Discrete Wavelet Transform Analysis Research Articles

Examining the interfacial behavior of non-Newtonian gas-liquid two-phase flow in horizontal square microchannels

This study investigates the flow dynamics of a non-Newtonian two-phase flow within a horizontal square microchannel. The experimental apparatus employed an acrylic channel with a side length of 8 × 10−4 m. Nitrogen served as the test gas, and the test liquids consisted of water and CMC (Carboxymethylcellulose) aqueous solutions at concentrations of 0.2 and 0.4 %wt. The superficial velocity of working gas and liquids spanned ranges of 0.26–20 m/s and 0.05–1.0 m/s, respectively. A differential pressure transducer was used to measure pressure gradients, while a high-speed video camera captured the flow behavior for analysis with a custom image processing technique. Nonlinear regression statistical analysis was applied to establish the criteria for flow pattern transition. Furthermore, signal processing techniques such as PSD (Power Spectral Density), DWT (Discrete Wavelet Transform), ANN (Artificial Neural Network), and Kolmogorov entropy were employed to analyze the flow behavior based on the pressure gradient signals from the differential pressure transducers. Our findings reveal the occurrence of bubbly, slug, slug-annular, and churn flow patterns. The nonlinear regression statistical analysis offered ambiguous results for determining flow pattern transitions. However, an empirical coefficient was obtained for the nondimensional liquid height. Moreover, the empirical nondimensional liquid height aligned well with the experimental values. The PSD and DWT analysis corroborated each other in clearly characterizing the flow pattern based on pressure gradient fluctuation and wavelet energy. The Kolmogorov entropy effectively captured the chaotic flow pattern. Furthermore, the ANN analysis demonstrated a solid agreement between the predicted and actual flow patterns.

Method for extracting pigment characteristic spectra from the phytoplankton absorption spectrum.

The extraction of pigment characteristic spectra from the phytoplankton absorption spectrum has high application value in phytoplankton identification and classification and in quantitative extraction of pigment concentrations. Derivative analysis, which has been widely used in this field, is easily interfered with by noisy signals and the selection of the derivative step, resulting in the loss and distortion of the pigment characteristic spectra. In this study, a method based on the one-dimensional discrete wavelet transform (DWT) was proposed to extract the pigment characteristic spectra of phytoplankton. DWT and derivative analysis were applied simultaneously to the phytoplankton absorption spectra of 6 phyla (Dinophyta, Bacillariophyta, Haptophyta, Chlorophyta, Cyanophyta, and Prochlorophyta) to verify the effectiveness of DWT in the extraction of pigment characteristic spectra.

Tumor Diagnosis against Other Brain Diseases Using T2 MRI Brain Images and CNN Binary Classifier and DWT.

