## 2 Multisensor Array Layout Scheme Based on the Spatial Distribution Characteristics of Rail Strain
### Layout Scheme of Multisensor Arrays in the Rail Cross-Section  
#### 2.2.1 Sensitivity of Different Layout Schemes to Wheel Flats  
Considering that the vertical rail responses surge intensively when wheel flats exist [29], measurement methods for vertical wheel-rail forces are feasible solutions to monitor the wheel defects. Conventional vertical wheel-rail forces measurement methods include: (1) sheer force method [30], (2) rail base bending moment method [31], (3) rail web bending moment method [32], and (4) rail web compression method [33]. Although they have different layout schemes (shown in Figure 6), they all achieve the purpose by establishing a relationship between the sensor outputs and the vertical loads.  
Although the sheer force method is widely used in field tests for wheel-rail force, it is not a suitable choice for the long-term monitoring of wheel flats because this method uses eight strain gauges to  
Figure 6: Commonly used wheel-rail force measurement methods: (**a**) Sheer force method; (**b**) rail base bending moment method; (**c**) rail web bending moment method; (**d**) rail web compression method.  
form a bridge which is vulnerable to water and electromagnetic environment. In addition, the baseline drift is inevitable for strain gauges during long-term service, making it impossible to stay consistent for a long period of time. The rail base bending moment method is not an ideal choice since all the sensors are required to be attached to the bottom of the rail along the longitudinal direction which makes it difficult to ensure the installation accuracy without replacing the rail.  
In contrast, the latter two methods, rail web bending moment and rail web compression, seem to have more potential for the long-term monitoring of wheel flats. For these methods, only two sensors need to be installed at the rail web. It is worth mentioning that the aim of this study is the recognition of wheel defects. Therefore, the sensors mounted on rails should capture the abnormal impact signals excited by wheel flats as effective as possible, rather than measure the exact dynamic loads. In view of this, we analyzed the sensitivity of these two methods under different defect conditions using the established refined rail response model. The predefined defect depths varied from 0 to 0.5 mm.  
As illustrated in Figure 7, the output signals of these two methods have similar characteristics. Each series of signals consists of a major trend reflecting the wheel passage, as well as the fluctuation induced by a wheel flat. As the depth of the wheel flat increases, the fluctuation becomes more intense.  
It is obvious that signals collected by the rail web compression method are much stronger than those of its counterpart. Therefore, the rail web compression method is considered to be more sensitive to wheel flat impact because the signals collected by the rail web bending moment method are essentially the longitudinal dynamic bending strains caused by the wheel loads. Since the sensors are mounted near the neutral axis, the strains are relatively small. By adjusting the sensor positions away from the neutral axis, the test results are further improved. It is, nevertheless, inevitable that the installation of sensors is hindered by track equipment such as fasteners and sleepers.  
Figure 7: Sensitivity of sensor layout schemes to wheel flats of different defect conditions: (**a**) Rail web bending moment method; (**b**) rail web compression method.