Threshold De-noising Method Research Articles

EMD-based noise reduction study of steel cored conveyor belt containing slag signal

This paper proposes a noise reduction technique that combines empirical mode decomposition (EMD) and wavelet thresholding to eliminate the noise interference caused by metal slag in the steel cord conveyor belt damage signal. Initially, the original signal undergoes decomposition by EMD into high- and low-frequency intrinsic mode function (IMF) components based on metal slag signal feature analysis. The wavelet threshold de-noising method is then applied to filter out the high-frequency noise while preserving the low-frequency IMF components. The IMF components containing slag noise are discarded, and the filtered signal and the low-frequency IMF components are used for signal reconstruction to obtain an optimal noise reduction effect. The study demonstrates that this method is more effective in suppressing metal slag noise, environmental noise, and other noise interferences than traditional EMD decomposition noise reduction and wavelet threshold noise reduction methods. This research provides a valuable reference for noise reduction in steel cord conveyor belt detection data.

CEEMDAN-LWT De-Noising Method for Pipe-Jacking Inertial Guidance System Based on Fiber Optic Gyroscope.

An inertial guidance system based on a fiber optic gyroscope (FOG) is an effective way to guide long-distance curved pipe jacking. However, environmental disturbances such as vibration, electromagnetism, and temperature will cause the FOG signal to generate significant random noise. The random noise will overwhelm the effective signal. Therefore, it is necessary to eliminate the random noise. This study proposes a hybrid de-noising method, namely complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN)-lifting wavelet transform (LWT). Firstly, the FOG signal is extracted using a sliding window and decomposed by CEEMDAN to obtain the intrinsic modal function (IMF) with N different scales and one residual. Subsequently, the effective IMF components are selected according to the correlation coefficient between the IMF components and the FOG signal. Due to the low resolution of the CEEMDAN method for high-frequency components, the selected high-frequency IMF components are decomposed with lifting wavelet transform to increase the resolution of the signal. The detailed signals of the LWT decomposition are de-noised using the soft threshold de-noising method, and then the signal is reconstructed. Finally, pipe-jacking dynamic and environmental interference experiments were conducted to verify the effectiveness of the CEEMDAN-LWT de-noising method. The de-noising effect of the proposed method was evaluated by SNR, RMSE, and Deviation and compared with the CEEMDAN and LWT de-noising methods. The results show that the CEEMDAN-LWT de-noising method has the best de-noising effect with good adaptivity and high accuracy. The navigation results of the pipe-jacking attitude before and after de-noising were compared and analyzed in the environmental interference experiment. The results show that the absolute error of the pipe-jacking pitch, roll, and heading angles is reduced by 39.86%, 59.45%, and 14.29% after de-noising. The maximum relative error of the pitch angle is improved from -0.74% to -0.44%, the roll angle is improved from 2.07% to 0.79%, and the heading angle is improved from -0.07% to -0.06%. Therefore, the CEEMDAN-LWT method can effectively suppress the random errors of the FOG signal caused by the environment and improve the measurement accuracy of the pipe-jacking attitude.

A new underwater acoustic signal denoising method based on modified uniform phase empirical mode decomposition, hierarchical amplitude-aware permutation entropy, and optimized improved wavelet threshold denoising

Underwater acoustic signal (UAS) denoising is base and prerequisite for UAS detection, recognition and classification. In order to perform UAS denoising effectively, a new UAS denoising method based on modified uniform phase empirical mode decomposition (MUPEMD), hierarchical amplitude-aware permutation entropy (HAAPE), and improved wavelet threshold denoising (IWTD) method optimized by sand cat swarm optimization (SCSO) (SIWTD), named MUPEMD-HAAPE-SIWTD, is proposed. Firstly, decompose original signal into a battery of intrinsic mode functions (IMFs) by MUPEMD. Secondly, determine the double threshold by HAAPE to classify signal into pure signal, mixed signal and noisy signal. Then, optimize IWTD by SCSO, so that it can adaptively select the optimal wavelet basis function to achieve the denoising of mixed signal. Finally, the denoised mixed signal is reconstructed with pure signal to obtain ultima denoised signal. The denoising experiments on Lorenz signal and Duffing signal demonstrate that signal-to-noise ratio can be improved by 9 dB–13 dB by the proposed method. The denoising experiments on simulating ship radiated noise signals and four kinds of actual ship radiated noise signals (https://www.aigei.com/, accessed on June 1, 2023) demonstrate that the proposed method makes phase diagram smoother and clearer, and makes the ability of suppressing noise higher.

