A New Wavelet Threshold Function and Denoising Application

The signal of wind turbine in vibration and noise testing is often very weak, and it subject to a variety of noise interference in the course of its transmission. The signal with the acceleration sensor caught is often manifested as the signal with weak characteristics in the context of strong noise. In signal analysis, signal de-noising is an indispensable key link. This paper adopting the Donoho's de-noising idea of wavelet threshold function {[1]}, improve and deeply research the Wavelet Threshold Function on the basis of the classical soft and hard threshold de-noising function. The improved threshold function is applied to the diagnosis of the vibration noise of the wind turbine. The signal is analyzed and the product is improved accordingly. The result indicates that the improved threshold function has obvious de-noising effects in comparing with the traditional soft and hard threshold function.

Acoustic emission (AE) detection, as a non-electrical detection method, is very suitable for effective fault detection of power equipment with a strong electromagnetic field. However, the AE signal collected at industrial sites often contains a lot of interference noise, affecting the analysis and prediction of faults. In this study, a wavelet denoising method based on a new threshold function is proposed, to achieve a noise reduction in the low signal-to-noise ratio (SNR) signals. Simulation experiment results show that the proposed threshold function not only overcomes the shortcomings of the discontinuous hard threshold function, but also solves the constant deviation of the soft threshold function. What’s more, the proposed function achieves a good adaptability. When SNR = 10 dB: The SNR of the new threshold is 20.6622, and the RMSE is 0.0026. The SNR of the hard threshold is 20.2246 and the RMSE is 0.0027, compared with the traditional hard threshold method, the SNR of the new threshold is increased by 2.16% and the root mean square error (RMSE) is reduced by 3.7%; the SNR of the soft threshold is 15.5656, and the RMSE is 0.0047, compared with the traditional soft threshold method, the new threshold has a 32.74% increase in SNR and a 40.43% reduction in RMSE. When SNR = -10 dB: The SNR of the new threshold is 4.2602, and the RMSE is 0.0172. The SNR of the hard threshold is 3.8558 and the RMSE is 0.0182, compared with the traditional hard threshold method, the SNR of the new threshold is increased by 10.49% and the RMSE is reduced by 5.49%; the SNR of the soft threshold is 2.1625, and the RMSE is 0.0212, compared with the soft threshold method, SNR is improved by 97% and RMSE is reduced by 18.87%. Performance analyses have proved that the improved wavelet denoising method can obtain a good noise reduction effect. It is very helpful for AE signal analysis with the generally low SNR, which can improve the accuracy of failure identification in subsequent acts.

Based on multi-resolution analysis of wavelet, this article is aimed at building a new soft threshold function for wavelet de-noising, to overcome the discontinuous disadvantage of the hard threshold function. In the area adjacent to the threshold, continuously adjustable nonlinear functions are introduced in piecewise to process the wavelet coefficients more carefully in this area. Consequently, large deviation caused by super-compression of wavelet coefficients when using traditional soft threshold could be avoided, and the nonlinearity of the system is able to be effectively kept. Using both signal to noise ratio (SNR) and mean square error (MSE) as the evaluation indicators, simulation results show that the improved method is more effective than the method based on traditional hard and soft threshold.

For the problem of denoising incomplete phenomenon appeared in the existing wavelet threshold methods, a new kind of threshold function and denoising method of parameter adjustable wavelet threshold is proposed. The traditional hard threshold and soft threshold wavelet had problems such as continuity and constant deviation. Firstly, to construct a new threshold function and theoretically proves the superiority of this new threshold function, as long as choosing the suitable parameter, the new threshold function has a better denoising effect than traditional thresholding function. Secondly, to reduce the deviation between wavelet coefficients and the original, the threshold value is changed with the change of decomposition scale. The experimental results demonstrate that by using the proposed method, whether the Gaussian noise or impulse noise, the signal-to-noise ratio (SNR) of image and the peak signal to noise ratio (PSNR) of image can be greatly improved and the mean square error (MSE) of the image was reduced, the denoising effect is better than other algorithms.