Brain tumors are diagnosed and classified manually and noninvasively by radiologists using Magnetic Resonance Imaging (MRI) data. The risk of misdiagnosis may exist due to human factors such as lack of time, fatigue, and relatively low experience. Deep learning methods have become increasingly important in MRI classification. To improve diagnostic accuracy, researchers emphasize the need to develop Computer-Aided Diagnosis (CAD) computational diagnostics based on artificial intelligence (AI) systems by using deep learning methods such as convolutional neural networks (CNN) and improving the performance of CNN by combining it with other data analysis tools such as wavelet transform. In this study, a novel diagnostic framework based on CNN and DWT data analysis is developed for the diagnosis of glioma tumors in the brain, among other tumors and other diseases, with T2-SWI MRI scans. It is a binary CNN classifier that treats the disease "glioma tumor" as positive and the other pathologies as negative, resulting in a very unbalanced binary problem. The study includes a comparative analysis of a CNN trained with wavelet transform data of MRIs instead of their pixel intensity values in order to demonstrate the increased performance of the CNN and DWT analysis in diagnosing brain gliomas. The results of the proposed CNN architecture are also compared with a deep CNN pre-trained on VGG16 transfer learning network and with the SVM machine learning method using DWT knowledge. To improve the accuracy of the CNN classifier, the proposed CNN model uses as knowledge the spatial and temporal features extracted by converting the original MRI images to the frequency domain by performing Discrete Wavelet Transformation (DWT), instead of the traditionally used original scans in the form of pixel intensities. Moreover, no pre-processing was applied to the original images. The images used are MRIs of type T2-SWI sequences parallel to the axial plane. Firstly, a compression step is applied for each MRI scan applying DWT up to three levels of decomposition. These data are used to train a 2D CNN in order to classify the scans as showing glioma or not. The proposed CNN model is trained on MRI slices originated from 382 various male and female adult patients, showing healthy and pathological images from a selection of diseases (showing glioma, meningioma, pituitary, necrosis, edema, non-enchasing tumor, hemorrhagic foci, edema, ischemic changes, cystic areas, etc.). The images are provided by the database of the Medical Image Computing and Computer-Assisted Intervention (MICCAI) and the Ischemic Stroke Lesion Segmentation (ISLES) challenges on Brain Tumor Segmentation (BraTS) challenges 2016 and 2017, as well as by the numerous records kept in the public general hospital of Chania, Crete, "Saint George". The proposed frameworks are experimentally evaluated by examining MRI slices originating from 190 different patients (not included in the training set), of which 56% are showing gliomas by the longest two axes less than 2 cm and 44% are showing other pathological effects or healthy cases. Results show convincing performance when using as information the spatial and temporal features extracted by the original scans. With the proposed CNN model and with data in DWT format, we achieved the following statistic percentages: accuracy 0.97, sensitivity (recall) 1, specificity 0.93, precision 0.95, FNR 0, and FPR 0.07. These numbers are higher for this data format (respectively: accuracy by 6% higher, recall by 11%, specificity by 7%, precision by 5%, FNR by 0.1%, and FPR is the same) than it would be, had we used as input data the intensity values of the MRIs (instead of the DWT analysis of the MRIs). Additionally, our study showed that when our CNN takes into account the TL of the existing network VGG, the performance values are lower, as follows: accuracy 0.87, sensitivity (recall) 0.91, specificity 0.84, precision 0.86, FNR of 0.08, and FPR 0.14. The experimental results show the outperformance of the CNN, which is not based on transfer learning, but is using as information the MRI brain scans decomposed into DWT information instead of the pixel intensity of the original scans. The results are promising for the proposed CNN based on DWT knowledge to serve for binary diagnosis of glioma tumors among other tumors and diseases. Moreover, the SVM learning model using DWT data analysis performs with higher accuracy and sensitivity than using pixel values.

Wavelet analysis of the EMG signal to assess muscle fatigue in the lower extremities during symmetric movement on a rowing ergometer

Purpose The aim of this publication is to propose a methodology to determine changes in fatigue in selected muscle groups of the lower extremity during dynamic and cyclical motion performed on a rowing ergometer. The study aims to use the discrete wavelet transform (DWT) to analyze electromyographic signals (EMG) recorded during diagnostic assessment of muscle and peripheral nerve electrical activity (electroneurography) using an electromyography device (EMG). Methods The analysis involved implementing calculations such as mean frequency (MNF) and median frequency (MDF) using the reconstructed EMG signal through DWT. The study examined the efficacy of DWT analysis in assessing muscle fatigue after physical exertion. Results The study obtained a negative regression coefficient for DWT analysis in all muscles except for the right gastrocnemius (GAS). The results suggest that DWT analysis can be an effective tool for evaluating muscle fatigue after physical exertion. Conclusions The use of DWT in the analysis of EMG signals during rowing ergometer exercises has shown promising results in assessing muscle fatigue. However, additional investigations are necessary to confirm and expand these findings. This publication addresses the literature gap on the determination of muscle fatigue considering motion analysis on a rowing ergometer using the discrete wavelet transform. Previous studies have extensively compared and analyzed methods such as the Fourier transform (FFT), short-time Fourier transform (STFT), and wavelet transform (WT) for muscle fatigue analysis. However, no previous work has specifically examined the assessment of muscle fatigue by incorporating DWT analysis with motion analysis on a rowing ergometer.