Partial discharge de-noising based on hybrid particle swarm optimization SWT adaptive threshold

A hybrid particle swarm optimization stationary wavelet adaptive threshold denoising (HPO-SWT-ATD) method was proposed to improve the adaptive ability of wavelet transform in partial discharge signal denoising. In the proposed method, the partial discharge signal is decomposed by stationary wavelet transform(SWT) and the multiorder differentiable function based on the Stein unbiased likelihood estimate (SURE) is used as the denoising threshold function. In threshold selection, the improved particle swarm optimization algorithm is used for global adaptive search to select the optimal denoising threshold. The de-noising experiments are carried out on the simulated partial discharge signals and the measured partial discharge signals.The experiment results show that, compared with the hard threshold method, particle swarm optimization threshold method, genetic algorithm optimization threshold method, Wiener filter method and modal decomposition method, the proposed method can better remove the white noise in the PD signal, and the denoising signal distortion degree is smaller.

Image Segmentation Analysis Using Otsu Thresholding and Mean Denoising for the Identification Coffee Plant Diseases

In Indonesia, coffee is one of the plantation products with a relatively high level of productivity and is a source of foreign exchange income for the country. However, unfortunately, certain factors can threaten productivity and quality in cultivating coffee plants, one of which is rust leaf disease. This disease causes disturbances in photosynthesis, thereby reducing plant yields. Therefore, to maintain and control productivity in coffee cultivation, this research carried out the process of observing coffee leaf images through segmentation using the Otsu Thresholding and Mean Denoising methods. The entire series of processes in this research was carried out using the Python programming language and succeeded in providing output in the form of image comparisons showing areas affected by Rust Leaf disease using the Otsu thresholding method alone and the Otsu thresholding method combined with a non-local means denoising algorithm. The test results prove that the Otsu thresholding method with the non-local means denoising algorithm has a smaller MSE value. It is the most optimal method for handling coffee leaf disease image segmentation with an accuracy level of 88%. It is hoped that this research can support farmers in providing insight into early detection of coffee plant diseases and increasing productivity through visual analysis.

Research on Improved Wavelet Threshold Denoising Method for Non-Contact Force and Magnetic Signals

In order to solve the problem of noise interference in the collected magneto mechanical signals, a new wavelet shrinkage threshold based on adaptive estimation is proposed. Based on the shortcomings of the traditional threshold function, an improved threshold function is proposed, and the parameters of the threshold function are solved by the improved genetic algorithm, and the optimal denoising effect is finally obtained. The new threshold function can not only make up the defects of each threshold function, ensure the continuity of threshold function, but also flexibly adjust the threshold to adapt to different noise conditions, and solve the deviation caused by inherent threshold function, and protect the useful information with noise signals.

Study on Optical Fiber Gas-Holdup Meter Signal Denoising Using Improved Threshold Wavelet Transform

