Wavelet Families Research Articles

High impedance fault detection in power distribution systems using wavelet transform and evolving neural network

This paper concerns how to apply an incremental learning algorithm based on data streams to detect high impedance faults in power distribution systems. A feature extraction method, based on a discrete wavelet transform that is combined with an evolving neural network, is used to recognize spatial–temporal patterns of electrical current data. Different wavelet families, such as Haar, Symlet, Daubechie, Coiflet and Biorthogonal, and different decomposition levels, were investigated in order to provide the most discriminative features for fault detection. The use of an evolving neural network was shown to be a quite appropriate approach to fault detection since high impedance faults is a time-varying problem. The performance of the proposed evolving system for detecting and classifying faults was compared with those of well-established computational intelligence methods: multilayer perceptron neural network, probabilistic neural network, and support vector machine. The results showed that the proposed system is efficient and robust to changes. A classification performance in the order of 99% is exhibited by all classifiers in situations where the fault patterns do not significantly change during tests. However, a performance drop of about 13–24% is exhibited by non-evolving classifiers when fault patterns suffer from gradual or abrupt change in their behavior. The evolving system is capable, after incremental learning, of maintaining its detection and classification performance even in such situations.

Wavelet multiresolution analysis and dyadic scalogram for detection of epileptiform paroxysms in electroencephalographic signals

Abstract Introduction Early detection of epilepsy by the review of large electroencephalographic (EEG) recordings is very stressful, time-consuming, and subjective for neurologists. Several automatic seizure detection systems have been proposed in the literature to solve this problem. Methods This study proposes two complementary wavelet-based approaches for detecting epileptiform paroxysms in EEG signals. First methodology applied the wavelet multiresolution analysis (MRA) to filter non-epileptiform activity in long-term EEG. Second methodology used the wavelet dyadic scalogram to analyze which scales were related to the epileptiform paroxysms. For tests, 65 wavelet functions were selected between daubechies, biorthogonal, symlets, reverse biorthogonal and coiflet wavelet families in order to evaluate their performance. Results For MRA, it was noted a better performance by using the db4 function, by reaching 48.30% of energy with 8 wavelet coefficients, 0.717658 of correlation and 36.799 of root mean square error (RMSE). For wavelet dyadic scalograms, were chosen bior3.9 and rbio1.5 functions, by reaching 77.98% of sensitivity, 94.08% of specificity, 87.87% of efficiency and 0.9613 of area under the curve (AUC value) by using bior3.9. Conclusion The presented approaches are highly complementary for a whole automatic seizure detection system by using the MRA as pre-processing stage to filter non-epileptiform activity, and wavelet dyadic scalogram for extracting desired features from filtered EEG signals.

Investigation of using wavelet analysis for classifying pattern of cyclic voltammetry signals

Wavelet analysis is an excellent technique for data processing analysis based on linear vector algebra since it has an ability to perform local analysis and is able to analyze an unspecific localized area of a large signal. In this work, the wavelet analysis of cyclic waveform was investigated in order to find the distinguishable feature from the cyclic data. The analyzed wavelet coefficients were proposed to be used as selected cyclic feature parameters. The cyclic voltammogram (CV) of different electrodes consisting of carbon nanotube (CNT) and several types of metal phthalocyanine (MPc) including CoPc, FePc, ZnPc and MnPc powders was used as several sets of cyclic data for various types of coffee. The mixture powder was embedded in a hollow Teflon rod and used as working electrodes. Electrochemical response of the fabricated electrodes in Robusta, blend coffee I, blend coffee II, chocolate malt and cocoa at the same concentrations was measured with scanning rate of 0.05V/s from -1.5 to 1.5V respectively to Ag/AgCl electrode for five scanning loops. The CV of blended CNT electrode with some MPc electrodes indicated the ionic interaction which can be the effect of catalytic oxidation of saccharides and/or polyphenol on the sensor surface. The major information of CV response can be extracted by using several mother wavelet families viz. daubechies (dB1 to dB3), coiflets (coiflet1), biorthogonal (Bior1.1) and symlets (sym2) and then the discrimination of these wavelet coefficients of each data group can be separated by principal component analysis (PCA). The PCA results indicated the clearly separate groups with total contribution more than 62.37% representing from PC1 and PC2.

