Elimination of end effects in local mean decomposition using spectral coherence and applications for rotating machinery

Local mean decomposition (LMD) is widely used in signal processing and fault diagnosis of rotating machinery as an adaptive signal processing method. It is developed from the popular empirical mode decomposition (EMD). Both of them have an open problem of end effects, which influences the performance of the signal decomposition and distort the results. Using the cyclostationary property of a vibration signal generated by rotating machinery, a novel signal waveform extension method is proposed to solve this problem. The method mainly includes three steps: waveform segmentation, spectral coherence comparison, and waveform extension. Its main idea is to automatically search the inside segment having similar frequency spectrum to one end of the analyzed signal, and then use its successive segment to extend the waveform, so that the extended signal can maintain temporal continuity in time domain and spectral coherence in frequency domain. A simulated signal is used to illustrate the proposed extension method and the comparison with the popular mirror extension and neural-network-based extension methods demonstrates its better performance on waveform extension. After that, combining the proposed extension method with normal LMD, the improved LMD method is applied to three experimental vibration signals collected from different rotating machines. The results demonstrate that the proposed waveform extension method based on spectral coherence can well extend the vibration signal, accordingly, errors caused by end effects would not distort the signal as well as its decomposition results.