Continuous Empirical Wavelets Systems

2020 ◽  
pp. 2050006 ◽  
Author(s):  
Jérôme Gilles
Keyword(s):  
Wavelet Transform ◽  
General Framework ◽  
Sufficient Conditions ◽  
Continuous Case ◽  
Reconstruction Formula ◽  
General Properties ◽  
Empirical Wavelet Transform ◽  
Mother Wavelets

The recently proposed empirical wavelet transform was based on a particular type of filter. In this paper, we aim to propose a general framework for the construction of empirical wavelet systems in the continuous case. We define a well-suited formalism and then investigate some general properties of empirical wavelet systems. In particular, we provide some sufficient conditions to the existence of a reconstruction formula. In the second part of the paper, we propose the construction of empirical wavelet systems based on some classic mother wavelets.

scholarly journals Low-Pass Filtering Empirical Wavelet Transform Machine Learning Based Fault Diagnosis for Combined Fault of Wind Turbines

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 975
Author(s):  
Yancai Xiao ◽  
Jinyu Xue ◽  
Mengdi Li ◽  
Wei Yang
Keyword(s):  
Machine Learning ◽  
Wavelet Transform ◽  
Fault Diagnosis ◽  
Wind Turbine ◽  
Wind Turbines ◽  
Gear Tooth ◽  
Support Vector ◽  
Grey Wolf Optimizer ◽  
Empirical Wavelet Transform ◽  
Low Pass

Fault diagnosis of wind turbines is of great importance to reduce operating and maintenance costs of wind farms. At present, most wind turbine fault diagnosis methods are focused on single faults, and the methods for combined faults usually depend on inefficient manual analysis. Filling the gap, this paper proposes a low-pass filtering empirical wavelet transform (LPFEWT) machine learning based fault diagnosis method for combined fault of wind turbines, which can identify the fault type of wind turbines simply and efficiently without human experience and with low computation costs. In this method, low-pass filtering empirical wavelet transform is proposed to extract fault features from vibration signals, LPFEWT energies are selected to be the inputs of the fault diagnosis model, a grey wolf optimizer hyperparameter tuned support vector machine (SVM) is employed for fault diagnosis. The method is verified on a wind turbine test rig that can simulate shaft misalignment and broken gear tooth faulty conditions. Compared with other models, the proposed model has superiority for this classification problem.

scholarly journals Fault Diagnosis of a Helical Gearbox Based on an Adaptive Empirical Wavelet Transform in Combination with a Spectral Subtraction Method

2019 ◽  
Vol 9 (8) ◽  
pp. 1696 ◽  
Author(s):  
Wang ◽  
Lee
Keyword(s):  
Wavelet Transform ◽  
Fault Diagnosis ◽  
Background Noise ◽  
Vibration Signal ◽  
Spectral Subtraction ◽  
Accurate Identification ◽  
Side Band ◽  
Empirical Wavelet Transform ◽  
Gear Fault ◽  
Fault Characteristic

Fault characteristic extraction is attracting a great deal of attention from researchers for the fault diagnosis of rotating machinery. Generally, when a gearbox is damaged, accurate identification of the side-band features can be used to detect the condition of the machinery equipment to reduce financial losses. However, the side-band feature of damaged gears that are constantly disturbed by strong jamming is embedded in the background noise. In this paper, a hybrid signal-processing method is proposed based on a spectral subtraction (SS) denoising algorithm combined with an empirical wavelet transform (EWT) to extract the side-band feature of gear faults. Firstly, SS is used to estimate the real-time noise information, which is used to enhance the fault signal of the helical gearbox from a vibration signal with strong noise disturbance. The empirical wavelet transform can extract amplitude-modulated/frequency-modulated (AM-FM) components of a signal using different filter bands that are designed in accordance with the signal properties. The fault signal is obtained by building a flexible gear for a helical gearbox with ADAMS software. The experiment shows the feasibility and availability of the multi-body dynamics model. The spectral subtraction-based adaptive empirical wavelet transform (SS-AEWT) method was applied to estimate the gear side-band feature for different tooth breakages and the strong background noise. The verification results show that the proposed method gives a clearer indication of gear fault characteristics with different tooth breakages and the different signal-noise ratio (SNR) than the conventional EMD and LMD methods. Finally, the fault characteristic frequency of a damaged gear suggests that the proposed SS-AEWT method can accurately and reliably diagnose faults of a gearbox.

Classification of Sleep Stages Using Multi-wavelet Time Frequency Entropy and LDA

2010 ◽  
Vol 49 (03) ◽  
pp. 230-237 ◽  
Author(s):  
K. Lweesy ◽  
N. Khasawneh ◽  
M. Fraiwan ◽  
H. Wenz ◽  
H. Dickhaus ◽  
...  
Keyword(s):  
Feature Extraction ◽  
Wavelet Transform ◽  
Discriminant Analysis ◽  
Sleep Stage ◽  
Continuous Wavelet ◽  
Eeg Signal ◽  
Linear Discriminant ◽  
Time Frequency ◽  
Mother Wavelets ◽  
Sleep Stage Scoring

Summary Background: The process of automatic sleep stage scoring consists of two major parts: feature extraction and classification. Features are normally extracted from the polysomno-graphic recordings, mainly electroencephalograph (EEG) signals. The EEG is considered a non-stationary signal which increases the complexity of the detection of different waves in it. Objectives: This work presents a new technique for automatic sleep stage scoring based on employing continuous wavelet transform (CWT) and linear discriminant analysis (LDA) using different mother wavelets to detect different waves embedded in the EEG signal. Methods: The use of different mother wave-lets increases the ability to detect waves in the EEG signal. The extracted features were formed based on CWT time frequency entropy using three mother wavelets, and the classification was performed using the linear discriminant analysis. Thirty-two data sets from the MIT-BIH database were used to evaluate the performance of the proposed method. Results: Features of a single EEG signal were extracted successfully based on the time frequency entropy using the continuous wavelet transform with three mother wavelets. The proposed method has shown to outperform the classification based on a CWT using a single mother wavelet. The accuracy was found to be 0.84, while the kappa coefficient was 0.78. Conclusions: This work has shown that wavelet time frequency entropy provides a powerful tool for feature extraction for the non-stationary EEG signal; the accuracy of the classification procedure improved when using multiple wavelets compared to the use of single wavelet time frequency entropy.

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