In view of the wheel state monitoring, the wheel vibration signal is often used to reflect the wheel state information, but the original vibration signal contains a lot of noise. In order to extract the effective wheel information, it is necessary to reduce the noise of the original vibration signal. The problems existing in the traditional wavelet threshold denoising method include unreasonable threshold setting, lack of continuity of hard threshold function and fixed deviation of wavelet coefficients processed by soft threshold function. In this paper, the traditional wavelet threshold denoising method is improved from threshold selection and threshold function, and an improved wavelet threshold denoising method is proposed. This method is used to reduce the noise of the measured wheelset vibration signal and compared with the traditional wavelet denoising method from evaluation indexes and graphical results. The results show that the improved wavelet threshold denoising method has better noise reduction effect.

In order to overcome the discontinuance of the hard thresholding function and the defect of seriously slashing singularity in the soft thresholding function, improve the denoising effect and detect the transformer partial discharge signal more accurately, in this paper an improved wavelet threshold denoising method is put forward through analyzing the interference noise of transformer partial discharge signals and studying various wavelet threshold denoising method, especially the wavelet threshold denoising method that overcomes the shortcomings of the hard and soft threshold. Simulation results show that the denoising effect of this method has been greatly improved than the traditional hard and soft threshold method. This method can be widely used in practical transformer partial discharge signal denoising.

Using wavelet analysis for non-stationary signal de-noising of electro-mechanical system is considered to be the best approach, and wavelet threshold de-noising method is the most simple method that needs the minimum amount of calculation. But this method in selecting threshold functions needs to be improved. Based on different domestic and foreign methods of improving threshold function, propose an improved bivariate threshold function. According to the simulation of non-stationary signal de-noising, the results show that the optimal de-noising results of different signals exist by taking different parameters. Compared with all the de-noising effects, application of the bivariate threshold function considering signal-to-noise ratio and mean square error is superior to the traditional soft and hard threshold functions. At the same time, it can significantly improve the filtering precision, and reserve the main signal details while effectively removing the noise well.

The relevant properties of the selected classical threshold function and selected threshold were compared and analyzed for the methods of noisy-image wavelet threshold de-noising. On the basis of this, a new wavelet threshold de-noising function was given in this paper. The new defined threshold function overcomes the shortcoming which the hard threshold function and the soft threshold function on higher derivatives are discontinuous by adding a variable. Theoretical analysis and experimental results show that, the constructed wavelet threshold de-noising function possess the better adaptability and de-noising effect. In the case of strong Gauss noise for the image, relatively soft threshold method, the PSNR of a new threshold de-noising method can be improved from 4dB to 6dB.

Unlike inflexible structure of soft and hard threshold function, a unified linear matrix form with flexible structure for threshold function is proposed. Based on the unified linear flexible structure threshold function, both supervised and unsupervised subband adaptive denoising frameworks are established. To determine flexible coefficients, a direct mean-square error (MSE) minimization is conducted in supervised denoising while Stein’s unbiased risk estimate as a MSE estimate is minimized in unsupervised denoising. The SURE rule requires no hypotheses or a priori knowledge about clean signals. Furthermore, we discuss conditions to obtain optimal coefficients for both supervised and unsupervised subband adaptive denoising frameworks. Applying an Odd-Term Reserving Polynomial (OTRP) function as concrete threshold function, simulations for polynomial order, denoising performance, and noise effect are conducted. Proper polynomial order and noise effect are analyzed. Both proposed methods are compared with soft and hard based denoising technologies—VisuShrink, SureShrink, MiniMaxShrink, and BayesShrink—in denoising performance simulation. Results show that the proposed approaches perform better in both MSE and signal-to-noise ratio (SNR) sense.

In the wavelet packet threshold denoising algorithm, retaining as many of the original signal wavelet packet coefficients as possible is necessary while eliminating noise. Due to the lack of an adaptive parameter, the traditional soft and hard threshold functions cannot be adjusted adaptively, and the useful signal is always mixed with noise, which leads to insecurity of the Internet of Things (IoT) application. Therefore, this paper discusses the significance and feasibility of sample entropy as an adaptive parameter in the wavelet packet threshold function. Furthermore, a new threshold function is proposed to improve the traditional wavelet packet denoising algorithm. The algorithm can process the wavelet packet coefficients differently for different noise backgrounds to achieve better denoising effect, thereby improving the security of the IoT. The simulation results show that compared with the classical wavelet packet threshold function, the proposed improved algorithm achieves better denoising effect and is beneficial to enhance the security of IoT applications.

