## 1 Introduction
For example, in the late 1990s [PERSON] [14] described an easy-to-measure method to detect track irregularity of short wavelength by using axle-box acceleration. [PERSON] and [PERSON] [15] reported a cheap and robust method for estimating wheel load and lateral force caused by short-wavelength track irregularity based on axle-box acceleration measurement, which is difficult to detect with a track inspection car. In particular, they analyzed the relationship between the wheel load, lateral force, and axle-box acceleration of the Shinkansen train. The study revealed that the maximum values of the wheel load and lateral force can be estimated by the use of axle-box acceleration. [PERSON] et al. [16] discussed the application of axle-box acceleration measurements to assess squats and insulated joints, and determined the quantitative relationship between track defects and the characteristics of excited axle-box acceleration through a finite element model. [PERSON] [17] detected track defects and track singularities with the aid of axle-box acceleration measurement, and did testing on the Metropolitan Rail Network of Valencia, Spain. The results determined the location of accelerometers on the train and identified track singularities and diverse track defects. However, little research has been reported on the quantitative correlation between wheel polygons and axle-box acceleration. Although [PERSON] et al. [18] used axle-box acceleration to detect wheel flats and other wheel damage, they could not assess the damage level of polygonized wheels. One promising, low cost, and relatively simple technique to determine wheel conditions is by detecting axle-box acceleration, so detecting axle-box accelerations for high-speed trains and their time-frequency characteristics merits further study to develop a method to detect wheel polygons. To detect wheel defects based on axle-box acceleration signal analysis, applying appropriate vibration signal processing techniques is essential to determine the state of wheel polygons. Axle-boxacceleration signals caused by polygonized wheels are non-stationary and nonlinear. In the past decades, researchers have proposed several random vibration signal processing approaches, such as short-time Fourier transform (STFT), wavelet transform (WT), Hilbert-Huang transform (HHT), and the Wigner-Ville distribution (WVD). However, the constant time and frequency resolution of STFT make it unsuitable for analyzing a non-stationary signal. In contrast, the time and frequency resolutions of WT are adaptive. For example, [PERSON] et al. [19] offered a wavelet survey applied for track diagnosis based on acceleration signal analysis of a running train, discussed the advantages and drawbacks of the discrete wavelet transform, the continuous wavelet transform and the wavelet packets, with respect to the classical Fourier analysis. [PERSON] and [PERSON] [20] proposed the wavelet local energy averaging approach and average signal wavelet decomposing application for rail wheel flats onboard detection using train acceleration signals. The numerical simulation results demonstrated that the proposed method was effective for monitoring localized rail wheel flats with sizes smaller than predefined threshold. Nevertheless, it is difficult to choose the mother wavelet at present. HHT is an adaptive method for time-frequency analysis, including empirical mode decomposition (EMD) and Hilbert transformation. [PERSON] et al. [18] utilized HHT based method to analyze axle-box vibration signal characteristics induced by railway out-of-round wheels. An energy principle algorithm was proposed to suppress mode-mixing phenomenon. The study results show that the revised HHT can be adopted to distinguish out-of-round wheels from normal wheels. However, the mode-mixing problem caused by the intermittent signal in the sifting EMD process still requires attention.