Entropy-Based Method of Choosing the Decomposition Level in Wavelet Threshold De-noising

Abstract

Abstract:In this paper, the energy distributions of various noises following normal, log-normal and Pearson-III distributions are first described quantitatively using the wavelet energy entropy (WEE), and the results are compared and discussed. Then, on the basis of these analytic results, a method for use in choosing the decomposition level (DL) in wavelet threshold de-noising (WTD) is put forward. Finally, the performance of the proposed method is verified by analysis of both synthetic and observed series. Analytic results indicate that the proposed method is easy to operate and suitable for various signals. Moreover, contrary to traditional white noise testing which depends on "autocorrelations", the proposed method uses energy distributions to distinguish real signals and noise in noisy series, therefore the chosen DL is reliable, and the WTD results of time series can be improved.

Wavelet-Based Analysis on the Complexity of Hydrologic Series Data under Multi-Temporal Scales

“…The variability of RS2 series is the most obvious because the value of its C v is 1.08, but the value of C v of RS5 series is just as little as 0.30; the skew degree of RS3 series is the most obvious with the C s value of 2.21, whereas the C s of RS4 series has the smallest value of í0.07; the RS5 series has the best auto-correlate characteristics because its R 1 is 0.96, but the R 1 of RS3 series has the smallest value of 0.29. To continue, we choose appropriate mother wavelets by using the method proposed in [26], and then remove noise in these series data by using the wavelet threshold de-noising (WTD) method proposed in [26,27], which is more effective than other traditional de-noising methods as discussed in [26,28,29]. The chosen wavelets are listed in Table 2, and the de-noising results are depicted in Figure 1.…”

“…Here, the authors suggest the wavelet threshold de-noising method proposed in [26,27] be used in practice, because by using it not only the appropriate mother wavelet can be chosen, but also reliable de-noising results of hydrologic series data can correspondingly be obtained, based on which the analytic results of complexity of hydrologic series data can be improved.…”

A Vibration Analysis Based on Wavelet Entropy Method of a Scroll Compressor

“…Chen et al [24] presented an evaluation method of bearing factory quality based on wavelet packet entropy flow manifold learning and applied it to detect different types of defects on the bearing components. Some applications of WE in signal analysis and processing have shown its outstanding performance in distinguishing real signals and noise in a noisy series [25] and fault-detecting for different stable and unstable power swing conditions [26].…”

Uncertainty Analysis of Decomposition Level Choice in Wavelet Threshold De-Noising

“…The white noise testing commonly used for DL choice in WTD cannot identify the real signals in observed series data and thus cannot meet the practical needs well [22]. The authors proposed in [23] a method of choosing DLs to improve wavelet threshold de-noising, whose basic idea is first to compare the difference of energy distributions between noisy series and noise, which are described by wavelet energy entropy (WEE), and then to choose the appropriate DL. Analyses of various examples verified the effectiveness of the proposed method, but in the analytic process by using it, the strictly quantitative criterion for comparing the difference of WEE was not given, therefore the chosen DL results based on the "extreme" would have inherent uncertainty.…”

“…In this study, the objective is to propose the criterion for quantifying the WEE difference between noisy series and noise by taking uncertainty into consideration, and to thus improve the DL choice method proposed in [23]. To achieve this purpose, in Section 2, the variations of WEE of various noises are analyzed and their uncertainties are described by using confidence intervals; then the DL choice method given in [23] is amended and improved.…”