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To ensure structural safety and integrity, a novel framework is developed for detecting the loosening of multi-bolt connections using wavelet entropy of vibro-acoustic modulation (VAM) signals. Wavelet entropy is employed as the dynamic index to capture the intricate time-frequency characteristics that are indicative of the connection status. Taking the wavelet entropy vectors as input, the proposed framework distinguishes itself by integrating a Transformer model for high-dimensional feature extraction with the recursive feature elimination (RFE) for essential feature selection, followed by a support vector machine (SVM) model for classification. Specifically, the Transformer model with innovative positional encoding capability helps to extract the time-dependent transient features that are sensitive to the bolt loosening. The RFE process reduces the data dimensionality while discerning the diagnostic information for more accurate classification. Through the experiment on a four-bolt joint, the identification results with cross-validation showed high accuracy and robustness of the proposed framework across various loosening cases. It outperformed the traditional SVM, long short-term memory network (LSTM), convolutional neural network (CNN)-SVM models without and with RFE, as well as the Transformer-SVM model without RFE, achieving an accuracy increase of 15.72%, 11.74%, 9.47%, 5.49%, and 5.06%, respectively. The proposed framework was demonstrated to be able to learn the damage-sensitive features more effectively from wavelet entropy data, marking a significant advancement in the health monitoring of engineering structures with high-strength bolt connections. [ABSTRACT FROM AUTHOR]

This study aimed to uncover the impact of COVID-19 on the leading cryptocurrency (Bitcoin) and on sustainable finance with specific attention to their potential long memory properties. In this article, the application of the selected methodologies is based on a fractal and entropy analysis of the econometric model in the financial market. To detect the regularity/irregularity property of a time series, approximate entropy is introduced to measure deterministic chaos. Using daily data for Bitcoin and sustainable finance, namely DJSW, Green Bond, Carbon, and Clean Energy, we examine long memory behaviour by employing a rescaled range statistic (R/S) methodology. The results of the research present that the returns of Bitcoin, the Dow Jones Sustainability World Index (DJSW), Green Bond, Carbon, and Clean Energy have a significant long memory. Contrastingly, an interdisciplinary approach, namely wavelet analysis, is also used to obtain complementary results. Wavelet analysis can provide warning information about turmoil phenomena and offer insights into co-movements in the time–frequency space. Our findings reveal that approximate entropy shows crisis (turmoil) conditions in the Bitcoin market, despite the nature of the pandemic's origin. Crucially, compared to Bitcoin assets, sustainable financial assets may play a better safe haven role during a pandemic turmoil period. The policy implications of this study could improve trading strategies for the sake of portfolio managers and investors during crisis and non-crisis periods. [ABSTRACT FROM AUTHOR]

The constant-Q Gabor atom is developed for spectral power, information, and uncertainty quantification from time–frequency representations. Stable multiresolution spectral entropy algorithms are constructed with continuous wavelet and Stockwell transforms. The recommended processing and scaling method will depend on the signature of interest, the desired information, and the acceptable levels of uncertainty of signal and noise features. Selected Lamb wave signatures and information spectra from the 2022 Tonga eruption are presented as representative case studies. Resilient transformations from physical to information metrics are provided for sensor-agnostic signal processing, pattern recognition, and machine learning applications. [ABSTRACT FROM AUTHOR]

Exploring the shape and direction of hidden cracks in a tunnel lining structure is one of the main objectives of ground penetrating radar (GPR) map interpretation. The most important factor that restricts the migration imaging of hidden cracks is the propagation velocity of electromagnetic waves. Determining the optimal electromagnetic wave velocity is the key to truthfully restoring the actual shape of hidden cracks. To study the GPR characteristic response signals of hidden cracks, forward simulation and model experiments of different cracks were performed. Subsequently, a method to determine the optimal electromagnetic wave velocity based on the wavelet entropy theory was proposed, and the frequency wavenumber domain migration (F-K) and Kirchhoff integral migration imaging method were combined. Horizontal, S-type, and inclined hidden fractures were examined by migration imaging. The results show that the radar characteristic response images of different cracks can be simulated forward by using the finite difference time domain method to write the fracture model instruction. Based on the wavelet entropy theory, the error range between the estimated value and true value was controlled within 4%. Taking the optimal electromagnetic wave velocity as the velocity parameter of the conventional migration method can make the migration more effective and suppress the interference of echo signals so that the diffraction wave converges, and the energy is more concentrated; thus, the real fracture morphology can be restored to the greatest extent. The research results can provide technical support for the fine detection of hidden quality defects in tunnel lining structures by GPR mapping. [ABSTRACT FROM AUTHOR]

Reliable operation of synchronous generators in hydroelectric power plants is crucial for avoiding unplanned stoppages that can incur substantial costs. The damper winding of salient pole synchronous generators (SPSGs) contributes to machine operation only during transient periods; however, it is a critical component that preserves the dynamic stability and protects the rotor in case of a fault. Consequently, detection of a broken damper bar (BDB) fault is vital for safe operation. Current methods for the BDB detection depend on visual inspection or offline tests. However, most of the recently proposed approaches have used invasive sensors that can detect BDB faults only during transient operation. In this article, a novel method is proposed based on a noninvasive sensor with high sensitivity to BDB faults that can identify a BDB fault either during transient operation or in the steady-state (SS) period. The effectiveness of the proposed method is validated by finite-element modeling and by experimental results from a 100-kVA custom-made SPSG. The proposed method is confirmed to provide a reliable and sensitive diagnosis of BDB faults during transient or SS operation, even in noisy environments. [ABSTRACT FROM AUTHOR]

