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Recently, the convolutional neural network (ConvNet) has a wide application in the classification of motor imagery EEG signals. However, the low signal-to-noise electroencephalogram (EEG) signals are collected under the interference of noises. However, the conventional ConvNet model cannot directly solve this problem. This study aims to discuss the aforementioned issues.

To solve this problem, this paper adopted a novel residual shrinkage block (RSB) to construct the ConvNet model (RSBConvNet). During the feature extraction from EEG signals, the proposed RSBConvNet prevented the noise component in EEG signals, and improved the classification accuracy of motor imagery. In the construction of RSBConvNet, the author applied the soft thresholding strategy to prevent the non-related motor imagery features in EEG signals. The soft thresholding was inserted into the residual block (RB), and the suitable threshold for the current EEG signals distribution can be learned by minimizing the loss function. Therefore, during the feature extraction of motor imagery, the proposed RSBConvNet de-noised the EEG signals and improved the discriminative of classification features.

Comparative experiments and ablation studies were done on two public benchmark datasets. Compared with conventional ConvNet models, the proposed RSBConvNet model has obvious improvements in motor imagery classification accuracy and Kappa coefficient. Ablation studies have also shown the de-noised abilities of the RSBConvNet model. Moreover, different parameters and computational methods of the RSBConvNet model have been tested on the classification of motor imagery.

Based on the experimental results, the RSBConvNet constructed in this paper has an excellent recognition accuracy of MI-BCI, which can be used for further applications for the online MI-BCI.

This paper aims to explore a new wavelet adaptive threshold de-noising method to resolve the shortcomings of wavelet hard-threshold method and wavelet soft-threshold method, which are usually used in gear fault diagnosis.

A new threshold function and a new determined method of threshold for each layer are proposed. The principle and the implementation of the algorithm are given. The simulated signal and the measured gear fault signal are analyzed, and the obtained results are compared with those from wavelet soft-threshold method, wavelet hard-threshold method and wavelet modulus maximum method.

The presented wavelet adaptive threshold method overcomes the defects of the traditional wavelet threshold method, and it can effectively eliminate the noise hidden in the gear fault signal at different decomposition scales. It provides more accurate information for the further fault diagnosis.

A new threshold function is adopted and the multi-resolution unbiased risk estimation is used to determine the adaptive threshold, which overcomes the defect of the traditional wavelet method.

Denoising of the vibration signal is crucial to identify a structure's damage. Based on noise frequency character, the “real” vibration signal can be gotten. The purpose of this paper is to propose a novel method for denoising a signal based on the wavelet transform.

The vibration signal with noise which can be collected by wireless network is decomposed by wavelet transform. In order to select optimal level of wavelet decomposition, based on noise's frequency, power spectral density is used. A soft thresholding method based on minimum mean‐variance is used for vibration signal de‐noising with Gaussian noise.

A novel method has been described in his paper. Based on the relationship between vibration signal's character and noise frequency, the way to get rid of noise is combined wavelet transform with power spectral density.

In order to select optimal level of wavelet decomposition, based on noise's frequency, power spectral density is used. A soft thresholding method based on minimum mean‐variance is used for vibration signal denoising with Gaussian noise.

The purpose of this paper is to apply the wavelet thresholding technique in order to analyze economic socio-political situations in Tunisia using textual data sets. This technique is used to remove noise from contingency table. A comparative study is done on correspondence analysis and classification results (using k-means algorithm) before and after denoising.

Textual data set is collected from an electronic newspaper that offers actual economic news about Tunisia. Both the hard and the soft-thresholding techniques are applied based on various Daubechies wavelets with different vanishing moments.

The results obtained have proved the effectiveness of wavelet denoising method in textual data analysis. On one hand, this technique allowed reducing the loss of information generated by correspondence analysis, ensured a better quality of representation of the factorial plan, neglected the interest of lemmatization in textual analysis and improved the results of classification by k-means algorithm. On the other hand, the proximities provided by the factorial visualization validate the economic situation of Tunisia during the studied period showing mainly a stable situation before the revolution and a deteriorated one after the revolution.

The results are the first to analyze economic socio-political relations using textual data. The originality of this paper comes also from the joint use of correspondence analysis and wavelet thresholding in textual data analysis.

In real working condition, signal is highly disturbed and even drowned by noise, which extremely interferes in detecting results. Therefore, this paper aims to provide an effective de-noising method for the debris particle in lubricant so that the ultrasonic technique can be applied to the online debris particle detection.

For completing the online ultrasonic monitoring of oil wear debris, the research is made on some selected wear debris signals. It applies morphology component analysis (MCA) theory to de-noise signals. To overcome the potential weakness of MCA threshold process, it proposes fuzzy morphology component analysis (FMCA) by fuzzy threshold function.

According to simulated and experimental results, it eliminates most of the wear debris signal noises by using FMCA through the signal comparison. According to the comparison of simulation evaluation index, it has highest signal noise ratio, smallest root mean square error and largest similarity factor.

The rapid movement of the debris particles, as well as the lubricant temperature, may influence the measuring signals. Researchers are encouraged to solve these problems further.

This paper includes implications for the improvement in the online debris detection and the development of the ultrasonic technique applied in online debris detection.

This paper provides a promising way of applying the MCA theory to de-noise signals. To avoid the potential weakness of the MCA threshold process, it proposes FMCA through fuzzy threshold function. The FMCA method has great obvious advantage in de-noising wear debris signals. It lays the foundation for online ultrasonic monitoring of lubrication wear debris.

