Wavelet Threshold Function Research Articles

A rolling bearing fault signal denoising algorithm that combines a new adaptive information entropy with a new wavelet threshold function

Abstract Mechanical fault diagnosis is of great significance to industrial automation, and extracting vibration fault signals is one of the important tasks in mechanical health monitoring and fault diagnosis. However, due to the complex working environment of rolling bearings, a large amount of noise makes it difficult to extract vibration fault signals. Denoising the vibration signal of bearings can remove interference noise, simplify the early identification of signal features, and thus improve diagnostic accuracy and mechanical maintenance efficiency. This paper proposes a rolling bearing fault signal denoising algorithm, which constructs a new feature extraction and denoising function. This method first decomposes the noisy signal into Intrinsic Mode Functions (IMFs) by Intrinsic Computing Expressive Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN). Secondly, a new adaptive information entropy threshold function is constructed to extract the noisy IMFs from it. Then, the noisy IMF signal is denoised by a new wavelet threshold function. Finally, the noise-free IMFs are reconstructed to reconstruct the denoised signal. To verify the actual performance of the algorithm, comparative experiments were conducted on a self-collected dataset and a public dataset, the results show that this method improves the continuity of signal reconstruction and can remove various types of vibration fault noise signals more effectively and accurately, \hl{thereby improving the fault detection accuracy by 2%-9%.

Joint sound denoising with EEMD and improved wavelet threshold for real-time drilling lithology identification

The present study proposes a joint denoising method for real-time drilling lithology identification based on drilling sound signals. The proposed method employs ensemble empirical mode decomposition (EEMD) for preliminary sound signal denoising while retaining the effective intrinsic mode function (IMF) components, which then undergo secondary denoising using the improved wavelet threshold function. Finally, the sound signal is reconstructed using the denoised IMF components. The experimental results show that the proposed method achieves a higher signal-to-noise ratio and lower root mean square error, reaching 12.94 and 0.0442, respectively. Furthermore, the proposed method demonstrated good performance in denoising rock drilling sound signals and successfully addressed issues including the susceptibility of sound signals to external interference, nonadaptive threshold selection in wavelet threshold denoising, and high reconstruction errors during EEMD in drilling environments. Simulation results show that the proposed method significantly improves the accuracy of lithology recognition by 23%, with a resulting accuracy of 72.58%.

An advanced adaptive algorithm driven by online blind noise level estimation for pedestrian positioning

An effective and universal positioning algorithm is essential for a highly reliable and accurate foot-mounted inertial pedestrian navigation system. Algorithm performance is significantly influenced by the accuracy of noise level estimation. This study introduces a novel blind noise estimation algorithm to reduce the impact of uncertain and variable system noise characteristics on positioning accuracy. The algorithm combines a quasi-population growth wavelet transform threshold with an adaptive window length adjustment strategy. Firstly, a quasi-population growth wavelet threshold function is employed to separate motion signals from noise and assess noise levels. Secondly, an adaptive sliding window strategy based on motion-noise correlation optimizing the balance between estimation precision and computational efficiency. These methods enable robust noise level estimation without prior knowledge and achieve real-time adjustments to the system noise matrix in Extended Kalman Filter of the inertial navigation system, thereby significantly enhancing navigation error suppression. The effectiveness of above methodologies has been experimentally validated.

Off-Design Operation and Cavitation Detection in Centrifugal Pumps Using Vibration and Motor Stator Current Analyses.

Centrifugal pumps are essential in many industrial processes. An accurate operation diagnosis of centrifugal pumps is crucial to ensure their reliable operation and extend their useful life. In real industry applications, many centrifugal pumps lack flowmeters and accurate pressure sensors, and therefore, it is not possible to determine whether the pump is operating near its best efficiency point (BEP). This paper investigates the detection of off-design operation and cavitation for centrifugal pumps with accelerometers and current sensors. To this end, a centrifugal pump was tested under off-design conditions and various levels of cavitation. A three-axis accelerometer and three Hall-effect current sensors were used to collect vibration and stator current signals simultaneously under each state. Both kinds of signals were evaluated for their effectiveness in operation diagnosis. Signal processing methods, including wavelet threshold function, variational mode decomposition (VMD), Park vector modulus transformation, and a marginal spectrum were introduced for feature extraction. Seven families of machine learning-based classification algorithms were evaluated for their performance when used for off-design and cavitation identification. The obtained results, using both types of signals, prove the effectiveness of both approaches and the advantages of combining them in achieving the most reliable operation diagnosis results for centrifugal pumps.

