Time-frequency Peak Filtering Research Articles

Adaptive block-matching and 4D denoising scheme for a distributed vibration sensing system

A noise reduction method based on the block-matching and 4D (BM4D) scheme is proposed to improve the signal-to-noise ratio (SNR) in distributed vibration sensing (DVS) systems. In the proposed scheme, the original Rayleigh backscattering (RBS) signal is converted into a three-dimensional image containing Rayleigh trajectory and energy information. The correlation between the time-domain and spatial-domain signals is then used to achieve the denoising operation. An experimental demonstration containing both one and two vibration points is conducted to verify the effectiveness of the proposed denoising scheme. The experimental results show that the BM4D scheme can provide higher SNR improvement than the current normalized least mean square (NLM), empirical mode decomposition combined with time-frequency peak filtering (EMD-TFPF), and BM3D schemes. Based on the BM4D scheme, the SNR is improved from 1.27 dB to 12.84 dB in the condition of one vibration point and from 6.23 dB to 20.14 dB in the condition of two vibration points. It is also indicated that the high-frequency noise of the vibration waveform after the denoising operation is mitigated by more than 30 dB, showing the potential for applications of accurate waveform characterization in cost-effective DVS systems.

MEMS Gyroscope Temperature Compensation Based on Improved Complete Ensemble Empirical Mode Decomposition and Optimized Extreme Learning Machine.

Herein, we investigate the temperature compensation for a dual-mass MEMS gyroscope. After introducing and simulating the dual-mass MEMS gyroscope's working modes, we propose a hybrid algorithm for temperature compensation relying on improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), sample entropy, time-frequency peak filtering, non-dominated sorting genetic algorithm-II (NSGA II) and extreme learning machine. Firstly, we use ICEEMDAN to decompose the gyroscope's output signal, and then we use sample entropy to classify the decomposed signals. For noise segments and mixed segments with different levels of noise, we use time-frequency peak filtering with different window lengths to achieve a trade-off between noise removal and signal retention. For the feature segment with temperature drift, we build a compensation model using extreme learning machine. To improve the compensation accuracy, NSGA II is used to optimize extreme learning machine, with the prediction error and the 2-norm of the output-layer connection weight as the optimization objectives. Enormous simulation experiments prove the excellent performance of our proposed scheme, which can achieve trade-offs in signal decomposition, classification, denoising and compensation. The improvement in the compensated gyroscope's output signal is analyzed based on Allen variance; its angle random walk is decreased from 0.531076°/h/√Hz to 6.65894 × 10-3°/h/√Hz and its bias stability is decreased from 32.7364°/h to 0.259247°/h.

A Temperature Compensation Approach for Micro-Electro-Mechanical Systems Accelerometer Based on Gated Recurrent Unit-Attention and Robust Local Mean Decomposition-Sample Entropy-Time-Frequency Peak Filtering.

MEMS accelerometers are significantly impacted by temperature and noise, leading to a considerable compromise in their accuracy. In response to this challenge, we propose a parallel denoising and temperature compensation fusion algorithm for MEMS accelerometers based on RLMD-SE-TFPF and GRU-attention. Firstly, we utilize robust local mean decomposition (RLMD) to decompose the output signal of the accelerometer into a series of product function (PF) signals and a residual signal. Secondly, we employ sample entropy (SE) to classify the decomposed signals, categorizing them into noise segments, mixed segments, and temperature drift segments. Next, we utilize the time-frequency peak filtering (TFPF) algorithm with varying window lengths to separately denoise the noise and mixed signal segments, enabling subsequent signal reconstruction and training. Considering the strong inertia of the temperature signal, we innovatively introduce the accelerometer's output time series as the model input when training the temperature compensation model. We incorporate gated recurrent unit (GRU) and attention modules, proposing a novel GRU-MLP-attention model (GMAN) architecture. Simulation experiments demonstrate the effectiveness of our proposed fusion algorithm. After processing the accelerometer output signal through the RLMD-SE-TFPF denoising algorithm and the GMAN temperature drift compensation model, the acceleration random walk is reduced by 96.11%, with values of 0.23032 g/h/Hz for the original accelerometer output signal and 0.00895695 g/h/Hz for the processed signal.

