## 1 Introduction  
A wheel flat is a faulty damage on the wheel tread caused by wheel-rail slipping contacts under train loads due to friction and wear. The wheel flat generates noise and vibration during train operation, and impacts to bearings, gears, motors, etc. Because these phenomena relate to operational life and derailment, anti-skid devices and lubrication have been applied.  
In general, small wheel flats are detected by periodical maintenance inspection. However, if there is a large flat with abnormal vibration and noise, they can be found through an unplanned investigation. Unacceptable wheel flats must be repaired in accordance with wheel safety criteria including detailed guidelines on flat size and numbers. Thus, it is necessary that the wheel flats are continuously detected and diagnosed for wheel rectification on time. These days, online monitoring on wheel conditions becomes more important due to high train speed.  
For CBM (Condition-Based Maintenance) on flat wheels, various vibration signal processing techniques [1] are applicable. They are very useful for detecting defects in rotating machines, such as gears [2, 3] and bearings [4, 5]. [PERSON] et al. [6] improved the fault detection rate of a bearing by combining the local mean decomposition and the ratio correction methods. [PERSON] et al. [7] suggested the spectrum whitening demodulation for a fault diagnosis on axle box bearing. [PERSON] [8] suggested a fault diagnosis method based on the analysis of thermal images for electric impact drills (EID). However, this is not appropriate for railway maintenance. [PERSON] et al. [9] suggested a time-frequency analysis method for detection and diagnosis of wheel flats. The time-frequency analysis method in the paper includes STFT (Short Time Fourier transform), WVT (Wigner Ville Transform), and WT (Wavelet Trans-form). However, the time-frequency analysis method is difficult to discriminate the defects because it is hard to set a predefined threshold value for a meaningful damage, and actual vibration signals in operation show various frequency bands. [PERSON] et al. [10] suggested a parallelogram method measuring the contact detection of wheel flats on rail. However, this method has a disadvantage that the flat signal is affected by measuring points on rail. [PERSON] and [PERSON] [11] suggested the cepstrum (the minimum distributed cepstrum) as a method which is useful for cyclic defect signal detections at constant velocity, but its effect has not been verified under variable running speed conditions. However, because many accelerations and decelerations take place during real operation of trains, an effective wheel-flat diagnosis algorithm is necessary considering a continuously varying train speed. Wheel flat is one of the main faults of railway vehicle and reduces ride quality too [12]. Thus, this paper studied a vibration signal processing algorithm for early detection of railway wheel flats considering variable train speed. Order and cepstrum analyses were used to effectively detect flats under variable speed conditions for real operation. During this signal processing, zero padding was implemented to facilitate signal detection. The cepstrum analysis was superior in diagnosing the existence of wheel flats with periodic signals, but not their sizes. In addition, to diagnose the size of flats, cross correlation analysis, a good method to diagnose the magnitude of the instantaneous impulse signal, was applied using a periodic signal of wheel flat in terms of repetitive rotation.  
Finally, to verify validity of the suggested algorithm, all the analysis procedures were performed and evaluated for wheel flat signals including wheel vibrations in actual field operation.