The optical fiber probe gas-holdup meter is a new logging tool, which can be used to measure the gas-holdup of oil-gas-water three-phase flow during production logging. In this paper, the wavelet transform is used to denoise the measured gas-holdup signal of the optical fiber probe. For the wavelet transform threshold de-noising method, the existing hard and soft threshold functions have certain defects. So we propose a wavelet transform denoising method with an improved threshold function, and use this method to denoise the measured gas-holdup signal of the optical fiber probe. The signal-to-noise ratio, root mean square error, smoothness, and correlation coefficient are used as the evaluation indexes of signal denoising effect. The improved threshold function is between the hard threshold function and the soft threshold function. It has the advantages of both hard and soft threshold functions, can effectively overcome the discontinuity of the hard threshold function and the constant deviation of the soft threshold function, and improves the denoising efficiency of the gas-holdup signal. The proposed method is applied to the synthetic data and the real gas-holdup signal of the optical fiber probe respectively. Compared with the traditional soft and hard threshold functions, the experiment results show that the improved threshold wavelet denoising method is feasible. And it is effective in the gas-holdup signal denoising, improving the signal-to-noise ratio, reducing root mean square error, and increasing the correlation coefficient. The proposed method preserves well the original features of the measured gas-holdup signal, which provides a reference for the signal processing and dynamic monitoring analysis of the subsequent oil-well downhole development.

Fast Sleep Stage Classification Using Cascaded Support Vector Machines with Single-Channel EEG Signals.

Long-term sleep stage monitoring is very important for the diagnosis and treatment of insomnia. With the development of wearable electroencephalogram (EEG) devices, we developed a fast and accurate sleep stage classification method in this study with single-channel EEG signals for practical applications. The original sleep recordings were collected from the Sleep-EDF database. The wavelet threshold denoising (WTD) method and wavelet packet transformation (WPT) method were applied as signal preprocessing to extract six kinds of characteristic waves. With a comprehensive feature system including time, frequency, and nonlinear dynamics, we obtained the sleep stage classification results with different Support Vector Machine (SVM) models. We proposed a novel classification method based on cascaded SVM models with various features extracted from denoised EEG signals. To enhance the accuracy and generalization performance of this method, nonlinear dynamics features were taken into consideration. With nonlinear dynamics features included, the average classification accuracy was up to 88.11% using this method. In addition, with cascaded SVM models, the classification accuracy of the non-rapid eye movement sleep stage 1 (N1) was enhanced from 41.5% to 55.65% compared with the single SVM model, and the overall classification time for each epoch was less than 1.7 s. Moreover, we demonstrated that it was possible to apply this method for long-term sleep stage monitor applications.

An Improved Wavelet Threshold Denoising Method for Health Monitoring Data: A Case Study of the Hong Kong-Zhuhai-Macao Bridge Immersed Tunnel

Tunnels generally operate underground or underwater in a complex environment. As a result, the health monitoring system is inevitably affected by various environmental factors, which introduces noise to the system. However, the noise contained in the monitoring sequence may disrupt structural damage identification and health state assessment as the real structural response may be overwhelmed by the noise. To properly eliminate the noise in an objective way, this study proposed an improved wavelet threshold denoising method. Firstly, it adopts a quantitative factor, namely the Sparse Index, to assist the selection of the best wavelet basis in numerous wavelet packages. Then, the decomposition layer and threshold are optimized by a comprehensive evaluation based on a variation coefficient method. At last, the application of the concrete strain health monitoring data of the Hong Kong-Zhuhai-Macao Bridge immersed tunnel verified the effectiveness of the proposed method. It is found that the combination of sym12 and five decomposition layers can obtain the best denoising results within the selected wavelet families and decomposition levels. Moreover, the proposed method achieves good denoising results under different fluctuation levels. Thus, the proposed method is reliable, can solve the problem of optimal parameter selection such as decomposition level and wavelet basis in wavelet denoising, and can be applied in the structural health monitoring of critical infrastructures.

Stock Closing Price Interval Prediction Based on CEEMDAN-WTD-Bilstm-Transformer Model

Stock price indices usually contain much noise and exhibit significant non-linearity, non-smoothness, and other complex characteristics. To address the complexity and long-term dependence of financial time series forecasting, a novel stock interval forecasting model based on Complete Ensemble Empirical Mode Decomposition with Adaptive Noise Analysis (CEEMDAN)-wavelet threshold de-noising (WTD) joint de-noising method and Transformer model improved by a Bi-directional Long Short-Term Memory model (BiLSTM) is proposed in this paper. First, based on CEEMDAN, the WTD method is incorporated to extract features from the basic ticker data of financial time series and use them as the input of the Transformer model. Meanwhile, the BiLSTM provides the time-series relationship among the input stock data for the Transformer to forecast the financial time series. Moreover, a hybrid sliding Kernel Density Interval Estimation (KDE) method to demonstrate the forecasting accuracy of financial time series. Using stock price index data, the prediction results are compared with those of traditional neural networks, and the results show that the stock interval prediction of the CEEMDAN-WTD-BiLSTM-Transformer model has a relatively high prediction accuracy, which achieves an improvement of 0.88%~3.62%.