Damage evolution in concrete is a complex phenomenon involving micro-cracks that originate from different material phases (mortar matrix, ITZ and aggregate), and culminate into a major crack. The information about the individual damaged material phases can provide major insights into the global failure behaviour, cracking path, and fracture processes. The evolution of damage, damage mechanisms and the material phase of origin of micro-cracks is highly influenced by the type of concrete (Normal and high strength). In order to investigate the evolution of damage in concrete of varying strength, notched beam specimens with different water-to-cement ratios have been prepared and tested under C M O D control. The evolution and growth of damage have been continuously monitored during testing through acoustic emission techniques. Based on acoustic emission results, it has been demonstrated that the damage progression in concrete can be better described as a function of the wavelet entropy of the AE events occurring during the entire loading duration, and therefore, an analytical model for the damage evolution has been proposed. The study reveals that, under the high-strength category, the level of deterioration reduces as the w / c ratio rises, while in normal-strength concrete, a reverse trend is observed. Furthermore, a novel approach has been proposed that utilizes wavelet entropy and amplitude to differentiate amongst various damaged material phases with the help of an unsupervised clustering algorithm. Normal-strength concrete with a w / c ratio of 0.4 has been used to demonstrate the proposed methodology and has been validated with the help of experiments performed on the mortar and the parent stone of aggregate. A higher occurrence of mode-I cracks compared to mode-II cracks across all material phases has been observed for the specimen. Additionally, ITZ and aggregate exhibit a greater proportion of tensile and shear cracking events than the matrix phase. In the end, a deep learning convolutional neural network (CNN) model is devised utilizing labelled scalogram images of the AE waveforms to discriminate between the various damaged material phases. A 10-fold training cross-validation of the dataset has been carried out to achieve a stable performance. The deep learning model performs well in discriminating the damaged material phases with high training, validation, and testing accuracy. • A damage variable based on wavelet entropy to evaluate the amount of deterioration in concrete has been proposed. • The damaged material phase identification with the help of acoustic emission event has been performed. • A convolutional neural network has been developed to discriminate between the AE events pertaining to different material phases. [ABSTRACT FROM AUTHOR]

It has become vital to effectively characterize the self-similar and regular patterns in time series marked by short-term and long-term memory in various fields in the ever-changing and complex global landscape. Within this framework, attempting to find solutions with adaptive mathematical models emerges as a major endeavor in economics whose complex systems and structures are generally volatile, vulnerable and vague. Thus, analysis of the dynamics of occurrence of time section accurately, efficiently and timely is at the forefront to perform forecasting of volatile states of an economic environment which is a complex system in itself since it includes interrelated elements interacting with one another. To manage data selection effectively and attain robust prediction, characterizing complexity and self-similarity is critical in financial decision-making. Our study aims to obtain analyzes based on two main approaches proposed related to seven recognized indexes belonging to prominent countries (DJI, FCHI, GDAXI, GSPC, GSTPE, N225 and Bitcoin index). The first approach includes the employment of Hurst exponent (HE) as calculated by Rescaled Range (R / S) fractal analysis and Wavelet Entropy (WE) in order to enhance the prediction accuracy in the long-term trend in the financial markets. The second approach includes Artificial Neural Network (ANN) algorithms application Feed forward back propagation (FFBP), Cascade Forward Back Propagation (CFBP) and Learning Vector Quantization (LVQ) algorithm for forecasting purposes. The following steps have been administered for the two aforementioned approaches: (i) HE and WE were applied. Consequently, new indicators were calculated for each index. By obtaining the indicators, the new dataset was formed and normalized by min-max normalization method' (ii) to form the forecasting model, ANN algorithms were applied on the datasets. Based on the experimental results, it has been demonstrated that the new dataset comprised of the HE and WE indicators had a critical and determining direction with a more accurate level of forecasting modeling by the ANN algorithms. Consequently, the proposed novel method with multifarious methodology illustrates a new frontier, which could be employed in the broad field of various applied sciences to analyze pressing real-world problems and propose optimal solutions for critical decision-making processes in nonlinear, complex and dynamic environments. [ABSTRACT FROM AUTHOR]

Electronic tongue mimics human gustatory sensation and is used to characterize and discriminate beverages and foods. Feature extraction plays a key role in improving the classification accuracy by preserving the distinct characteristics while reducing high dimensionality of data generated from electronic tongue. This paper presents a new feature extraction method based on stationary wavelet singular entropy for a developed electronic tongue system to classify pasteurized cow milk. The electronic tongue consists of an array of five working electrodes along with a reference and a counter electrode to characterize milk sample. The feature extraction of acquired data is done by computing stationary wavelet transform to obtain detail and approximate coefficients at different level of decomposition. These coefficients are processed using singular value decomposition followed by calculation of entropy to obtain stationary wavelet singular entropy values. These values form the feature set and feed to two classifiers, k-nearest neighbor and back propagation artificial neural network, and their classification accuracy is evaluated with variation in their model parameters. The proposed method is compared with other wavelet transform-entropy methods in terms of classification accuracy, which indicates that the proposed method is more effective in discriminating milk samples. [ABSTRACT FROM AUTHOR]

Postdisaster search and rescue is an important application of ultra‐wideband radar system, which mainly detects survivors by their respiratory‐motion response. In the application of detecting multiple human targets, owing to faint amplitude of human chest movement and high attenuation of electromagnetic wave, the motionless living human targets cannot be discriminated accurately, especially in a complex rescue condition with dynamic clutter interference. In this article, on account of the significant difference of frequency components between the echo signal of tested target and that of illusive target produced by dynamic clutter, an algorithm based on wavelet entropy is proposed. Compared with the reference algorithms of adaptive line enhancement and energy accumulation, the wavelet entropy can accurately detect multiple human targets under the condition of dynamic clutter interference, even though the human targets stand far away locate in the shadowing region caused by the closer one. [ABSTRACT FROM AUTHOR]

Ordinary microphone cannot accurately reflect authentic human feelings in the sound quality testing and evaluation. By contrast, professional artificial head system can produce similar results with human feelings through the simulation of human auditory system, but it is expensive and unable to occupy the driver's seat to record the vehicle sound. Here we design a portable system based on self-adaptive neural network (NN) which can obtain the result of sound quality evaluation similar with the artificial head. The system consists of binaural microphone, signal conditioning units (SCU), and mobile phone. Firstly, sound is perceived by binaural microphone, processed by SCU, and collected by mobile phone. Initial sound quality objective parameters are calculated after noise reduction for sound signals and then the accurate objective parameters can be obtained from the initial parameters through the trained NN model. To train the model, the portable system and the HEAD system are simultaneously used to collect sound sample as the input and output sample sets under different conditions. After the input samples are preprocessed, wavelet entropy eigenvalues based on the best tree wavelet packet analysis are calculated along with psychoacoustic parameters of all the samples. Finally, we obtain the combined feature vectors and successfully train the model. Checked by the practical data, the relative error of sound quality objective parameters produced by the NN model is less than 5% compared with the HEAD system, which conforms to general engineering requirements. This inexpensive and user-friendly portable system paves a new way in the sound quality testing and evaluation that are highly desirable for vehicle acoustical designs and improvements. [ABSTRACT FROM AUTHOR]