Comparison of Wavelet Family Performances in ECG Signal Denoising

The heart is considered the most important organ of our body that controls the circulation of blood throughout the body. Measured heartbeat signals can be further analyzed in order to know the health condition of a person. The challenge of ECG signal measurement and analysis is how to remove the noises imposed on the signal that is interfered from many different sources, such as internal noise in sensor devices, power line interference, muscle activity, and body movements. This paper implemented wavelet transform to reduce the noise imposed on the ECG signal to get a closely actual heart signal. ECG data used in this research are three digitized recorded ECG data obtained from MIT-BIH Arrhythmia Database. The first step is generating the noisy ECG signal as the input system by adding 1W WGN signal into the original ECG signal. Then DWT is applied to extract the noisy ECG signal. Some DWT’s parameters, threshold selection (rule, type, rescaling), decomposition level, and desired wavelet family are varied to get the best denoised output signal. All results are recorded to be compared. Based on the results, the best DWT parameter for ECG signal denoising is obtained by Symlet wavelet when the decomposition level is set to 3, with soft thresholding, in rigrsure thresholding rule.

Intelligent facial emotion recognition based on stationary wavelet entropy and Jaya algorithm

AimEmotion recognition based on facial expression is an important field in affective computing. Current emotion recognition systems may suffer from two shortcomings: translation in facial image may deteriorate the recognition performance, and the classifier is not robust. MethodTo solve above two problems, our team proposed a novel intelligent emotion recognition system. Our method used stationary wavelet entropy to extract features, and employed a single hidden layer feedforward neural network as the classifier. To prevent the training of the classifier fall into local optimum points, we introduced the Jaya algorithm. ResultsThe simulation results over a 20-subject 700-image dataset showed our algorithm reached an overall accuracy of 96.80 ± 0.14%. ConclusionThis proposed approach performs better than five state-of-the-art approaches in terms of overall accuracy. Besides, the db4 wavelet performs the best among other whole db wavelet family. The 4-level wavelet decomposition is superior to other levels. In the future, we shall test other advanced features and training algorithms.

Appearance and characterization of fruit image textures for quality sorting using wavelet transform and genetic algorithms.

The proposed method is nondestructive fruit quality assessment method. The experimental results has proven that Genetic algorithm along with wavelet textures feature has potential to discriminate fruit quality. Finally, it can be concluded that discussed method is an accurate, reliable, and objective tool to determine fruit quality namely Mango and Guava, and might be applicable to in-line sorting systems.

Studies on the sparsifying operator in compressive digital holography.

In compressive digital holography, we reconstruct sparse object wavefields from undersampled holograms by solving an ℓ1-minimization problem. Applying wavelet transformations to the object wavefields produces the necessary sparse representations, but prior work clings to transformations with too few vanishing moments. We put several wavelet transformations belonging to different wavelet families to the test by evaluating their sparsifying properties, the number of hologram samples that are required to reconstruct the sparse wavefields perfectly, and the robustness of the reconstructions to additive noise and sparsity defects. In particular, we recommend the CDF 9/7 and 17/11 wavelet transformations, as well as their reverse counter-parts, because they yield sufficiently sparse representations for most accustomed wavefields in combination with robust reconstructions. These and other recommendations are procured from simulations and are validated using biased, noisy holograms.

A New Construction of Boundary Interpolating Wavelets for Fourth Order Problems

In this article we introduce a new mixed Lagrange–Hermite interpolating wavelet family on the interval, to deal with two types (Dirichlet and Neumann) of boundary conditions. As this construction is a slight modification of the interpolating wavelets on the interval of Donoho, it leads to fast decomposition, error estimates and norm equivalences. This new basis is then used in adaptive wavelet collocation schemes for the solution of one dimensional fourth order problems. Numerical tests conducted on the 1D Euler–Bernoulli beam problem, show the efficiency of the method.