A method for reducing transient electromagnetic Noise: Combination of variational mode decomposition and wavelet denoising algorithm

The transient electromagnetic method (TEM) is used to detect mineral resources and mined-out areas, to eliminate the secondary field signal noise interference, this paper proposes an algorithm for denoising the TEM signal based on Variational Mode Decomposition (VMD) and Wavelet Threshold Denoising (WTD) methods. The Grey Wolf Optimization (GWO) algorithm solves the parameter combination (K, α) in the VMD, and the K intrinsic mode functions (IMFs) are then obtained using the decomposed TEM signal. Subsequently, all IMFs are analyzed according to the correlation coefficient and divided into signal modes, mixed modes, and invalid modes. Finally, the mixed modes are denoised by WTD, the signal and denoised modes are combined. To validate the effectiveness of the VMD-WTD algorithm, the method was compared in simulations with the Ensemble Empirical Mode Decomposition (EEMD) algorithm and various other methods previously developed to improve the TEM, its performance in a field experiment was also confirmed.

Weak Signal Detection Based on Lifting Wavelet Threshold Denoising and Multi-Layer Autocorrelation Method

To solve the problem that the weak signal is difficult to detect under a strong background noise, a detection method based on lifting wavelet threshold denoising and multi-layer autocorrelation method is proposed. Firstly, the original signal is denoised by lifting wavelet threshold to improve the signal-to-noise ratio. Secondly, the multi-layer autocorrelation function of the noise-reconstructed signal is calculated, and its time-frequency signature are analyzed. Finally, the combined algorithm is used on weak signals with low signal-to-noise ratio to extract weak signal features. Simulation and experimental results demonstrate that the proposed method can detect weak signal features buried in the heavy noise effectively. The proposed method is compared with the traditional noise reduction method, which reflects its effectiveness and superiority.

Enhancement method of weak Lidar signal based on adaptive variational modal decomposition and wavelet threshold denoising

Aiming to identify and detect the weak signal of lidar, a cascade method of adaptive variational modal decomposition (VMD) and wavelet threshold (WT) denoising is proposed in this paper. Firstly, VMD is used to decompose the echo signal, and the criterion of adaptive mode selection is improved. Furthermore, the “db4” wavelet and soft threshold denoising method are used to process the denoised signal by AVMD. The optimal threshold value is obtained by minimizing Stein's unbiased risk estimator. In order to verify the superity of the proposed method, Bumps signal is employed in simulation. When the input signal-to-noise ratio (SNR) is −3dB, the SNR of proposed method can reach 7.8587 dB. Compared with three methods, the SNR of proposed method is the highest under different input SNRs. The real Lidar signal is recorded to be denoised. The root mean square errors of WT-db4, EMD-DT, SVD-WT and the proposed method are 0.0046, 0.0044, 0.0044 and 0.0043. Compared with three state-of-art denoising methods, the proposed denoising method can effectively eliminate the spike noise and fully retain the echo signal.

A signal de-noising method for a MEMS gyroscope based on improved VMD-WTD

To reduce the influence of MEMS gyroscope random errors on navigation systems, the improved variational mode decomposition-wavelet threshold de-noising (WTD) method is proposed in this paper. First, to suppress the endpoint effect caused by the signal truncation and Hilbert transform during decomposition, the triangular waveform matching method is used to search for the waveform which most matches the endpoints in the whole signal. Secondly, the grid search algorithm is used to select the optimal parameters for the extended signal to realize the optimal decomposition. Finally, all the components are analyzed to determine autocorrelation characteristics. According to the variance of the autocorrelation function, all the components can be divided into noise components, mixed components and signal components. The noise components are directly removed, and the mixed components are de-noised using the WTD method. Then, the signal components and the mixed components are reconstructed after de-noising. Analysis of simulation and measured data de-noising experiments proves the effectiveness of the proposed method. For the static signal, the mean square error (MSE) of the proposed method is reduced by 10.1% and the signal to noise ratio (SNR) is increased by 14.2%. For the dynamic signal, the MSE of the proposed method decreases by 16.9% and the SNR increases by 18.8%.