Symbolic aggregate approximation is an important way to extract time series features. However，traditional symbol aggregation approximation methods have many defects，such as the averaged segment number, equal segmentation interval, and mutation information that cannot accurately reflect the non-stationary sequence. Aiming at the abovementioned problems, we establish a new time series SAX model by introducing the local mean decomposition and a segmentation algorithm for improving wavelet entropy. The basic principle of the model is to denoise the original sequences by the local mean decomposition technique, obtain the segmentation number by the sliding window threshold method, and use SAX notation to represent the symbols，and the KNN classifier is used to realize classification performance test. Based on this improved model，we carry out an empirical test. The results show that the algorithm can effectively extract the information features of the sequences, has a high fitness degree， and achieves the purpose of dimensionality reduction. And more importantly, it improves the classification accuracy of the KNN classification algorithm in SAX notation. [ABSTRACT FROM AUTHOR]

We propose a method for finding a priori undefined structures of unknown temporal fluctuations for frequency oscillators of various intensities as part of the output signals of synchronized dynamical systems. Unlike traditional approaches, the developed method is based on the continuous wavelet transform of the observed signal and is efficient in cases when frequency characteristics of the desired pattern are close to the noise characteristics of the output signal. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the performance of the 12 entropy-based features for the monitoring and detection of bearing faults. These entropy measures were proposed both in time, frequency and time–frequency domain. Probability mass function (PMF) was extracted from the time waveforms using four different methods: (i) via power spectral density, (ii) via ordinal pattern distribution, (iii) via wavelet packet tree and iv) ensemble empirical mode decomposition. Three different entropy measures were used in the article: (i) Shannon entropy, (ii) Rényi entropy and (iii) Jensen–Rényi divergence. A new bearing produces a vibration time series characterised by random noise without prominent periodic content. As soon as a fault develops, impulses are produced, what excites structural resonances generating a train of impulse responses. As defect grows, it becomes a distributed fault, and then no sharp impulses are generated but rather an amplitude modulated random noise signal. The proposed methodology has been applied to detect bearing faults by the analysis of two real bearing datasets, from run-to-failure experiments. Three bearings that presented different defects in the test (inner race fault, rolling elements fault and outer race fault) were analysed to validate the performance of the entropy-based features. The modified Z-score has been implemented and used as an index to detect changes of the entropy features. The results clearly demonstrate that the proposed approach represents a valuable non-parametric tool for early detection of anomalies in bearings vibration signals. Highlights • We study 12 entropy-based features for monitoring and detection of bearing faults. • The proposed methodology is tested on two real bearing vibration signal datasets. • Entropy is shown to be a valuable tool for early detection of anomalies in bearings. [ABSTRACT FROM AUTHOR]

A wavelet-matched filter bank is considered as a brain stroke diagnostic scheme to yield multiscale analysis and joint time-scale representation of microwave backscattered signal from a radiated head. Gaussian-modulated sinusoidal signal of 3-GHz bandwidth is radiated sequentially by an antenna at different locations around the head. An anatomically realistic 3-D-head model and a numerical analysis technique based on a finite-difference time-domain convolution approach are adopted to formulate the electromagnetic wave propagation in dispersive domain represented by fourth-order Debye model. The variance in the calculated scalogram and the Shannon wavelet entropy of the filtered backscattered signals in time/scale plane at spatial antennas around the head would play a crucial role to detect the defection in the computational domain. Beside the cost and scarce availability of expensive stroke diagnostic tools, we claim that the proposed microwave diagnosis scheme can be a promising, efficient portable tool. Finally, noisy backscattered signal is considered to study its impact on the wavelet quantities as relative energy and entropy. Wavelet entropy in time domain is found to be less sensitive to the noise in the processed signal. [ABSTRACT FROM AUTHOR]

Fatigue driving is bringing more and more serious harm, but there are various reasons for fatigue driving, it is still difficult to test the driver's fatigue. This paper defines a method to test driver's fatigue based on the EEG, and different from other researches into fatigue driving, this paper mainly takes the fatigue features of EEG signals in fatigue state and uses wavelet entropy as the feature extraction method to analyze the features of wavelet entropy and spectral entropy features as well as the classification accuracy under the same classifier. The SVM is used to show the classifier's results. The accuracy of the driver fatigue state monitoring using the wavelet entropy is 90.7%, which is higher than the use of spectral entropy as the characteristic accuracy rate of 81.3%. The results show that the frequency characteristics of EEG can be well applied to driving fatigue testing, but different frequency feature calculation methods will affect the classification accuracy. [ABSTRACT FROM AUTHOR]

• Effect of notch-to-depth ratio on flexural and fracture properties of UHPGC notched beams is investigated by four-point bending test. • AE energy is used to characterize the fracture process of UHPGC notched beams. • The correlation between fracture energy and cumulative AE energy is evaluated. • The wavelet entropy evolution model during loading process is constructed to provide early warning prior to reach the peak load. An ecological ultra-high-performance glass sand concrete (UHPGC) was prepared by partially replacing quartz sand in traditional ultra-high-performance concrete (UHPC) with glass sand recycled from waste glass. The four-point bending tests of UHPGC notched beams with different notch-depth ratios (0.2, 0.3, 0.4, and 0.5) were carried out, while acoustic emission (AE) monitoring was employed at the whole fracture process. Flexural toughness and residual flexural tensile strength were used to evaluate the flexural properties. Meanwhile, fracture energy and fracture toughness were used to evaluate the fracture properties. The results reveal that notch-depth ratio exhibits a significant effect on the flexural and fracture performances of UHPGC notched beams. The residual flexural tensile strength, flexural toughness, fracture energy and fracture toughness decrease with the increase of notch depth. Moreover, AE energy parameters can favorably characterize the differences of energy release in the fracture processes of UHPGC beams with different notch depths, and favorable correlations are observed between cumulative AE energy and fracture energy. Besides, AE wavelet entropy are constructed based on wavelet packet transform (WPT) of AE waveforms, and the evolution model of wavelet entropy is established. By comparing with the evolution process of AE energy information entropy, it is proved that the maximum point of wavelet entropy can be used as the key point to predict the peak load. [ABSTRACT FROM AUTHOR]