Forecasting the Electric Energy Supply in Duhok Province using Proposed Methods Based on Wavelet Analysis and Sarima Methods

Many applications have been done in the field of using wavelet analysis for time series analysis. In this study, we used the quarterly data of Electric Energy Supply in Duhok Province-Iraq in Megawatt which represents a sample size (46) observations during the period 2004 and 2015.we aim to describe how wavelet de-noising can be used in time series forecasting and improve the forecasting quality through presenting some proposed methods based on wavelet analysis and SARIMA method and applying on real data and make comparison between methods depending on some statistical criteria.Results from the analysis showed the superiority of the three proposed methods and showed that we can get more information from a series when using Wavelet-SARIMA method and this leads to enhance the classical SARIMA model in forecasting. Furthermore, after many empirical experiments with many wavelet families, it has been found that Daubechies, Coiflets, Discrete Meyer(dmey) and Symlet wavelets are very suitable when denoising the data and out of these four wavelet families, the Daubechies and Discrete Meyer performed better.

Development of a coupled wavelet transform and evolutionary Levenberg‐Marquardt neural networks for hydrological process modeling

AbstractThis research aims to present a general framework by which the most appropriate wavelet parameters including mother wavelet, vanishing moment, and decomposition level can be chosen for a joint wavelet transform and machine learning model. This study is organized in 2 parts: the first part presents an evolutionary Levenberg‐Marquardt neural network (ELMNN) model as the most effective machine learning configuration, and the second part describes how the wavelet transform can be effectively embedded with the developed ELMNN model. In this research, the rainfall and runoff time series data of 2 distinct watersheds at 2 different time scales (daily and monthly) were used to build the proposed hybrid wavelet transform and ELMNN model. The conclusions of this study showed that the Daubechies wavelet more than other wavelet families is capable to extract the informative features of hydrologic series. The vanishing moment and decomposition level of this mother wavelet should be selected based on the watershed behavior and the time resolution of rainfall and runoff time series, respectively. The verification results for both watersheds at daily and monthly time scales indicated root mean square error, peak value criterion, low value criterion, and Kling‐Gupta efficiency as about 0.017, 0.021, 0.023, and 0.91, respectively.

Automatic identification of epileptic EEG signals through binary magnetic optimization algorithms

Epilepsy is a class of chronic neurological disorders characterized by transient and unexpected electrical disturbances of the brain. The automated analysis of the electroencephalogram (EEG) signal can be instrumental for the proper diagnosis of this mental condition. This work presents a systematic assessment of the performance of different variants of the binary magnetic optimization algorithm (BMOA), two of which are introduced here, while serving as feature selectors for epileptic EEG signal identification. In this context, the optimum-path forest classifier was adopted as a classification model, whereas different wavelet families were considered for EEG feature extraction. In order to compare the performance of the improved BMOA variants against the traditional one, as well as other metaheuristic techniques, namely particle swarm optimization, binary bat algorithm, and genetic algorithm, we employed a well-known EEG benchmark dataset composed of five classes of EEG signals (two of which comprising normal patients with eyes open or closed, and the remaining comprising ill patients with different levels of epilepsy). Overall, the results evidenced the robustness of the proposed BMOA and its variants.

Off-Line Handwritten Signature Recognition by Wavelet Entropy and Neural Network

Handwritten signatures are widely utilized as a form of personal recognition. However, they have the unfortunate shortcoming of being easily abused by those who would fake the identification or intent of an individual which might be very harmful. Therefore, the need for an automatic signature recognition system is crucial. In this paper, a signature recognition approach based on a probabilistic neural network (PNN) and wavelet transform average framing entropy (AFE) is proposed. The system was tested with a wavelet packet (WP) entropy denoted as a WP entropy neural network system (WPENN) and with a discrete wavelet transform (DWT) entropy denoted as a DWT entropy neural network system (DWENN). Our investigation was conducted over several wavelet families and different entropy types. Identification tasks, as well as verification tasks, were investigated for a comprehensive signature system study. Several other methods used in the literature were considered for comparison. Two databases were used for algorithm testing. The best recognition rate result was achieved by WPENN whereby the threshold entropy reached 92%.

