Application of wavelet threshold method based on optimized VMD to ECG denoising

To address the noise issue in the measured vibration signals of spillway radial gate discharge, this paper utilizes the Multiverse Optimization Algorithm (MVO) to optimize the number of decomposition modes (K) and the penalty factor (α) in Variational Mode Decomposition (VMD). This approach ensures improved efficiency of VMD decomposition while maintaining accuracy. Subsequently, the obtained Intrinsic Mode Functions (IMFs) from VMD decomposition are classified based on Multi-scale Permutation Entropy (MPE). IMFs are divided into pure components and noisy components; the noisy components are processed with Wavelet Threshold Denoising (WTD), while the pure components are overlaid and reconstructed to obtain the denoised vibration signal of the gate. Comprehensive comparisons involving artificial signal simulations, gate flow-induced vibration model tests, and numerical simulations lead to the following conclusions: compared to other algorithms, the proposed combined denoising method (MVO-VMD-MPE-WTD) achieves the highest signal-to-noise ratio (SNR) in both the frequency and time domains for artificial signals, while yielding the lowest mean square error (MSE). In the gate flow-induced vibration model tests, the method significantly reduces noise in the vibration signals and effectively preserves characteristic information. The error in preserving characteristic information across model tests and numerical simulations is kept below 1%. Furthermore, compared to other optimization algorithms, the MVO demonstrates higher computational efficiency. The parameter-optimized combined denoising method proposed in this study provides insights into denoising measured vibration signals of hydraulic spillway radial gates and other drainage structures, and it opens possibilities for exploring more efficient optimization algorithms for achieving online monitoring in the future.

In order to separate the valid ECG signals from the undesired artifacts, the neighboring coefficients thresholding scheme with a level dependent threshold estimator was employed in our study. The noisy ECG signals were obtained by adding three types of noise to the synthetic ECG signal and real ECG signals. Experimental results show that our method can effectively suppress the noise and is better than the hard thresholding method. Comparing the hard thresholding, the average SNR improvement of the results denoised by the neighboring coefficients scheme was increased by 0.767dB.

Original lidar return signals are covered by high levels of noise that seriously affect the accuracy of subsequent data processing and inversion. Therefore, it is important to separate the effective signal from the returned signal with noise interference. In this paper, an efficient denoising method based on the variational mode decomposition (VMD) algorithm optimized using the global search strategy-based whale algorithm and the total variational stationary wavelet transform (GSWOA-VMD-SWTTV) is proposed, and this method is applied to denoising of lidar return signals. First, the global search strategy-based whale optimization algorithm (GSWOA) is used to acquire the optimal parameters of the VMD algorithm adaptively, and the lidar return signal is then decomposed by global search strategy-based whale optimization algorithm (GSWOA)-VMD. The effective modal components are then determined using the cross-correlation coefficient method from the decomposed modal components, and total variation stationary wavelet denoising is performed on each effective mode. Finally, the effective modes are reconstructed to obtain a clean lidar return signal. Moreover, to provide further verification of the effectiveness of the proposed method, it is compared with the ensemble empirical mode decomposition (EEMD) method, the complete EEMD with adaptive noise (CEEMDAN) method, the singular value decomposition (SVD) method, and the wavelet threshold method under sunny, cloudy, and dusty weather conditions. The experimental results demonstrate the superior noise reduction performance of the proposed algorithm, which can filter out strong noise from the signal while retaining the complete signal details without distortion; additionally, the proposed method has the highest signal-to-noise ratio and lowest mean square error.

