Title: Fractal description and fractal dimension estimation of the wheel-rail rolling noise in high-speed railway

Author(s): HAO Qiushi; SHEN Yi; WANG Yan; ZHANG Xin; LIU Jian;

Affiliation(s): Department of Control Science and Engineering, Harbin Institute of Technology; Department of Instrumentation Science and Technology, Harbin Institute of Technology

Abstract: A fractal analysis method is proposed to investigate the wheel-rail rolling noise, in which statistics of the noise’s increments with different scales are studied. It is proven that the noise has fractality and can be described by the fractional Brownian motion (FBM). On this basis, the power-law relation of the FBM regarding the variance of its wavelet coefficients and the fractal dimension is utilized to estimate the fractal dimension. Comparisons of fractal dimensions are made among noises at different speeds and the rail defect AE signals of crack propagations. It is revealed that the fractal dimension of the noise is stochastic and its estimations at different speeds distribute in a small margin below 2 with mean 1.5666. Moreover, the fractal dimension is irrelevant to the speed and is an intrinsic feature of the noise. Thus, the noises with different speeds can be modeled by an identical FBM. On the contrary, fractal dimensions of AE signals of crack propagations are all above 2 and the modeling requirement of the FBM is not met. Therefore, the fractal dimension can be taken advantage of as a distinct feature, too. The work extracts the fractal dimension of the wheel-rail rolling noise as the intrinsic feature and offers an effective analysis approach for the description of wheel-rail rolling noise and defect detection in high-speed railway.