Improved multiscale coded dispersion entropy: A novel quadratic-coded health indicator of rolling bearings

Abstract Dispersion entropy (DE) is widely used to quantify the complexity of nonlinear time series. In order to improve the ability to capture fault characteristics, a novel approach called coded dispersion entropy (CDE) has been introduced in recent years. CDE aims to expand the number of possible dispersion patterns and enhance the encoding of similar dispersion patterns. However, the coding method of CDE ignores the amplitude differences between dispersion elements and average elements, resulting in the inaccurate assignment of samples. Additionally, CDE is unable to extract effective information from other time scales. These limitations hinder the ability of CDE to effectively characterize faults. This paper proposes an improved multiscale coded dispersion entropy (IMCDE) to solve these limitations. The method introduces the interval scaling factor "R" and utilizes the sum and difference between the mean element and R as new coding boundaries. This approach addresses the sensitivity issue of the CDE coding mode towards smaller amplitude differences by the reasonable quadratic coding mode. Additionally, a composite coarse-graining process is introduced to rearrange the first coarse-grained point in sequence, resulting in multiple sets of sequences. The average probability of the same dispersion pattern at each scale is calculated to correct the entropy error. The experimental results from two sets of bearing faults demonstrate the effectiveness of this method in extracting critical features associated with faulty bearings. Furthermore, the method showed higher classification accuracy compared to multiscale dispersion entropy (MDE) and multiscale coded dispersion entropy (MCDE). Additionally, it exhibited smaller classification error than MDE and MCDE.