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1、附 录附录 A 外文资料翻译Machanical Systerms and Signal Processing 13 (2010)Performance enhancement of ensemble empirical mode decompositionAbstractEnsemble empirical mode decomposition (EEMD) is a newly developed method aimed at eliminating mode mixing present in the original empirical mode decomposition (EMD
2、). To evaluate the performance of this new method, this paper investigates the effect of two parameters pertinent to EEMD: the amplitude of added white noise and the number of ensemble trials. A test signal with mode mixing that mimics realistic bearing vibration signals measured on a bearing test b
3、ed was developed to enable quantitative evaluation of the EEMD and provide guidance on how to choose the two parameters appropriately for bearing signal decomposition. Subsequently, a modified EEMD (MEEMD) method is proposed to reduce the computational cost of the original EEMD method as well as imp
4、roving its performance. Numerical evaluation and systematic study using vibration data measured on an experimental bearing test bed verified the effectiveness and computational efficiency of the proposed MEEMD method for bearing defect diagnosis.1. IntroductionIn recent years, timefrequency and time
5、-scale analysis techniques such as short time Fourier transform (STFT) 1 and wavelet transform 2, 3 have been increasingly investigated for non-stationary and/or nonlinear signal processing in machine health diagnosis. These techniques, while having shown to be successful in various applications, ar
6、e non-adaptive in nature. As a result, once the window type or a base wavelet has been chosen, the analysis function remains the same during the subsequent signal decomposition process. In comparison, the HilbertHuang transform (HHT) 4,5 decomposes a signal into a set of intrinsic mode functions (IM
7、Fs) through the empirical mode decomposition (EMD) process, thus only involving the signal being analyzed itself instead of requiring an analysis function to be convoluted with. As a result, it presents a data-driven approach to dealing with non-stationarity and/or nonlinearity in the signal. While
8、the HHT technique has been applied to various fields, such as machine health monitoring and structural damage detection 611, filtering and denoising 12,13, and bioscience 1416, a problem that has remained existing in the EMD process is the mode mixing, which results from signal intermittency 1720. T
9、o improve the EMD method, the ensemble empirical mode decomposition (EEMD) method has been recently proposed to eliminate mode mixing 21. Essentially, EEMD repeatedly decomposes the original signal with added white noise into a series of IMFs, by applying the original EMD process, and treats the (en
10、semble) means of the corresponding IMFs during the repetitive process as the final EEMD decomposition result.This paper investigates the effect of two parameters the amplitude of added noise and the number of ensemble trials on the performance of the EEMD method. After introducing the theoretical ba
11、ckground of the EEMD process, a simulated signal that presents the mode mixing phenomenon is developed to facilitate quantitative evaluation of the two parameters. Furthermore, it is proposed to replace white noise with noise of finite bandwidth for the EEMD process to improve computational efficien
12、cy. Subsequently, both numerical evaluations on a test signal that mimic realistic bearing vibration signal and experimental study on vibration signals measured on a bearing test bed have verified the effectiveness of the improved EEMD method for bearing defect diagnosis. Comparison with the origina
13、l EMD and EEMD methods has demonstrated that the modified EEMD (MEEMD) method is more effective and computationally efficient, and is well suited for applications involving rotary machine health diagnosis.2. Modified EEMD methodWhile the EEMD method solves the problem of mode mixing, the large numbe
14、r of ensemble trails presents a high computational load. Improving the computational efficiency of EEMD is thus desired. The purpose of adding white noise is to facilitate that components in different scales of the signal are properly projected onto scales of reference established by the white noise
15、 21. This means the low frequency part of the added white noise will affect the decomposition results of the EEMD process (i.e. reducing mode mixing in the decomposed IMFs), as long as it covers the frequency range of the signal of interest. In comparison, the high-frequency section of the added whi
16、te noise has no effect. This indicates that improvement on the Computational efficiency of the EEMD process can be achieved by replacing white noise with a band-limited noise to be added to the signal to be decomposed. Such replacement will effectively reduce the number of ensemble trials required to obtain meaningful IMFs. Technically, band-limited noise can be obtained by low-pass filtering the white noise, with the cut-off frequency being the upper limit
