Time-frequency Peak Filtering Method Research Articles

A noise reduction method of rolling bearing based on empirical wavelet transform and adaptive time frequency peak filtering

The vibration signal of rolling bearing with variable operating conditions contains complex interference components, which will cause low fault diagnosis accuracy, especially in strong noise case. To solve this problem, we proposed a noise reduction method of rolling bearing with variable operating based on empirical wavelet transform and adaptive time-frequency peak filtering (EWT-ATFPF). Firstly, empirical wavelet transform is used to obtain different frequency intrinsic mode functions (IMFs). Secondly, a modified adaptive window length formula for time-frequency peak filtering (TFPF) is constructed by combining the sampling ratio index and a fault sensitivity indicator that calculated by kurtosis and correlation coefficients of IMFs, which can better characterize the impact components. Thirdly, to balance noise reduction effect and the fidelity of IMFs, we proposed an improved TFPF method by adaptively adjusting its windows length. The adaptive method could be carried out using the proposed fault sensitivity indicator and window length formula, and the denoising IMFs could be obtained by ATFPF. Finally, the denoising vibration signal is reconstructed by using the denoising IMFs. The performance of fault diagnosis of the proposed method is verified by using simulated signal and bearing fault test data. The results show that the proposed EWT-ATFPF method could effectively achieve noise reduction under variable operating conditions.

Random Noise Suppression Method of Micro-Seismic Data Based on CEEMDAN-FE-TFPF

As rock fractures caused by micro-seismic events has potential safety hazards to underground workers, it is often necessary to accurately locate the micro-seismic source for hidden danger investigation. Micro-seismic data are generated in complex underground environments which are significantly affected by random noise. These data greatly influence subsequent micro-seismic source location, energy estimation, and disaster monitoring. In this paper, a new denoising method based on Time-Frequency Peak Filtering (TFPF) and Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN) is proposed for micro-seismic data. Micro-seismic data are decomposed into several Intrinsic Mode Functions (IMFs) by CEEMDAN. Then, discriminant factors are used to determine which IMF needs to be denoised by TFPF. Finally, the denoised result is reconstructed by inverse CEEMDAN. By comparing and analyzing different entropies, Fuzzy Entropy (FE) is selected as the best discriminant factor. The CEEMDAN-FE-TFPF denoising method can effectively avoid the influence of fixed window length of the conventional TFPF method. The effectiveness and superiority of this method are verified by experiments of synthetic and actual data.

Processing of Underground Nuclear Magnetic Resonance Data for Underground River Detection: A Case Study in Doumo Tunnel, Guizhou, China

Underground nuclear magnetic resonance (NMR) is introduced to detect the risk of groundwater-induced disasters in the underground engineering such as tunnels and mines. However, underground NMR is in practice often limited to the extremely low signal-to-noise ratios (SNRs). On the one hand, small coils are necessary to be used to detect water in the narrow underground space, which decreases the amplitude of the excited signal. On the other hand, the weak signal is submerged in quite serious electromagnetic noise which is generated from the electrical installations. The low SNRs emphasize the importance of using an optimal post-processing strategy to obtain the reliable underground NMR data. The objective of this paper is to explain the processing of underground NMR data taking the detection of the underground river in Doumo Tunnel as an example. We have evaluated the noise condition in Doumo Tunnel and the noise level of 0.6760 nV/m2 was found in this area. At such a high noise level, the reliable underground NMR signal is difficult to be extracted and the credible depth profile of water content is unable to be provided. Then, we have analyzed the noise interference. Although de-spiking algorithm and reference-based noise cancellation method were applied to remove the major noise sources, the underground NMR signal is still invisible. There is still a lot of additive noise remained, so time-frequency peak filtering method is further used to suppress the remaining noise. The performance of the proposed post-processing strategy is tested on the underground NMR data from the underground river. The result was consistent with the geological structure, which is demonstrated to be able to directly provide a security pre-warning of the underground engineering.

Random noise suppression of seismic data by time–frequency peak filtering with variational mode decomposition

Random noise suppression is of great importance in seismic processing and interpretation, and time–frequency peak filtering (TFPF) is a classic denoising approach. In TFPF, pseudo Wigner–Ville distribution (PWVD) is used to linearise the given signal for an unbiased estimation of the instantaneous frequency. However, window length is a trade-off parameter for preserving valid signals and attenuating random noise. A long window length may cause loss of the desired signal, whereas a short window length may be inadequate to suppress noise. To ensure a good trade-off between signal preservation and noise reduction, empirical mode decomposition (EMD) has been introduced into the TFPF method. Although the EMD-TFPF method can achieve good results, the mode mixing problem in EMD is non-negligible. In this article, we introduce variational mode decomposition (VMD) to overcome the mode mixing problem. VMD decomposes a signal into an ensemble of modes that own their respective centre frequencies. Thus, the modes obtained by VMD contain less noise, which simplifies selection of the window width of TFPF. Therefore, we propose the VMD-based TFPF (VMD-TFPF) method to suppress random noise. Synthetic and field seismic data examples are employed to illustrate the superior performance of the proposed method in attenuating random noise and preserving the desired signal.