FOURIER AND WAVELET ANALYSIS OF PRESSURE FLUCTUATIONS IN GAS-NON-NEWTONIAN LIQUID TWO-PHASE FLOWS IN A MICROCHANNEL

The purpose of this study was to analyze the characteristics of gas-non-Newtonian liquid flow patterns in microchannels using signal processing techniques including power spectral density (PSD) and discrete wavelet transform (DWT) analyses. Square microchannels measuring 0.8 × 0.8 mm were used in this study. Water, 0.1 percent by weight (wt%) xanthan gum (XG) aqueous solution, and 0.2 wt% XG were employed as the working liquids, while nitrogen gas was used as the working gas. The superficial velocities of the liquid and gas were varied between 0.05 and 1 m/s and 0.26 and 7.8 m/s, respectively. The flow patterns were recorded using a high-speed camera, while the pressure drop was measured using a differential pressure transducer. The pressure gradient data were analyzed using signal processing techniques to characterize the flow patterns. Furthermore, PSD and DWT analyses were found to effectively describe the characteristics of the flow pattern.

Discrete Wavelet Transform Analysis of the Electroretinogram in Autism Spectrum Disorder and Attention Deficit Hyperactivity Disorder

BackgroundTo evaluate the electroretinogram waveform in autism spectrum disorder (ASD) and attention deficit hyperactivity disorder (ADHD) using a discrete wavelet transform (DWT) approach.MethodsA total of 55 ASD, 15 ADHD and 156 control individuals took part in this study. Full field light-adapted electroretinograms (ERGs) were recorded using a Troland protocol, accounting for pupil size, with five flash strengths ranging from –0.12 to 1.20 log photopic cd.s.m–2. A DWT analysis was performed using the Haar wavelet on the waveforms to examine the energy within the time windows of the a- and b-waves and the oscillatory potentials (OPs) which yielded six DWT coefficients related to these parameters. The central frequency bands were from 20–160 Hz relating to the a-wave, b-wave and OPs represented by the coefficients: a20, a40, b20, b40, op80, and op160, respectively. In addition, the b-wave amplitude and percentage energy contribution of the OPs (%OPs) in the total ERG broadband energy was evaluated.ResultsThere were significant group differences (p < 0.001) in the coefficients corresponding to energies in the b-wave (b20, b40) and OPs (op80 and op160) as well as the b-wave amplitude. Notable differences between the ADHD and control groups were found in the b20 and b40 coefficients. In contrast, the greatest differences between the ASD and control group were found in the op80 and op160 coefficients. The b-wave amplitude showed both ASD and ADHD significant group differences from the control participants, for flash strengths greater than 0.4 log photopic cd.s.m–2 (p < 0.001).ConclusionThis methodological approach may provide insights about neuronal activity in studies investigating group differences where retinal signaling may be altered through neurodevelopment or neurodegenerative conditions. However, further work will be required to determine if retinal signal analysis can offer a classification model for neurodevelopmental conditions in which there is a co-occurrence such as ASD and ADHD.

