Transition Permutation Entropy and Transition Dissimilarity Measure: Efficient Tools for Fault Detection of Railway Vehicle Systems

The ordinal pattern is an essential tool to extract the information in time series. However, little attention has been paid to the transition probability matrix of ordinal patterns, which affects the accuracy and comprehensiveness of the extracted information. In this article, we propose a transition permutation entropy (TPE) and a transition dissimilarity measure (TDM) through the transition matrix. The TPE can evaluate the complexity of systems. The TDM measures the dissimilarity between systems through the dynamic transition and the probability distribution of ordinal patterns. The proposed methods are comprehensively evaluated by simulation experiments and vehicle dynamic response data. The results show that both the TPE and the TDM can distinguish complex systems and locate the rail corrugation. The combination of the TDM, multidimensional scaling, and neural networks can be used for fault detection and is better than other distance calculation methods.