This study proposes a wavelet-based multi-resolution modeling approach for statistical downscaling of GCM variables to mean monthly precipitation for five locations at Krishna Basin, India. Climatic dataset from NCEP is used for training the proposed models (Jan.’69 to Dec.’94) and are applied to corresponding CanCM4 GCM variables to simulate precipitation for the validation (Jan.’95–Dec.’05) and forecast (Jan.’06–Dec.’35) periods. The observed precipitation data is obtained from the India Meteorological Department (IMD) gridded precipitation product at 0.25 degree spatial resolution. This paper proposes a novel Multi-Scale Wavelet Entropy (MWE) based approach for clustering climatic variables into suitable clusters using k-means methodology. Principal Component Analysis (PCA) is used to obtain the representative Principal Components (PC) explaining 90–95% variance for each cluster. A multi-resolution non-linear approach combining Discrete Wavelet Transform (DWT) and Second Order Volterra (SoV) is used to model the representative PCs to obtain the downscaled precipitation for each downscaling location (W-P-SoV model). The results establish that wavelet-based multi-resolution SoV models perform significantly better compared to the traditional Multiple Linear Regression (MLR) and Artificial Neural Networks (ANN) based frameworks. It is observed that the proposed MWE-based clustering and subsequent PCA, helps reduce the dimensionality of the input climatic variables, while capturing more variability compared to stand-alone k-means (no MWE). The proposed models perform better in estimating the number of precipitation events during the non-monsoon periods whereas the models with clustering without MWE over-estimate the rainfall during the dry season. [ABSTRACT FROM AUTHOR]

The chaos characteristics for system complexity, e.g. randomness and fractality, are generally ignored when researchers study the complex behaviour of precipitation time series, which makes it difficult to elicit adequate information for such series. The main objective of this study was to diagnose the complexity of seasonal precipitation by using wavelet entropy and mean wavelet entropy, and to find the complex system of spatial variation in seasonal precipitation for the sub-areas of Jiansanjiang Administration in China as a case study. The results illustrate that the complexity characteristic of the seasonal precipitation series is greatest in the North sub-area, lowest in the Middle sub-area, and intermediate in the South sub-area; topography and agricultural development are the key driving factors of the complex dynamic variation in the local seasonal precipitation time series. This study provides a basis for analysing the trend in development of complex precipitation time series and realizing the sustainable use of regional water resources. [ABSTRACT FROM AUTHOR]

Ultra-wide band (UWB) radar for short-range human target detection is widely used to find and locate survivors in some rescue missions after a disaster. The results of the application of bistatic UWB radar for detecting multi-stationary human targets have shown that human targets close to the radar antennas are very often visible, while those farther from radar antennas are detected with less reliability. In this paper, on account of the significant difference of frequency content between the echo signal of the human target and that of noise in the shadowing region, an algorithm based on wavelet entropy is proposed to detect multiple targets. Our findings indicate that the entropy value of human targets was much lower than that of noise. Compared with the method of adaptive filtering and the energy spectrum, wavelet entropy can accurately detect the person farther from the radar antennas, and it can be employed as a useful tool in detecting multiple targets by bistatic UWB radar. [ABSTRACT FROM AUTHOR]

In the context of systematic optimization and intelligent upgrade of the mineral production， the assessment and quantification of the operators’ behavioral factors need to be investigated to further enhance productivity and quality of the products. A real-time analysis method based on the electroencephalography (EEG) characteristics was presented in grinding process. To begin with， the δ， θ， α， and β rhythms in different brain regions were extracted using wavelet decomposition. Then the wavelet entropy can be obtained by calculating the energy sequence distribution of different wavelet coefficient vectors. According to the comparison of the entropy values， the specific brain region was selected. Through wavelet time-frequency analysis， (α+β)/(δ+θ+α+β) was determined as the spectral characteristic. Finally， the results of real-time analysis using B-spline curve and sliding window showed that the physiological indicators can reflect the trend of the granularity curves and assess the operators’ influence factors objectively to some extent. [ABSTRACT FROM AUTHOR]

Traveling surges are commonly adopted in protection devices of high-voltage direct current (HVDC) transmission systems. Lightning strikes also can produce large-amplitude traveling surges which lead to the malfunction of relays. To ensure the reliable operation of protection devices, recognition of traveling surges must be considered. Wavelet entropy, which can reveal time-frequency distribution features, is a potential tool for traveling surge recognition. In this paper, the effectiveness of wavelet entropy in characterizing traveling surges is demonstrated by comparing its representations of different kinds of surges and discussing its stability with the effects of propagation distance and fault resistance. A wavelet entropy-based recognition method is proposed and tested by simulated traveling surges. The results show wavelet entropy can discriminate fault traveling surges with a good recognition rate. [ABSTRACT FROM AUTHOR]

This paper presents a constant speed rotating machines fault analysis method to maximize incipient fault signatures based on computed order tracking with adaptive filter and cyclic logarithmic envelope spectrum (CLES) tools. First, adaptive filter reduces not-concerned harmonic components and measurement artefacts from a vibration signal. To accurately and precisely select the step size in the process of the LMS-type adaptive filter, a new method is proposed based on wavelet entropy (WE). Then, a tacho signal is generated from vibration signal and computed order tracking is performed using this tacho signal. Finally, to reduce the effect of second-order cyclostationarity, CLES tool is used to analyze the incipient fault features. Simulations are carried out and the performances of WE and CLES are compared with traditional method. Furthermore, vibration signals of real experimental data are used to verify the robustness of the proposed method. The experimental results show that the proposed method can effectively maximize the incipient fault signatures of rotating machines. [ABSTRACT FROM AUTHOR]

