# An Optimal Resonant Frequency Band Feature Extraction Method Based on Empirical Wavelet Transform
## 1 Introduction
At the same time, [PERSON] also noted in their work that the proposed method did not give recommendations for the scale-space parameters under different noise intensities. The above literature shows that the improvement of EWT mostly focuses on how to optimize the division of the spectrum. Since the randomness of noise is reflected as the uncertainty of spectrum division, it is difficult to construct the optimal filter only by studying the spectral features. Therefore, by effectively analyzing the characteristics carried by each empirical mode, the optimal resonance band constructed by the data-driven method will have better universality and stronger robustness to noise. In the event of a local failure in a rolling bearing, a periodic instantaneous impact is generated, and the bearing system is stimulated to resonate and decay exponentially [18]. [PERSON] proposed Spectral Kurtosis (SK) [19] and Fast Kurtogram (FK) [20] based on an envelope analysis to determine the center frequency and bandwidth of the optimal resonance band. Nevertheless, in the case of a low SNR, the center frequency obtained by the Kurtogram is inaccurate and the bandwidth is too wide. Meanwhile, it is a research hotspot in recent years to determine the center frequency position by fully considering the cyclostationality of fault signal. When the studied signal has a cyclostationary component, the square envelope spectrum will show a peak value at the specific cyclic frequency of the phenomenon [21]. Based on this characteristic, [PERSON] et al. proposed a Protrugram method [22] based on the narrowband envelope spectrum kurtosis. Unfortunately, this method still has the problem that the bandwidth needs to be preset, and the ideal effect is not achieved when there is noise interference [23]. To capture the impulsiveness and cyclostationarity of the signal, [PERSON] et al. used Shannon entropy as a reflection of the transient deviation of the signal, equated the negative entropy with kurtosis to measure the energy fluctuation in the spectrum, creatively combining Kurtogram with Protrugram, and proposed the average spectral Negentropy (ASN) method by measuring the negative entropy in square envelope and square envelope spectrums respectively, which is very important to precisely locate the fault frequency center of bearings [24]. One point worth improving is this method uses the average partitioning of each level for the segmentation of the spectrum, which is rough and lacks physical significance. Meanwhile, it can be observed that the precise location of the center frequency is the key to determine the optimal resonance frequency band. After consulting, we found that the combination of entropy and decomposition methods has been extensively used for noise elimination, evaluation of mechanical operation state, identification of fault types and so on. For example, [PERSON] et al. applied transfer entropy to multivariate empirical mode decomposition to improve the robustness of detection while mitigating the mode mixing phenomenon [25]. [PERSON] uses the multiscale-dispersion entropy to identify the noise IMFs decomposed by the complete ensemble empirical mode, which plays a role in de-noising [26]. [PERSON] et al. applied the improved time-frequency entropy to EWT by constructing a classifier to identify the type of fault in the rolling bearing [27]. Inspired by the above literature, we firstly apply the idea of combining entropy with decomposition method to the task of accurately constructing the optimal fault frequency band. It is worth noting that in actual operating conditions, abnormal impulse interference is often accompanied by strong randomness, and the increase of entropy may not always be associated with an increase in dynamic complexity, which may present multiple high values on different frequency bands, and it is still difficult to determine the optimal fault center location [28; 29]. Therefore, how to improve the ASN part of the proposed method to make it more accurate and robust is another core issue of this paper.