Showing papers on "Continuous wavelet transform published in 2019"

PyWavelets: A Python package for wavelet analysis

Abstract: 1 Department of Radiology, Cincinnati Children’s Hospital Medical Center, Cincinnati, OH, USA 2 Department of Radiology, University of Cincinnati School of Medicine, Cincinnati, OH, USA 3 Scion, 49 Sala Street, Private Bag 3020, Rotorua 3046, New Zealand 4 FPInnovations, 2665 East Mall, Vancouver, BC V6T 1Z4, Canada 5 Department of Biochemistry, University of Cambridge, Old Addenbrookes Site, 80 Tennis Court Road, Cambridge, CB2 1GA, United Kingdom 6 None

Generalized wavelets and hypergroups

Abstract: 1. Hypergroups 2. Wavelets and the Windowed Spherical Fourier Transform on Gelfand Pairs 3. Generalized Wavelets and Generalized Continuous Wavelet Transforms on Hypergroups 4. Harmonic Analysis, Generalized Wavelets and the Generalized Continuous Wavelet Transform Associated with the Spherical Mean Operator 5. Generalized Radon Transforms on Generalized Hypergroups 6. Inversion of Generalized Radon Transforms Using Generalized Wavelets 7. Product Formulas and Generalized Hypergroups 8. Harmonic Analysis, Generalized Wavelets and the Generalized Continuous Wavelet Transform on Chebli-Trimeche 9. Hypergroups Harmonic Analysis, Generalized Wavelets and the Generalized Continuous Wavelet Transform Associated with Laguerre Functions 10. Generalized Wavelets and Generalized Continuous Wavelet Transforms on Semisimple Lie Groups and on Cartan Motion Groups

Time-frequency analysis for bearing fault diagnosis using multiple Q-factor Gabor wavelets

Abstract: Rolling element bearings are key and also vulnerable machine elements in rotating machinery. Fault diagnosis of rolling element bearings is significant for guaranteeing machinery safety and functionality. To accurately extract bearing diagnostic information, a time-frequency analysis method based on continuous wavelet transform (CWT) and multiple Q-factor Gabor wavelets (MQGWs) (termed CMQGWT) is introduced in this paper. In the CMQGWT method, Gabor wavelets with multiple Q-factors are adopted and sets of the continuous wavelet coefficients for each Q-factor are combined to generate time-frequency map. By this way, the resolution of the CWT time-frequency map can be greatly increased and the diagnostic information can be accurately identified. Numerical simulation is carried out and verified the effectiveness of the proposed method. Case studies and comparisons with the continuous Morlet wavelet transform (CMWT) and the tunable Q-factor wavelet transform (TQWT) demonstrate the effectiveness and superiority of the CMQGWT for bearing diagnostic information extraction and fault identification.

Application of Continuous Wavelet Transform and Convolutional Neural Network in Decoding Motor Imagery Brain-Computer Interface

Abstract: The motor imagery-based brain-computer interface (BCI) using electroencephalography (EEG) has been receiving attention from neural engineering researchers and is being applied to various rehabilitation applications. However, the performance degradation caused by motor imagery EEG with very low single-to-noise ratio faces several application issues with the use of a BCI system. In this paper, we propose a novel motor imagery classification scheme based on the continuous wavelet transform and the convolutional neural network. Continuous wavelet transform with three mother wavelets is used to capture a highly informative EEG image by combining time-frequency and electrode location. A convolutional neural network is then designed to both classify motor imagery tasks and reduce computation complexity. The proposed method was validated using two public BCI datasets, BCI competition IV dataset 2b and BCI competition II dataset III. The proposed methods were found to achieve improved classification performance compared with the existing methods, thus showcasing the feasibility of motor imagery BCI.

Demodulated High-Order Synchrosqueezing Transform With Application to Machine Fault Diagnosis

Abstract: Time–frequency analysis (TFA) is considered as a useful tool to extract the time-variant features of the nonstationary signal. In this paper, a new method called demodulated high-order synchrosqueezing transform (DHST) is proposed. The DHST introduces a two-step algorithm, namely, demodulated transform and high-order synchrosqueezing method to achieve a compact time–frequency representation (TFR) while enabling the reconstruction of the signal from TFR. The performance of the proposed DHST method in this paper is validated by both the simulated and experimental signals including bat echolocation and a vibration signal. The results show that the proposed TFA method is more effective in processing the nonstationary signals with fast varying instantaneous frequency.

