Composite Interpolated Hierarchical Dispersion Entropy: A Novel and Robust Algorithm for Mechanical Fault Diagnosis

The hierarchical dispersion entropy (HDE) algorithm, which combines hierarchical decomposition and dispersion entropy (DE), can extract multifrequency features from bearing signals. However, the data compression phenomenon caused by the nonoverlapped average and difference operators filters a large amount of dynamic information hidden in hierarchical nodes. In addition, relying on a fixed mapping function, i.e., normal cumulative distribution function (NCDF), the node components cannot be accurately mapped to the proper categories. These deficiencies negatively affect the characterization performance of HDE on bearing damages. Therefore, the composite interpolated HDE with generalized Gaussian distribution (CIHDE
$_{\text {GGD}}{)}$
algorithm is developed in this article to eliminate the limitations of HDE. In this algorithm, an interpolated hierarchical decomposition scheme is designed to supplement the intrinsic dynamic information and weaken the influence of data compression. Meanwhile, based on the generalized Gaussian distribution (GGD), an optimization strategy for the mapping function is further developed to dynamically fit the distributions of node components. The simulation experiments prove that benefited by the improvements, the CIHDEGGD can better extract the frequency features from different types of nonlinear signals in comparison with HDE. Afterward, the iterative Davies–Bouldin index (iDBI) feature selection method is developed to filter the redundant information and refine the features. The experimental results demonstrate that the diagnostic vector obtained by CIHDEGGD and iDBI is more sensitive than those of traditional methods. Consequently, based on the combination of CIHDEGGD and iDBI, the satisfactory identification results for different types of rolling bearing damages can be obtained.