Relative Wavelet Energy Research Articles

Application of continuous‐time wavelet entropy for detection of cardiac repolarisation alternans

Prognostic utility of microvolt T-wave alternans (TWAs) has been established since its clinical acceptance as markers for malignant ventricular arrhythmias, leading to sudden cardiac death. Accurate detection of TWA from surface electrocardiography is a challenge because of invisible nature of the phenomenon. A novel TWA detection scheme based upon analysis of continuous-time wavelet entropy (CTWE) trend of consecutive ventricular repolarisation complexes is presented. The CTWE is computed using relative wavelet energy coefficients of continuous wavelet transform. Variety of simulated alternan waveforms, wavelet functions, frequency bands and noise levels are used to test the algorithm. The algorithm achieves a sensitivity of 100% at signal-to-noise ratio (SNR) >35 dB for all the selected wavelet functions and sensitivities of 99.5, 97 and 92% for Symlet4, Mexican Hat and truncated Morlet functions, respectively, at 30 dB SNR. A performance improvement of 5 dB is achieved by only computing the wavelet coefficients at the optimal frequency band. This study concludes that CTWE can successfully characterise the heterogeneity of cardiac repolarisation and detect TWA phenomenon.

Linear Analysis of Epileptic Forms in the Electroencephalogram

In our study, we investigated the properties of electroencephalogram (EEG) of humans experiencing epileptic seizures. By applying linear methods, such as spectral analysis and wavelet transformation, we compared characteristics of EEGs of patients suffering from epilepsia with the characteristics of EEGs of healthy individuals. Our goal was to establish the real effect of epileptic attacks in frequency domains, distinguishing them from various types of artifacts caused by mental and physical activities in humans. The frequency range of 1 to 2 Hz was found to be interesting, where we have detected a power spectral density peak typical of epileptic seizures. Also, we have shown that there exists an anomalous distribution of the relative wavelet energy of the signal within this frequency range. We also showed that the frequency range 7.97 to 15.94 Hz can serve as an indicator of preictal activity in the EEG signal.

CLASSIFICATION OF EEG SIGNALS IN NORMAL AND DEPRESSION CONDITIONS BY ANN USING RWE AND SIGNAL ENTROPY

EEG is useful for the analysis of the functional activity of the brain and a detailed assessment of this non-stationary waveform can provide crucial parameters indicative of the mental state of patients. The complex nature of EEG signals calls for automated analysis using various signal processing methods. This paper attempts to classify the EEG signals of normal and depression patients using well-established signal processing techniques involving relative wavelet energy (RWE) and artificial feedForward neural network. High frequency noise present in the recorded signal is removed using total variation filtering (TVF). Classification of the frequency bands of EEG signals into appropriate detail levels and approximation level is carried out using an eight-level multiresolution decomposition method of discrete wavelet transform (DWT). Parseval's theorem is used for calculating the energy at different resolution levels. RWE analysis gives information about the signal energy distribution at different decomposition levels. Both RWE and feedforward Network are used to classify the signals from normal controls and depression patients. The performance of the artificial neural network was evaluated using the classification accuracy and its value of 98.11% indicates a great potential for classifying normal and depression signals.

Relative wavelet energy and wavelet entropy based epileptic brain signals classification

Purpose Manual analysis of EEG signals by an expert is very much time consuming due to the long length of EEG recordings. The suitable computerized analysis is essentially required to differentiate among the normal, interictal and ictal (epileptic) EEGs.

Fault diagnosis of roller bearing based on relative wavelet energy

Fault diagnosis of roller bearing based on relative wavelet energy

Impairment of Erythrocytes Incubated in Glucose Medium: A Wavelet-Information Theory Analysis

This study investigates the effects produced by an increased concentration of glucose in a suspending medium on the erythrocytes Information Theory quantifiers. Erythrocytes, which were obtained from eight healthy volunteers, were washed and incubated in vitro with glucose solutions at different concentrations. The measured Wavelet-based Information Theory quantifiers include the Relative Wavelet Energy (RWE), the Normalized Total Wavelet Shannon Entropy (NTWS), MPR-Statistical Complexity Measure (SCM) and entropy-complexity plane. The results show that the increase in glucose concentration does not produce significant changes on the RWE, while significant ones on the NTSE, which combined with SCM values allow to identify different behaviour for all the different populations in the entropy-complexity plane. Modification in the hemorheological properties of cells could be clearly detected with these Wavelet-based Information Theory quantifiers.

Fault diagnosis of ball bearings using continuous wavelet transform

Bearing failure is one of the foremost causes of breakdown in rotating machines, resulting in costly systems downtime. This paper presents a methodology for rolling element bearings fault diagnosis using continuous wavelet transform (CWT). The fault diagnosis method consists of three steps, firstly the six different base wavelets are considered in which three are from real valued and other three from complex valued. Out of these six wavelets, the base wavelet is selected based on wavelet selection criterion to extract statistical features from wavelet coefficients of raw vibration signals. Two wavelet selection criteria Maximum Energy to Shannon Entropy ratio and Maximum Relative Wavelet Energy are used and compared to select an appropriate wavelet for feature extraction. Finally, the bearing faults are classified using these statistical features as input to machine learning techniques. Three machine learning techniques are used for faults classifications, out of which two are supervised machine learning techniques, i.e. support vector machine (SVM), artificial neural network (ANN) and other one is an unsupervised machine learning technique, i.e. self-organizing maps (SOM). The methodology presented in the paper is applied to the rolling element bearings fault diagnosis. The Meyer wavelet is selected based on Maximum Energy to Shannon Entropy ratio and the Complex Morlet wavelet is selected using Maximum Relative Wavelet Energy criterion. The test result showed that the SVM identified the fault categories of rolling element bearing more accurately for both Meyer wavelet and Complex Morlet wavelet and has a better diagnosis performance as compared to the ANN and SOM. Features selected using Meyer wavelet gives higher faults classification efficiency with SVM classifier.