A New Approach for Motor Imagery Classification Based on Sorted Blind Source Separation, Continuous Wavelet Transform, and Convolutional Neural Network.

Abstract: Brain-Computer Interfaces (BCI) are systems that allow the interaction of people and devices on the grounds of brain activity. The noninvasive and most viable way to obtain such information is by using electroencephalography (EEG). However, these signals have a low signal-to-noise ratio, as well as a low spatial resolution. This work proposes a new method built from the combination of a Blind Source Separation (BSS) to obtain estimated independent components, a 2D representation of these component signals using the Continuous Wavelet Transform (CWT), and a classification stage using a Convolutional Neural Network (CNN) approach. A criterion based on the spectral correlation with a Movement Related Independent Component (MRIC) is used to sort the estimated sources by BSS, thus reducing the spatial variance. The experimental results of 94.66% using a k-fold cross validation are competitive with techniques recently reported in the state-of-the-art.

Real-Time Wavelet-Based Grid Impedance Estimation Method

Abstract: This letter presents a novel method to estimate the grid impedance based on stationary discrete wavelet packet transform (SDWPT). The proposed method uses a steady-state technique, by injecting an interharmonic current into the grid and measuring the voltage response at the point of common coupling to estimate the grid impedance. The proposed method employed a standard three-phase photovoltaic system interconnected to the grid to validate its effectiveness experimentally. Comparisons with a discrete Fourier transform- and continuous wavelet transform-based impedance estimation approaches demonstrate the performance of proposed method. Besides, the proposed SDWPT-based impedance estimation provided accurate experimental results, which make it viable for real-time applications.

Joint Time–Frequency Scattering

Abstract: In time series classification and regression, signals are typically mapped into some intermediate representation used for constructing models. Since the underlying task is often insensitive to time shifts, these representations are required to be time-shift invariant. We introduce the joint time–frequency scattering transform, a time-shift invariant representation that characterizes the multiscale energy distribution of a signal in time and frequency. It is computed through wavelet convolutions and modulus non-linearities and may, therefore, be implemented as a deep convolutional neural network whose filters are not learned but calculated from wavelets. We consider the progression from mel-spectrograms to time scattering and joint time–frequency scattering transforms, illustrating the relationship between increased discriminability and refinements of convolutional network architectures. The suitability of the joint time–frequency scattering transform for time-shift invariant characterization of time series is demonstrated through applications to chirp signals and audio synthesis experiments. The proposed transform also obtains state-of-the-art results on several audio classification tasks, outperforming time scattering transforms and achieving accuracies comparable to those of fully learned networks.

Identification of Fusarium Head Blight in Winter Wheat Ears Using Continuous Wavelet Analysis

Abstract: Fusarium head blight in winter wheat ears produces the highly toxic mycotoxin deoxynivalenol (DON), which is a serious problem affecting human and animal health. Disease identification directly on ears is important for selective harvesting. This study aimed to investigate the spectroscopic identification of Fusarium head blight by applying continuous wavelet analysis (CWA) to the reflectance spectra (350 to 2500 nm) of wheat ears. First, continuous wavelet transform was used on each of the reflectance spectra and a wavelet power scalogram as a function of wavelength location and the scale of decomposition was generated. The coefficient of determination R2 between wavelet powers and the disease infestation ratio were calculated by using linear regression. The intersections of the top 5% regions ranking in descending order based on the R2 values and the statistically significant (p-value of t-test < 0.001) wavelet regions were retained as the sensitive wavelet feature regions. The wavelet powers with the highest R2 values of each sensitive region were retained as the initial wavelet features. A threshold was set for selecting the optimal wavelet features based on the coefficient of correlation R obtained via the correlation analysis among the initial wavelet features. The results identified six wavelet features which include (471 nm, scale 4), (696 nm, scale 1), (841 nm, scale 4), (963 nm, scale 3), (1069 nm, scale 3), and (2272 nm, scale 4). A model for identifying Fusarium head blight based on the six wavelet features was then established using Fisher linear discriminant analysis. The model performed well, providing an overall accuracy of 88.7% and a kappa coefficient of 0.775, suggesting that the spectral features obtained using CWA can potentially reflect the infestation of Fusarium head blight in winter wheat ears.

