A novel mathematical morphology spectrum entropy based on scale-adaptive techniques

Mathematical morphology spectrum entropy is a signal feature extraction method based on information entropy and mathematical morphology. The scale of structure element is a critical parameter, whose value determines the accuracy of feature extraction. Existing scale selection methods depend on experiment parameters or external indicators including noise ratio, fault frequencies, etc. In many cases, existing methods obtain fix scale and they are not suitable for quantifying the performance degradation and the fault degree of bearings. There are few researches on scale selection based on the properties of mathematical morphology spectrum. In this study, a scale-adaptive mathematical morphology spectrum entropy (AMMSE) is proposed to improve the scale selection. To support the proposed method, two properties of the mathematical morphology spectrum (MMS), namely non-negativity and monotonic decreasing, are proved. It can be concluded from the two properties that the feature loss of MMS decreases with the increase of scale. Based on the conclusion, two adaptive scale selection strategies are proposed to automatically determine the scale by reducing the feature loss of MMS. AMMSE is the integration of two strategies. Compare to the existing methods, AMMSE is not constrained by the information of the experiment and the signal. The scale of AMMSE changes with the signal characteristics and is no longer fixed by experimental parameters. The parameters of AMMSE are more generalizable as well. The presented method is applied to identify fault degree on CWRU bearing data set and evaluate performance degradation on IMS bearing data set. The experiment result shows that AMMSE has better results in both experiments with the same parameters.