Improved wavelet packet denoising algorithm using fuzzy threshold and correlation analysis for chaotic signals

When the wavelet packet is used to extract signal, the result is greatly affected by the coefficient quantization threshold. It is difficult for the threshold to reflect the current state of the signal accurately, which leads to the failure of signal extraction. A novel method of extracting signal based on fuzzy threshold for wavelet packet is proposed in this paper. The wavelet packet decomposition coefficient is quantified by fuzzy threshold method. The concept of the maximum value of noise to signal ratio is given to characterize the signal's strength compared to the noise in the simulation experiment. The frequency distribution probability is computed. The maximum value of noise to signal ratio and the frequency distribution probability are used as fuzzy input. To make the computing of fuzzy threshold conveniently, the fuzzy output is set by fixed value. The simulation results show that the method can meet the needs of different frequency signals, compared to conventional filtering and matched filtering, the novel method can inhibit the influence of the noise on the signal effectively, enhance the signal extraction ability and improve the detection distance.

The vibration signals of diesel include excess noise that must be eliminated before extraction of characteristic parameters. Firstly, the effects of vibration-signal de-noising among Fourier transform, wavelet decomposition and wavelet packet decomposition are compared. Secondly, singular value decomposition is applied to de-noising vibration signals. Finally, a new de-noise method integrated with wavelet packet and singular value is presented. In this method, vibration signals are decomposed by wavelet packet, and the wavelet packet coefficient is de-noised by singular value decomposition again. The results indicate that the new de-noising method is the best. The SNR (signal-to-noise ratio) of the vibration signals of a diesel cylinder lid is the highest. The diesel vibration waveforms of combustion and valve become clear and the extracted characteristic parameters become more precise.

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.

It was suggested that spectrum estimation can be accomplished by applying wavelet denoising methodology to wavelet packet coefficients derived from the logarithm of a spectrum estimate. The particular algorithm we consider consists of computing the logarithm of the multitaper spectrum estimator, applying an orthonormal transform derived from a wavelet packet tree to the log multitaper spectrum ordinates, thresholding the empirical wavelet packet coefficients, and then inverting the transform. For a small number of tapers, suitable transforms/partitions for the logarithm of the multitaper spectrum estimator are derived using a method matched to statistical thresholding properties. The partitions thus derived starting from different stationary time series are all similar and easily derived, and any differences between the wavelet packet and discrete wavelet transform (DWT) approaches are minimal. For a larger number of tapers, where the chosen parameters satisfy the conditions of a proven theorem, the simple DWT again emerges as appropriate. Hence, using our approach to thresholding and the method of partitioning, we conclude that the DWT approach is a very adequate wavelet-based approach and that the use of wavelet packets is unnecessary.

Partial discharge (PD) in insulators will not only lead to the gradual degradation of insulation performance but even cause power system failure in serious cases. Because there is strong noise interference in the field, it is difficult to accurately locate the position of the PD source. Therefore, this paper proposes a three-dimensional spatial localization method of the PD source with a four-element ultra-high-frequency (UHF) array based on improved wavelet packet dynamic threshold denoising and the generalized cross-correlation algorithm. Firstly, considering the field noise interference, the PD signal is decomposed into sub-signals with different frequency bands by the wavelet packet, and the corresponding wavelet packet coefficients are extracted. By using the improved threshold function to process the wavelet packet coefficients, the PD signal with low distortion rate and high signal-to-noise ratio (SNR) is reconstructed. Secondly, in order to solve the problem that the amplitude of the first wave of the PD signal is small and the SNR is low, an improved weighting function, , is proposed, which is based on the self-power spectral density of the signal and is adjusted by introducing an exponential factor to improve the accuracy of the first wave arrival time and time difference calculation. Finally, the influence of different sensor array shapes and PD source positions on the localization results is analyzed, and a reasonable arrangement scheme is found. In order to verify the performance of the proposed method, simulation and experimental analysis are carried out. The results show that the improved wavelet packet denoising algorithm can effectively realize the separation of PD signal and noise and improve the SNR of the localization signal with low distortion rate. The improved weighting function significantly improves the estimation accuracy of the time difference between UHF sensors. With the sensor array designed in this paper, the relative localization error is 3.46%, and the absolute error is within 6 cm, which meets the requirements of engineering applications.

Classification of electroencephalogram (EEG) signals is an important task in the brain computer interface system. This paper presents two combination strategies of feature extraction on EEG signals. In the first strategy, Autoregressive coefficients and approximate entropy are calculated respectively, and the features are obtained by assembling them. In the second strategy, the EEG signals are first decomposed into sub-bands by wavelet packet decomposition. Wavelet packet coefficients are then sent to the autoregressive model to calculate autoregressive coefficients, which are used as features extracted from the original EEG signals. These features are fed to support vector machine for classifying the EEG signals. The classification accuracy has been used for evaluating the classification performance. Experimental results in five mental tasks show that the combination strategies can effectively improve the classification performance when the order of autoregressive model is greater than 5, and the second strategy is superior to the first one in terms of the classification accuracy.

This paper proposes a new method for building time series model to predict machine vibration values. Instead of building a time series model based on the raw machine vibration signal, the vibration signal will be first decomposed into different levels using wavelet packet decomposition (WPD). Sub-signals can be reconstructed from those wavelet packet coefficients. Time series model is built for each of those sub-signals, using adaptive neuro-fuzzy inference system (ANFIS). The final prediction value is the sum of the prediction values of all the models. Comparing to the other two methods, which are building ANFIS model based on the raw vibration signal and building ANFIS models based on the sub-signals generated with discrete wavelet decomposition, experimental results show that the method using ANFIS and WPD outperforms the other two methods.

