LMSST-Based 2-D Multiscale Time-Frequency Reverse Dispersion Entropy and Its Application in Fault Diagnosis of Rolling Bearing

Multiscale reverse dispersion entropy (MRDE
$_{\text {1-D}}$
) can effectively evaluate the complexity and nonlinear dynamic mutation behavior of 1-D signals. However, the representation of vibration signal complexity within the time domain is primarily represented, with the inherent nonlinear dynamic properties in the frequency domain being ignored. Inspired by 2-D dispersion entropy (DE
$_{\text {2-D}}$
), a novel nonlinear dynamic method termed 2-D time-frequency reverse dispersion entropy (TFRDE
$_{\text {2-D}}$
) is presented. Meanwhile, for the purpose of quantifying the complexity of the time-frequency distribution (TFD) of time series at multiscales, another complexity measurement method called LMSST-based 2-D multiscale time-frequency reverse dispersion entropy (LMSST-MTFRDE
$_{\text {2-D}}$
) is introduced by combining TFRDE
$_{\text {2-D}}$
with the LMSST for TFD computation and the 2-D coarse-graining process. Subsequently, a novel fault diagnosis method for rolling bearings is developed by combining LMSST-MTFRDE
$_{\text {2-D}}$
with a support vector machine optimized through the firefly algorithm (FA-SVM). Finally, the fault diagnosis method proposed in this article is applied to evaluate the test data for rolling bearings in comparison to the MRDE
$_{\text {1-D}}$
and other similar methods. As a result, a higher level of stability in fault feature extraction and increased rates of fault recognition are demonstrated by the proposed fault diagnosis method.