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.

High-G MEMS Accelerometer Calibration Denoising Method Based on EMD and Time-Frequency Peak Filtering.

In order to remove noise generated during the accelerometer calibration process, an accelerometer denoising method based on empirical mode decomposition (EMD) and time-frequency peak filtering (TFPF) is proposed in this paper. Firstly, a new design of the accelerometer structure is introduced and analyzed by finite element analysis software. Then, an algorithm combining EMD and TFPF is proposed for the first time to deal with the noise of the accelerometer calibration process. Specific steps taken are to remove the intrinsic mode function (IMF) component of the high frequency band after the EMD decomposition, and then to use the TFPF algorithm to process the IMF component of the medium frequency band; meanwhile, the IMF component of the low frequency band is reserved, and finally the signal is reconstructed. The reconstruction results show that the algorithm can effectively suppress the random noise generated during the calibration process. The results of spectrum analysis show that EMD + TFPF can effectively protect the characteristics of the original signal and that the error can be controlled within 0.5%. Finally, Allan variance is used to analyze the results of the three methods to verify the filtering effect. The results show that the filtering effect of EMD + TFPF is the most obvious, being 97.4% higher than the original data.

Precision Enhancement by Compensation of Hemispherical Resonator Gyroscope Dynamic Output Errors

In order to compensate for the hemispherical resonator gyroscope (HRG) dynamic output drift errors, a novel compensation method is presented. Through deriving the resonator motion equations and analyzing the mechanism of HRG dynamic output drift errors, it is found that the resonator defect nonuniformity is the main cause of the HRG dynamic output errors. By analyzing the mechanisms of these errors, the influence of these error sources is interacted and coupled, and it is difficult to analyze HRG output error mechanism and establish an error model comprehensively. We proposed a compensation prediction model for the HRG dynamic output to suppress the influence of these errors comprehensively. To establish the high precision HRG dynamic output compensation model, we proposed an improved variational mode decomposition (VMD) method to achieve an accurate HRG output. First, we used VMD to decompose the HRG output, and the optimal VMD decomposition parameters are achieved by genetic algorithm. In order to better achieve the effective information, the decomposed components of HRG drift are classified using the sample entropy. Then the mixed components are further processed using time frequency peak filtering. Finally, the accurate HRG output is achieved by reconstructing all the effective components. The accurate HRG output is used to construct the training set, and the high-precision HRG dynamic output prediction model is established by long short-term memory. The software compensation of the HRG dynamic output drift is realized by the prediction model. The experiment shows that the HRG dynamic output drift is mainly produced by the resonator nonuniformity, and it is strongly correlated with the standing wave azimuth, which verifies the correctness of the mechanism analysis. The HRG dynamic drift peak-peak value decreases to 5.715×10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-3</sup> °/s, which verifies the effectiveness of the compensation method.

A Hybrid Algorithm for Noise Suppression of MEMS Accelerometer Based on the Improved VMD and TFPF

High-G MEMS accelerometer (HGMA) is a new type of sensor; it has been widely used in high precision measurement and control fields. Inevitably, the accelerometer output signal contains random noise caused by the accelerometer itself, the hardware circuit and other aspects. In order to denoise the HGMA’s output signal to improve the measurement accuracy, the improved VMD and TFPF hybrid denoising algorithm is proposed, which combines variational modal decomposition (VMD) and time-frequency peak filtering (TFPF). Firstly, VMD was optimized by the multi-objective particle swarm optimization (MOPSO), then the best decomposition parameters [kbest, abest] could be obtained, in which the permutation entropy (PE) and fuzzy entropy (FE) were selected for MOPSO as fitness functions. Secondly, the accelerometer voltage output signals were decomposed by the improved VMD, then some intrinsic mode functions (IMFs) were achieved. Thirdly, sample entropy (SE) was introduced to classify those IMFs into information-dominated IMFs or noise-dominated IMFs. Then, the short-window TFPF was selected for denoising information-dominated IMFs, while the long-window TFPF was selected for denoising noise-dominated IMFs, which can make denoising more targeted. After reconstruction, we obtained the accelerometer denoising signal. The denoising results of different denoising algorithms in the time and frequency domains were compared, and SNR and RMSE were taken as denoising indicators. The improved VMD and TFPF denoising method has a smaller signal distortion and stronger denoising ability, so it can be adopted to denoise the output signal of the High-G MEMS accelerometer to improve its accuracy.