In this paper, a novel method for stator interturn short circuit fault diagnosis in induction motors using the wavelet packet analysis is presented. Wavelet packet analysis is the extension of wavelet analysis and decompose signal into the equal bandwidth, it can achieve better decomposition result than wavelet analysis does. In the operating induction motor, electromagnetic torque is sensitive to the asymmetry due to the fault. Research indicate that the interturn short circuit fault will give rise to the sidebands at some given harmonic components of the electromagnetic torque signal and some certain frequency components change evidently, the distribution of the energy in the certain frequency bands alter as well. In the proposed method, electromagnetic torque signal is analyzed via wavelet packet decomposition and the wavelet packet coefficients are extracted. Based on each coefficient's energy eigenvalue, an eigenvector is set up. The presence of the short circuit fault makes the eigenvector change by a special rule, and the fluctuation of the load or supply unbalance make it change in another way, so it is immune to the variety of load and supply. Experimental results demonstrate the validity and effectiveness of this method.

Fault degradation assessment of water hydraulic motor by impulse vibration signal with Wavelet Packet Analysis and Kolmogorov–Smirnov Test

In order to extract the week fault features contained in the vibration signal of the mechanical equipment, a new de-nosing method based on dual-tree complex wavelet packet transform (DTCWPT) and principal manifold was proposed. Firstly, the vibration signals were decomposed into several sub-frequency bands by DTCWPT, the Shannon entropy was used to seek the best basis of DTCWPT, and a new adaptive threshold function was employed to denoise the wavelet packet coefficients on the best basis of the real part and imaginary part of DTCWPT via the de-noising criterion, then the wavelet packet coefficients were reconstructed into a high dimensional space. Secondly, t-distributed stochastic neighbor embedding (t-SNE) was performed to extract a low dimensional manifold, the proposed threshold function was further applied to process the low dimensional manifold, aiming at separate the signal and noise, the principal manifold was reconstructed by the method of spectral regression analysis, thus, the signals were reconstructed back into one dimensional time series after eliminating the noise. Finally, a simulated signal and a real bearing fault signal were used to validate the proposed method, the results have demonstrated that the proposed method has a good performance of nonlinear noise reduction, and can extract fault features of rolling bearing effectively.

A human face representation and recognition system, based on the wavelet packet method and the best basis selection algorithm, is proposed. Through conducting a set of experiments on three groups of training sets, the optimal transform basis (called the face basis), the best filter, and the best decomposition level are identified for the face image class. A face image is represented in a compressed form by its wavelet packet coefficients. For recognition, the compressed input face image is then compared against a database of compressed images of the known faces. The recognition results are presented.

Driver behavior and intention recognition affects traffic safety. Many scholars use the steering wheel angle, distance of the brake pedal, distance of the accelerator pedal, and turn signal as input data to identify driver behaviors and intentions. However, in terms of time, the acquisition of these parameters has a relative delay, which lengthens the identification time. Therefore, this study uses drivers’ EEG (electroencephalograph) data as input parameters to identify driver behaviors and intentions. The key to the driving intention recognition of EEG signals is to reduce their noise. Noise interference has a significant influence on EEG driving intention recognition. To substantially denoise EEG signals, this study selects wavelet transform theory and wavelet packet transform technology, collects the EEG signals during driving, uses the threshold noise reduction method on EEG signals to reduce noise, and achieves noise reduction through wavelet packet reconstruction. After the wavelet packet coefficients of EEG signals are obtained, the energy characteristics of the wavelet packet coefficients are extracted as input to the Bayesian theoretical model for driver behavior and intention recognition. Results show that the maximum recognition rate of the Bayesian theoretical model reaches 82.6%. Early driver behavior and intention recognition has important research significance for traffic safety and sustainable traffic development.

In order to improve the denoising effect of the pulsar signal, a new denoising method is proposed in the no-subsampling wavelet packet domain based on the local Laplace prior model. First, we count the true noise-free pulsar signal’s wavelet packet coefficient distribution characteristics and construct the true signal wavelet packet coefficients’ Laplace probability density function model. Then, we estimate the denosied wavelet packet coefficients by using the noisy pulsar wavelet coefficients based on maximum a posteriori criteria. Finally, we obtain the denoisied pulsar signal through no-subsampling wavelet packet reconstruction of the estimated coefficients. The experimental results show that the proposed method performs better when calculating the pulsar time of arrival than the translation-invariant wavelet denoising method.

Electroconvulsive therapy (ECT) is an effective treatment for severe depression. In this paper, we have used an algorithm based on wavelet packet (WP) analysis of EEG signals to detect seizures induced by ECT. After determining dominant frequency bands in the ictal period during ECT, the energy ratio of these bands was computed using the corresponding WP coefficients. This ratio was then used as an index to recognize seizure periods. Four different approaches to detect ECT seizures were employed in 41 EEG recordings from nine patients. Sensitivity in ECT seizure detection ranged from 76 to 95% while the false detection rate ranged from 6 to 13.

An efficient wavelet-based feature selection (FS) method is proposed in this paper for subject recognition using ground reaction force measurements. Our approach relies on a local fuzzy evaluation measure with respect to patterns that reveal the adequacy of data coverage for each feature. Furthermore, FS is driven by a fuzzy complementary criterion (FuzCoC) which assures that those features are iteratively introduced, providing the maximum additional contribution with regard to the information content given by the previously selected features. On the basis of the principles of FuzCoC, we develop two novel techniques. At Stage 1, wavelet packet (WP) decomposition of gaits is accomplished to obtain a set of discriminating frequency sub-bands. A computationally simple FS method is then applied at Stage 2, providing a compact set of powerful and complementary features, from WP coefficients. The quality of our approach is validated via comparative analysis against existing methods on gait recognition.