The threshold-based method has been used at the last stage of most QRS detection for monitoring many cardiac diseases including arrhythmias detection. The method also been proven to achieve good detection accuracy in clean and high-quality ECG signal. However, the threshold-based method is sensitive to noise and the performance of detectors will be affected by low-quality ECG signal data. The numerous types of noise and different abnormal morphological of ECG signal will produce low-quality of signal. Because of that, the performance of the threshold-based method to detect the QRS complex in low-quality ECG signals should be investigated. In this paper, to assess the QRS detection on noisy ECG signal, the performance of threshold-based method is evaluated. Two experiments were performed using MIT-BIH Noise Stress Test data and MIT-BIH Arrhythmia data to assess the algorithm performance. The performance of the algorithm was then analysed and presented. This paper shows the capability of the threshold-based detection method to identify QRS complex in noisy ECG signals.

Removing noise from ECG signals is still a very frequently discussed topic. There are many challenges that make this problem more complex. These challenges are driven by the widespread use of ECG devices such as monitoring a heart disease of patients and a heart rate of athletes namely when reading and sending ECG signal data is done, there is a lot of noise that contaminates ECG signals, one of which is white Gaussian noise. In this research, noise elimination is done by using Variation mode decomposition (VMD) and Nonlocal Means (NLM) method. Denoising using the NLM technique approach is very effective in removing white Gaussian noise but it suffers from the issue of under-averaging in the high-frequency QRS-complex region and the VMD method which is the development of the Empirical Mode Decomposition (EMD) method has better capability to decompose the signal into several modes. By using the advantages of each method, we are capable of achieving good performance in removing noise from the ECG signals. Testing of the proposed method was performed using MIT-BIH arrhythmias database, which was given Gaussian white noise with different SNR levels. Measurements were made using three levels of measurement matrices i.e. Signal for Ratio Noise Enhancement (SNRimp), Mean Square Error (MSE) and Percentage root mean square difference (PRD). In addition, we may use methods that are compatible with state-of-the-art noise removal methods on ECG signals i.e. the DWT thresholding, EMD soft thresholding, EMD + Wavelet, NLM, M-EMD+NLM, and DWT+NLM. The end result is a method that is capable of producing a slightly higher SNRimp, a lower MSE and PRD value.

Partial discharge evaluation is a principal method for assessing insulation conditions in power transformers. Traditional singular value decomposition (SVD) approaches, however, face issues like high residual noise and loss of signal details in white noise suppression. This article introduces an advanced denoising algorithm integrating SVD, variational mode decomposition (VMD), and wavelet thresholding to effectively address mixed noise in on-site power transformer assessments. The algorithm initially employs SVD to suppress mixed noise, specifically targeting narrowband interference by decomposing the noisy signal and nullifying the corresponding singular values. Post-SVD, the signal is further processed through VMD, with its modal components refined via wavelet thresholding. The final reconstruction of these denoised components effectively eliminates white noise. Applied to an input signal with a signal-to-noise ratio of -27.593 dB, the proposed method achieves a postdenoising ratio of 13.654 dB. Comparative analysis indicates its superiority over existing algorithms in mitigating white noise and narrowband interference and more accurately restoring the partial discharge signal.

Long-span bridges are susceptible to damage, aging, and deformation in harsh environments for a long time. Therefore, structural health monitoring (SHM) systems need to be used for reasonable monitoring and maintenance. Among various indicators, bridge displacement is a crucial parameter reflecting the bridge's health condition. Due to the simultaneous bearing of multiple environmental loads on suspension bridges, determining the impact of different loads on displacement is beneficial for the better understanding of the health conditions of the bridges. Considering the fact that extreme gradient boosting (XGBoost) has higher prediction performance and robustness, the authors of this paper have developed a data-driven approach based on the XGBoost model to quantify the impact between different environmental loads and the displacement of a suspension bridge. Simultaneously, this study combined wavelet threshold (WT) denoising and the variational mode decomposition (VMD) method to conduct a modal decomposition of three-dimensional (3D) displacement, further investigating the interrelationships between different loads and bridge displacements. This model links wind speed, temperature, air pressure, and humidity with the 3D displacement response of the span using the bridge monitoring data provided by the GNSS and Earth Observation for Structural Health Monitoring (GeoSHM) system of the Forth Road Bridge (FRB) in the United Kingdom (UK), thus eliminating the temperature time-lag effect on displacement data. The effects of the different loads on the displacement are quantified individually with partial dependence plots (PDPs). Employing testing, it was found that the XGBoost model has a high predictive effect on the target variable of displacement. The analysis of quantification and correlation reveals that lateral displacement is primarily affected by same-direction wind, showing a clear positive correlation, and vertical displacement is mainly influenced by temperature and exhibits a negative correlation. Longitudinal displacement is jointly influenced by various environmental loads, showing a positive correlation with atmospheric pressure, temperature, and vertical wind and a negative correlation with longitudinal wind, lateral wind, and humidity. The results can guide bridge structural health monitoring in extreme weather to avoid accidents.