A Resonance Demodulation Method Based on Harmonic Wavelet Transform for Rolling Bearing Fault Diagnosis

Resonance demodulation technique is widely employed to diagnose faults of rolling bearings. In order to reduce the energy leakage influence of the traditional demodulated resonance method, a new approach based on harmonic wavelet transform (HWT) is proposed to extract the fault characteristics of rolling bearing. From the results of the numerical simulation analysis, this method is proven to be efficient in detecting the impact signal clouded in noises. Moreover, this article proposes a resonance demodulation scheme, which can obtain the optimal HWT parameters automatically to construct the proper sub-frequency band filter by calculating the relative wavelet energy of the different sub-frequency band. It solves the shortcoming in which a resonance frequency band filter is chosen manually. The proposed scheme is successfully applied to detect the fault of rolling bearings of a tilting mechanism in a converter mill.

Entropy changes in brain function

The traditional way of analyzing brain electrical activity, on the basis of electroencephalography (EEG) records, relies mainly on visual inspection and years of training. Although it is quite useful, of course, one has to acknowledge its subjective nature that hardly allows for a systematic protocol. In the present work quantifiers based on information theory and wavelet transform are reviewed. The “relative wavelet energy” provides information about the relative energy associated with different frequency bands present in the EEG and their corresponding degree of importance. The “normalized total wavelet entropy” carries information about the degree of order–disorder associated with a multi-frequency signal response. Their application in the analysis and quantification of short duration EEG signals (event-related potentials) and epileptic EEG records are summarized.

Evidence of self-organization in brain electrical activity using wavelet-based informational tools

In the present work, we show that appropriate information-theory tools based on the wavelet transform (relative wavelet energy; normalized total wavelet entropy, H ; generalized wavelet complexity, C W ), when applied to tonic–clonic epileptic EEG data, provide one with valuable insights into the dynamics of neural activity. Twenty tonic–clonic secondary generalized epileptic records pertaining to eight patients have been analyzed. If the electromyographic activity is excluded the difference between the ictal and pre-ictal mean entropic values ( Δ H = 〈 H ( ictal ) 〉 - 〈 H ( pre - ictal ) 〉 ) is negative in 95% of the cases ( p < 0.0001 ) , and the mean complexity variation ( Δ C W = 〈 C W ( ictal ) 〉 - 〈 C W ( pre - ictal ) 〉 ) is positive in 85% of the cases ( p = 0.0002 ) . Thus during the seizure entropy diminishes while complexity grows. This is construed as evidence supporting the conjecture that an epileptic focus in this kind of seizures triggers a self-organized brain state characterized by both order and maximal complexity.

Wavelet analysis of generalized tonic-clonic epileptic seizures

The analysis of generalized tonic-clonic seizures is usually difficult with quantitative EEG techniques due to muscle artifact. We applied two quantifiers based on the Wavelet Transform to evaluate 20 seizures from eight consecutive patients admitted for video-EEG monitoring. We studied the relative wavelet energy and the wavelet entropy over time. In 16 20 events we found significant decremental activity in the relative wavelet energy associated with frequency band 0.8– 3.2 Hz (delta activity) at the seizure onset, indicating that the seizure is dominated by medium frequency bands 3.2– 12.8 Hz (theta and alpha bands). In 19 20 events the mean wavelet entropy presents lower values during the ictal period compared to the pre-ictal period, indicating that the associated dynamic is more ordered and simple. Thus the employed tools show good accuracy for detecting changes in the system dynamic. We conclude that this behavior could be induced by frequency tuning in the neuronal activity triggered by an hypothetic epileptic focus.

Wavelet entropy: a new tool for analysis of short duration brain electrical signals

Since traditional electrical brain signal analysis is mostly qualitative, the development of new quantitative methods is crucial for restricting the subjectivity in the study of brain signals. These methods are particularly fruitful when they are strongly correlated with intuitive physical concepts that allow a better understanding of brain dynamics. Here, new method based on orthogonal discrete wavelet transform (ODWT) is applied. It takes as a basic element the ODWT of the EEG signal, and defines the relative wavelet energy, the wavelet entropy (WE) and the relative wavelet entropy (RWE). The relative wavelet energy provides information about the relative energy associated with different frequency bands present in the EEG and their corresponding degree of importance. The WE carries information about the degree of order/disorder associated with a multi-frequency signal response, and the RWE measures the degree of similarity between different segments of the signal. In addition, the time evolution of the WE is calculated to give information about the dynamics in the EEG records. Within this framework, the major objective of the present work was to characterize in a quantitative way functional dynamics of order/disorder microstates in short duration EEG signals. For that aim, spontaneous EEG signals under different physiological conditions were analyzed. Further, specific quantifiers were derived to characterize how stimulus affects electrical events in terms of frequency synchronization (tuning) in the event related potentials.