Fractal Analysis And Application Of Rail Corrugations

Fractal is a new branch of nonlinear science and has been used more and more widely in the other fields of science. Because of fractal theory can be applied to describe the nature of the irregularity and non-integrable geometry of the system self-similarity, it can also be used to analyze the fractal nature of rail corrugations. In this paper, we will analyze the fractal character of rail corrugations by using the box-count estimator, the H-W estimator, variogram estimator and the variation estimator methods, and on this basis, we will compare the characteristics of four methods in the analysis of time series or spatial sequence, and then we will analyze how fractal dimension of rail corrugations will alter when corrugations become bigger. Then we will introduce a new multifractal method can be used for for analyzing time series or spatial sequence, that is generalized q-th order entropy based on the ren'yi entropy, and we will use the generalized q-th order entropy method to analyze the multifractality of rail corrugations series which have been fitted by the fractal interpolation function. The significance of the proposed method is that we can use the fractal dimension or multifractality to distinguish of rail corrugations, and at the same time, it also maybe provides a more flexible way for dealing with the problem of corrugation.