Abstract
A method of step characteristic trend extraction based on logistic functions and envelopes (LFEs) is proposed in this paper. Compared with the existing trend extraction methods, the LFE method can determine the starting position of the step trend using a logistic function and extract the local trend using upper and lower envelopes. This method enhances the extraction accuracy and reduces the computation time. To verify the effectiveness of the LFE method, a simulated signal with a step trend feature was compared with the five-spot triple smoothing method, wavelet transform method and empirical mode decomposition-based method. All of these methods were applied to a real shock signal. The results demonstrate that the LFE method can reliably and accurately extract the trends with step characteristics based on less prior knowledge. Moreover, the proposed technique is suitable for industrial online applications.
Highlights
A method of step characteristic trend extraction based on logistic functions and envelopes (LFEs) is proposed in this paper
The accuracy of the trend extraction based on wavelet transform is affected by the wavelet basis function and decomposed layer number, and these two parameter values must be determined by empirical knowledge and experimental comparison[9]
The empirical mode decomposition (EMD) method has attracted the attention of researchers because it does not require predetermining the basis function and adaptive decomposition
Summary
A method of step characteristic trend extraction based on logistic functions and envelopes (LFEs) is proposed in this paper. To verify the effectiveness of the LFE method, a simulated signal with a step trend feature was compared with the five-spot triple smoothing method, wavelet transform method and empirical mode decomposition-based method. Dybala and Zimroz[13] proposed a method of IMF identification based on the Pearson correlation coefficient of each IMF and the empirically determined local mean of the original signal These methods do not avoid the problem of mode mixing during the EMD process. This paper is organized as follows: in “Trend extraction by LFE method” section describes the step characteristics of the trends in signals that are collected in an impact vibration test by piezoelectric acceleration sensors. This paper proposes a method using a logistic function and upper and lower envelopes to extract the step characteristic trend.
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