The influence of ripple on DC energy measurement and the improvement of wavelet threshold function filtering method

DC energy has been applied in the construction of DC power grids, photovoltaic power generation, energy storage, and rapid charging of electric vehicles. The application of DC energy is of great significance for energy conservation, emission reduction, carbon reduction, and efficiency increase. In this paper, the reasons for the decrease in DC energy measurement accuracy caused by ripples in voltage and current are analyzed. The minimum requirements of ripples for DC energy meters are analyzed, and the traditional filtering method based on wavelet threshold is studied. An optimized and fast iterative wavelet threshold function was designed, the current signal of electric vehicle charging was selected, and the effectiveness of the algorithm proposed in this paper was verified through simulation.

Leakage detection method of underground heating pipeline based on improved wavelet threshold function

For urban heating pipeline network, the intelligent and precise detection is an important guarantee for urban heating infrastructure of the safe and low-carbon operation. Heating pipe network was directly buried in the soil and difficult to detect the leakage point due to lack of non-excavation detection method for rapid repair. An improved noise reduction algorithm of the wavelet threshold function coupled with the acoustic method was used for the directly buried pipe leakage detection. Large-scale leakage experimental tests were used to validate the reliability. The influences of temperature, pressure, flowrates and leakage distance on the frequency and time domains were then investigated. Results show that the improved threshold function could well detect the leakage for directly buried hot water heating pipes. When the temperature increases, the leakage frequency domain spreads from 200 - 800 Hz to 50–1500 Hz. The pressure, flow rate, and leak point location could affect the amplitude feature. The accuracy ranges of the improved method in the different location, temperature and pressure and flowrates are separately 0.11–2.36%, 0.11–1.96%,0.11–3.49% and 0.16–1.55%, respectively.

Research on denoising the temperature monitoring signal of a distributed optical fiber downhole cable

Aiming at the noise mixed in the downhole cable skin temperature signal measured by the BOTDR distributed fiber optic sensing temperature measurement system, a new improved wavelet threshold function is proposed, and denoising experiments are completed based on the MATLAB platform for the measured cable skin temperature signal. The denoising results of several threshold function methods are compared and analyzed from the aspects of graphical intuitive comparison as well as quantitative evaluation indicators. The results show that the improved threshold function denoising fiber optic temperature monitoring signal has a higher SNR and lower RMSE, there is no obvious distortion phenomenon, and the denoising performance is significantly improved compared with the traditional threshold function, which has a high application value.

A hybrid denoising approach for PPG signals utilizing variational mode decomposition and improved wavelet thresholding.

Photoplethysmography (PPG) signals are sensitive to motion-induced interference, leading to the emergence of motion artifacts (MA) and baseline drift, which significantly affect the accuracy of PPG measurements. The objective of our study is to effectively eliminate baseline drift and high-frequency noise from PPG signals, ensuring that the signal's critical frequency components remain within the range of 1 ∼ 10Hz. This paper introduces a novel hybrid denoising method for PPG signals, integrating Variational Mode Decomposition (VMD) with an improved wavelet threshold function. The method initially employs VMD to decompose PPG signals into a set of narrowband intrinsic mode function (IMF) components, effectively removing low-frequency baseline drift. Subsequently, an improved wavelet thresholding algorithm is applied to eliminate high-frequency noise, resulting in denoised PPG signals. The effectiveness of the denoising method was rigorously assessed through a comprehensive validation process. It was tested on real-world PPG measurements, PPG signals generated by the Fluke ProSim™8 Vital Signs Simulator with synthesized noise, and extended to the MIMIC-III waveform database. The application of the improved threshold function let to a substantial 11.47% increase in signal-to-noise ratio (SNR) and an impressive 26.75% reduction in root mean square error (RMSE) compared to the soft threshold function. Furthermore, the hybrid denoising method improved SNR by 15.54% and reduced RMSE by 37.43% compared to the improved threshold function. This study proposes an effective PPG denoising algorithm based on VMD and an improved wavelet threshold function, capable of simultaneously eliminating low-frequency baseline drift and high-frequency noise in PPG signals while faithfully preserving their morphological characteristics. This advancement establishes the foundation for time-domain feature extraction and model development in the domain of PPG signal analysis.