Intelligent chatter detection using image features and support vector machine

Abstract: Chatter is a self-excited vibration that affects the part quality and tool life in the machining process. This paper introduces an intelligent chatter detection method based on image features and the support vector machine. In order to reduce the background noise and highlight chatter characteristics, the average FFT is applied to identify the dominant frequency bands that divide the time-frequency image of the short-time Fourier transform into several sub-images. The non-stationary properties of the machining conditions are quantified using sub-images features. The area under the receiver operating characteristics curve ranks the extracted image features according to their separability capabilities. The support vector machine is designed to automatically classify the machining conditions and select the best feature subset based on the ranked features. The proposed method is verified by using dry micro-milling tests of steel 1040 and high classification accuracies for both the stable and unstable tests are obtained. In addition, the proposed method is compared with two additional methods using either image features from the continuous wavelet transform or time-domain features. The results present a better classification performance than the two additional methods, indicating the efficiency of the proposed method for chatter detection.

Defect identification in friction stir welding using continuous wavelet transform

Abstract: The manuscript reports on detection of defect that arises during friction stir welding using continuous wavelet transform (CWT) on force signal. The vertical force during welding undergoes sudden change due to presence of defects. These localized defects are detected accurately with the help of continuous wavelet transform scalogram (CWT coefficients’ gray scale image). Statistical feature of variance is used on scale of 1 of transformed signal to localize the defects. The experiments of welding are conducted on the work piece of AA 1100 with varying tool rotational speed (1000, 2000, 3000 rpm) and transverse velocity (50, 75 and 125 mm/min). The manuscript also presents the comparison of results obtained using discrete wavelet transform and CWT of force signals and shows better localization and determination of degree of defect are possible through CWT analysis.

Fall Detection Using Multiple Bioradars and Convolutional Neural Networks.

Abstract: A lack of effective non-contact methods for automatic fall detection, which may result in the development of health and life-threatening conditions, is a great problem of modern medicine, and in particular, geriatrics. The purpose of the present work was to investigate the advantages of utilizing a multi-bioradar system in the accuracy of remote fall detection. The proposed concept combined usage of wavelet transform and deep learning to detect fall episodes. The continuous wavelet transform was used to get a time-frequency representation of the bio-radar signal and use it as input data for a pre-trained convolutional neural network AlexNet adapted to solve the problem of detecting falls. Processing of the experimental results showed that the designed multi-bioradar system can be used as a simple and view-independent approach implementing a non-contact fall detection method with an accuracy and F1-score of 99%.

Characterization of Analytic Wavelet Transforms and a New Phaseless Reconstruction Algorithm

Abstract: We obtain a characterization of all wavelets leading to analytic wavelet transforms (WT). The characterization is obtained as a byproduct of the theoretical foundations of a new method for wavelet phase reconstruction from magnitude-only coefficients. The cornerstone of our analysis is an expression of the partial derivatives of the continuous WT, which results in phase–magnitude relationships similar to the short-time Fourier transform setting and valid for the generalized family of Cauchy wavelets. We show that the existence of such relations is equivalent to analyticity of the WT up to a multiplicative weight and a scaling of the mother wavelet. The implementation of the new phaseless reconstruction method is considered in detail and compared to previous methods. It is shown that the proposed method provides significant performance gains and a great flexibility regarding accuracy versus complexity. In addition, we discuss the relation between scalogram reassignment operators and the wavelet transform phase gradient and present an observation on the phase around zeros of the WT.

The Spectral Graph Wavelet Transform: Fundamental Theory and Fast Computation

Abstract: The spectral graph wavelet transform (SGWT) defines wavelet transforms appropriate for data defined on the vertices of a weighted graph. Weighted graphs provide an extremely flexible way to model the data domain for a large number of important applications (such as data defined on vertices of social networks, transportation networks, brain connectivity networks, point clouds, or irregularly sampled grids). The SGWT is based on the spectral decomposition of the \(N\times N\) graph Laplacian matrix \(\mathscr {L}\), where N is the number of vertices of the weighted graph. Its construction is specified by designing a real-valued function g which acts as a bandpass filter on the spectrum of \(\mathscr {L}\), and is analogous to the Fourier transform of the “mother wavelet” for the continuous wavelet transform. The wavelet operators at scale s are then specified by \(T_g^s = g(s\mathscr {L})\), and provide a mapping from the input data \(f\in \mathbb {R}^N\) to the wavelet coefficients at scale s. The individual wavelets \(\psi _{s,n}\) centered at vertex n, for scale s, are recovered by localizing these operators by applying them to a delta impulse, i.e. \(\psi _{s,n} = T_g^s \delta _n\). The wavelet scales may be discretized to give a graph wavelet transform producing a finite number of coefficients. In this work we also describe a fast algorithm, based on Chebyshev polynomial approximation, which allows computation of the SGWT without needing to compute the full set of eigenvalues and eigenvectors of \(\mathscr {L}\).

