# Research on Wheel Flat Recognition Based on Wayside Wheel-Rail Force
## 2 Wheel-Rail Force Detection and Concatenation Method of Train Operation State Detect System (TODS)  
Wheel-rail force detection methods are categorized into vehicle-mounted and wayside systems. Due to spatial limitations, wheel-rail forces measured on the track generally exhibit discrete and intermittent characteristics. In contrast, wheel-rail forces measured via vehicle-mounted sensors are typically continuous in both spatial and temporal dimensions. For wheel fault identification, wayside detection offers the most cost-effective solution. By attaching strain gauges to the rail web, this method measures wheel-rail forces within the span between two sleepers [31]. An alternative approach involves replacing sleepers with force sensors to monitor vertical forces at specific rail intervals. Among these, the shear strain gauge method is particularly efficient and economical, prompting extensive targeted research by scholars in recent years [32; 33; 34; 35; 36]. However, a critical limitation exists: the shear method can only capture wheel-rail forces within a single sleeper span. As a train passes through the detection zone, the collected data reflects only a small segment of the wheel thread. To overcome this, multiple detection zones are required so that combined data from all channels can cover the entire wheel circumference. Data from these parallel channels must then be integrated into a unified system, concatenated according to temporal and spatial sequences, to reconstruct continuous wheel-rail force profiles for each wheel.  
Figure 2: Research route.  
Figure 3 illustrates TODS' wheel-rail force concatenation principle. The system employs the shear force method across 14 consecutive rail spans. For railway freight car wheels with a diameter of 840 mm, it has been proven that 14 test sections can cover the entire wheel surface [31]. As a wheel traverses the effective detection zone, each segment measures a partial wheel surface profile, followed by a data-free \"blank zone\" where no force monitoring occurs. During the first wheel rotation, the combined test zones cannot fully cover the entire tread. To achieve complete surface detection, the system extends the cumulative detection length, through proximity switch to detect the exact time when wheel entry/exit the detection zone, and split the data of each channel between the time, and then join the data in a single vector, and finally generate a complete, continuous wheel-rail force profile for each wheel.  
Figure 4 illustrates the rail-mounted proximity switch configuration. The sensing assembly is integrated into a custom-designed fixture comprising three rail clamps, a mounting base, a proximity switch carrier, two proximity switches, and two strain gauge guard plates. The entire fixture is anchored via the mounting base. The proximity switches are mounted on the carrier with a longitudinal center-to-center spacing of 240 mm, positioned directly above the shear measurement points on both rail sides. The switch tops are maintained at a 45 mm vertical clearance from the rail surface to ensure safety against rolling stock gauge intrusions. The proximity switch carrier attaches to the mounting base  
Figure 3: Principle of wheel–rail force measurement. Discrete wheel–rail force detection section (**a**), principle of force continuity (**b**).  
through two bottom circular holes, while the fixture secures to the rail foot via two bottom rail clamps and one opposing side clamp. As a wheel traverses the detection zone, the proximity switches record entry and exit timestamps. These timestamps enable the extraction of zone-specific wheel-rail force data, which are then temporally aligned and concatenated with data from adjacent segments (see Figure 4), forming a complete circumferential force profile. This design offers dual advantages: it avoids structural modification of the track and rail (since it is a non-intrusive installation method), ensuring low installation cost, while enabling simultaneous detection of additional wheel defects such as misalignment.