Ultrasound signal processing based on joint GWO-VMD wavelet threshold functions

To overcome the problem of noise interference in the ultrasonic echo signal received by the probe in ultrasonic nondestructive testing, a method of ultrasonic signal processing using the jointed wavelet threshold function of GWO-VMD (Grey Wolf Optimisation, Variational Mode Decomposition) is proposed. The method first uses the GWO algorithm to optimise the VMD parameters to find the optimal parameter combination penalty factor α and decomposition modulus number K, and then uses the correlation coefficient method to differentiate between the desired signal and noise components after decomposition to obtain the intrinsic mode function (IMF) components. Secondly, the noise components are processed by combining the improved wavelet threshold function algorithm, and lastly, each modal component is restored to produce a denoised signal. Experimental results show that the method improves the signal-to-noise ratio (SNR) by 2.55%, reduces the root mean square error (RMSE) by 3.8%, preserves more useful information, and is more effective in denoising.

ОПТИМІЗАЦІЯ АЛГОРИТМУ ПАКЕТНОЇ ВЕЙВЛЕТ-ФІЛЬТРАЦІЇ СИГНАЛІВ

A wavelet packet filtering algorithm has been developed, which includes cyclic movement along the branches of the wavelet packet tree with a constraint on each branch of the approximation and detail coefficients until the minimum root-mean-square error is attained, with the optimal parameters of the wavelet threshold and threshold function. To calculate the root-mean-square error of filtering, after each cycle of processing the wavelet decomposition coefficients, the signal is reconstructed in the time domain. In the next cycle, the received signal is decomposed into approximation and detail coefficients until the root-mean-square error reaches a minimum for all possible values of the basic wavelet-threshold and the threshold function. The study was conducted with twenty of the most commonly used signals, including signals with linear and non-linear frequencies. To confirm the efficiency of packet wavelet filtering, a comparative analysis with the known methods based on a common threshold of detail coefficients at all levels of wavelet decomposition is given. Keywords: wavelet analysis, packet wavelet filtering, entropy, threshold function, threshholding.

Neutron image denoising method based on adaptive new wavelet threshold function

Neutron radiography is an important nondestructive testing technique in the industrial field. Due to the influence of various factors in the neutron imaging process, the image quality will be reduced. Aiming at the Gaussian-Poisson mixed noise in neutron images, an adaptive new wavelet threshold function denoising method is proposed to reduce the influence of noise on neutron images. The basic idea is to transform the Gaussian-Poisson mixed noise into a noise that approximately follows the Gaussian distribution by generalized Anscombe transformation, and then use Particle Swarm Optimization (PSO) algorithm and wavelet threshold function denoising method to remove the mixed noise in the image. The new wavelet threshold function overcomes the problems of discontinuity in the traditional hard threshold function and fixed deviation in the wavelet coefficient of the traditional soft threshold function, and has the adjustment factor, which can combine the advantages of the traditional soft and hard threshold functions. PSO algorithm is used to find the optimal adjustment factor for image denoising. In addition, the new wavelet threshold function is continuous and smooth at the threshold, avoiding excessive strangulation of wavelet coefficients. By analyzing the fixed threshold defect, a threshold selection formula that decreases with the number of decomposition layers is proposed. The results of Matlab software experiments show that the new method can significantly improve the Peak Signal-to-Noise Ratio (PSNR) and reduce the Mean Square Error (MSE) of noisy images compared with the other four methods in removing Gaussian-Poisson mixed noise. Therefore, the new method can retain more image details and effectively improve the quality of neutron images.