EFFECT OF WAVELET DE-NOISING ON THE CLASSIFICATION OF PIG BEHAVIOUR

To efficiently eliminate the noise generated by the triaxial accelerometer when collecting pigs’ behavioural data, this paper adopted SNR and MSE as the indexes to evaluate the de-noising effect of pigs’ acceleration signal under various combinations of wavelet basis, decomposition layer, threshold rule and threshold function. Based on the optimal wavelet parameter combinations, the de-noised data were divided into a training dataset and test dataset to conduct a 3-fold cross validation. The results showed that Db4 wavelet can achieve a satisfactory de-noising effect when used as a wavelet basis for 8 layers wavelet decomposition based on Rigrsure threshold rules and the new improved threshold function. As a result, compared with traditional wavelet hard threshold de-noising, soft threshold de-noising and EMD de-noising method, the improved threshold function improved the stability of signal filtering, which was shown to be more practical, effective and feasible. As such, wavelet de-noising was found to significantly improve the classification accuracy of all four behaviour classes (lying, standing, walking and exploring) considered for this study, and the overall major mean accuracy was improved from 0.680 to 0.826.

An improved denoise method based on EEMD and optimal wavelet threshold for model building of OPAX

To improve the accuracy of Operational Path Analysis with Exogeneous Inputs (OPAX) model by excluding the noise interference sufficiently in the vehicle operating condition data (time-domain vibration signal), the combined noise reduction method of Ensemble Empirical Mode Decomposition (EEMD) and wavelet threshold was used. Since the noise content of each noisy intrinsic mode functions (IMFs) decomposed by EEMD is uncertain, the effective signal element in the less noisy IMFs affects the accuracy of the first-layer wavelet coefficients to estimate the noise variance, the EEMD and wavelet particle swarm optimization sample entropy threshold denoising (EEMD-WPSE) method is presented in terms of information entropy. In this method, the sample entropy of the eliminated noise is used as the information cost function, together with the particle swarm optimization algorithm to find the optimal wavelet threshold of each high-frequency noisy IMFs. After denoising the simulation signal, it is found that the combination of EEMD-WPSE threshold with hard threshold function, soft threshold function and half-soft threshold function identifying higher SNR and lower RMSE, are given to demonstrate the higher universality of the proposed method. The method is applied to the noise reduction processing of the automobile operating condition data for constructing the OPAX model, and the degree of similarity between the synthesized responses of the care-target point obtained by the OPAX model and the measured responses under the second order operational condition are observed, as it turned out, the calculation results of SNR and RMSE indicated that EEMD-WPSE can better promote the accuracy of OPAX model in terms of noise reduction.

Data-driven early fault diagnostic methodology of permanent magnet synchronous motor

Permanent magnet synchronous motor (PMSM) is one of the common core power components in modern industrial systems. Early fault diagnosis can avoid major accidents and plan maintenance in advance. However, the features of early faults are weak, and the symptoms are not obvious. Meanwhile, the fault signal is often overwhelmed by noise. Accordingly, fault diagnosis for early faults is difficult, and the diagnostic accuracy is generally low. A Bayesian-network-based data-driven early fault diagnostic methodology of PMSM is proposed with vibration and acoustic emission data. The wavelet threshold denoising and minimum entropy deconvolution methods are used to improve the signal-to-noise ratio. The complementary ensemble empirical mode decomposition method is used to extract signal eigenvalues, and Bayesian networks are applied to identify the early, middle, and permanent faults. Experimental data carried out with Tyco ST8N80P100V22E medium PMSM are used to train the fault diagnostic model and validate the proposed fault diagnostic methodology. Result shows that the accuracy for early faults is more than 90% when acoustic emission signal is used, and it is higher than the accuracy with vibration signal. The influence of load on diagnostic accuracy is also investigated, and it indicates that the accuracy with acoustic emission signal is higher than that with vibration signal under different loads.

