Soft Threshold Denoising Research Articles

MSTD: a framework for rolling bearing fault diagnosis based on multi-scale and soft-threshold denoising

ABSTRACT In real industrial environments, the data collected is often subject to noise interference, which leads to challenges for traditional deep learning fault diagnosis models, including insufficient autonomous learning capabilities, complex feature extraction processes, and sensitivity to noise. To address these issues, this paper proposes a bearing fault diagnosis convolutional neural network based on multi-scale and soft-threshold denoising (MSTD). In this model, Poly Kernel Feature Fusion (PKFF) is utilised to extract high-quality features from raw vibration data, enhancing the model’s ability to recognise complex fault patterns; Residual anchor attention (RAA) reduces redundancy and irrelevant information between channels, optimising inter-channel information to ensure the model’s effectiveness when handling multi-channel data; Soft threshold CG (ST-CG) utilises a soft-threshold denoising method to suppress noise after feature extraction, thereby more clearly revealing fault characteristics. Soft-threshold processing not only enhances the model’s noise resistance but also preserves critical fault information, enabling the model to maintain high diagnostic accuracy even under low signal-to-noise ratio conditions. The proposed model demonstrates outstanding performance on the CWRU and MFS-MG datasets, exhibiting superior feature extraction capabilities and robustness in high-noise environments compared to other models, significantly improving diagnostic accuracy and noise resistance.

Projection generalized correntropy twin support vector regression

A projection generalized maximum correntropy twin support vector regression algorithm is proposed. The generalized correntropy function is added into the loss function of adaptive filtering, maximizing which can suppress the interference of noise or outliers.Considering the fact that single-shift projection twin support vector regression cannot observe local information of samples, a complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) combined with wavelet soft threshold denoising is used to assign weights to samples. The CEEMDAN is used to decompose the original data, calculate the Pearson correlation coefficient between the mode functions and the original data. The mode with low correlation is filtered by wavelet based algorithm with soft-threshold to get the reconstructed samples after noise reduction. Smaller weights will be assigned to reconstructed samples with significant differences from the original data, while larger weights will be assigned to reconstructed samples with smaller differences. Similarly, the empirical risk term in the cost function is also assigned calculated weights to improve the robustness. Due to the use of empirical mode decomposition, the proposed method is particularly suitable for processing non-stationary data. Experimental results on artificial and UCI datasets verified the effectiveness of the algorithm.

The univariate model for long-term wind speed forecasting based on wavelet soft threshold denoising and improved Autoformer

Accurate wind speed prediction is crucial for effective wind power grid integration and energy dispatching. Recent research has explored the combination of decomposition algorithms with forecast models to form hybrid models, aiming to enhance wind speed prediction accuracy. However, these traditional decomposition techniques often lead to high time costs in practical applications, as they require new wind speed sequences to be appended to historical long sequences for decomposition before entering the forecast model. To overcome this challenge, this study introduces and improves the Autoformer model, applying it for the first time to long-term univariate wind speed forecasting. By incorporating decomposition technology as a sub-module of the forecast model, Autoformer not only solves the high time cost issue found in conventional hybrid models but also retains the benefits of decomposition technology in time series processing.Furthermore, in this paper, the decomposition module of Autoformer is replaced with the Mixture of Expert Decomposition Module (MOEDecomp) to better extract complex trend elements of wind speed series. Combined with the auto-correlation mechanism, sequential attention is paid to wind speed for extracting time dependencies in long series. Additionally, the Wavelet Soft Threshold Denoising (WSTD) algorithm is utilised for noise reduction in wind speed sequences. To evaluate the model's performance, two multi-step forecasting strategies were employed to predict wind speeds for the forthcoming 24, 48, 72, 96, and 120 h using four datasets. Experimental results demonstrate that the proposed model surpasses 15 comparative models in terms of prediction accuracy, generalization ability, and handling uncertain data.

