Cubic spline interpolation-based refined composite multiscale dispersion entropy and its application to bearing fault identification

Abstract

As a powerful tool, dispersion entropy (DE) has good capability to measure the irregularity and complexity of nonlinear systems, so it is extensively utilized in the field of structural health monitoring. However, traditional multiscale dispersion entropy (MDE) will suffer from down-sampling as the scale factor increases, which compresses some intrinsic feature information, so that the representation ability of MDE for nonlinear system is significantly restrained. Aiming at this problem, a new method called cubic spline interpolation-based refined composite multiscale dispersion entropy (CSIRCMDE) is proposed. In this frame, the coarse-graining series are regarded as knots to calculate the interpolative points in different sub-sections. Then, the obtained coarse-graining samples and interpolative samples are used to construct interpolation series to capture the potential vibration characteristics and constrain the down-sampling phenomenon. Finally, the first coarse-graining point is gradually shifted back to make multiple groups of interpolation series, and the entropy values are rectified by calculating mean pattern probabilities at the same scale. Through these steps, CSIRCMDE can grasp sufficient feature information to reduce entropy errors and overcome the dependence on sample size compared with traditional algorithms, which is demonstrated by simulation and noise signals. Furthermore, two types of bearing damage experiments prove that CSIRCMDE has good capability to characterize the bearing states, therefore, based on the proposed algorithm, the classification model that can fully identify different bearing faults is established.