Research on vibration effect of tunnel blasting based on an improved Hilbert–Huang transform

Through a tunnel-blasting project, the effect of tunnel-blasting vibration has been analyzed from the perspective of vibration energy transfer. The non-linear regression method was used to obtain the prediction equation for blast vibration velocity based on the field blast vibration data. Then, the maximum charge per delay of the blasting construction of the tunnel was obtained through the formula inversion. Based on the traditional Hilbert transform, a novel Hilbert–Huang transform (HHT) analysis method considering Complete Ensemble Empirical Mode Decomposition with Adaptive Noise decomposition (CEEMDAN) and wavelet packet threshold de-noising method has been proposed, the feasibility of which was verified using the field blast vibration signals. It has been proved that the improved HHT analysis method can be used to analyze the influence of the different blasting vibration parameters on the regular distribution of vibration energy. In addition, the dimensional analysis method was used to establish the blasting vibration energy prediction model. The results of this research show that the improved HHT analysis method can solve the problem of modal aliasing caused by the traditional decomposition method, and can obtain the purified main modal components, which improves the adaptability of HHT analysis. In addition, with the increase of the distance between blast area and the maximum charge per delay, the high-frequency energy of the blasting signal gradually weakens, while the dominant energy frequency band diverts to the low-frequency band. The methods and conclusions of this research can provide a certain reference for the controlled blasting construction in similar cases.

Accuracy improvement of quantitative LIBS analysis of coal properties using a hybrid model based on a wavelet threshold de-noising and feature selection method.

A hybrid model based on a wavelet threshold de-noising (WTD) and recursive feature elimination with cross-validation (RFECV) method was proposed to improve the measurements in quantitative analysis of coal properties using laser-induced breakdown spectroscopy (LIBS). First, a modified threshold of WTD was proposed based on wavelet coefficient theory. Interference of noise in the LIBS spectrum was reduced by using this modified method. Then, the RFECV method was applied to extract effective features from the de-noised LIBS spectrum. Finally, support vector regression (SVR) models of coal properties were established by the selected features. A validation set was used to verify the effectiveness and robustness of the hybrid model. The improvement of the hybrid model on the quantitative analysis of each index of coal properties (heat value, ash, volatile content) was studied and discussed. By using the proposed model, the determination coefficient (R2), root mean square error of prediction, average relative error, and relative standard deviation were all significantly improved over the original spectra model. The results demonstrated that the proposed model could effectively improve the accuracy and precision of LIBS quantitative analysis for coal properties.

A novel bat algorithm with double mutation operators and its application to low-velocity impact localization problem

The low-velocity impact localization in the plate structure of the ship is a critical problem which can be considered as a nonlinear optimization problem. The bat algorithm (BA) has been widely used to solve nonlinear optimization problems. However, the standard BA exhibits poor performance on complex problems because of its premature convergence. In this study, a novel bat algorithm with double mutation operators (TMBA), in which a modified time factor and two mutation operators are integrated, is proposed to enhance BA’s performance on nonlinear optimization problems. Classical benchmark functions are employed to analyze the contributions of the three modifications and demonstrate the significant improvement of TMBA. For the low-velocity impact localization problem, the low-velocity impact localization system based on fiber Bragg grating (FBG) sensors is utilized to receive the impact signals. The wavelet threshold de-noising method and the generalized cross-correlation method are both applied to the extraction of time differences between the impact signals. Then, the proposed algorithm and several well-known optimization algorithms are adopted to solve the minimization fitness function which is established using the triangulation method. The statistical results indicate that TMBA is more feasible and effective for solving the low-velocity impact localization problem.