A Hybrid De-Noising Algorithm for the Gear Transmission System Based on CEEMDAN-PE-TFPF

In order to remove noise and preserve the important features of a signal, a hybrid de-noising algorithm based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (CEEMDAN), Permutation Entropy (PE), and Time-Frequency Peak Filtering (TFPF) is proposed. In view of the limitations of the conventional TFPF method regarding the fixed window length problem, CEEMDAN and PE are applied to compensate for this, so that the signal is balanced with respect to both noise suppression and signal fidelity. First, the Intrinsic Mode Functions (IMFs) of the original spectra are obtained using the CEEMDAN algorithm, and the PE value of each IMF is calculated to classify whether the IMF requires filtering, then, for different IMFs, we select different window lengths to filter them using TFPF; finally, the signal is reconstructed as the sum of the filtered and residual IMFs. The filtering results of a simulated and an actual gearbox vibration signal verify that the de-noising results of CEEMDAN-PE-TFPF outperforms other signal de-noising methods, and the proposed method can reveal fault characteristic information effectively.

Application of Sample Entropy Based LMD-TFPF De-Noising Algorithm for the Gear Transmission System

This paper investigates an improved noise reduction method and its application on gearbox vibration signal de-noising. A hybrid de-noising algorithm based on local mean decomposition (LMD), sample entropy (SE), and time-frequency peak filtering (TFPF) is proposed. TFPF is a classical filter method in the time-frequency domain. However, there is a contradiction in TFPF, i.e., a good preservation for signal amplitude, but poor random noise reduction results might be obtained by selecting a short window length, whereas a serious attenuation for signal amplitude, but effective random noise reduction might be obtained by selecting a long window length. In order to make a good tradeoff between valid signal amplitude preservation and random noise reduction, LMD and SE are adopted to improve TFPF. Firstly, the original signal is decomposed into PFs by LMD, and the SE value of each product function (PF) is calculated in order to classify the numerous PFs into the useful component, mixed component, and the noise component; then short-window TFPF is employed for the useful component, long-window TFPF is employed for the mixed component, and the noise component is removed; finally, the final signal is obtained after reconstruction. The gearbox vibration signals are employed to verify the proposed algorithm, and the comparison results show that the proposed SE-LMD-TFPF has the best de-noising results compared to traditional wavelet and TFPF method.

Simultaneous denoising and preserving of seismic signals by multiscale time-frequency peak filtering

Time frequency peak filtering has been successfully applied to eliminate pervasive random noise in the time-frequency domain. The linearity of the signal is crucial for denoising in the time frequency peak filtering method. We usually apply pseudo Wigner–Ville distribution to make the signal locally linear in time. However, there is a pair of contradiction in window length selection for pseudo Wigner–Ville distribution. If we choose a short window length for pseudo Wigner–Ville distribution in the time frequency peak filtering, it leads to good preservation for signals, but the denoising performance is relatively poor. So the contradiction between the signal preservation and noise attenuation cannot be solved by a fixed window length. In this paper, we present a multiscale time frequency peak filtering to solve this problem. In the novel method, we adopt a Laplacian pyramid to decompose the seismic data into multiple scale components. These components have different frequencies. Then a short window length can be chosen for signal-dominant scale to preserve the signal and a long window length is applied to noise-dominant scale by the time frequency peak filtering to suppress more noise. We test the performance of our proposed method on both synthetic and real seismic data. Tests demonstrate that the multiscale time frequency peak filtering based on Laplacian pyramid can eliminate the random noise more effectively and preserve events of interest better than the conventional time frequency peak filtering.

Seismic random noise attenuation and signal-preserving by multiple directional time-frequency peak filtering

Time-frequency peak filtering (TFPF) is an effective method for seismic random noise attenuation. The linearity of the signal has a significant influence on the accuracy of the TFPF method. The higher the linearity of the signal to be filtered is, the better the denoising result is. With this in mind, and taking the lateral coherence of reflected events into account, we do TFPF along the reflected events to improve the degree of linearity and enhance the continuity of these events. The key factor to realize this idea is to find the traces of the reflected events. However, the traces of the events are too hard to obtain in the complicated field seismic data. In this paper, we propose a Multiple Directional TFPF (MD–TFPF), in which the filtering is performed in certain direction components of the seismic data. These components are obtained by a directional filter bank. In each direction component, we do TFPF along these decomposed reflected events (the local direction of the events) instead of the channel direction. The final result is achieved by adding up the filtering results of all decomposition directions of seismic data. In this way, filtering along the reflected events is implemented without accurately finding the directions. The effectiveness of the proposed method is tested on synthetic and field seismic data. The experimental results demonstrate that MD–TFPF can more effectively eliminate random noise and enhance the continuity of the reflected events with better preservation than the conventional TFPF, curvelet denoising method and F–X deconvolution method.

Spatiotemporal Time–Frequency Peak Filtering Method for Seismic Random Noise Reduction

The time-frequency peak filtering (TFPF) is an effective method for seismic random noise reduction. To achieve a higher level of noise suppression in seismic records, we propose a novel approach in which we apply the TFPF method in Radon domain. This method, called spatiotemporal TFPF, can be applied with different types of Radon transforms (linear, parabolic, etc.) depending on the geometry of the reflection. The new method is similar to the principle of ridgelet, which is doing 1-D wavelet in linear Radon domain so that there is a parameter representing direction brought in the filtering process. Although the ridgelet has the wonderful ability to process reflection events with linearly changing characteristics, for curving events, it shows lack of effectiveness. With this in mind, and taking the superiority of TFPF into consideration, the new method as mentioned previously is proposed. Thus, it breaks the limitation of doing filtering in linear Radon domain to make the filtering more flexible and plays the advantage of TFPF in denoising. Using both synthetic and real seismic data, we show the better performance of the new method in random noise reduction and higher continuity and clarity of reflection events compared to the conventional TFPF.