Nonlinear vibration analysis and defect characterization using entropy measure-based learning algorithm in a defective rolling element bearings

Rolling element bearings (REBs) constitute a crucial element in rotating machinery, and their malfunction is one of the most common reasons for unplanned outages and shutdowns. As a result, monitoring the health of REBs, detecting and diagnosing the size and location of faults, and assessing their degradation have been the subject of extensive research. In the last few decades, several signal processing techniques such as Fast Fourier transform, Wavelet transform, Hilbert transform, artificial neural network, and recurrence plot (RP), among others, have been proposed for the diagnosis and prognosis of REBs. However, most of these techniques provide only a qualitative diagnosis while ignoring the quantitative aspect of the faults. The current work proposes a novel entropy-based fault detection approach and grading the condition of bearings from noisy time history measurements. Entropy-based measures based on Kullback–Leibler and Shannon entropy from vibration signals have been used for grading the condition of bearings. Subsequently, these entropy basis measures have been successfully tested on vibration signatures from various bearing fault types occurring at different locations. The results indicate a one-to-one relation between fault severity and its entropy measure. Moreover, each type of bearing fault has been shown to have a well-defined entropy measure, for different faults lie on a nearly linear locus. In addition to the field and experimental data obtained in the workshop, a nonlinear vibration model under the combined effect of the unbalanced and non-Gaussian Poisson loading has been developed to obtain the acceleration time waveform for the fault severity assessment. The noisy nonlinear model takes into account the Hertizian contact force between the ball and races, internal clearance, race waviness, varying compliances, and localized defects. The adaptive time stepping (ATSP) numerical integration combined with the Brownian tree is used to obtain the nonlinear vibration response. The results show the effectiveness of the proposed algorithm in the diagnosis and prognosis of various types of REB faults.