A novel similarity measure based on dispersion-transition matrix and Jensen–Fisher divergence and its application on the detection of rail short-wave defects

In this paper, we first propose dispersion transition entropy (DTE) to measure inner dynamical complexity of signals or time series from the perspective of states transition between consecutive dispersion patterns, and then introduce a new similarity measure based upon the Jensen–Fisher divergence (JFD) between dispersion-transition distributions. The numerical experiments prove that DTE is immune to the data length but more sensitive to the state or characteristic changes compared with traditional dispersion entropy. In addition, the results of tests on white noise and 1/f noise are consistent with the complexity theory in present researches. Then the new similarity measure exhibits superior performances on distinguishing chaotic time series from stochastic processes since JFD enlarges the local difference or changes between dispersion-transition matrices. Especially, for the axle box acceleration vibration signals of rail detection, the dispersion-transition distributions of normal, rail corrugation and impact signals are significantly dissimilar. By estimating the JFD between the probability distributions of two successive sliding windows, rail corrugation and impact defects can be identified and located.