Muscle fatigue detection in upper limbs during the use of the computer mouse using discrete wavelet transform: A pilot study

BackgroundDue to the current global situation of the pandemic, computer use has increased and has become essential for working and studying. Hence, detection of muscle fatigue associated with computer mouse use is essential to prevent musculoskeletal disorders, since it is considered a precursor of some musculoskeletal injuries. ObjectiveThis study aims to detect muscle fatigue in the shoulder and forearm caused by repetitive and continuous strain associated with the computer mouse, using the discrete wavelet transform (DWT) to prevent musculoskeletal disorders. MethodsTen participants performed a one-direction tapping task on a computer with four difficulty levels while the shoulder and forearm signals were recorded. We used twelve wavelet functions for DWT analysis. Then, power, MNF, and MDF features were extracted from the wavelet coefficients to detect muscle fatigue. ResultsSpectral changes using MNF and MDF of wavelet coefficients of Coif5 and Db6 functions showed significant shiftings towards low frequencies with magnitudes of 20.2 Hz and 26.5 Hz for the shoulder, and 18.9 Hz and 25.6 Hz for the forearm in the fourth decomposition level when the task difficulty increased, indicating muscle fatigue. ConclusionThis study demonstrated that high-precision computer mouse tasks may cause muscle fatigue, and it can be effectively detected by extracting spectral features of the EMG signal to help clinicians and physiotherapists to prevent severe musculoskeletal disorders. In future work, we will optimize the feature extraction method.

Evaluation of Total Nitrogen in Water via Airborne Hyperspectral Data: Potential of Fractional Order Discretization Algorithm and Discrete Wavelet Transform Analysis

Controlling and managing surface source pollution depends on the rapid monitoring of total nitrogen in water. However, the complex factors affecting water quality (plant shading and suspended matter in water) make direct estimation extremely challenging. Considering the spectral response mechanisms of emergent plants, we coupled discrete wavelet transform (DWT) and fractional order discretization (FOD) techniques with three machine learning models (random forest (RF), bagging algorithm (bagging), and eXtreme Gradient Boosting (XGBoost)) to mine this potential spectral information. A total of 567 models were developed, and airborne hyperspectral data processed with various DWT scales and FOD techniques were compared. The effective information in the hyperspectral reflectance data were better emphasized after DWT processing. After DWT processing the original spectrum (OR), its sensitivity to TN in water was maximally improved by 0.22, and the correlation between FOD and TN in water was optimally increased by 0.57. The transformed spectral information enhanced the TN model accuracy, especially for FOD after DWT. For RF, 82% of the model R2 values improved by 0.02~0.72 compared to the model using FOD spectra; 78.8% of the bagging values improved by 0.01~0.53 and 65.0% of the XGBoost values improved by 0.01~0.64. The XGBoost model with DWT coupled with grey relation analysis (GRA) yielded the best estimation accuracy, with the highest precision of R2 = 0.91 for L6. In conclusion, appropriately scaled DWT analysis can substantially improve the accuracy of extracting TN from UAV hyperspectral images. These outcomes may facilitate the further development of accurate water quality monitoring in sophisticated global waters from drone or satellite hyperspectral data.

Energy eigenvalues and neural network analysis for broken bars fault diagnosis in induction machine under variable load: experimental study

In this paper, a technique primarily based on the discrete wavelet transform (DWT) and the slip associated with a neural network (NN) for classification and fault detection of broken rotor bars in an induction machine has been proposed. The calculated energy in each decomposition level obtained by the DWT analysis and the slip of the motor are used as input to the classifier in order to diagnose the healthy and faulty classes. The advantage of this method lays in the use of one single current sensor with the slip factor in order to detect the presence of the fault and identify the number of broken bars under different load conditions. The DWT analysis is proposed to overcome the limitation of the Fourier analysis and it is mainly adapted for the non-stationary signals. Moreover, the slip factor is applied as a second input on the classifier of NN to eliminate the problem of low-load. Feed-forward multi-layer Perceptron neural network is chosen as a technique to classify the fault in an induction machine. This technique is performed and validated by experimental data.