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.

Noise Reduction Method of Φ-OTDR System Based on EMD-TFPF Algorithm

The phase-sensitive optical time domain reflectometry ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula> -OTDR) system has been gradually applied to vertical seismic profile exploration due to its excellent anti-electromagnetic interference, extremely high resolution and sensitivity, and wide detection range. However, the actual data is often disturbed by random noise, which seriously affects the system’s ability to recognize low-frequency disturbances. In order to suppress the background noise and improve the signal-to-noise ratio (SNR), a fusion noise reduction method based on empirical mode decomposition and time-frequency peak filtering (EMD-TFPF) algorithm is studied and introduced. In terms of seismic exploration data processing, the algorithm has good denoising performance. Using the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula> -OTDR system based on optical synchronous reference heterodyne detection as the experimental platform, the EMD-TFPF noise reduction algorithm is applied to the position information and compared with the VSS-NLMS, VMD-NWT and EMD-soft methods. Experimental results show that under the conditions of 0.1 Hz and 5 V vibration interference, the EMD-TFPF method improves the SNR to 37.6 dB, which is much higher than the other three noise reduction algorithms. In addition, this method broadens the low-frequency response range of the system to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−5</sup> Hz. The improvement of the system’s ability to recognize low-frequency disturbance events will undoubtedly accelerate the practical process of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Phi $ </tex-math></inline-formula> -OTDR system in seismic exploration.

A Novel Parallel Processing Model for Noise Reduction and Temperature Compensation of MEMS Gyroscope.

To eliminate the noise and temperature drift in an Micro-Electro-Mechanical Systems (MEMS) gyroscope’s output signal for improving measurement accuracy, a parallel processing model based on Multi-objective particle swarm optimization based on variational modal decomposition-time-frequency peak filter (MOVMD–TFPF) and Beetle antennae search algorithm- Elman neural network (BAS–Elman NN) is established. Firstly, variational mode decomposition (VMD) is optimized by multi-objective particle swarm optimization (MOPSO); then, the best decomposition parameters [kbest,abest] can be obtained. Secondly, the gyroscope output signals are decomposed by VMD optimized by MOPSO (MOVMD); then, the intrinsic mode functions (IMFs) obtained after decomposition are classified into a noise segment, mixed segment, and drift segment by sample entropy (SE). According to the idea of a parallel model, the noise segment can be discarded directly, the mixed segment is denoised by time-frequency peak filtering (TFPF), and the drift segment is compensated at the same time. In the compensation part, the beetle antennae search algorithm (BAS) is adopted to optimize the network parameters of the Elman neural network (Elman NN). Subsequently, the double-input/single-output temperature compensation model based on the BAS-Elman NN is established to compensate the drift segment, and these processed segments are reconstructed to form the final gyroscope output signal. Experimental results demonstrate the superiority of this parallel processing model; the angle random walk of the compensated gyroscope output is decreased from 0.531076 to 5.22502 × 10−3°/h/√Hz, and its bias stability is decreased from 32.7364°/h to 0.140403°/h, respectively.

An Approach to 1/f Noise Detection Based on Adaptive T-ATFPF Algorithm

The generation of 1/f noise is closely related to the quality defects of IGBT devices. In the process of detecting IGBT single tube noise, thermal noise and shot noise show obvious white noise characteristics in the low frequency band, which are detected under the background of strong white noise 1/f noise can characterize the performance of IGBT devices. Therefore, on the basis of the Time-Frequency Peak Filtering (TFPF) algorithm, a two-dimensional time-domain adaptive T-ATFPF algorithm is proposed, and the adaptive segmentation is realized by means of the confidence interval crossing criterion based on Chebyshev’s inequality. Variable window length,use a small window length to process the signal section, which retains more detailed information of the effective signal.Use a larger window length to process the buffer section to ensure a smooth transition.Use the large window length to process the noise section, which more effectively suppresses randomness for noise, apply T-ATFPF to artificial synthesis model and actual model. Experimental results indicate that compared with the conventional algorithm, the improved method can better recover 1/f noise, and the ratio of signal to noise is greatly improved by about 1.3dB.

