Denoising Method of Train Vibration Signal Based on Improved Wavelet Threshold

In order to improve the effects of denoising, this paper introduces the basic principles of wavelet threshold denoising and traditional structures threshold functions. Meanwhile, it proposes wavelet threshold function and fixed threshold formula which are both improved here. First, this paper studies the problems existing in the traditional wavelet threshold functions and introduces the adjustment factors to construct the new threshold function basis on soft threshold function. Then, it studies the fixed threshold and introduces the logarithmic function of layer number of wavelet decomposition to design the new fixed threshold formula. Finally, this paper uses hard threshold, soft threshold, Garrote threshold, and improved threshold function to denoise different signals. And the paper also calculates signal-to-noise (SNR) and mean square errors (MSE) of the hard threshold functions, soft thresholding functions, Garrote threshold functions, and the improved threshold function after denoising. Theoretical analysis and experimental results showed that the proposed approach could improve soft threshold functions with constant deviation and hard threshold with discontinuous function problems. The proposed approach could improve the different decomposition scales that adopt the same threshold value to deal with the noise problems, also effectively filter the noise in the signals, and improve the SNR and reduce the MSE of output signals.

Vibration component separation by iteratively using stochastic resonance with different frequency-scale ratios

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.

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

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.

HighlightsWhat are the main findings?A joint denoising framework (ICFO–SVMD–improved wavelet thresholding) is proposed which adaptively optimizes SVMD parameters and sub-band thresholds for nonlinear, non-stationary vibration signals.Simulation and experimental results on bearing and gearbox vibration data show that the proposed method outperforms VMD, SVMD, VMD–WTD, CFO–SVMD, and traditional wavelet denoising in terms of SNR, RMSE, RVR, and SER while better preserving transient fault features.What are the implications of the main findings?The proposed method provides a robust preprocessing tool for vibration-based condition monitoring under strong noise, improving the reliability of fault feature extraction and fault diagnosis in rotating machinery.The ICFO–SVMD–WTD framework is generic and can be extended to other noisy engineering signals that require joint decomposition and adaptive thresholding.Non-stationary, multi-component vibration signals in rotating machinery are easily contaminated by strong background noise, which masks weak fault features and degrades diagnostic reliability. This paper proposes a joint denoising method that combines an improved cordyceps fungus optimization algorithm (ICFO), successive variational mode decomposition (SVMD), and an improved wavelet thresholding scheme. ICFO, enhanced by Chebyshev chaotic initialization, a longitudinal–transverse crossover fusion mutation operator, and a thinking innovation strategy, is used to adaptively optimize the SVMD penalty factor and number of modes. The optimized SVMD decomposes the noisy signal into intrinsic mode functions, which are classified into effective and noise-dominated components via the Pearson correlation coefficient. An improved wavelet threshold function, whose threshold is modulated by the sub-band signal-to-noise ratio, is then applied to the effective components, and the denoised signal is reconstructed. Simulation experiments on nonlinear, non-stationary signals with different noise levels (SNR = 1–20 dB) show that the proposed method consistently achieves the highest SNR and lowest RMSE compared to VMD, SVMD, VMD–WTD, CFO–SVMD, and WTD. Tests on CWRU bearing data and gearbox vibration signals with added −2 dB Gaussian white noise further confirm that the method yields the lowest residual variance ratio and highest signal energy ratio while preserving key fault characteristic frequencies.

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.

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.

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.

Based on the Multi-analysis wavelet threshold denosing method which is put forward by D. L. Dohono and I. M. Johnstone, a new threshold function is posed. This new threshold function has many advantages over the classical soft and hard threshold function. It is clear in physics meaning and simple in expression. The experimental results show that this improved method is effective in removing white noise, and gives better RMSE performance and SNR gains than soft and hard threshold methods, and makes it possible to embody the advantages of the wavelet threshold denoising method more fully.

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.

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.

Rotating devices such as gears often generate fault vibration signals during eration. Under the interference of strong external noise, it is often difficult to extract these weak fault feature. To this end, a method based on Complementary Ensemble Empirical Mode Decomposition (CEEMD) and Singular Spectrum Analysis (SSA) is proposed to reduce the noise of the gear signals. Firstly, original vibration signals are decomposed into a series of intrinsic mode functions (IMFs) by CEEMD, and the reconstructed signals are obtained after the some IMFs are removed according to evaluation coefficients. Then, the reconstructed signals are further denoised using SSA. After singular value decomposition, grouping and reconstruction, the denoised time series are obtained. The actual gear vibration signals from the QPZZ-II rotating machinery fault simulation rig are used to verify the effectiveness of the proposed method. The results of comparing with the different denoising methods show that the presented method can effectively depress the strong noise, and extract weak fault feature.

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.

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.