A detailed understanding of key signal characteristics has enabled the use of artificial neural networks (ANN) for feature detection and classification of EEG signals in clinical research. The present study is performed to classify EEG signals of normal and depression patients with wavelet parameters as key input features. The characteristics of depression cannot be made out by visual inspection of EEG records unlike epilepsy which is well characterized by sudden recurrent and transient waveforms. In this study, a comparison is made between the performance of feedforward neural network (FFNN) and probabilistic neural network (PNN) while classifying the EEG signals of normal and depression patients. Classification capabilities of both the methods are validated with the EEG recordings from 30 normal controls and 30 depression patients. One-way ANOVA provided a statistical significant difference between the two classes of EEG signals recorded. Preprocessing for feature extraction is done using discrete wavelet transform (DWT). The time domain and relative wavelet energy (RWE) features calculated from the sub-bands are given as a set of input to the neural network. Another set of feature used independently for training the network is the wavelet entropy (WE). The FFNN achieved a classification accuracy of 100% and PNN gave an accuracy of 58.75% with time domain and wavelet energy as the input features. With wavelet entropy as the input feature, FFNN further showed 98.75% classification accuracy while PNN gave an accuracy of only 46.5%. The results indicate that FFNN with the given input features is more suitable for the classification of EEG signals with mood changing depressive disorders. [ABSTRACT FROM AUTHOR]

Most spectral background subtraction methods rely on the difference in frequency response of background compared with characteristic peaks. It is difficult to extract accurately the background components from the spectrum when characteristic peaks and background have overlaps in frequency domain. An improved background estimation algorithm based on iterative wavelet transform (IWT) is presented. The wavelet entropy principle is used to select the best wavelet basis. A criterion based on wavelet energy theory to determine the optimal iteration times is proposed. The case of energy dispersive X-ray spectroscopy is discussed for illustration. A simulated spectrum with a prior known background and an experimental spectrum are tested. The processing results of the simulated spectrum is compared with non-IWT and it demonstrates the superiority of the IWT. It has great significance to improve the accuracy for spectral analysis. [ABSTRACT FROM AUTHOR]

Objective To assess whether there is a difference in the background activity in the ripple band (80–200 Hz) between epileptic and non-epileptic channels, and to assess whether this difference is sufficient for their reliable separation. Methods We calculated mean and standard deviation of wavelet entropy in 303 non-epileptic and 334 epileptic channels from 50 patients with intracerebral depth electrodes and used these measures as predictors in a multivariable logistic regression model. We assessed sensitivity, positive predictive value (PPV) and negative predictive value (NPV) based on a probability threshold corresponding to 90% specificity. Results The probability of a channel being epileptic increased with higher mean ( p = 0.004) and particularly with higher standard deviation ( p < 0.0001). The performance of the model was however not sufficient for fully classifying the channels. With a threshold corresponding to 90% specificity, sensitivity was 37%, PPV was 80%, and NPV was 56%. Conclusions A channel with a high standard deviation of entropy is likely to be epileptic; with a threshold corresponding to 90% specificity our model can reliably select a subset of epileptic channels. Significance Most studies have concentrated on brief ripple events. We showed that background activity in the ripple band also has some ability to discriminate epileptic channels. [ABSTRACT FROM AUTHOR]

The aim of this article is to describe the relationship between consciousness and epilepsy. Epilepsy is a neurological disorder which can be seen all over the world. It can be diagnosed by the brain's electrical activity (EEG). The determination of epileptic attacks by EEG signals is quite common in both clinical and research fields. During epileptic seizures, the brain dynamics that make up the graph consist of abnormalities in EEG signals. In this study, the relation between epilepsy and consciousness will be investigated by using wavelet entropy and artificial neural networks. [ABSTRACT FROM AUTHOR]

Global change, as a combination of climate change, human activities on watersheds and the river flow regulation, causes intense changes in hydrological cycles and, consequently, threatens the good ecological status of freshwater biological communities. This study addresses how and whether the combination of climatic drivers and local human impacts may alter the metabolism of freshwater communities. We identified a few factors modulating the natural water flow and quality in 25 point spread within the Ebro river Basin: waste water spills, industrial spills, reservoir discharges, water withdrawals, agricultural use, and the presence of riparian forests. We assessed their impacts on the freshwater metabolism as changes in the annual cycle of both gross primary production—GPP – and ecosystem respiration—ER –. For this purpose, daily data series were analyzed by continuous wavelet transformation, allowing for the assessment of the metabolic ecosystem Frequency Spectrum Patterns (FSPs). Changes in the behavior of ecosystem metabolism were strongly associated with local characteristics at each sampling point, however in 20 out of 25 studied points, changes in metabolic ecosystem FSP were related to climatic change events (the driest period of the last 140 years). The changes in FSP indicate that severe impacts on how biological communities use carbon sources occur as a result of the human water management – too much focus on human needs – during intense climatic events. Results show that local factors, and specially the flow regulation, may modulate the impact of global change. As example those points exposed to a more intense anthropization showed a clear disruption – and even disappearance – of the annual FSP. This information may help managers to understand the action mechanisms of non-climatic factors at ecosystem level, leading to better management policies based on the promotion of ecosystem resilience. The method here presented may help on improving the calculation of ecological flows to maintain the river metabolic annual cycles as close as possible to the natural ones. [ABSTRACT FROM AUTHOR]

Background and objective Hydrocephalus comprises a number of conditions characterised by clinical symptoms, dilated ventricles and anomalous cerebrospinal fluid (CSF) dynamics. Infusion tests (ITs) are usually performed to study CSF circulation and in the preoperatory evaluation of patients with hydrocephalus. The study of intracranial pressure (ICP) signals recorded during ITs could be useful to gain insight into the underlying pathophysiology of this condition and to further support treatment decisions. In this study, two wavelet parameters, wavelet turbulence ( WT ) and wavelet entropy ( WE ), were analysed in order to characterise the variability, irregularity and similarity in spectral content of ICP signals in hydrocephalus. Methods One hundred and twelve ICP signals were analysed using WT and WE . These parameters were calculated in two frequency bands: B 1 (0.15–0.3 Hz) and B 2 (0.67–2.5 Hz). Each signal was divided into four artefact-free epochs corresponding to the basal, early infusion, plateau and recovery phases of the IT. We calculated the mean and standard deviation of WT and WE and analysed whether these parameters revealed differences between epochs of the IT. Results Statistically significant differences ( p  < 1.70⋅10 −3 , Bonferroni-corrected Wilcoxon signed-rank tests) in pairwise comparisons between phases of ITs were found using the mean and standard deviation of WT and WE . These differences were mainly found in B 2 . Conclusions Wavelet parameters like WT and WE revealed changes in the signal time-scale representation during ITs. Statistically significant differences were mainly found in B 2 , associated with ICP pulse waves, and included a higher degree of similarity in the spectral content, together with a lower irregularity and variability in the plateau phase with respect to the basal phase. [ABSTRACT FROM AUTHOR]