Wavelet de-noising method is often used in the processing of magnetotelluric (MT) signal, and the wavelet hard and soft threshold de-noising method are the most popular although there is much room for improvement in the threshold function selection and threshold determination. A new adaptive wavelet threshold de-noising method was proposed by selecting a new threshold function and presenting an adaptive method for obtaining optimal threshold based on the multi-resolution Stein unbiased risk estimation. New threshold function and an adaptive method to determine threshold were discussed, and the principle and implementation of the algorithm were given. The simulated signal and the measured MT data contaminated by impulse interference were analyzed, and the obtained results were compared with those of the conventional wavelet hard and soft threshold de-noising methods. The results show that the proposed method overcomes the defects of the traditional wavelet soft and hard threshold due to a new threshold function, and a new method to determine the threshold of each layer is applied and provides an adaptive method for filtering MT data in the wavelet domain that requires a minimum of human intervention. The presented de-noising method is very suitable for suppressing the impulse interference for MT data and can get higher signal-to-noise ratio than the traditional wavelet threshold de-noising methods. After de-noising, the accurate data is loaded for further impedance estimation and geological interpretation.

Broiler sound signal filtering method based on improved wavelet denoising and effective pulse extraction

The measurement of downhole engineering parameters is greatly disturbed by the working environment. Effective de-noising methods are required for processing logging-while-drilling (LWD) acquisition signals, in order to obtain downhole engineering parameters accurately and effectively. In this paper, a new de-noising method for measuring downhole engineering parameters was presented, based on a feedback method and a wavelet transform threshold function. Firstly, in view of the mutability and density of downhole engineering data, an improved wavelet threshold function was proposed to de-noise the signal, so as to overcome the shortcomings of data oscillation and deviation caused by the traditional threshold function. Secondly, due to the unknown true value, traditional single denoising effect evaluation cannot meet the requirements of quality evaluation very well. So the root mean square error (RMSE), signal-to-noise ratio (SNR), smoothness (R) and fusion indexs (F) are used as the evaluation parameters of the de-noising effect, which can determine the optimal wavelet decomposition scale and the best wavelet basis. Finally, the proposed method was verified based on the measured downhole data. The experimental results showed that the improved wavelet de-noising method could reduce all kinds of interferences in the LWD signal, providing reliable measurement for analyzing the working status of the drilling bit.

Electric energy signals are often contaminated by noise during the collection process, which affects the accurate positioning of disturbances. The discontinuity of traditional hard threshold functions can lead to oscillations, while excessive smoothness of soft threshold functions can lead to signal distortion. The optimized threshold function and scale adaptive processing on the selection of the threshold are proposed. The wavelet thresholding method is used to process voltage sag, rise, and interrupt signals containing noise. The denoised signal is decomposed into five scale wavelets using db7 wavelet and detected by using wavelet transform modulus maximum and signal singularity principle. Experiments have shown that optimized threshold and threshold function not only effectively denoise but also retain the effective mutation point information in the original signal, and the new method is reliable in detection.

Stock is one type of long-term investment in the capital market. The stock movement indicator that is most often used in analysis by investors is the Indonesia Composite Index (ICI). ICI data is a variety of time series data, so it can be analyzed using forecasting. One forecasting method that can be used is the wavelet thresholding method. The wavelet threshold can analyze stationary, non-stationary, and nonlinear time series data by producing smooth estimates. The wavelet threshold has a wavelet filter and threshold parameters and threshold functions that can be used in analyzing. In this study MSE was assessed from several wavelet filters namely haar, daubechies, and coiflets filters at levels 1 to 7 with the thresholding function namely soft thresholding and thresholding parameters, namely minimax thresholding and sure thresholding. The data used is IHGS data in 2018 totaling 240 data. Based on the data analysis performed, MSE was obtained which means that the best filter provided in order 2 wavelet coiflet filter at level 2 and thresholding parameter is sure of thresholding with MSE value of 0.0094