Chromatography Denoising with Improved Wavelet Thresholding Based on Modified Genetic Particle Swarm Optimization

The wavelet threshold functions are widely used in oil chromatography denoising because high-quality signals are the basis for Dissolved Gas Analysis (DGA), which determines the accuracy of transformer fault monitoring. However, there are certain limitations of the wavelet threshold functions, such as the Pseudo-Gibbs phenomenon and improper threshold selection. To this purpose, a modified genetic particle swarm optimization-based improved threshold function denoising method (MGPSO-ITF) is proposed. Specifically, the method constructs a new parametric threshold function that possesses high-order derivability and a small constant deviation. To obtain optimal values for the tunable parameters, MGPSO is employed, which outperforms other methods in identifying the optimum and achieving fast convergence. The simulation results demonstrate that the enhanced thresholding function yields a higher Signal-to-Noise Ratio (SNR), higher Noise Suppression Ratio (NSR), and smaller Root Mean Square Error (RMSE) compared to prior methods. Specifically, for the originally relatively smooth signal, MGPSO-ITF does not over-correct it to cause distortion. Furthermore, experiments on measured signals illustrate that the MGPSO-ITF is highly effective at denoising and preserving the original signal properties. Particularly in cases where peak deformation is prominent, the algorithm outperforms both hard and soft thresholding methods, achieving a reduction of 2.934% and 1.029% in peak area error, respectively.

Denoising Method of Hydro-turbine Vibration Signal Based on Joint WOA-VMD and Improved Wavelet Threshold

Comparing to the untreated signal, the traditional wavelet thresholding functions decomposed and reconstructed signal has a constant error. Variational mode decomposition (VMD) sets different penalty factor α and mode decomposition layer K during signal processing will lead to the final noise reduction results. Therefore, this paper introduces the Whale Optimization Algorithm (WOA)-VMD and improved wavelet threshold denoising for oscillation signal disposal of hydraulic turbine. Firstly, WOA was used to optimize the VMD decomposition parameters α and K with the local minimum of envelope entropy as the objective function, and the optimal noise reduction effect was obtained. Secondly, the vibration signals with noise were deconstructed into K intrinsic mode functions (IMF) after VMD, and their thresholds were set. Furthermore, the IMF component below the threshold value is denoised again by improving the wavelet threshold value. Finally, the IMF reorganization after de-noising is used to obtain the final noise reduction signal. Through the verification analysis, the combination of WOA-VMD and improved wavelet threshold function denoising method could effectively filter the noise in the signal and significantly improve the noise reduction effect of the hydraulic turbine vibration signal.

Parameter Optimisation of Wavelet Denoising for Pulsed Eddy Current Signals Based on Particle Swarm Optimisation Algorithm

ABSTRACT To ensure the reliable operation of high voltage cables, it is crucial to routinely inspect the lead sealing using pulsed eddy current. But nevertheless, the signals can be impacted by noise in actual engineering. While retaining the useful high-frequency information in the original signal, wavelet denoising can filter the clutter efficiently. However, previous research on wavelet denoising has only used it as a straightforward filtering tool, ignoring the impact of changing the parameters on the actual denoising effect. In this study, a more accurate evaluation index called P NCC is constructed for pulsed eddy current testing signals with a focus on maintaining the peak information. This index is then adopted as a fitness function for the particle swarm optimisation algorithm to determine the befitting wavelet denoising parameters and denoised signals. The results show that the signal-to-noise ratio of the signals after denoising is approximately 25 dB, and the distortion at the peak position is stable at about 1%. It demonstrates that the comprehensive index P NCC is a reliable metric for assessing the quality of pulsed eddy current signals. The optimal wavelet denoising parameters for pulsed eddy current signals are found to be the Sym 4 wavelet, 10-layer decomposition and Median threshold function.

