# Research on Wheel Flat Recognition Based on Wayside Wheel-Rail Force
## 1 Introduction
(2015) (2015) proposed a hybrid model for predicting ground vibrations from discrete wheel-rail irregularities (e.g., flats, welds). [PERSON] et al. (2016) (2016) formulated flat impact force expressions under hypothetical conditions, while [PERSON] et al. (2016) developed a history-dependent nonlinear rubber spring model using fractional calculus for heavy-haul trains with nonlinear suspensions, comparing it with traditional Kelvin-Voigt models under flat impacts and random track irregularities. In 2017, [PERSON] et al. (2017) analyzed passenger car vertical dynamics via wheel-rail vertical forces, evaluating ride stability with wheel flats. [PERSON] et al. (2018) numerically characterized new and worn flat geometries using vehicle-track coupling dynamics and non-Hertzian contact theory, developing a high-speed train model to assess bogie responses. [PERSON] et al. (2019) (2018) systematically studied vehicle-track parameters and flat defects, analyzing wheel-rail force interactions and impact-speed relationships. [PERSON] (2019) (2019) constructed a 3D model considering flat length, width, and depth, investigating multi-dimensional effects on wheel-rail dynamics. Recent studies highlight technological innovations: [PERSON] et al. (2020) (2020) developed a wheel flat detection system using reflective optical sensors to measure laser spot movements for impact force monitoring and defect identification. [PERSON] et al. (2021) integrated vehicle component and track elastic vibrations into a rigid-flexible coupling model, analyzing system vibration characteristics. [PERSON] et al. (2020) (2020) fitted flat models using field data, establishing coupled locomotive-track dynamics to analyze time-frequency domain responses. [PERSON] et al. (2021) used multisensor arrays and proposed a wheel flat recognition method that can position its location precisely. [PERSON] et al. (2021) (2021) applied FEM and multi-body dynamics to study flat effects on vehicle dynamics during turnout crossings, evaluating speed and flat size impacts. [PERSON] et al. (2021) (2021) investigated dynamic impact loads considering speed and wheel diameter variations, providing insights into operational safety margins. Following extensive research on wheel flats by scholars in recent years, the mechanisms of wheel-rail impact and the effects of flats on vehicle dynamics have been fundamentally clarified. Leveraging the impact characteristics and interaction patterns of wheel flats, diverse detection methods have emerged. Among these, wheel-rail force-based approaches are most widely adopted, including China's TPDS (Truck Performance Detection System) (2017; 2018; 2019; 2020) developed by the China Academy of Railway Sciences and TTCI's (Transportation Technology Center Inc.) WILD (Wheel Impact Load Detector) system in the U.S. In prior work (2019), the authors proposed a novel detection method: the Train Operation State Detection System (TODS), which uses a discrete wheel-rail force connecting method to detect spatial continuous wheel-rail force. This method offers advantages of reliable data acquisition, low installation cost, and less track damage (2019). However, since traditional wheel-rail force detection relies on discontinuous sampling data--distinct from directly measured continuous wheel-rail forces on the wheel itself--questions remain about whether conventional impact models and feature recognition algorithms are compatible with this new detection framework. Further investigation is required to validate the applicability of existing impact formulations and diagnostic algorithms for discontinuous force data. To develop a reliable wheel flat recognition method for the TODS, this study simulates discrete wheel-rail forces to match the actual TODS measurement characteristics, analyzing the correlation between wheel flats and wheel-rail force signatures.