On the diagnosis of idiopathic Parkinson’s disease using continuous wavelet transform complex plot

Abstract: Gait analysis provides valuable motor deficit quantitative information about Parkinson’s disease patients Detection of gait abnormalities is key to preserving healthy mobility The goal of this paper is to propose a novel gait analysis and continuous wavelet transform-based approach to diagnose idiopathic Parkinson’s disease First, we eliminate the noise resulting from orientation changes of test subjects by filtering the continuous wavelet transform output below 08 Hz Next, we analyze the complex plot output above 08 Hz, which takes an ellipse, and calculate the area using $$95\%$$ confidence level We found out that this ellipse area, along with the mean continuous wavelet transform output value, and the peak of the temporal signal are excellent features for classification Experiments using Artificial Neural Networks on the Physionet database produced an accuracy of $$976\%$$ Furthermore, we have shown an association between the Parkinson’s disease severity stage and the ellipse complex plot area with a 978% overall accuracy Based on the results, we could effectively recognize the gait patterns and distinguish apart Parkinson’s disease patients with varying severity from healthy individuals

Separating the EoR signal with a convolutional denoising autoencoder: a deep-learning-based method

Abstract: When applying the foreground removal methods to uncover the faint cosmological signal from the epoch of reionization (EoR), the foreground spectra are assumed to be smooth. However, this assumption can be seriously violated in practice since the unresolved or mis-subtracted foreground sources, which are further complicated by the frequency-dependent beam effects of interferometers, will generate significant fluctuations along the frequency dimension. To address this issue, we propose a novel deep-learning-based method that uses a 9-layer convolutional denoising autoencoder (CDAE) to separate the EoR signal. After being trained on the SKA images simulated with realistic beam effects, the CDAE achieves excellent performance as the mean correlation coefficient ($\bar{\rho}$) between the reconstructed and input EoR signals reaches $0.929 \pm 0.045$. In comparison, the two representative traditional methods, namely the polynomial fitting method and the continuous wavelet transform method, both have difficulties in modelling and removing the foreground emission complicated with the beam effects, yielding only $\bar{\rho}_{\text{poly}} = 0.296 \pm 0.121$ and $\bar{\rho}_{\text{cwt}} = 0.198 \pm 0.160$, respectively. We conclude that, by hierarchically learning sophisticated features through multiple convolutional layers, the CDAE is a powerful tool that can be used to overcome the complicated beam effects and accurately separate the EoR signal. Our results also exhibit the great potential of deep-learning-based methods in future EoR experiments.

A Novel Method to Detect Multiple Arrhythmias Based on Time-Frequency Analysis and Convolutional Neural Networks

Abstract: Electrocardiogram (ECG) is an efficient and commonly used tool for detecting arrhythmias. With the development of dynamic ECG monitoring, an effective and simple algorithm is needed to deal with large quantities of ECG data. In this study, we proposed a method to detect multiple arrhythmias based on time-frequency analysis and convolutional neural networks. For a short-time (10 s) single-lead ECG signal, the time-frequency distribution matrix of the signal was first obtained using a time-frequency transform method, and then a convolutional neural network was used to discriminate the rhythm of the signal. ECG data in multiple databases were used and were divided into 12 classes. Finally, the performance of three kinds of time-frequency transform methods are evaluated, including short-time Fourier transform (STFT), continuous wavelet transform (CWT), and pseudo Wigner-Ville distribution (PWVD). The best result was obtained by STFT, with an accuracy of 96.65%, an average sensitivity of 96.47%, an average specificity of 99.68%, and an average F1 score of 96.27%, respectively. Especially, the area under curve (AUC) value is 0.9987. The proposed method in this work may be efficient and valuable to detect multiple arrhythmias for dynamic ECG monitoring.

Classification of Motor Functions from Electroencephalogram (EEG) Signals Based on an Integrated Method Comprised of Common Spatial Pattern and Wavelet Transform Framework.