Spatio-temporal characterization of rainfall in Bangladesh: an innovative trend and discrete wavelet transformation approaches

The analysis of detailed characteristics of rainfall is of utmost importance for understanding water resources, irrigation, and agriculture. This study investigated detailed characteristics of rainfall of Bangladesh from 1966 to 2019. Rainfall features like the precipitation concentration index (PCI) and seasonality index (SI) were estimated to characterize spatial patterns of rainfall regimes, and innovative trend analysis (ITA) and percent bias (PBIAS) were used to detect the trend, and its reliability was tested by using the Mann–Kendall (MK) or modified Mann–Kendall (mMK) test. The magnitude of changes was computed by using Sen’s slope estimator (Q), and discrete wavelet transform (DWT) was employed to find out the dominant periodicity of the trend of annual series. SI and PCI revealed that rainfall is mainly seasonal and markedly with the long dry season, and the distribution of rainfall is irregular for the major portion of Bangladesh. The result of ITA and PBIAS showed a similar trend for all the stations and time scales. ITA showed that 23 stations experienced significant (α = < 0.05) increasing (39.13%) and decreasing (39.13%) trends in annual rainfall. For the seasonal scale, post-monsoon rainfall is dominated by significant increasing trend (60.87%), whereas winter rainfall is dominated by significant decreasing trend (65.28%); besides, both decreasing and increasing trends were found in pre-monsoon and monsoon in Bangladesh. The analysis of DWT confirmed that 4- to 16-year periodic cycle was the dominant component for annual rainfall. The results of detailed analysis of rainfall will be helpful for policymakers and scientists to focus on regional-scale planning about flood and drought situation of the country that will be ultimately helpful for agricultural development and environmental planning.

Characterization of the anteroposterior center of pressure in upright position in type 2 diabetics with peripheral diabetic neuropathy and paired healthy controls

Peripheral diabetic neuropathy (PDN) is a complication of type 2 diabetes (T2DM) that impairs posture control and increases the risk of falling. The aim of this study was to characterize the anteroposterior center of pressure (COP-AP) in the time and the frequency domains in the T2DM/PDN group in relation to the control group. To that end we: (1) evaluated the efficacy of using both linear and non-linear discrete wavelet transform (DWT) analyses to evaluate oscillation patterns in the anteroposterior center of pressure (COP-AP) in the bipedal position in terms of time and frequency and (2) established input parameters for a model for predicting the risk of falling.This study included an experimental sample of 30 people with T2DM/PDN matched by gender, age, weight and height with a control sample of 30 healthy individuals. Unreported techniques for analyzing the COP-AP literature were assessed for their capacity to model patient bodily stability in the proprioceptive, visual and vestibular systems. To measure COP-AP, five tests were performed under different conditions as outlined in the Romberg Test using the “PEDAR System” for measuring plantar pressure. DWTs were used to calculate excursion parameters, average speeds, range, RMS values, the average maximum and minimum amplitude, power spectral densities and energy percentages in 11 frequency bands (D1 to D10 and A10). There were significant differences between the two study groups in terms of the calculated linear parameters (p<0.05). Using linear and non-linear DWT analyses, a preliminary characterization of COP-AP patterns was achieved. DWT could be used alongside linear analysis to determine the effect changes in these systems have on postural oscillation in people with T2DM.

Wavelet based real-time monitoring of electrical signals in Distributed Generation (DG) integrated system

In this paper, Hilbert-Huang Transform (HHT) and Discrete Wavelet Transform (DWT) based methods are employed on line to monitor the deviation in electrical quantities of the power system integrated with distributed generation. HHT employs an Empirical Mode Decomposition (EMD) method i.e. decomposition of the signal into Intrinsic Mode Functions (IMFs) in such a way that they are sorted from the highest frequency to the lowest frequency whereas, Wavelet Transform (WT) decomposes the signal into components that are indicative of signal details and trend. This paper presents a comparative analysis of HHT and DWT with the motive to provide the guidelines for deciding which one of these techniques is more suitable for Power Quality (PQ) event analysis in the case of Distributed Generation (DG) integrated system, in real-time domain. From the comparative analysis, it is observed that DWT is more precise in comparison with HHT in determining PQ events in real-time domain with high resolution. This work further explores the potential of WT for the real time application in measuring, monitoring, and analyzing the electrical signals during the occurrence of voltage sag, swell and harmonics. Real time implementation of WT necessitates signal sections to be serially processed. Towards the same, signal samples are collected in a buffer and then subjected to WT to extract the inherent details. The processing of the signal gives attributes that help in identifying the type of disturbance. Performance of the proposed method is tested through simulations on MATLAB/Simulink platform along with the experimental validation of the technique. Results reveal that the application of WT, in real time, can accurately detect the instant of disturbances with minimum delay to analyze the PQ issues.

