![]() Therefore, only a limited choice of wavelets is available to meet the orthogonal decomposition and reconstruction-requirement of filter banks used in Discrete Wavelet Transform (DWT). Wavelet basis functions (mother wavelets) have different shapes and are localized in both the time and frequency domains. The Wavelet Transform (WT) is an extension of the FT application to non-stationary and non-linear signals, where time-dependent frequency information of the signal is identified using the rescaled and modulated wavelet basis functions. ![]() To be able to improve the estimation of PSD wavelength & amplitude characteristics, it is essential to remove outliers and trends (DC signal) in the track geometry data, which requires the application of procedures for the analysis of non-stationary signals. For STFT, however, the choice of the time window width is not straightforward, calibration is required to achieve the appropriate time and frequency resolution. Due to the non-stationary nature of track geometry signals, the spatial/time dependence of the local wavelength information for FT can only be approximated by decomposing the measurement signal into near-stationary sections (STFT, GD-i.e., Gabor distribution). The Power Spectral Density (PSD) produced by the Fourier transform can extract the dominant wavelengths and their amplitude from the track geometry parameters but does not provide information about their local representation. The Fourier Transform (FT) decomposes the signal into a linear combination of sine and cosine functions. This analysis can elucidate the wavelengths and positions of track irregularities that affect vehicle responses. The sensitive wavelengths of the track irregularities are obtained from the proper allocation of wavelength ranges in the Fourier Amplitude Spectrum of the original signal and the Fourier transform of the components detected by the Variational Mode Decomposition. During the time series analysis of the track gauge, the cumulative difference from the mean value is calculated, which makes it possible to distinguish the track section constructed with non-standard initial track gauges. In addition to the conventional time and frequency domain analysis, auto-adaptive signal decomposition techniques are used on four pre-selected track sections. The parameters of the track gauge and the left and right rail alignment are considered to identify their characteristic wavelengths and the locations of their waveforms. This paper deals with the time-frequency characteristic analysis for track geometry irregularities using field data recorded by a comprehensive track inspection train.
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