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.

Efficient noise reduction for the free induction decay signal from a proton precession magnetometer with time-frequency peak filtering.

The proton precession magnetometer (PPM) is a commonly used device to measure the varying magnetic field. Since the frequency of the PPM sensing free induction decay (FID) signal is proportional to the magnetic field, the signal-to-noise ratio (SNR) is always a critical issue that influences the measurement accuracy severely due to the external interferences such as harmonic noise and random noise. In this study, to boost the SNR of the FID signal, an effective filtering algorithm based on time-frequency peak filtering (TFPF) analyzed with pseudo-Wigner-Ville distribution (PWVD) is proposed. Through pre-treating the collected noisy FID signal with frequency modulation and instantaneous frequency estimation using the peak value of the time-frequency characterization, the embedded noise can be decorrelated and the relative pure FID signal can be detected regardless of the impact of varying noise levels. The superiority of the proposed synaptic noise reduction framework, namely, TFPF-PWVD, was found by comparing it with state-of-the-art approaches under the same conditions. The results illustrated that even though in a strong-noisy scenario, the proposed TFPF-PWVD based approach still achieved the best SNR for the yielded sensing FID and the minimum standard deviation for the observed magnetic field data, which can enhance the geomagnetic measuring performance of a PPM.

Seismic signal de-noising using time–frequency peak filtering based on empirical wavelet transform

Seismic noise suppression plays an important role in seismic data processing and interpretation. The time–frequency peak filtering (TFPF) is a classical method for seismic noise attenuation defined in the time–frequency domain. Nevertheless, we obtain serious attenuation for the seismic signal amplitude when choosing a wide window of TFPF. It is an unsolved issue for TFPF to select a suitable window width for attenuating seismic noise effectively and preserving valid signal amplitude effectively. To overcome the disadvantage of TFPF, we introduce the empirical wavelet transform (EWT) to improve the filtered results produced by TFPF. We name the proposed seismic de-noising workflow as the TFPF based on EWT (TFPF-EWT). We first introduce EWT to decompose a non-stationary seismic trace into a couple of intrinsic mode functions (IMFs) with different dominant frequencies. Then, we apply TFPF to the chosen IMFs for noise attenuation, which are selected by using a defined reference formula. At last, we add the filtered IMFs and the unprocessed ones to obtain the filtered seismic signal. Synthetic data and 3D field data examples prove the validity and effectiveness of the TFPF-EWT for both attenuating random noise and preserving valid seismic amplitude.

Strong random noise attenuation by shearlet transform and time-frequency peak filtering

Directional wavelet transforms combined with coefficient thresholding are very competitive in denoising seismic signals. However, these techniques struggle when the coefficients of signal and noise have comparable magnitudes. To better address this problem, we have developed an improvement to this method by applying time-frequency peak filtering (TFPF) to the directional wavelet coefficients. TFPF consists of computing the instantaneous frequency of a frequency-modulated analytic signal. The use of a longer or shorter smoothing window helps to emphasize either signal or remove random noise. In our method, we use the shearlet transform as a directional wavelet transform and estimate signal dips based on the cumulative energy in each decomposition direction. TFPF is then applied to the fine-scale wavelet coefficients to enhance signal and remove high-frequency noise. Coefficient thresholding is applied to all other scales. Experimental results demonstrate that our algorithm can effectively eliminate strong random noise and preserve events of interest.