Denoising of Laser Self-Mixing Interference by Improved Wavelet Threshold for High Performance of Displacement Reconstruction

This article proposes an improved wavelet threshold denoising for laser self-mixing interference signals. The improved wavelet threshold function exhibits smoothness and continuity near the threshold. By replacing hard or soft wavelet threshold with the improved wavelet threshold, it can eliminate the generation of fake self-mixing interference peaks due to local oscillation induced by hard wavelet threshold, as well as the loss of self-mixing interference peaks due to over-smoothness induced by the soft wavelet threshold. Compared with hard and soft wavelet threshold denoising, theoretical simulations and experimental results demonstrate that the displacement of vibrations are well reconstructed based on the improved wavelet threshold denoising.

Effect of vitamin energy drinks on relieving exercise-induced fatigue in muscle group by ultrasonic bioimaging data analysis.

This work was aimed to analyze the effect of vitamin energy drink on muscle fatigue by surface electromyography (SEMG) and ultrasonic bioimaging (USBI). 20 healthy men were selected to do increasing load fatigue test. Surface electromyographic signals and ultrasonic biological images were collected based on wavelet threshold function with improved thresholds. Time domain and frequency domain characteristic integrated electromyography (IEMG), root mean square amplitude (RMS), average power frequency (MPF), and surface and deep muscle morphological changes were analyzed. Hemoglobin concentration (HB), red blood cell number (RBC), mean volume of red blood cell (MCV), blood lactic acid (BLA), malondialdehyde (MDA), and phosphocreatine kinase (CK) were measured. 1) the Accuracy (94.10%), Sensitivity (94.43%), Specificity (93.75%), and Precision (94.07%) of the long and short-term memory (LSTM) specificity for muscle fatigue recognition were higher than those of other models. 2) Compared with the control group, the levels of BLA, MDA, and CK in the experimental group were decreased and HB levels were increased after exercise (P < 0.05). 3) IEMG and RMS of the experimental group were higher than those of the control group, and increased with time (P < 0.05). 4) The mean amplitude of the response signal decreased with time. Compared with the control group, the surface muscle thickness, deep muscle thickness, total muscle thickness, contrast, and homogeneity (HOM) decreased in the experimental group; while the angular second moment (ASM) and contrast increased, showing great differences (P < 0.05). Surface electromyographic signal and ultrasonic biological image can be used as auxiliary monitoring techniques for muscle fatigue during exercise. Drinking vitamin energy drinks before exercise can relieve physical fatigue to a certain extent and promote the maintenance of muscle microstructure.

Infrared image enhancement algorithm based on improved wavelet threshold function and weighted guided filtering

Aiming at the problems such as the poor visual effect of infrared thermal imaging under low illumination conditions, an enhanced infrared image recognition method based on wavelet decomposition is proposed for this paper. First, according to wavelet decomposition, the infrared image is divided into a low-frequency sub-band (LFS) and high-frequency sub-band (HFS) in each orientation, and HFS in each orientation is denoised using a modified wavelet threshold function to strengthen the denoising effect of the infrared image; Second, the multi-scale Retinex (MSR) algorithm based on weighted guided filtering (WGIF) is used to evaluate the component of illumination in the basic layer of the LFS, and the WGIF-segmented detail layer images are fused with the MSR processed ones to effectively highlight the texture details of the LFS; Finally, the LFS and the HFS are wavelets reconstructed (WR) to obtain the infrared enhanced images. This paper applies the algorithm to a low-resolution (resolution 32x32 pixels) infrared thermal imaging module, and the results of combining subjective and objective evaluation indexes show that the overall property index of the algorithm in this paper is superior to other contrasting algorithms and can effectively improve the infrared image quality.

Multi-Leakage Source Localization of Safety Valve Based on Uniform Circular AE Array and Improved MUSIC Algorithm.

