An Improved Method for Mitigating End Effects in Empirical Mode Decomposition and Its Applications to Track Irregularity Analysis

One of the most important problems in Empirical Mode Decomposition (EMD) applications is mitigation of the end effects. The mirror extrema extending method is an effective method to deal with it. When mirror extrema extending is used to solve the end effects, it must put the mirror at the local extrema point. Aiming at this problem, a method of combining the mirror extension with a grey neural network is proposed to extend the data. The grey neural network is adopted to forecast an extrema point forward and backward, and then the mirror extrema extending is used to mitigate the end effects. To evaluate the end effects, five common end-effect mitigation methods of EMD have been compared, including the mirror extrema extending method, the BP neural network prediction method, the support vector regression machines prediction method, the self-adaptive matching extending method, and the grey neural network mirror extrema extending method. The five end-effect mitigation methods are evaluated quantitatively and compared through energy, the correlation coefficient of the decomposed signal and the original signal, and operation time. Results show that the grey neural network mirror extrema extending method is the best option among the five methods. Finally, the method is applied to analyze track irregularity and achieve satisfactory results.