An integrated method based on refined composite multivariate hierarchical permutation entropy and random forest and its application in rotating machinery

Fault feature extraction of rotating machinery is crucial and challenging due to its nonlinear and nonstationary characteristics. In order to resolve this difficulty, a quality nonlinear fault feature extraction method is required. Hierarchical permutation entropy has been proven to be a promising nonlinear feature extraction method for fault diagnosis of rotating machinery. Compared with multiscale permutation entropy, hierarchical permutation entropy considers the fault information hidden in both high frequency and low frequency components. However, hierarchical permutation entropy still has some shortcomings, such as poor statistical stability for short time series and inability of analyzing multichannel signals. To address such disadvantages, this paper proposes a new entropy method, called refined composite multivariate hierarchical permutation entropy. Refined composite multivariate hierarchical permutation entropy can extract rich fault information hidden in multichannel signals synchronously. Based on refined composite multivariate hierarchical permutation entropy and random forest, a novel fault diagnosis framework is proposed in this paper. The effectiveness of the proposed method is validated using experimental and simulated signals. The results demonstrate that the proposed method outperforms multivariate multiscale fuzzy entropy, refined composite multivariate multiscale fuzzy entropy, multivariate multiscale sample entropy, multivariate multiscale permutation entropy, multivariate hierarchical permutation entropy, and composite multivariate hierarchical permutation entropy in recognizing the different faults of rotating machinery.