Reversible integer wavelet transform for blind image hiding method.

In this article, a blind data hiding reversible methodology to embed the secret data for hiding purpose into cover image is proposed. The key advantage of this research work is to resolve the privacy and secrecy issues raised during the data transmission over the internet. Firstly, data is decomposed into sub-bands using the integer wavelets. For decomposition, the Fresnelet transform is utilized which encrypts the secret data by choosing a unique key parameter to construct a dummy pattern. The dummy pattern is then embedded into an approximated sub-band of the cover image. Our proposed method reveals high-capacity and great imperceptibility of the secret embedded data. With the utilization of family of integer wavelets, the proposed novel approach becomes more efficient for hiding and retrieving process. It retrieved the secret hidden data from the embedded data blindly, without the requirement of original cover image.

Wavelet transform with generalized beta wavelets for seismic time-frequency analysis

Using the continuous wavelet transform (CWT), the time-frequency analysis of reflection seismic data can provide significant information to delineate subsurface reservoirs. However, CWT is limited by the Heisenberg uncertainty principle, with a trade-off between time and frequency localizations. Meanwhile, the mother wavelet should be adapted to the real seismic waveform. Therefore, for a reflection seismic signal, we have developed a progressive wavelet family that is referred to as generalized beta wavelets (GBWs). By varying two parameters controlling the wavelet shapes, the time-frequency representation of GBWs can be given sufficient flexibility while remaining exactly analytic. To achieve an adaptive trade-off between time-frequency localizations, an optimization workflow is designed to estimate suitable parameters of GBWs in the time-frequency analysis of seismic data. For noise-free and noisy synthetic signals from a depositional cycle model, the results of spectral component using CWT with GBWs display its flexibility and robustness in the adaptive time-frequency representation. Finally, we have applied CWT with GBWs on 3D seismic data to show its potential to discriminate stacked fluvial channels in the vertical sections and to delineate more distinct fluvial channels in the horizontal slices. CWT with GBWs provides a potential technique to improve the resolution of exploration seismic interpretation.

Noise reduction for lidar returns using self-adaptive wavelet neural network

Lidar has been widely applied in many fields, such as meteorology and environment. However, because lidar returns are very weak, the influence of noise on useful signal is very serious. To obtain useful lidar return signals from raw data, a self-adaptive method combining wavelet analysis and a neural network that suppresses noise is proposed, in which the orthogonal Daubechies wavelet family serves as node functions in the hidden layer of the neural network, a search algorithm is selected to optimize the parameters and thresholds, and the Levenberg–Marquardt algorithm is adopted in the neural network gradient algorithm. Some comparative experiments were carried out to verify the feasibility of the noise reduction method and the results showed that the signal-to-noise ratio (SNR) of the common wavelet threshold denoising method is about 10, while that of the self-adaptive wavelet neural network denoising method is more than 20. From the experimental results, it can be seen that the wavelet neural network denoising method has less distortion and a higher SNR value than other methods, giving it superior performance.

Effectively Interpreting Discrete Wavelet Transformed Signals [Lecture Notes

Following two decades of research focusing on the discrete wavelet transform (DWT) and driven by students' high level of questioning, I decided to write this essay on one of the most significant tools for time-frequency signal analysis. As it is widely applicable in a variety of fields, I invite readers to follow this lecture note, which is specially dedicated to show a practical strategy for the interpretation of DWT-based transformed signals while extracting useful information from them. The particular focus resides on the procedure used to find the time support of frequencies and how it is influenced by the wavelet family and the support size of corresponding filters.