The purpose of this paper is to reduce the destructive effects of existing unavoidable noises contaminating temperature data in inverse heat conduction problems (IHCP) utilizing the wavelets.

For noise reduction, sensor data were treated as input to the filter bank used for signal decomposition and implementation of discrete wavelet transform. This is followed by the application of wavelet denoising algorithm that is applied on the wavelet coefficients of signal components at different resolution levels. Both noisy and de‐noised measurement temperatures are then used as input data to a numerical experiment of IHCP. The inverse problem deals with an estimation of unknown surface heat flux in a 2D slab and is solved by the variable metric method.

Comparison of estimated heat fluxes obtained using denoised data with those using original sensor data indicates that noise reduction by wavelet has a potential to be a powerful tool for improvement of IHCP results.

Noise reduction using wavelets, while it can be implemented very easily, may also significantly relegate (or even eliminate) conventional regularization schemes commonly used in IHCP.

The purpose of this paper is to investigate the condition of insulation in high-voltage equipments using partial discharge (PD) measurements. It proposes the methods to eliminate several noises like white noise, random noise and discrete spectral interferences which severely pollutes the PD signals. The study aims to remove these noises from the PD signal effectively by preserving the signal features.

This paper employs fast Fourier transform, discrete wavelet transform and translational invariant wavelet transform (TIWT) for denoising the PD signals. The simulated damped exponential pulse and damped oscillatory pulse with low- and high-level noises and a measured PD signal are considered for this analysis. The conventional wavelet denoising approach is also improved by estimating the automated global optimum threshold value using genetic algorithm (GA). The statistical parameters are evaluated and compared. Among these methods, GA-based TIWT approach provides robustness and reduces computational complexity.

This paper provides effective condition monitoring of power apparatus using GA-based TIWT approach. This method provides the low value of mean square error, pulse amplitude distortion and also high reduction in noise level due to its robustness and reduced computational complexity. It suggests that this approach works well for both signals immersed in noise as well as for noise immersed in signals.

Because of the chosen PD signals, the research results may lack for multiple discharges. Therefore, researchers are encouraged to test the proposed propositions further.

The paper includes implication for the development of online testing for equipment analysis and diagnostics during normal operating condition. Corrective actions can be planned and implemented, resulting in reduced unscheduled downtime.

This PD-based analysis often present well in advance of insulation failure, asset managers can monitor it over time and make informed strategic decisions regarding the repair or replacement of the equipment. These predictive diagnostics help society to prioritize investments before an unexpected outage occurs.

This paper provides an enhanced study of condition monitoring of HV power apparatus by which life time of insulation can be increased by taking preventive measures.

The real challenges in online crack detection testing based on guided waves are random noise as well as narrow-band coherent noise; and to achieve efficient structural health assessment methodology, magnificent extraction of noise and analysis of the signals are essential. The purpose of this paper is to provide optimal noise filtering technique for Lamb waves in the diagnosis of structural singularities.

Filtration of time-frequency information of guided elastic waves through the noisy signal is investigated in the present analysis using matched filtering technique which “sniffs” the signal buried in noise and most favorable mother wavelet based denoising methods. The optimal wavelet function is selected using Shannon’s entropy criterion and verified by the analysis of root mean square error of the filtered signal.

Wavelet matched filter method, a newly developed filtering technique in this work and which is a combination of the wavelet transform and matched filtering method, significantly improves the accuracy of the filtered signal and identifies relatively small damage, especially in enormously noisy data. A comparative study is also performed using the statistical tool to know acceptability and practicability of filtered signals for guided wave application.

The proposed filtering techniques can be utilized in online monitoring of civil and mechanical structures. The algorithm of the method is easy to implement and found to be successful in accurately detecting damage.

Although many techniques have been developed over the past several years to suppress random noise in Lamb wave signal but filtration of interferences of wave modes and boundary reflection is not in a much matured stage and thus needs further investigation. The present study contains detailed information about various noise filtering methods, newly developed filtration technique and their efficacy in handling the above mentioned issues.

The purpose of this paper is to identify significant factors of environmental variables and pollutants that have an effect on PM_2.5 through wavelet and regression analysis.

In order to provide stable data set for regression analysis, multiresolution analysis using wavelets is conducted. For the sampled data, multicollinearity among the independent variables is removed by using principal component analysis and multiple linear regression analysis is conducted using PM_2.5 as a dependent variable.

It is found that few pollutants such as NO₂, NO_x, SO₂, benzene and environmental factors such as ambient temperature, solar radiation and wind direction affect PM_2.5. The regression model developed has high R² value of 91.9 percent, and the residues are stationary and not correlated indicating a sound model.

The research provides a framework for extracting stationary data and other important features such as change points in mean and variance, using the sample data for regression analysis. The work needs to be extended across all areas in India and for various other stationary data sets there can be different factors affecting PM_2.5.

Control measures such as control charts can be implemented for significant factors.

Rules and regulations can be made more stringent on the factors.

The originality of this paper lies in the integration of wavelets with regression analysis for air pollution data.

Multiresolution representations of data are classical tools in image processing applications. The purpose of this paper is to discuss a particular problem, obtaining good reconstructions of noise images.

A nonlinear multiresolution scheme within Harten's framework corresponding to a nonlinear cell‐average technique is used for color image denoising.

This paper finds it is possible, for example, to apply the theoretical framework to case studies in internationally operating companies delivering a mix of goods and services.

The present study provides a starting point for further research in the denoising problems using nonlinear techniques.

Moreover, the proposed framework has proven to be useful in improving the classical linear multiresolution approaches.