Background Because acute ethanol (EtOH) administration is known to influence cognitive processes by impairing hippocampal function, electrophysiological responses of the hippocampus following EtOH exposure warrant investigation. To mimic in vivo conditions, we recorded and analyzed critical firing characteristics of the neuronal population dynamically, particularly in the hippocampal region, before and after acute EtOH administration. Methods Microelectrodes were inserted in the hippocampus CA1 region of 21 Institute of Cancer Research mice. The mice were divided into 3 groups, including an EtOH injection group (1.5 g/kg), a saline injection group (1.5 g/kg), and a negative control group that received no injection. A data acquisition system was employed to detect the local field potentials ( LFPs) and spike potentials following acute EtOH administration. Various multichannel electrophysiological signals were collected in vivo in each group at 60 minutes, from which the firing rate and wavelet entropy ( WE) were analyzed further. Results Firing rates began to decline at 20 minutes postinjection and then gradually recovered from 40 to 60 minutes. In contrast, 20 minutes post-injection, WE increased maximally and then returned to normal from 40 to 60 minutes ( p < 0.05). Pronounced changes in the relative energy of theta and alpha oscillations were also observed after 20 minutes of alcohol exposure and recovery occurred by 60 minutes ( p < 0.05). Conclusions A major mechanism of EtOH's action on the hippocampus is neurotransmitter blocking in the form of excitatory neuron inhibition in vivo. Changes in hippocampal spikes coincided with changes in LFPs during the entire time course of acute EtOH administration. The correlation between spikes and LFPs suggests that they jointly affect encoding in hippocampus. [ABSTRACT FROM AUTHOR]

An accurate diagnosis is important for the medical treatment of patients suffering from brain diseases. Magnetic resonance (MR) images are commonly used by technicians to assist preclinical diagnosis. The classification of MR images of normal and pathological brains poses a challenge from the technological point of view, since MR imaging generates a large information set that reflects the conditions of the brain. In this paper, we present a computer-assisted diagnosis method based on wavelet entropy (WE) of the feature space approach and a feed-forward neural network (FNN) classification method for improving the brain diagnosis accuracy by means of MR images. The most relevant image feature is selected as the WE, which is used to train an FNN classifier. The results using tenfold cross validation of 64 images show that the average accuracy attainable is 100.00%. It can be easily seen from the data that the proposed classifier can detect abnormal brains from normal controls with excellent performance, which can compete with the latest methods. © 2016 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc. [ABSTRACT FROM AUTHOR]

The activities of the brain and the heart are dynamic, chaotic, and possibly intrinsically coordinated. This study aims to investigate the effect of Mindfulness-Based Stress Reduction (MBSR) program on the chaoticity of electronic activities of the brain and the heart, and to explore their potential correlation. Electroencephalogram (EEG) and electrocardiogram (ECG) were recorded at the beginning of an 8-week standard MBSR training course and after the course. EEG spectrum analysis was carried out, wavelet entropies (WE) of EEG (together with reconstructed cortical sources) and heart rate were calculated, and their correlation was investigated. We found enhancement of EEG power of alpha and beta waves and lowering of delta waves power during MBSR training state as compared to normal resting state. Wavelet entropy analysis indicated that MBSR mindfulness meditation could reduce the chaotic activities of both EEG and heart rate as a change of state. However, longitudinal change of trait may need more long-term training. For the first time, our data demonstrated that the chaotic activities of the brain and the heart became more coordinated during MBSR training, suggesting that mindfulness training may increase the entrainment between mind and body. The 3D brain regions involved in the change in mental states were identified. [ABSTRACT FROM AUTHOR]

For the modeling of complex and nonlinear crude oil price dynamics and movement, wavelet analysis can decompose the time series and produce multiple economically meaningful decomposition structures based on different assumptions of wavelet families and decomposition scale. However, the determination of the optimal model specification will critically affect the forecasting accuracy. In this paper, we propose a new wavelet entropy based approach to identify the optimal model specification and construct the effective wavelet entropy based forecasting models. The wavelet entropy algorithm is introduced to determine the optimal wavelet families and decomposition scale, that will produce the improved forecasting performance. Empirical studies conducted in the crude oil markets show that the proposed algorithm outperforms the benchmark model, in terms of conventional performance evaluation criteria for the model forecasting accuracy. [ABSTRACT FROM AUTHOR]

Vibration-based condition monitoring and fault diagnosis is an effective approach to maintain the reliable operation of a scroll compressor. Unfortunately, the vibration signal from the scroll compressor always has characteristics of being non-linear and non-stationary, which makes vibration signal analysis and fault feature extraction very difficult. To extract the significant fault features, a vibration analysis method based on Wavelet entropy is proposed in this paper. Two forms of the wavelet entropy, namely the wavelet space feature spectrum entropy (WSFSE) and the wavelet energy spectrum entropy (WESE), are defined to depict instantaneous characteristics of the local variation of the vibration signal. Four types of mechanical faulty vibration signal, namely unbalanced rotor, malfunctioning scroll, loosened mechanical assembly, and loosened bearing, are analyzed by using the proposed approach. The experimental results show that feature components and energy distribution of each fault signal is accurately identified and revealed, which proves that the combined application of WSFSE and WESE approach is a successful scheme for the vibration analysis of scroll compressors. [ABSTRACT FROM AUTHOR]

A novel method of quantifying the effectiveness of the suppression of ventricular activity from electrocardiograms (ECGs) in atrial fibrillation is proposed. The temporal distribution of the energy of wavelet coefficients is quantified by wavelet entropy at each ventricular beat. More effective ventricular activity suppression yields increased entropies at scales dominated by the ventricular and atrial components of the ECG. Two studies are undertaken to demonstrate the efficacy of the method: first, using synthesised ECGs with controlled levels of residual ventricular activity, and second, using patient recordings with ventricular activity suppressed by an average beat template subtraction algorithm. In both cases wavelet entropy is shown to be a good measure of the effectiveness of ventricular beat suppression. [ABSTRACT FROM AUTHOR]