Smoothing denoising method of spatial filtering image based on Contourlet transform

This paper studies the threshold denoising problem of image in Contourlet transform domain, and proposes a smoothing denoising method of spatial filtering image based on Contourlet transform. This method combined with Contourlet transform can highlight the advantages of image edge information and direction information. The image is decomposed by using the Contourlet transform algorithm, and then the spatial filtered image is obtained. Based on the threshold estimation of the Contourlet coefficient of the Treelet difference variable and the soft threshold denoising of the high-frequency coefficient, the spatial filtered image denoising is realized. Then, aiming at the unsmooth denoising problem of the spatial filtered image, the spatial filtered image filtering smoothing processing method based on generalized Laplace distribution is used to solve the unsmooth denoising problem of the spatial filtered image. The experimental results show that this method has strong smoothing denoising ability and obvious application effect.

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.

An enhanced K-SVD denoising algorithm based on adaptive soft-threshold shrinkage for fault detection of wind turbine rolling bearing

Due to nonstationary operating conditions of wind turbines and surrounding harsh working environments, the impulse features induced by bearing faults are always overwhelmed by heavy noise, which brings challenges to accurately detect rolling bearing faults. Sparse representation exhibits excellent performance in nonstationary signal analysis, but it is closely bound up with the degree of similarity between the atoms in a dictionary and signals. Therefore, this paper investigates an enhanced K-SVD denoising method based on adaptive soft-threshold shrinkage to achieve high-precision extraction of impulse signals, and applies it to fault detection of generator bearing of wind turbines. An adaptive sparse coding shrinkage soft-threshold denoising is first proposed to remove noise and harmonic interference in the residual term of dictionary updating, so that the updated atoms show obvious impact characteristics. Furthermore, a soft-threshold shrinkage function with adaptive threshold is designed to further suppress clutter in atoms of the learned dictionary, so as to obtain an optimized dictionary for recovering impulse signals. Two actual engineering cases are selected for analysis, and the envelope spectrum correlation kurtosis corresponding to the results obtained by the proposed method is significantly higher than that of other comparison methods, thus verifying its superiority in detecting rolling bearing faults.

Efficient Massive Machine Type Communication (mMTC) via AMP

We propose efficient and low-complexity multiuser detection (MUD) algorithms for Gaussian multiple access channel (G-MAC) for short-packet transmission in massive machine type communications. To do so, we first formulate the G-MAC MUD problem as a sparse signal recovery problem and obtain the exact and approximate joint prior distribution of the sparse vector to be recovered. Then, we employ the Bayesian approximate message passing (AMP) algorithms with the optimal separable and nonseparable minimum mean squared error (MMSE) denoisers for soft decoding of the sparse vector. The effectiveness of the proposed MUD algorithms for a large number of devices is supported by simulation results. For packets of 8 information bits, while the state-of-the-art AMP with soft-threshold denoising achieves 8/100 of the upper bound at Eb/N0 = 4 dB, the proposed algorithms reach 4/7 and 1/2 of the upper bound.

A Novel Denoising Algorithm Based on Wavelet and Non-Local Moment Mean Filtering

Denoising is the basis and premise of image processing and an important part of image preprocessing. Denoising can effectively improve image quality, which contributes to subsequent image processing such as image segmentation, feature extraction, and so on. In this paper, we propose a novel image denoising method based on wavelet transform and nonlocal moment mean filtering approach (NMM). The noisy image is firstly denoised by a wavelet-based soft-thresholding denoising technique and NMM is then utilized to further eliminate the rest noises. Meanwhile, the fusion of moment invariants increases the robustness of our denoising algorithm due to the invariance of image scaling, translation, and rotation of color moments. Experiments show that our algorithm achieves a better denoising effect compared with some other denoising approaches.

Soft threshold denoising and video data fusion-relevant low-quality 3D face recognition

Soft threshold denoising and video data fusion-relevant low-quality 3D face recognition

Patient-specific method for predicting epileptic seizures based on DRSN-GRU

Epilepsy is one of the most common neurological disorders worldwide and can cause the brain to stop working properly or even endanger the life of the patient. Epilepsy prediction is a prerequisite for seizure control, allowing preventive measures to mitigate damage or control seizures. It has been found that abnormal brain activity begins some time before a seizure, which is known as the pre-ictal state. In this study, we reconsidered the temporal scope of the pre-ictal period and divided it into multiple temporal windows. A patient-specific seizure prediction method based on deep residual shrinkage network (DRSN) and gated recurrent unit (GRU) was then proposed. The temporal dependency of the signal of different time windows in the pre-ictal period is modeled by introducing GRU into a DRSN. In addition, automatic feature extraction is achieved by applying soft threshold denoising and attention mechanism inside the neural network. The proposed method was tested on four patients reasonably selected from the CHB-MIT scalp EEG dataset, which achieved a sensitivity of 90.54%, an AUC value of 0.88, and a false prediction rate of 0.11/h. The results obtained by our method are compared with the recent epilepsy prediction methods. Compared with the being among the best method, our method still has a little gap, but it also shows a new idea and some advantages.

