Abstract
As a novel data mining approach, a wavelet entropy algorithm is used to perform entropy statistics on wavelet coefficients (or reconstructed signals) at various wavelet scales on the basis of wavelet decomposition and entropy statistic theory. Shannon wavelet energy entropy, one kind of wavelet entropy algorithm, has been taken into consideration and utilized in many areas since it came into being. However, as there is wavelet aliasing after the wavelet decomposition, and the information set of different-scale wavelet decomposition coefficients (or reconstructed signals) is non-additive to a certain extent, Shannon entropy, which is more adaptable to extensive systems, couldn’t do accurate uncertainty statistics on the wavelet decomposition results. Therefore, the transient signal features are extracted incorrectly by using Shannon wavelet energy entropy. From the two aspects, the theoretical limitations and negative effects of wavelet aliasing on extraction accuracy, the problems which exist in the feature extraction process of transient signals by Shannon wavelet energy entropy, are discussed in depth. Considering the defects of Shannon wavelet energy entropy, a novel wavelet entropy named Tsallis wavelet energy entropy is proposed by using Tsallis entropy instead of Shannon entropy, and it is applied to the feature extraction of transient signals in power systems. Theoretical derivation and experimental result prove that compared with Shannon wavelet energy entropy, Tsallis wavelet energy entropy could reduce the negative effects of wavelet aliasing on accuracy of feature extraction and extract transient signal feature of power system accurately.
Highlights
Transient feature extraction is an important part of signal analysis, and as a new feature extraction algorithm, wavelet entropy has attracted the attention of experts and scholars all over the world.Wavelet entropy is a combination of wavelet decomposition and entropy statistics theories, and it has the advantages of multi-resolution analysis and complexity evaluation for time-varying signals, which means that the macro and micro aspects of some special signals could be researched in the timefrequency domain
Starting with an analysis of wavelet aliasing and feature extraction effects, this paper studied the working mechanism and the suitable scope of Tsallis wavelet energy entropy (TWEE), analyzes the relationship and difference between TWEE
Entropy statistics theories and wavelet decomposition algorithmw are the academic foundation of wavelet entropy, the choice of entropy has a direct impact on the signal analysis results
Summary
Transient feature extraction is an important part of signal analysis, and as a new feature extraction algorithm, wavelet entropy has attracted the attention of experts and scholars all over the world. Wavelet entropy is a combination of wavelet decomposition and entropy statistics theories, and it has the advantages of multi-resolution analysis and complexity evaluation for time-varying signals, which means that the macro and micro aspects of some special signals could be researched in the timefrequency domain. Most research on wavelet entropy involves engineering applications of Shannon wavelet energy entropy (SWEE), but its physical meanings, working mechanism, and application principle have not been well discussed yet. In view of the abovementioned facts, in this paper, the theoretical basis of SWEE has been analyzed, and the emphasis of research was placed on the working mechanism for feature extraction of transient signals. Starting with an analysis of wavelet aliasing and feature extraction effects, this paper studied the working mechanism and the suitable scope of TWEE, analyzes the relationship and difference between TWEE and SWEE and provides the initial principle of non-extensivity index selection. The experimental results show that TWEE is better than SWEE in analyzing transient signals
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