A novel entropy-based sparsity measure for prognosis of bearing defects and development of a sparsogram to select sensitive filtering band of an axial piston pump

Abstract

This study aims to establish a novel entropy-based sparsity measure for two main purposes: first is for the prognosis of bearing defects, secondly it is employed to construct sparsogram for identifying sensitive filtering band to carry out envelope analysis for identifying defects in the complex hydraulic machinery (axial piston pump). The newly developed symmetrized directed divergence measure is first authenticated after satisfying the necessary conditions such as convexity, non-negativity and symmetric properties and then reformulated to generate another novel probabilistic entropy measure. The entropy measure so obtained has been mathematically proven to satisfy all essential conditions as laid down by Shannon such as permutationally symmetric, degeneracy, separability, continuity, concavity, maximum value, and non-negativity. Furthermore, the proclaimed probabilistic entropy measure is modified to become a novel sparsity measure that can satisfy all of the six intuitive sparse attributes. The sparsity measure so obtained is applied in two ways. First application is of defect degradation monitoring of the rolling element bearing. Here, LSTM network is used for the carrying out defect prognosis. The degradation monitoring has been carried out on the life time accelerating data of IMS and PRONOSTIA. Second application of the proposed sparsity measure is for the development of a sparsogram for selecting the suitable filtering band to carry out envelop analysis, needed to identify bearing defects in the axial piston pump. To authenticate the validity of the proposed sparsogram, a comparative study has also been done with the existing tool such as fast Kurtogram, spectral kurtosis and Protugram.