The safety valve is the core component of the pressure-relief protection device for pressure-bearing special equipment. When the safety valve leaks, the medium of the pressure vessel will be lost and wasted, which may cause safety accidents. With the aim to solve the problem of accurately locating the multiple leakage sources of safety valves, a localization method combining a uniform circular array acoustic emission detection and an improved multiple signal classification (MUSIC) algorithm is proposed. First, an improved wavelet threshold function denoising method is introduced to extract acoustic emission signals with high SNR, thereby reducing the rank of the covariance matrix, weakening the noise dispersion caused by eigenvalue reconstruction, avoiding signal and noise cross-confusion, and improving positioning accuracy. By introducing a windowed fast Fourier transform (FFT) frequency division processing link to obtain narrowband signal, the premise of using MUSIC positioning algorithm is established. In addition, a forward/backward spatial smoothing algorithm is introduced in the decoherence link to reduce co-channel interference, reduce the rank loss of the signal covariance matrix, and improve the positioning accuracy of the algorithm. The results show that when the working pressure is 0.70 MPa, 0.75 MPa, and 0.80 MPa, the deviation between the azimuth angle and elevation angle positioning results of each leakage source obtained by the improved MUSIC algorithm and the actual angle does not exceed 2°, and the relative error does not exceed 3.5%. Therefore, the improved MUSIC algorithm can accurately locate multiple leakage sources of the safety valve, and as the working pressure of the safety valve increases, the positioning accuracy of the improved MUSIC algorithm also increases accordingly.

An Improved Microseismic Signal Denoising Method of Rock Failure for Deeply Buried Energy Exploration

Microseismic monitoring has become a well-known technique for predicting the mechanisms of rock failure in deeply buried energy exploration, in which noise has a great influence on microseismic monitoring results. We proposed an improved microseismic denoising method based on different wavelet coefficients of useful signal and noise components. First, according to the selection of an appropriate wavelet threshold and threshold function, the useful signal part of original microseismic signal was decomposed many times and reconstructed to achieve denoising. Subsequently, synthetic signals of different types (microseismic noise, microseismic current, microseismic noise current) and with various signal-to-noise ratios (SNRs, −10~10) were used as test data. Evaluation indicators (mean absolute error μ and standard deviation error σ) were established to compare the denoising effect of different denoising methods and verify that the improved method is more effective than the traditional denoising methods (wavelet global threshold, empirical mode decomposition and wavelet transform–empirical mode decomposition). Finally, the proposed method was applied to actual field microseismic data. The results showed that the microseismic signal (with different types of noise) could be fully denoised (car honk, knock, current and construction noise, etc.) without losing useful signals (pure microseismic), suggesting that the proposed approach provides a good basis for the subsequent evaluation and classification of rock burst disasters.

A Random Error Suppression Method Based on IGWPSO-ELM for Micromachined Silicon Resonant Accelerometers.

There are various errors in practical applications of micromachined silicon resonant accelerometers (MSRA), among which the composition of random errors is complex and uncertain. In order to improve the output accuracy of MSRA, this paper proposes an MSRA random error suppression method based on an improved grey wolf and particle swarm optimized extreme learning machine (IGWPSO-ELM). A modified wavelet threshold function is firstly used to separate the white noise from the useful signal. The output frequency at the previous sampling point and the sequence value are then added to the current output frequency to form a three-dimensional input. Additional improvements are made on the particle swarm optimized extreme learning machine (PSO-ELM): the grey wolf optimization (GWO) is fused into the algorithm and the three factors (inertia, acceleration and convergence) are non-linearized to improve the convergence efficiency and accuracy of the algorithm. The model trained offline using IGWPSO-ELM is applied to predicting compensation experiments, and the results show that the method is able to reduce velocity random walk from the original 4.3618 μg/√Hz to 2.1807 μg/√Hz, bias instability from the original 2.0248 μg to 1.3815 μg, and acceleration random walk from the original 0.53429 μg·√Hz to 0.43804 μg·√Hz, effectively suppressing the random error in the MSRA output.