Adaptive wavelet-enriched hierarchical finite element model for polycrystalline microstructures

This paper proposes an adaptive, wavelet-enriched hierarchical finite element model (FEM) to enhance computational efficiency and solution accuracy for heterogeneous domains of anisotropic elastic materials. It is motivated by the need to overcome shortcomings of conventional methods like the standard FEM or fast Fourier transformation (FFT) based method for analyzing deformation in large polycrystalline microstructures. The multi-resolution wavelet functions are advantageous for selection of an optimal set of functions that can adaptively enrich the solution space with a prescribed level of accuracy. The proposed method introduces a discretization space that conforms to the profile of the solution sought. The method engages a second generation family of wavelets with a lifting scheme to generate hierarchical interpolation functions. An iterative algorithm efficiently calculates estimates of the solution from the previous iterate using a modified Jacobi method. The adaptive FE method performs significantly better than uniformly refined FEM in validation tests with focus on the convergence rate and error mitigation. A polycrystalline microstructure with elastically anisotropic grains is simulated by the adaptive wavelet-enriched hierarchical method, showing high convergence rates.

A Study on Image Denoising using Higher Decomposition Method Based on Wavelet Transform

The Wavelet change is in certainty an unbounded arrangement of different changes, contingent upon the legitimacy work utilized for its calculation. Picture generally gets contorted amid securing, preparing and progress. As wavelet change has many preferences over other strategy, for example, best restriction and multiresolution properties. Wavelet change utilized different strategies for picture denoising, for example, Visu Recoil yet this method have hindrance that it deliver over smoothening of picture which causes obscure in the edges. So to defeat such issue we have proposed new strategy by changing the Visu recoil thresholding systems. We have contrasted our proposed strategy and the Visu thresholding strategy on the premise of PSNR esteem for various wavelet families, for example, Haar, Daubechies, Biorthogonal, Symlet and Coiflet.

Implementation of wavelet packet transform and non linear analysis for emotion classification in stroke patient using brain signals

Abstract Emotion perception in stroke patients is affected since there is abnormality in the brain. Here, researchers focused on the impact of left brain damage and right brain damage towards emotion recognition. Due to the impaired emotion recognition, it is a challenge for stroke patients to express themselves in daily communication. Hence, it is inspiring to see the possibility to predict patient’s emotional state so as to prevent recurrent stroke. In this work, electroencephalograph (EEG) of 19 left brain damage patients (LBD), 19 right brain damage patients (RBD) and 19 normal control (NC) are collected as database. During data collection, six emotions (sad, disgust, fear, anger, happy and surprise) are induced by using audio visual stimuli. After normalization, EEG signals are filtered by using Butterworth 6th order band-pass filter at the cut-off frequencies of 0.5 Hz and 49 Hz. Then, wavelet packet transform (WPT) technique is implemented to localize five frequency bands: alpha (8 Hz–13 Hz), beta (13 Hz–30 Hz), gamma (30 Hz–49 Hz), alpha-to-gamma (8 Hz–49 Hz), beta-to-gamma (13 Hz–49 Hz). In WPT, four wavelet families are chosen: daubechies 4 (db4), daubechies 6 (db6), coiflet 5 (coif5) and symmlet 8 (sym8). Hurst exponents are extracted from each band and wavelet family and are classified by using K-nearest Neighbour (KNN) and Probabilistic Neural Network (PNN). Two classifications are done: comparison between three groups and comparison between six emotions. The results showed that all the H values are anti-correlated (0

Speed and security improvements of distance protection based on Discrete Wavelet and Hilbert transform

In order to maintain power system stability, modern transmission networks demand a high fault detection speed. At the same time, a high level of protection security is required, since each protection maloperation might lead to a system blackout and high economic loss. The protection speed and security represent conflicting requirements fundamentally limited by the Heisenberg’s Uncertainty Principle. Traditional line protection approach relies on fundamental frequency phasor estimation based on Discrete Fourier Transform. There are also various Discrete Wavelet Transform algorithms, typically based on Daubechies wavelet families, which may be used to estimate phasors. In this paper wavelet families other than Daubechies are evaluated as methods for estimating phasors. Two new algorithms based on Reverse Biorthogonal mother wavelets are presented and compared to the previous solutions. The protection speed and security are evaluated via a very demanding test formed on the basis of several thousands of fault simulations, as well as on 60 fault records from 400kV and 220kV transmission networks.