Railway foreign body vibration signal detection based on wavelet analysis

Based on the wavelet packet analysis method with time-frequency analysis characteristics, the measurement signal of the vibration system is processed for noise reduction, the soft-hard threshold compromise wavelet denoising method used has the advantages of soft threshold and hard threshold denoising, and through the introduction of compromise factors, signal processing can be performed more flexibly in signal analysis. For the denoised signal, the fundamental wavelet time-energy spectrum analysis, the main components of the signal can be clearly displayed, and according to the distribution of its energy in each frequency band, the signal characteristics can be displayed intuitively. Experimental results show: It can be determined that there is a foreign body intrusion incident at a position 520 m away from the monitoring point, rather than a normal train travel incident. In fact, we are walking back and forth at a distance of about 520 m from the monitoring point, simulating the intrusion of illegal foreign objects such as pedestrians and livestock beside the railroad tracks prove that analysis and judgment can be known, the wavelet analysis proposed by the author can realize the monitoring and judgment of some illegal foreign body intrusion incidents such as pedestrians and livestock.

RDTS Noise Reduction Method Based on ICEEMDAN-FE-WSTD

Aiming at the problem of temperature measurement error caused by the noise signal on the Raman-based distributed optical fiber temperature sensor (RDTS), a noise reduction method based on the improved complete ensemble empirical mode decomposition with adaptive noise, fuzzy entropy, and the wavelet soft threshold denoising (ICEEMDAN-FE-WSTD) is proposed. First, ICEEMDAN is used to decompose the input signal, and noise intrinsic mode functions (IMFs) are determined by calculating the FE value of each IMF. Then, noise IMFs are denoised by the WSTD method. Finally, the noise reduction results are obtained by combining the denoised IMFs with the remaining useful signal IMFs for reconstruction. The advantages of the proposed method in terms of denoising and character extraction are verified by the simulation signal experiment with different signal-to-noise ratios (SNRs). The temperature measurement experiments are carried out with heating areas set at 40 °C, 45 °C, 50 °C, 55 °C, and 60 °C. Taking the 40 °C temperature measurement experiment as an example, after the temperature measurement signal is denoised by the proposed method, the maximum temperature measurement error in the heating area is reduced by 1.07 °C, the SNR is increased by 4.83 dB, and the root-mean-square error (RMSE) is reduced by 0.77. The temperature drift of RDTS signals after noise reduction by the proposed method is also effectively suppressed, and the maximum temperature measurement error at 2.28 km is reduced by 1.43 °C. The denoising results of the proposed method are compared with the other six noise reduction methods in this article, and the proposed method has the best performance.

Multi-Step Short-Term Wind Speed Prediction Models Based on Adaptive Robust Decomposition Coupled with Deep Gated Recurrent Unit

Accurate wind speed prediction is a premise that guarantees the reliable operation of the power grid. This study presents a combined prediction model that integrates data preprocessing, cascade optimization, and deep learning prediction to improve prediction performance. In data preprocessing, the wavelet soft threshold denoising (WSTD) is employed to filter the blurring noise of the original data. Then, the robust empirical mode decomposition (REMD) and adaptive variational mode decomposition (AVMD) are adopted to carry out a two-stage adaptive decomposition. Spearman correlation is used to quantify the mode that need to be decomposed for the second time. In the cascade optimization, the hybrid grey wolf algorithm (HGWO) is employed to optimize the parameters of the VMD and the gated recurrent unit (GRU), which overcomes the problem of empirical parameter adjustment. The HGWO is also adopted in the prediction strategy to optimize the GRU model to predict the grouped intrinsic mode functions (IMFs). Lastly, the final wind speed prediction result is obtained by superimposing the values of all the predicted models. The proposed model was validated with the measured wind speed data of the four quarters in the Bay area of China and was compared with 20 models of the classic method to further evaluate the effectiveness of the model. The results show that the whole process of the proposed model is adaptive, the final multi-step prediction performance is good, and high prediction accuracy can be attained.