This work introduces for the first time the application of wavelet entropy (WE) to detect episodes of the most common cardiac arrhythmia, atrial fibrillation (AF), automatically from the electrocardiogram (ECG). Given that AF is often asymptomatic and usually presents very brief initial episodes, its early automatic detection is clinically relevant to improve AF treatment and prevent risks for the patients. After discarding noisy TQ intervals from the ECG, the WE has been computed over the median TQ segment obtained from the 10 previous noise-free beats under study. In this way, the P-waves or the fibrillatory waves present in the recording were highlighted or attenuated, respectively, thus enabling the patient's rhythm identification (sinus rhythm or AF). Results provided a discriminant ability of about 95%, which is comparable to previous works. However, in contrast to most of them, which are mainly based on quantifying RR series variability, the proposed algorithm is able to deal with patients under rate-control therapy or with a reduced heart rate variability during AF. Additionally, it also presents interesting properties, such as the lowest delay in detecting AF or sinus rhythm, the ability to detect episodes as brief as five beats in length or its integration facilities under real-time beat-by-beat ECG monitoring systems. Consequently, this tool may help clinicians in the automatic detection of a wide variety of AF episodes, thus gaining further knowledge about the mechanisms initiating this arrhythmia. [ABSTRACT FROM AUTHOR]

With the aim of developing an accurate pathological brain detection system, we proposed a novel automatic computer-aided diagnosis (CAD) to detect pathological brains from normal brains obtained by magnetic resonance imaging (MRI) scanning. The problem still remained a challenge for technicians and clinicians, since MR imaging generated an exceptionally large information dataset. A new two-step approach was proposed in this study. We used wavelet entropy (WE) and Hu moment invariants (HMI) for feature extraction, and the generalized eigenvalue proximal support vector machine (GEPSVM) for classification. To further enhance classification accuracy, the popular radial basis function (RBF) kernel was employed. The 10 runs of k-fold stratified cross validation result showed that the proposed "WE + HMI + GEPSVM + RBF" method was superior to existing methods w.r.t. classification accuracy. It obtained the average classification accuracies of 100%, 100%, and 99.45% over Dataset-66, Dataset-160, and Dataset-255, respectively. The proposed method is effective and can be applied to realistic use. [ABSTRACT FROM AUTHOR]

Epilepsy is a neurological disorder characterized by the sudden abnormal discharging of brain neurons that can lead to encephalographic (EEG) abnormalities. In this study, data was obtained from epileptic patients with intracranial depth electrodes and analyzed using wavelet entropy algorithms in order to locate the epileptic foci. Significant increases in the wavelet entropy of the epileptic signals were identified during multiple episodes of clinical seizures. The results indicated that the algorithm was capable of identifying entropy changes in the epileptic sources. Furthermore, the correlations among the electrocorticogram (ECoG) signals of different channels determined using the amplitude-amplitude coupling method verified that the epileptic foci exhibited significantly higher coupling strengths. Thus, cross frequency coupling (CFC) could be an inspiration to energy and signal transitive mode of seizure and, thereby, improve diagnostic processes. [ABSTRACT FROM AUTHOR]

The aim of the present study was to characterize the neural network reorganization during a cognitive task in schizophrenia (SCH) by means of wavelet entropy (WE). Previous studies suggest that the cognitive impairment in patients with SCH could be related to the disrupted integrative functions of neural circuits. Nevertheless, further characterization of this effect is needed, especially in the time-frequency domain. This characterization is sensitive to fast neuronal dynamics and their synchronization that may be an important component of distributed neuronal interactions; especially in light of the disconnection hypothesis for SCH and its electrophysiological correlates. In this work, the irregularity dynamics elicited by an auditory oddball paradigm were analyzed through synchronized-averaging (SA) and single-trial (ST) analyses. They provide complementary information on the spatial patterns involved in the neural network reorganization. Our results from 20 healthy controls and 20 SCH patients showed a WE decrease from baseline to response both in controls and SCH subjects. These changes were significantly more pronounced for healthy controls after ST analysis, mainly in central and frontopolar areas. On the other hand, SA analysis showed more widespread spatial differences than ST results. These findings suggest that the activation response is weakly phase-locked to stimulus onset in SCH and related to the default mode and salience networks. Furthermore, the less pronounced changes in WE from baseline to response for SCH patients suggest an impaired ability to reorganize neural dynamics during an oddball task. [ABSTRACT FROM AUTHOR]

ABSTRACT A novel millimeter-wave radar speech sensor based on vibration detection developed in our laboratory can penetrate nonmetal barriers to obtain speech signals, which expands traditional speech detection techniques. However, the radar speech signals are usually corrupted by nonuniform noises that include radar noise, electrocircuit noise, and so on. The article, therefore, proposed an improved Wiener filter method based on wavelet entropy (WE) to suppress the nonuniform noise. The utilization of WE contributes to the high efficiency of the algorithm for suppressing nonuniform radar noise. WE point detection can provide a basis through which radar noise can be accurately estimated and updated in an adaptive manner, resulting in accurate a priori signal-to-noise ratios obtained from updated noise estimations and reduction of nonuniform noise. The results from spectrogram and mean opinion score demonstrate that the radar nonuniform noise can be reduced efficiently, and the radar speech quality was improved effectively. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:1184-1189, 2014 [ABSTRACT FROM AUTHOR]

Performance monitoring and fault diagnosis for the critical component of bogie is very important. Simulation data of high speed train bogie fault signal was selected in the data experiment. Based on multiresolution analysis, wavelet entropies were extracted to reflect the complexity level of the vibration signal on scales. In the high dimension composed by several wavelet entropy features, the dates from four fault patterns were classified and recognition rate is above 90% when the speed over 200 km/h. The wavelet entropy feature is effective for fault signal analysis of high speed train bogie. [ABSTRACT FROM AUTHOR]

The interface between steel bar and concrete plays an important role in retaining the strength of reinforced concrete structures. When the interface is damaged by cracking, de-bonding between the two materials and/or other kinds of damage, significant degradation of the structural performances will occur owing to loss of composite actions. In this study, wave propagation on several steel bars embedded in two concrete plates with different de-bonding scenarios is tested. Piezoelectric actuators and sensors are attached to steel bars for recording input and response signals. This paper uses the wavelet transform combined with the wavelet packet decomposition, component energy and Shannon entropy to analyse the experimental results. The results demonstrate that both damage index and relative entropy are sensitive to the existence of de-bonding damage and change linearly with de-bonding length when there is only a single de-bonding damage, while energy and entropy distribution are largely influenced by the property of the excitation signal. When multiple de-bonding exists, however, both the damage index and relative entropy have no such clear tendency. [ABSTRACT FROM AUTHOR]