Abstract: In this work, an algorithm for the classification of six motor functions from an electroencephalogram (EEG) signal that combines a common spatial pattern (CSP) filter and a continuous wavelet transform (CWT), is investigated. The EEG data comprise six grasp-and-lift events, which are used to investigate the potential of using EEG as input signals with brain computer interface devices for controlling prosthetic devices for upper limb movement. Selected EEG channels are the ones located over the motor cortex, C3, Cz and C4, as well as at the parietal region, P3, Pz and P4. In general, the proposed algorithm includes three main stages, band pass filtering, CSP filtering, and wavelet transform and training on GoogLeNet for feature extraction, feature learning and classification. The band pass filtering is performed to select the EEG signal in the band of 7 Hz to 30 Hz while eliminating artifacts related to eye blink, heartbeat and muscle movement. The CSP filtering is applied on two-class EEG signals that will result in maximizing the power difference between the two-class dataset. Since CSP is mathematically developed for two-class events, the extension to the multiclass paradigm is achieved by using the approach of one class versus all other classes. Subsequently, continuous wavelet transform is used to convert the band pass and CSP filtered signals from selected electrodes to scalograms which are then converted to images in grayscale format. The three scalograms from the motor cortex regions and the parietal region are then combined to form two sets of RGB images. Next, these RGB images become the input to GoogLeNet for classification of the motor EEG signals. The performance of the proposed classification algorithm is evaluated in terms of precision, sensitivity, specificity, accuracy with average values of 94.8%, 93.5%, 94.7%, 94.1%, respectively, and average area under the receiver operating characteristic (ROC) curve equal to 0.985. These results indicate a good performance of the proposed algorithm in classifying grasp-and-lift events from EEG signals.

An Improved Cyclic Modulation Spectral Analysis Based on the CWT and its Application on Broken Rotor Bar Fault Diagnosis for Induction Motors

Abstract: Induction motors (IMs) are widely used in many manufacturing processes and industrial applications. The harsh work environment, long-time enduring, and overloads mean that it is subjected to broken rotor bar (BRB) faults. The vibration signal of IMs with BRB faults consists of the reliable modulation information used for fault diagnosis. Cyclostationary analysis has been found to be effective in identifying and extracting fault feature. The estimators of cyclic modulation spectrum (CMS) and fast spectral correlation (FSC) based on the short-time fourier transform (STFT) have higher cyclic frequency resolution, which has proven efficient in demodulating second order cyclostationary (CS2) signals. However, these two estimators have limitations of processing the maximum cyclic frequency αmax that is smaller than Fs/2 (Fs is the sampling frequency) according to Nyquist’s Theorem. In addition, they have lower carrier frequency resolution due to the fixed window size used in STFT. In order to resolve the initial shortcomings of the CMS and FSC methods, in this paper, we extended the analysis of CMS algorithm based on the continuous wavelet transform (CWT), which enlarged the maximum cyclic frequency range to Fs/2 and provides higher carrier frequency resolution because the CWT has the advantage of multi-resolution analysis. The reliability and applicability of the proposed method for fault components localization were validated by CS2 simulation signals. Compared to CMS and FSC methods, the proposed approach shows better performance by analyzing vibration signals between healthy motor and faulty motor with one BRB fault under 0%, 20%, 40%, and 80% load conditions.

Diagnostics of mechanical and electrical faults in induction motors using wavelet-based features of vibration and current through support vector machine algorithms for various operating conditions

Abstract: Fault diagnosis of induction motors (IMs) is always a challenging task in the practical industrial field, and it is even more challenging in the case of inadequate information of IM working conditions. In this paper, a new methodology for fault detection has been proposed for IMs to detect various electrical and mechanical faults as well as their severities, where the data are unavailable at required operating conditions (i.e., speed and load) based on wavelet and support vector machine (SVM). For this, the radial, axial and tangential vibrations, and three-phase current signals are acquired from IMs having different faults. The acquired time domain signal is then transformed to time–frequency signals using continuous wavelet transform (CWT). Ten different base wavelets are used to investigate the impact of different wavelet function on the fault diagnosis of IMs. Statistical features are extracted based on the CWT, and then appropriate feature(s) are selected using the wrapper model. These features are fed to the SVM to detect whether a defect has occurred. The fault detection is performed for identical speed and load case using a number of mother wavelets. To analyze the robustness of the present system, diagnosis is attempted for various operational conditions of IMs. The result showed that the feature(s) selected using the Shannon wavelet diagnose, the fault categories of IM more accurately as compared to other wavelets, and remarkably found to be robust at all working conditions of IMs. The work is finally extended to perform the fault diagnosis when limited information is available for the training. From the results, it is observed that the proposed methodology does not only take care of the practical problem of unavailability of data at different operating conditions, but also shows good performance and takes low computation time, which are vital requirements of a condition monitoring and diagnostic system.