Study on the Wavelet Threshold Noise Reduction Technique Based on MATLAB

In the process of image processing, image acquisition, conversion and transmission are often affected by imaging equipment and external environmental noise impact, so that the image degradation. The follow-up image processing of digital image noise influence is bigger, so there are very important realistic meanings to remove image noise. Image denoising is an extensive image pretreatment technology, the purpose is to improve the image SNR, highlight the expectations of the image features. Modern image noise reduction technology is very much, and each has its advantages and disadvantages, in the process of image processing, image acquisition, conversion and transmission are often affected by imaging equipment and external environmental noise impact, so that the image degradation. The follow-up image processing of digital image noise influence is bigger, so there are very important realistic meanings to remove image noise. Image denoising is an extensive image pretreatment technology, the purpose is to improve the image SNR, highlight the expectations of the image features. Modern image noise reduction technology is very much, and each has its advantages and disadvantages, among them, wavelet threshold denoising is a denoising technique can have good treatment of Gauss noise, wavelet threshold denoising is divided into soft threshold and hard threshold denoising, for different noise, can take different threshold denoising, can get very good the effect of. MATLAB is a very good software, and her language is simple and powerful, can finish all kinds of simulation of signal processing, especially the simulation of image denoising. Among them, wavelet threshold denoising is a denoising technique can have good treatment of Gauss noise, wavelet threshold denoising is divided into soft threshold and hard threshold denoising, for different noise, can take different threshold denoising, can get very good effect. MATLAB is a very good software, and her language is simple and powerful, can finish all kinds of simulation of signal processing, especially the simulation of image denoising.

Calibration Analysis of High-G MEMS Accelerometer Sensor Based on Wavelet and Wavelet Packet Denoising.

High-G accelerometers are mainly used for motion measurement in some special fields, such as projectile penetration and aerospace equipment. This paper mainly explores the wavelet threshold denoising and wavelet packet threshold denoising in wavelet analysis, which is more suitable for high-G piezoresistive accelerometers. In this paper, adaptive decomposition and Shannon entropy criterion are used to find the optimal decomposition layer and optimal tree. Both methods use the Stein unbiased likelihood estimation method for soft threshold denoising. Through numerical simulation and Machete hammer test, the wavelet threshold denoising is more suitable for the dynamic calibration of a high-G accelerometer. The wavelet packet threshold denoising is more suitable for the parameter extraction of the oscillation phase.

Application of Improved Wavelet Threshold in Denoising of ECG Signals

The ECG signal is susceptible to interference from the external environment during the acquisition process, affecting the analysis and processing of the ECG signal. After the traditional soft-hard threshold function is processed, there is a defect that the signal quality is not high and the continuity at the threshold is poor. An improved threshold function wavelet denoising is proposed, which has better regulation and continuity, and effectively solves the shortcomings of traditional soft and hard threshold functions. The Matlab simulation is carried out through a large amount of data, and various processing methods are compared. The results show that the improved threshold function can improve the denoising effect and is superior to the traditional soft and hard threshold denoising.

Water leak location based on improved dual-tree complex wavelet transform with soft thresholding de-noising