It is an important practical problem to accurately recognize whether biological tissue is denatured during high intensity focused ultrasound (HIFU) treatment. Ultrasonic scattering echo signals are related to some physical properties of biological tissues. According to the characteristics of ultrasonic scattering echo signals, the recognition of denatured biological tissues is studied based on the variational mode decomposition (VMD) and multi-scale permutation entropy (MPE) in this paper. The ultrasonic echo signals are decomposed into various modal components by the VMD. The noise components and the useful components are separated according to the power spectrum information entropy of various modal components. The separated useful signals are reconstructed and the MPE are extracted. Furthermore, Gustafson-Kessel (GK) fuzzy clustering analysis is employed to obtain the standard clustering center, and the recognition of denatured biological tissues is carried out by Euclid approach degree and principle of proximity. The proposed method is applied to ultrasonic scattering echo signal during HIFU treatment. In order to determine the parameters of MPE algorithm for ultrasonic scattering echo signals, the embedding dimension of the MPE is discussed, and the scale factor of the MPE algorithm is optimized by genetic algorithm. When the delay time and the embedding dimension are 2 and 7 respectively, the MPE values decrease with scale factor increasing. Assuming that the scale factor is 12 from optimization results, the 293 ultrasonic scattering echo signals from normal tissues and denatured tissues are analyzed by the MPE. It is found that the MPE values of the denatured tissues are higher than those of the normal tissues. The MPE can be used to distinguish normal tissues and denatured tissues. Comparing with the recognition methods of the EMD-MPE-GK fuzzy clustering method and the VMD-WE-GK fuzzy clustering, the proposed method has good clustering performance and separability. Its partition coefficient (PC) is close to 1 and the Xie-Beni (XB) index is smaller. There are fewer feature points in the overlap region between MPE features of denatured tissues and normal tissues. The recognition results of denatured biological tissues in this experimental environment show that the recognition rate based on this method is higher, reaching up to 93.81%.

Due to the complexity and variability of automotive bearing fault vibration signals, as well as the challenges in feature extraction, a novel automotive bearing fault diagnosis method based on an improved SSA-VMD algorithm is proposed in this paper. Firstly, the number of modes (K) and the penalty factor (α) in the variational mode decomposition (VMD) algorithm are optimized by the Sparrow Search Algorithm (SSA). Secondly, the VMD using optimized parameters is used to decompose the automotive bearing fault vibration signal into a series of modal components. Modal components with larger kurtosis values are selected for reconstruction and feature extraction. Lastly, the feature vectors are input into a kernel extreme learning machine (KELM) model for fault recognition. A comparative analysis is conducted between the improved SSA-VMD method and the original SSA-VMD method in automotive bearing fault diagnosis. Experimental results demonstrate that the improved SSA-VMD method is satisfactory in extracting characteristic information from automotive bearing fault vibration signals and achieves higher fault diagnosis accuracy.

