impact position which is most difficult for adjacent sensors to recognize. The most unfavorable impact position is generally the middle position between every two sensors. When the wheel flat hits exactly this position, the impact signals collected by sensors are weakest.  
The most unfavorable impact positions of the above plans are marked with P\({}_{\text{imp}}\). By adjusting the initial time of the simulation, the wheel flat impacts are ensured to occur just at those most unfavorable positions. Figure 12 shows the output signals of Plan I, where wheel flat impact occurs in the middle of the sleeper spacing. The wheel flat causes a sudden change in the signals of both adjacent sensors. Even when the wheel defect is very slight, for example, 0.1 mm, the sensors still completely capture the abnormal responses. As the depth increases, the sudden change becomes more intense.  
Figure 13 shows the output signals of Plan II where the wheel flat impact occurs right above the sleeper. Compared to Plan I, the signals of Plan II are much weaker, even if the wheel flat depth reaches 0.5 mm. When applied to the field test, the impact signals are likely to be submerged in system noises.  
Figure 12: Output signals of Plan I under its most unfavorable condition: (**a**) Without wheel flat; (**b**) wheel flat depth of 0.1 mm; (**c**) wheel flat depth of 0.3 mm; and (**d**) wheel flat depth of 0.5 mm.  
Plan III is essentially a combination of Plan I and Plan II. As shown in Figure 14, although the distance between sensors is halved, the test effects are not necessarily improved. Contrarily, the output signals are very dissimilar because the sensors are mounted in two different situations. In the middle of the sleeper spacing, the rail is relatively free in the vertical direction. Most of the wheel flat impact energy is dissipated through the vertical rigid body motion of the rail, leading to the smaller compression strain at the rail web. Therefore, the responses of sensors installed in these locations, like \(S_{2}\), are much weaker. Whereas for the rail above the sleepers, it cannot freely vibrate because of the restraints of sleepers. The impact energy is mostly converted into elastic potential energy of the rail. As a result, these sensors, like \(S_{3}\), have stronger output signals.  
However, the fusion of multiple sensors is reliable only when the sensors are mounted in identical situations. Otherwise, the adjacent sensors have different transfer functions to the same excitation. This means that signals sampled by sensors are based on different baselines. Therefore, Plan III is not suitable for the sensor arrangement. By comparison, Plan I is considered as the best option.  
Figure 14: _Cont._  
Figure 13: Output signals of Plan II under its most unfavorable condition: (**a**) Without wheel flat; (**b**) wheel flat depth of 0.1 mm; (**c**) wheel flat depth of 0.3 mm; and (**d**) wheel flat depth of 0.5 mm.