Water leakage control emerges as a prime concern among researchers and water utility companies due to ever-increasing water loss level. Acoustic leak detection technique is a promising and widely used approach. Unfavorably, the deficiency of this method is that acoustic waves are interfered by undesirable noise and presence of multi-modal dispersive wave. The conventional correlation-based method assumes leak noise propagates as a single non-dispersive wave and this leads to unreliable detection method. This paper concerns on noise reduction through an improved de-noising method and leak localization by considering wave dispersion. Wavelet de-noising is a common de-noising method used in past leak detection works. But it has shortcomings of frequency aliasing and shift-variant due to DWT decomposition. Therefore, a shift-invariant Dual Tree Complex Wavelet Transform (DTCWT) is introduced here to substitute DWT for wavelet de-noising. DTCWT will decompose the signal into several bandwidths then soft thresholding is applied to remove noise by eliminating the irrelevant signals. Multilevel DTCWT decomposition aids to tackle the problem encountered by basic localization method because the wave velocity is evaluated based on the dominant frequency and dispersion curve. Experimental results show that the proposed de-noising method outperforms ordinary wavelet de-noising. Besides, the method effectively removes noise and makes the peak of cross-correlation function more pronounced and hence it is achievable to increase leak localization accuracy. The proposed method outweighs other methods by offering the lowest false trips occurrence and minimal localization error of 3.33%. A field test result proved that the method is able to locate the leak in a 235-meter-long, underground buried pipe with a minimal error of 2.63% which is 57% lower than the conventional method.

Research on Speech Signal Denoising Algorithm Based on Wavelet Analysis

In this paper, wavelet analysis is used to remove noise superimposed on the speech signal to achieve denoising of the speech signal. The prepared speech signal is superimposed with Gaussian white noise with different signal-to-noise ratios, and is removed by using a forced noise removal processing method and a given threshold denoising processing method; The wavelet soft and hard threshold denoising method is used to separately superimpose different Gaussian white noise speech signals, and the hard threshold and soft threshold denoising are respectively performed, and different wavelets are used for processing; Four threshold selection methods are used to denoise the noisy signal using different wavelets. The denoising effects of these methods are simulated in MATLAB software, and combined with the signal-to-noise ratio of the signal after denoising, the denoising effects of various methods are judged. Experimental results show that soft threshold denoising is slightly better than hard threshold denoising. Among the four threshold selection methods, Rigrsure rule denoising is the best. Although other methods are effective, they are not obvious.

A novel deep learning ensemble model with data denoising for short-term wind speed forecasting

Wind speed forecasting plays a pivotal role in the security and economy of the power system operation. However, accurate prediction on the wind speed value is still quite challenging due to three features of wind speed: randomness, fluctuation and unpredictability. Though many previous works have studied decomposition-based methods for preprocessing, these methods are difficult to use in actual prediction, since the newly acquired data will greatly affect the values of the initial decomposed subsequences. To solve this problem, a good solution referred as the wavelet soft threshold denoising (WSTD) is proposed herein, which is also systematically introduced for the first time. Moreover, a novel deep learning method gated recurrent unit (GRU) is successfully developed to be combined with WSTD to forecast the wind speed series in this paper. In the ensemble WSTD-GRU model, the WSTD is applied to filter the redundant information from the original data of wind speed series; GRU, which is particularly advantageous for learning the features in case of cooperating with WSTD, is adopted to predict the future multi-step wind speed values. Also, the parameters of the GRU are adjusted by cross-validated grid-search, and they are visualized in the paper. In experiments, thirty-five commonly used models are involved for comparison to evaluate the forecasting performance of the proposed model, through the datasets from four sites in the United States covering a wide range of longitudes. Finally, a superior performance of this methodology with relatively high accuracy, fast forecasting speed, small volatility of results and good adaptability is verified by the test results of case studies aforementioned.

Gamma spectrum denoising method based on improved wavelet threshold

Adverse effects in the measured gamma spectrum caused by radioactive statistical fluctuations, gamma ray scattering, and electronic noise can be reduced by energy spectrum denoising. Wavelet threshold denoising can be used to perform multi-scale and multi-resolution analysis on noisy signals with small root mean square errors and high signal-to-noise ratios. However, in traditional wavelet threshold denoising methods, there are signal oscillations in hard threshold denoising and constant deviations in soft threshold denoising. An improved wavelet threshold calculation method and threshold processing function are proposed in this paper. The improved threshold calculation method takes into account the influence of the number of wavelet decomposition layers and reduces the deviation caused by the inaccuracy of the threshold. The improved threshold processing function can be continuously guided, which solves the discontinuity of the traditional hard threshold function, avoids the constant deviation caused by the traditional soft threshold method. The examples show that the proposed method can accurately denoise and preserves the characteristic signals well in the gamma energy spectrum.