Phase Function Effects on Identification of Terahertz Spectral Signatures Using the Discrete Wavelet Transform

We describe the application of the Discrete Wavelet Transform (DWT) in extracting the characteristic absorption signatures of materials from terahertz reflection spectra. We compare the performance of different mother wavelets, including Daubechies, Least Asymmetric (LA), and Coiflet, based on their phase and gain functions and filter lengths. We show that the phase functions of the wavelet and scaling filters result in spectral shifts to the absorption lines in the wavelet domain. We provide a solution by calculating advancement coefficients necessary to achieve effective zero-phase-function DWT. We demonstrate the utility of this signal processing technique using α-lactose monohydrate/polyethylene samples with different levels of rough surface scattering. In all cases, the DWT-based algorithm successfully extracts resonant signatures at 0.53 and 1.38 THz, even when they are obscured by the rough surface scattering effects. The DWT analysis with accompanying phase corrections can be utilized as a robust technique for material identification in non-destructive evaluation (NDE) using terahertz spectroscopy.

Ring analysis of multifocal oscillatory potentials (mfOPs) in cCSNB suggests near-normal ON-OFF pathways at the fovea only.

To investigate the center-periphery distribution of ON and OFF retinal responses in complete congenital stationary night blindness (cCSNB). Photopic full-field flash ERGs (photopic ffERGs) and OPs (photopic ffOPs) and slow m-sequence (to enhance OP prominence) mfERGs (and filtered mfOPs) evoked by a 37 hexagon stimulus array were recorded from normal subjects and cCSNB patients. Discrete wavelet transform (DWT) analysis of photopic ffERGs and mfERGs was also performed in order to assess the contribution of the ON and OFF retinal pathways (i.e., OFF-to-ON ratio) in both cohorts. As expected, the photopic ffERG (and ffOPs) responses in cCSNB were devoid of the first two of the three OPs (i.e., OP2 and OP3 and OP4) normally seen on the ascending limb of the b-wave. A similar finding was also noted in the mfERGs (and mfOPs) of ring 4. In contrast, the mfERGs (and mfOPs) of ring 1 included all three OPs. DWT analysis revealed that while in normal subjects, the OFF-to-ON ratio of mfERGs slightly increased from rings 1 to 4 (from 0.61 ± 0.03 to 0.78 ± 0.04; p < 0.05; median: from 0.62 to 0.79; p < 0.05), in cCSNB this ratio increased significantly more [from 0.73 ± 0.13 (ring 1) to 1.18 ± 0.17 (ring 4); p < 0.05; median: 0.78 to 1.22; p < 0.05], hence from a normal ON-dominated ratio (central ring) to an OFF-dominated ratio (peripheral ring). Our results show a clear discrepancy of ON and OFF mfOP components in cCSNB. Responses originating from the most central ring (i.e., ring 1) disclosed a near-normal electrophysiological contribution (as revealed with the presence of OP2, OP3 and OP4 as well as with the DWT OFF-to-ON ratio) of the retinal ON and OFF pathways in mfERG (and mfOPs) responses compared to responses from the more peripheral ring (and ffOP) which are devoid of the ON OPs (i.e., OP2 and OP3).