Aiming at the problem that the signals received by MEMS vector hydrophones are mixed with a large amount of external environmental noise, and inevitably produce baseline drift and other distortion phenomenons which made it difficult for the further signal detection and recognition, a joint denoising method (VMD-NWT) based on variational mode decomposition (VMD) and nonlinear wavelet threshold (NWT) processing is proposed. The main frequency of the noisy signal is first obtained by Fourier transform. Then the noisy signal is decomposed by VMD to obtain the IMF components. The center frequency and correlation coefficient of each IMF component further determine that the IMF components belong to noise IMF components, noisy IMF components or pure IMF components. Then the pure IMF components are reserved, the noise IMF components are removed, and the noisy IMF components are denoised by NWT processing method with new threshold function as a whole. Finally, the denoised IMF components and the pure IMF components are reconstructed to obtain the denoised signal to realize the extraction of useful signals and baseline drift removal. Compared with complete ensemble empirical mode decomposition with adaptive noise combined with wavelet threshold processing method (CEEMDAN-WT), ensemble empirical mode decomposition combined with wavelet threshold processing method (EEMD-WT), and single wavelet threshold processing method with compromised function between hard and soft threshold (ZWT), the VMD-NWT in this paper has the advantages of less calculation and simple implementation. The simulation comparison experiments verify that the VMD-NWT is superior to CEEMDAN-WT, EEMD-WT, and ZWT. Then VMD-NWT is applied to process the measured data obtained from the Fenji experiment conducted by the North University of China. Simulation and lake trial results show that VMD-NWT has better denoising effect and can realize baseline drift removal. So the proposed VMD-NWT has certain practical research value.

In this paper, we propose a novel method of removal of baseline wander noise from a noisy ECG signal. We have shown that the original (clean) ECG signal can be modeled as a 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order fractional Brownian motion (fBm) process, while the baseline wander noise can be modeled as a 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> order fBm process. We use the eigenvectors of the auto-covariance matrix of the 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order fBm process characterizing the original ECG signal to design an M-channel uniformly decimated filterbank. Noisy ECG signal is fed to this filterbank and the subband signals are processed for removal of baseline wander noise. Performance comparison with other baseline wander removal methods shows the efficacy of the proposed method.

In this paper, we propose a novel method for baseline wander removal from a noisy ECG signal. We use projection operator based approach to remove baseline wander noise from the ECG signal. The noise subspace is generated using sample functions of the first order fBm processes characterizing baseline wander noise. The orthogonal projection of noisy ECG signal onto the noise subspace provides an estimate of baseline wander noise. The estimated noise is subtracted from the noisy input signal to obtain noise-free ECG signal. Performance comparison with other baseline wander removal methods shows the efficacy of the proposed method.

Considering the noise problem of the acquisition signals from mechanical transmission systems, a novel denoising method is proposed that combines Variational Mode Decomposition (VMD) with wavelet thresholding. The key innovat... | Find, read and cite all the research you need on Tech Science Press

Rolling bearings serve as one of the critical elements in rotating machines, and ensuring its fault-free operation is essential for the overall safety and efficiency of the equipment. In recent years, data driven fault diagnosis techniques are extensively proposed for detecting faults in rolling bearing due to rising demands from industry. This work introduces a model for identifying the faults in rolling bearings using variational mode decomposition (VMD), multifractal detrended fluctuation analysis (MFDFA) and optimized one dimensional convolutional neural network (O-1D-CNN). Firstly, with the prevalent noise present in the original vibration signal, a wavelet threshold denoising (WTD) model is employed to effectively denoise the raw vibration signals. Secondly by recognizing the inherent nonlinearity of rolling bearing vibration signals, the VMD technique and MFDFA are exploited for extracting meaningful features. Finally, the features are classified using the O-1D-CNN where the network is an integration of the hybrid red deer algorithm (HRDA) and 1D-CNN. The proposed model is applied to the datasets from experiments and from the Case Western Reserve University (CWRU) for comparison and verification. The results demonstrate that the proposed method has a maximum fault classification accuracy of 99.5% and 99.7% based on the experimental and CWRU dataset respectively.

Study on tool wear state recognition algorithm based on spindle vibration signals collected by homemade tool condition monitoring ring