Sensor fault diagnosis is necessary to ensure the normal operation of a gas turbine system. However, the existing methods require too many resources and this need can't be satisfied in some occasions. Since the sensor readings are directly affected by sensor state, sensor fault diagnosis can be performed by extracting features of the measured signals. This paper proposes a novel fault diagnosis method for sensors based on wavelet entropy. Based on the wavelet theory, wavelet decomposition is utilized to decompose the signal in different scales. Then the instantaneous wavelet energy entropy (IWEE) and instantaneous wavelet singular entropy (IWSE) are defined based on the previous wavelet entropy theory. Subsequently, a fault diagnosis method for gas turbine sensors is proposed based on the results of a numerically simulated example. Then, experiments on this method are carried out on a real micro gas turbine engine. In the experiment, four types of faults with different magnitudes are presented. The experimental results show that the proposed method for sensor fault diagnosis is efficient. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a decentralized damage identification method using wavelet signal analysis tools embedded on wireless smart sensors (Imote2) has been proposed and experimentally validated. The damage identification analysis is decentralized by calculating discrete wavelet coefficients for acceleration in Imote2 sensors and transmitting the wavelet coefficients to a base station for damage identification through wavelet entropy indices. The wavelet entropy is modified to serve as a damage-sensitive signature that can be obtained both at different spatial locations and time stations to indicate existence of damage. It is known that wavelet-based approaches have clear advantages over Fourier transform-based ones for damage identification, since the wavelet transform allows for a wider choice of basis functions. This flexibility allows the wavelet transform to isolate changes in a signal that may be difficult to detect using other transform methods. To assess the reliability of the measurement signals, the wireless sensors have been compared with reference wired sensors. The proposed decentralized method for damage identification is verified via experimental tests using two laboratory structures: a three-story shear building structure and a three-dimensional truss bridge structure. [Copyright &y& Elsevier]

Abstract: Fatigue in human drivers is a serious cause of road accidents. Hence, it is important to devise methods to detect and quantify the fatigue. This paper presents a method based on a class of entropy measures on the recorded Electroencephalogram (EEG) signals of human subjects for relative quantification of fatigue during driving. These entropy values have been evaluated in the wavelet domain and have been validated using standard subjective measures. Five types of entropies i.e. Shannon’s entropy, Rényi entropy of order 2 and 3, Tsallis wavelet entropy and Generalized Escort-Tsallis entropy, have been considered as possible indicators of fatigue. These entropies along with alpha band relative energy and (α + β)/δ 1 relative energy ratio have been used to develop a method for estimation of unknown fatigue level. Experiments have been designed to test the subjects under simulated driving and actual driving. The EEG signals have been recorded along with subjective assessment of their fatigue levels through standard questionnaire during these experiments. The signal analysis steps involve preprocessing, artifact removal, entropy calculation and validation against the subjective assessment. The results show definite patterns of these entropies during different stages of fatigue. [ABSTRACT FROM AUTHOR]

A large number of studies reveal that repetitive TMS (rTMS) can have strong influences on cortical functions, even though the effect is very dependent on the stimulation parameters. At the same time, it is commonly acknowledged that acupuncture plays an important role in traditional Chinese medicine, and it is indeed receiving more and more attentions from the world. It is likely that a combination of acupuncture and magnetic stimulation which is non-invasive, painless and secure could give rise to treatments with substantial medical significance. This study discusses (a) the difference of EEG with pre- and post-stimulations at two different acupoints including Zusanli (St36) and Hegu (LI4) with three different frequencies (0.5 Hz, 1 Hz and 3 Hz) based on complexity analysis; (b) the character of the somatosensory evoked potentials(SEPs) in response to acupoint stimulation (Hegu) and mock point stimulation. The result indicates that different acupoints can induce different brain activity under the same stimulation correlated with the physical properties of the acupoints; and P150 can be observed after acupoint stimulation whereas mock point stimulation does not produce the same effect. [ABSTRACT FROM AUTHOR]

Abstract: Computer assisted automated detection is highly inevitable for recognizing neurological disorders, as it involves continuous monitoring of Electroencephalogram (EEG) signal. Being a non-stationary signal, suitable analysis is essential for EEG to differentiate the normal EEG and epileptic seizures. This paper highlights the importance of entropy based features to recognize the normal EEGs, and ictal as well as interictal epileptic seizures. Three non-linear features, such as, wavelet entropy, sample entropy, and spectral entropy are used to extract quantitative entropy features from the given EEG time using two neural network models, namely, recurrent Elman network (REN) and radial basis network (RBN) are then incorporated for the purpose of classification. The stationary properties of the EEG are exploited by estimating entropies at various time frames and the performance of the proposed scheme is evaluated using specificity, sensitivity and classification accuracy. From the experimental results, it is found that among the different entropies applied, the wavelet entropy features with recurrent Elman networks yields 99.75% and 94.5% accuracy for detecting normal vs. epileptic seizures and interictal focal seizures respectively. [Copyright &y& Elsevier]

Abstract: The ability to detect and classify the type of fault plays a great role in the protection of power system. This procedure is required to be precise with no time consumption. In this paper detection of fault type has been implemented using wavelet analysis together with wavelet entropy principle. The simulation of power system is carried out using PSCAD/EMTDC. Different types of faults were studied obtaining various current waveforms. These current waveforms were decomposed using wavelet analysis into different approximation and details. The wavelet entropies of such decompositions are analyzed reaching a successful methodology for fault classification. The suggested approach is tested using different fault types and proven successful identification for the type of fault. [Copyright &y& Elsevier]

In this study, an intelligent system based on genetic-support vector machines (GSVM) approach is presented for classification of the Doppler signals of the heart valve diseases. This intelligent system deals with combination of the feature extraction and classification from measured Doppler signal waveforms at the heart valve using the Doppler ultrasound. GSVM is used in this study for diagnosis of the heart valve diseases. The GSVM selects of most appropriate wavelet filter type for problem, wavelet entropy parameter, the optimal kernel function type, kernel function parameter, and soft margin constant C penalty parameter of support vector machines (SVM) classifier. The performance of the GSVM system proposed in this study is evaluated in 215 samples. The test results show that this GSVM system is effective to detect Doppler heart sounds. The averaged rate of correct classification rate was about 95%. [Copyright &y& Elsevier]