A novel empirical reconstruction Gauss decomposition method and its application in gear fault diagnosis

This paper proposes a novel signal decomposition method, empirical reconstruction Gaussian decomposition (ERGD). ERGD comprises two key steps: spectrum segmentation based on the unimodal symmetry hypothesis and reconstruction decomposition strategy. ERGD puts forward the unimodal symmetry hypothesis along with the corresponding unimodal symmetry estimation method. Building upon this, ERGD presents a novel spectrum segmentation approach that adaptively divides the spectrum into energy-concentrated and unimodal symmetry segments, thereby circumventing issues of over-segmentation. The reconstruction decomposition strategy defines a series of alpha factor generalized Gaussian filters and then reconstructs them into ideal filter banks in order to accomplish signal decomposition. The ideal filter banks can effectively eliminate noise in the segment. It is worth mentioning that ERGD has the ability to adaptively adjust the overlap and attenuation properties of the ideal filter, which can effectively suppress noise interference. As a new signal decomposition method, ERGD is capable of decomposing signals into a series of Gaussian intrinsic mode functions (GIMFs) possessing orthogonality. Applying ERGD to gear fault diagnosis, both simulation and experimental signal analysis results demonstrate the excellent performance of the proposed method in signal decomposition. It significantly contributes to the attainment of precise gear fault diagnosis and holds practical value.