Application of SNMF-MSS in low-frequency seismic noise suppression in desert areas

Noise suppression is an important step in seismic data processing. Various geographical environments make random noise in the acquired seismic records different in characteristics. Random noise in desert areas has non-Gaussian, non-linearity, non-stationary and heterogeneity. What is more, its frequency range is generally below 15 Hz, showing distinct low-frequency characteristics. Therefore, it brings much difficulty to the suppression of desert noise. Most of the existing noise suppression methods perform well on the condition of high-frequency noise, but perform worse for low-frequency noise because the denoising process of some methods depends on the waveform of noisy signal. And in some transformed methods, signal and noise are mixed with each other in the transformed domain. Thus, to resolve this problem, this paper presents a novel multiband spectrum separation (MSS) method based upon sparse nonnegative matrix factorization (SNMF) algorithm. It firstly decomposes noisy signal into some sub-signals of different narrow frequencies bands. Then, signal and noise components of these sub-signals are further separated by spectral unmixing in time-frequency domain. Several groups of experiments were carried out on synthetic records and real seismic data in Tarim oilfield in the northwest of China. Moreover, we compare its denoising effect with time-frequency peak filtering (TFPF), empirical mode decomposing (EMD) and Radon transform methods. The experimental and comparison results demonstrate that the proposed SNMF-MSS method performs better than the other three methods in the aspect of low-frequency suppression and weak signal recovery.

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.

MEMS Accelerometer Calibration Denoising Method for Hopkinson Bar System Based on LMD-SE-TFPF

High-G MEMS accelerometer (HGMA) is widely used in the aerospace field and the precise control of missiles. Therefore, its calibration accuracy is critical to sensor performance and the overall control system. In order to decrease the influence of noise on the HGMA output signal, a hybrid denoising algorithm which is based on the Time-frequency peak filtering (TFPF), Local mean decomposition (LMD) and Sample entropy (SE) has been proposed in this article. For the problem that the TFPF algorithm is limited in the choice of window length, LMD and SE are used to distinguish components, which can improve the TFPF algorithm effectively. It provides a better balance between noise reduction and signal fidelity. Firstly, the noise-containing signal can be decomposed by LMD to obtain PFs. Secondly, calculate the sample entropy values of each PFs, then divide the signal into mixed component, useful component and noise component according to the similarity of sample entropy. Thirdly, the mixed component can use long-window TFPF to reduce noise, the short-window TFPF can reduce the noise for the useful component, and the noise component can be wiped off directly. Finally, the useful component and the mixed component are both reconstructed to form the final denoised signal. Experiments have showed that this method can not only remove noise (the noise of static signal is reduced by 91.76%, the signal-noise ratio of dynamic signal has increased to 17.6), but also retain the details of frequency and amplitude (the shock peak amplitude error is 0.062% and the vibration amplitude error is 0.04%). Therefore, this method can reduce the noise of the High-G MEMS accelerometer signal with maintaining the characteristics of the original signal, thereby greatly improves the performance of the accelerometer, making it widely used.

Random Noise Suppression of Magnetic Resonance Sounding Oscillating Signal by Combining Empirical Mode Decomposition and Time-Frequency Peak Filtering

Magnetic resonance sounding (MRS) signals are always corrupted by random noise. Although time-frequency peak filtering (TFPF) has been proven to be an effective method to suppress the random noise, it shows shortcomings when processing the oscillating high-frequency MRS signal at about 2 kHz. In this study, a new method combining empirical mode decomposition (EMD) and TFPF is proposed to overcome the TFPF limitation when processing the MRS oscillating signal. With the help of EMD decomposition characteristics, the random-noise-corrupted MRS oscillating signal is first decomposed into several different components which contain frequencies ranging from the highest to the lowest ones. Then, the components which do not have signal frequency are discarded to bring down the level of random noise. The residual components are further processed by TFPF, respectively, based on the theory of instantaneous frequency estimation and the property of noise accumulation. Finally, the de-noised result is obtained by reconstructing the processed components. The numerical simulations on synthetic signals embedded in both artificial noise and real noise show the combined method can improve the signal-to-noise ratios and reduce the uncertainties of signal parameters. In addition, the combined method is applied following a standard processing scheme in field data, and better results are also obtained.

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.