Trend Analysis of Seasonal Precipitation (1960–2013) in Subregions of Hunan Province, Central South China Using Discrete Wavelet Transforms

AbstractIn this study, trends of seasonal precipitation are investigated in subregions of Hunan Province in China over 1960–2013 by discrete wavelet transform (DWT) and Mann–Kendall (MK) tests. The main purpose of trend analysis is to detect the most dominant periodic components affecting the observed trends of seasonal precipitation in each subregion. For this purpose, the homogeneous precipitation regions are first delineated by combining rotated empirical orthogonal functions with agglomerative hierarchical clustering. Results suggest dividing the precipitation of Hunan Province into five subregions for winter and three subregions for spring, summer, and autumn. Delineated subregions for each season show strongly coherent spatial patterns, all of which are along the strip extending in the southwest–northeast direction. After regionalization, areal seasonal precipitation series in each subregion are decomposed into several detail and approximation component subseries, and then the decomposed subseries are analyzed by three types of MK tests. Results reveal that winter and summer precipitations experience an increasing trend in all of the divisions—winter precipitation in southeast-central and southern Hunan and summer precipitation in southwest-central Hunan especially exhibit a statistically significant tendency. However, spring and autumn precipitations show a nonsignificant decreasing trend in all of the divisions. Results from DWT and sequential MK analyses suggest that detail component 1 (plus approximation) of seasonal precipitations in all subregions is the most dominant periodic mode affecting their observed trends, except for summer precipitation in the subregion of southern Hunan, where detail component 2 is the most dominant one. Therefore, short-term periodicity (2–4 yr) is the most influential in affecting the observed trends of seasonal precipitation over Hunan Province.

A study of characteristic extraction for transformer oscillation wave based on DWT analysis

In order to improve the reliability of transformer winding state evaluation method, the analysis of oscillation wave based on high voltage direct current (HVDC) power supply is proposed. Firstly, different noise reduction methods are adopted dealing with the measured oscillation wave data, and a suitable noise reduction method for field experiments is obtained. Then the discrete wavelet transform (DWT) is applied on denoising data. Finally, the characteristics that can be used to evaluate the state of windings are obtained by analysing the wavelet detailed signals. The results show that the waveform characteristics of windings obtained by discrete wavelet transform have good repeatability and can reflect the differences between different windings.

High-impedance fault detection in medium-voltage distribution network using computational intelligence-based classifiers

This paper presents the high-impedance fault (HIF) detection and identification in medium-voltage distribution network of 13.8 kV using discrete wavelet transform (DWT) and intelligence classifiers such as adaptive neuro-fuzzy inference system (ANFIS) and support vector machine (SVM). The three-phase feeder network is modelled in MATLAB/Simulink to obtain the fault current signal of the feeder. The acquired fault current signal for various types of faults such as three-phase fault, line to line, line to ground, double line to ground and HIF is sampled using 1st, 2nd, 3rd, 4th and 5th level of detailed coefficients and approximated by DWT analysis to extract the feature, namely standard deviation (SD) values, considering the time-varying fault impedance. The SD values drawn by DWT technique have been used to train the computational intelligence-based classifiers such as fuzzy, Bayes, multi-layer perceptron neural network, ANFIS and SVM. The performance indices such as mean absolute error, root mean square error, kappa statistic, success rate and discrimination rate are compared for various classifiers presented. The results showed that the proffered ANFIS and SVM classifiers are more effective and their performance is substantially superior than other classifiers.

