Two-dimensional composite multi-scale time–frequency reverse dispersion entropy-based fault diagnosis for rolling bearing

Multi-scale dispersion entropy (MDE_1D) is an effective nonlinear dynamic tool to characterize the complexity of time series and has been extensively applied to mechanical fault diagnosis. However, with the increase of scale factor, the values of MDE_1D often fluctuate largely, resulting in poor stability. Besides, it only extracts the complexity information from the time domain of vibration signal, while the complexity information in the frequency domain is ignored. To enhance the stability of MDE_1D and extract the complexity characteristics from the time–frequency domain of vibration signal, this paper first develops a two-dimensional multi-scale reverse dispersion entropy (MRDE_2D), inspired by the MDE_1D and two-dimensional multi-scale dispersion entropy (MDE_2D) through introducing the “distance information from white noise”. Then a two-dimensional multi-scale time–frequency reverse dispersion entropy (MTFRDE_2D) combined with time–frequency analysis is proposed. After that, considering that the length of the coarse-grained sequence used in the multi-scale coarse-grained process of MTFRDE_2D will become shorter and shorter with the increase of scale factor, resulting in a loss of potentially useful information, the two-dimensional composite multi-scale time–frequency reverse dispersion entropy (CMTFRDE_2D) is proposed through using the composite coarse-grained process. The effectiveness and advantages of CMTFRDE_2D algorithm are demonstrated by analyzing different kinds of noise signals. Following that, a new rolling bearing fault diagnosis method is proposed based on the CMTFRDE_2D for feature extraction and gravitational search algorithm optimized support vector machine for mode identification. The proposed fault diagnosis method is employed on two rolling bearing test data sets and also compared with the existing MTFRDE_2D,- MRDE_2D,- MDE_2D,- and MDE_1D-based fault diagnosis methods. The analysis results reveal that the proposed fault diagnosis method can successfully extract the fault information from rolling bearing vibration signals in time–frequency domain and can accurately identify different fault locations and severities of rolling bearings with certain advantages.