applied sciences  
The Wheel Flat Identification Based on Variational Modal Decomposition--Envelope Spectrum Method of the Axelbox Acceleration  
[PERSON], [PERSON],*, [PERSON], [PERSON], [PERSON] and [PERSON]  
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of an efficient method to identify the wheel flat is still the subject of many researches at present. The wheel flat identification method are mainly divided into two groups: the wayside method and the on-board method. The wayside method monitors the wheel status with a series of sensors mounted on the rail. [PERSON] et al. [6] adopted the envelope spectrum to detect the wheel flat signal based on the shear force of the rail. [PERSON] et al. [7] fused the data measured by multiple stress sensors and correlated it with the circumferential position of the wheel. [PERSON] et al. [8] proposed a two-step important point selection method based on the time series with the multilayered sensing device. Besides the aforementioned methods, other types of technology, such as ultrasonic [9; 10; 11] and fiber optic sensing technology [12; 13; 14; 15], are also reported in the researches of wheel flat identification. However, wayside detection can only detect the wheel flat in a fixed section, and the partial wheel conditions information provided by limited number of sensors reduces the overall reliability of the wheel flat identification [16]. The on-board method monitors the wheel status in real-time by placing the sensors on the vehicle components. The closer the sensor is to the wheelset, the more vibration information of the wheel is reflected. To extract the vibration characteristics of the wheel, more accurate signal analysis methods are needed when the sensor is far away from the wheelset. [PERSON] et al. [17] used the adaptive noise canceling to process the axlebox acceleration signal with flat and compared it with other time-frequency analysis methods. [PERSON] et al. [18] proposed a time domain index to identify the wheel flat faults, and validated its feasibility by field test on the freight vehicle. [PERSON] et al. [19] transformed the vibration signals from time domain to rotating angular domain with a combined method based on the cepstrum analysis and the order analysis. [PERSON] et al. [20] designed a one-dimensional convolutional neural network. [PERSON] et al. [21] recorded the bearing adapter acceleration signals on a 1:4 scale bogie test rig, and validated the feasibility of wheel flat analogue fault detector device. The on-board method is lower-cost and the sensor installed on the vehicle is easily maintained. In this work, we will focus on the on-board method to detect the wheel flat. Although the on-board monitoring method was adopted in the above study, the quantitative correspondence between the expansion of the flat and the index still needs further study. The axlebox is in direct contact with the wheelset, and the characteristics of high frequency vibration between wheel and rail are reflected in it. Meanwhile, the axlebox acceleration is always influenced by the complex wheel-rail excitation (e.g., the track irregularities, wheel polygon and wheel flat). The impact characteristics of the wheel flat are easily covered by interference signal especially in the early wheel flat faults. The accuracy extraction of the wheel flat characteristics makes it a challenge for the wheel flat identification by using the axlebox acceleration. Therefore, the advanced signal processing methods need to be employed to process the fault signal. As an adaptive signal decomposition method, empirical mode decomposition (EMD) [22] was adopted in the wheel flat identification [23; 24]. However, its end effect and mode mixing in signal decomposition limits the widely application [25]. As the alternative of EMD, variational mode decomposition (VMD) was proposed by [PERSON] [26], which effectively makes up for the shortcomings of EMD.