Evaluation of Leaf N Concentration in Winter Wheat Based on Discrete Wavelet Transform Analysis

Leaf nitrogen concentration (LNC) is an important indicator for accurate diagnosis and quantitative evaluation of plant growth status. The objective was to apply a discrete wavelet transform (DWT) analysis in winter wheat for the estimation of LNC based on visible and near-infrared (400–1350 nm) canopy reflectance spectra. In this paper, in situ LNC data and ground-based hyperspectral canopy reflectance was measured over three years at different sites during the tillering, jointing, booting and filling stages of winter wheat. The DWT analysis was conducted on canopy original spectrum, log-transformed spectrum, first derivative spectrum and continuum removal spectrum, respectively, to obtain approximation coefficients, detail coefficients and energy values to characterize canopy spectra. The quantitative relationships between LNC and characteristic parameters were investigated and compared with models established by sensitive band reflectance and typical spectral indices. The results showed combining log-transformed spectrum and a sym8 wavelet function with partial least squares regression (PLS) based on the approximation coefficients at decomposition level 4 most accurately predicted LNC. This approach could explain 11% more variability in LNC than the best spectral index mSR705 alone, and was more stable in estimating LNC than models based on random forest regression (RF). The results indicated that narrowband reflectance spectroscopy (450–1350 nm) combined with DWT analysis and PLS regression was a promising method for rapid and nondestructive estimation of LNC for winter wheat across a range in growth stages.

A Harmonic Detection Method for Distributed Generation Connected Grid System Using DWT and HHT

In distributed generation (DG) connected grid system, there is serious harmonic pollution caused by the wide use of inverter units and nonlinear loads. The traditional detection methods (such as Fast Fourier Transform and wavelet analysis) heavily depend on synchronous signal detection or basis functions selection, which don’t satisfy the requirements of the harmonic detection of the micro-grid environment. Therefore, a novel method combining discrete wavelet transform (DWT) with Hilbert–Huang transform (HHT) is proposed to detect and analyze the harmonic. The method uses multi resolution analysis of DWT to process the original signal. Then, a series of intrinsic mode function (IMF) components are obtained from the processed signal by using Empirical Mode Decomposition (EMD) algorithm. Thirdly, the fundamental component and harmonic are extracted from the IMF components. Finally, the frequency and amplitude of the signal are calculated by using the HHT. Simulation results demonstrate that the proposed algorithm has high precision and good real-time characteristics. Furthermore, the proposed algorithm satisfies the requirements of the harmonic detection of the DG connected grid system.

Analysis of pattern electroretinogram signals of early primary open-angle glaucoma in discrete wavelet transform coefficients domain.

To evaluate discrete wavelet transform coefficients and identify descriptors of pattern electroretinogram (PERG) waveforms in order to determine PERG characteristics for optimizing the diagnosis of early primary open-angle glaucoma (POAG). Pattern electroretinogram was performed in 30 normal eyes and 30 eyes with primary open-angle glaucoma according to the ISCEV protocol. The check size was 0.8° and 16°, and the color was black/white in both groups. The results were analyzed in time domain (TD) and discrete wavelet transform (DWT) using the MATLAB software. The mean value, standard deviation, and relative energy of level 6 and 7 detail coefficients (d6, d7) and level 7 approximation coefficients (a7) of Daubechies 4 (db4), Daubechies 8 (db8), Symlet 5 (sym5), Symlet 7 (sym7), and Coiflet 5 (coif5) wavelets were calculated. In all the mentioned wavelets, DWT descriptors were extracted. Signals were reconstructed by inverse DWT. All data obtained by TD and DWT analyses were compared between the two groups. In both check sizes, a significant attenuation of N95 amplitude was seen in the patient group. The relative energy of a7 of db8 increased significantly in the POAG group in the 0.8° check size. In larger check stimuli, the relative energy of d7 of coif5 decreased significantly and the standard deviation of d7 of sym7 increased markedly in glaucomatous patients (P < 0.05). In small stimuli, N95 descriptor (7N) of db8 had the highest value and showed a significant increase as compared to the POAG group. In the 16° check size, there was no significant difference. A strong correlation was seen between reconstructed signals and originals (r = 0.99). The DWT can quantify PERG responses more accurately. In agreement with TD and wavelet coefficients domain results, 7N of db8 decomposition can be used as a good indicator for early detection of POAG.