Improved 2-D Multiscale Fractional Dispersion Entropy: A Novel Health Condition Indicator for Fault Diagnosis of Rolling Bearings

The multiscale dispersion entropy (MDE), which measures the irregularity or chaos of 1-D univariate time series through a dispersion pattern, is a useful tool to extract features from bearing signals. However, the stable dynamical characteristics of bearing signals are commonly hidden in high-dimensional state spaces, which cannot be easily captured by MDE. A large number of fractional chaotic information is filtered due to the application of integer-order pattern probability, negatively impacting the characterization performance of MDE on nonlinear signals. Therefore, an improved 2-D multiscale fractional dispersion entropy (IMFDE2-D) is proposed to overcome the shortcomings of MDE. In IMFDE2-D, the proper state space is constructed to reveal the high-dimensional dynamic characteristics of bearing signals. Meanwhile, the 2-D fractional dispersion pattern is developed to scan the space structure and supplement the fractional chaotic information. Furthermore, the first point of 2-D coarse-graining process is diagonally moved to alleviate the space compression, which further improves the stabilities of entropy metrics. The Logistic and Hénon maps demonstrate that IMFDE2-D has a better capability to describe the states of complex systems compared with MDE. To establish the intelligent health condition identification scheme, a novel feature selection algorithm called iterative Davies–Bouldin index (iDBI) is further designed to refine entropy features. The experimental results demonstrate that under the condition of supervised learning, IMFDE2-D–iDBI achieves the average accuracies of 100% and 99.91%, respectively, in various bearing experiments. Furthermore, even with an unsupervised classifier, the average accuracies can still reach 95.57% and 100%, which are much higher than those of traditional indicators.