Mother Wavelet Research Articles

Separation of the overlapped vitamin B1 and B3 voltammetric peaks by means of Continuous Wavelet Transform and differentiation

Due to the indubitable role of vitamins in maintaining human health, a lot of attention has been paid to the methods and analytical procedures of their determination. Voltammetric methods are of particular interest as they do not involve complex sample preparation, however, close values of the redox potential of some vitamins may result in peak overlapping, hindering the quantitative analysis. This paper addresses the separation of overlapped reduction peak of vitamins B1 and B3 by means of Continuous Wavelet Transform (with appropriately selected mother wavelets) and differentiation of the recorded voltammograms. These numerical algorithms allowed to obtained linear, single-variable calibration functions that comply with the applied in analytical chemistry criteria regarding the correlation coefficients and the limit of detection and quantification. Their relatively simple implementation does not include any manual interpretation step; thus, these algorithms provide impartial and reproducible results. The proposed methodology has been applied in the determination of vitamins B1 and B3 in dietary supplements, providing results consistent with the declaration of the manufacturer.Graphic abstract

Selection of suitable mother wavelet along with vanishing moment for the effective detection of crack in a beam

Presence of crack in a beam causes a slope discontinuity at the crack location in the operational deflection shape (ODS). Detecting the slope discontinuity in ODS can reveal the presence of crack in a beam. Wavelet transform is a powerful technique to detect discontinuity in a signal. Efficient detection of the crack using wavelet transform depends primarily upon the wavelet family and the number of vanishing moments. In the present work, suitable mother wavelet along with optimum number of vanishing moment is obtained for the effective detection of crack in a beam. Crack detectability is defined to quantify the effectiveness of different mother wavelet and vanishing moments. Finite element analysis is used for getting the simulated ODS. Higher resolution measurement of ODS is the requisite for effective wavelet based crack detection. Photographic method is used for obtaining the high resolution measurement of ODS for the experimental verification. The present methodology works well with the experimentally obtained ODS of the cracked beam. It is capable of detecting crack near the end support also.

Deep learning of resting-state electroencephalogram signals for three-class classification of Alzheimer’s disease, mild cognitive impairment and healthy ageing

Objective. This study aimed to produce a novel deep learning (DL) model for the classification of subjects with Alzheimer’s disease (AD), mild cognitive impairment (MCI) subjects and healthy ageing (HA) subjects using resting-state scalp electroencephalogram (EEG) signals. Approach. The raw EEG data were pre-processed to remove unwanted artefacts and sources of noise. The data were then processed with the continuous wavelet transform, using the Morse mother wavelet, to create time-frequency graphs with a wavelet coefficient scale range of 0–600. The graphs were combined into tiled topographical maps governed by the 10–20 system orientation for scalp electrodes. The application of this processing pipeline was used on a data set of resting-state EEG samples from age-matched groups of 52 AD subjects (82.3 ± 4.7 years of age), 37 MCI subjects (78.4 ± 5.1 years of age) and 52 HA subjects (79.6 ± 6.0 years of age). This resulted in the formation of a data set of 16197 topographical images. This image data set was then split into training, validation and test images and used as input to an AlexNet DL model. This model was comprised of five hidden convolutional layers and optimised for various parameters such as learning rate, learning rate schedule, optimiser, and batch size. Main results. The performance was assessed by a tenfold cross-validation strategy, which produced an average accuracy result of 98.9 ± 0.4% for the three-class classification of AD vs MCI vs HA. The results showed minimal overfitting and bias between classes, further indicating the strength of the model produced. Significance. These results provide significant improvement for this classification task compared to previous studies in this field and suggest that DL could contribute to the diagnosis of AD from EEG recordings.

An Approach on MCSA-Based Fault Detection Using Discrete Wavelet Transform and Fault Classification Based on Deep Neural Networks

This paper presents a novel approach on motor current signature analysis (MCSA) forbroken Rotor Bar fault and High Contact Resistance fault using stator current signals as an input from the three phases of Induction motors. Discrete Wavelet Transform is preferred over the Fast Fourier Transform (FFT). Fast Fourier Transform (FFT) converts signals from time domain to frequency domain on the other hand Discrete Wavelet Transform (DWT) gives complete three-dimensional information of the signal, frequency, amplitude, and the time where the frequency components exist. In wavelet analysis, thesignal is converted into scaled and translated version of mother wavelet, which is very irregular so cannot be predicted. Hence, mother wavelets are more appropriate for predicting the local behavior of the signal including irregularities and spikes. In this research features are extracted using DWT and then features are trained in Deep NN sequential model for the purpose of classification of the faults. In this research, MATLAB software has been used for building the motor model in Simulink environment and PyCharm software is used to implement Deep NN for getting accuracy and classification results. This research helps in early detection of the faults that assists in prevention from unscheduled downtimes in industry, economy loss and production loss as well.

Selection of a mother wavelet as identification pattern for the detection of cracks in shafts

Nowadays, there are many methods to detect and diagnose defects in mechanical components during operation. The newest methods that can be found in the literature are based on intelligent classification systems and evaluation of patterns to obtain a diagnosis; however, there is not any standard method to assess features. Wavelet packet transform allows to obtain interesting patterns for evaluating the condition of rotating elements. To perform this calculation, it is necessary to select a series of parameters that affect the resulting pattern. These parameters are the decomposition level and the mother wavelet function. A detailed methodology for the selection of the mother wavelet is proposed, which is the aim of this work, to obtain the most suitable patterns in the diagnostic task. This proposed methodology is applied to data obtained from a rotating shaft with a crack located at the change of section. These signals were measured at low rotation frequency (below the critical rotation frequency) and without eccentricity, where detection becomes more complex.

Applying Wavelet Analysis to Assess the Ultra Low Frequency (ULF) Geomagnetic Anomalies prior to the M6.1 Banten Earthquake (2018)

The M6.1 Banten earthquake (EQ) occurred on January 23, 2018. The EQ epicenter was in Lebak Regency, Banten. The epicenter distance from the ULF geomagnetic station installed in Banten Province is about 100 km. Applying wavelet analysis on the geomagnetic time series data, we assess the ultra-low frequency (ULF) geomagnetic anomaly related to the M6.1 Banten EQ. We focused on the frequency of 0.02 Hz for the analysis of the spectral density ratio based on wavelet. We applied the Morlet wavelet as the mother wavelet in this study. The spectral density ratio analysis based on the Morlet wavelet presents the existence of the ULF geomagnetic anomalies prior to the M6.1 Banten EQ. The global geomagnetic index, Dst, did not show any peculiarity when the anomalies prior to the EQ exist. Then, we concluded that the anomaly is possibly related to the Banten EQ.

Wavelet-Gaussian process regression model for forecasting daily solar radiation in the Saharan climate

AbstractForecasting solar radiation is fundamental to several domains related to renewable energy where several methods have been used to predict daily solar radiation, such as artificial intelligence and hybrid models. Recently, the Gaussian process regression (GPR) algorithm has been used successfully in remote sensing and Earth sciences. In this paper, a wavelet-coupled Gaussian process regression (W–GPR) model was proposed to predict the daily solar radiation received on a horizontal surface in Ghardaia (Algeria). For this purpose, 3 years of data (2013–15) have been used in model training while the data of 2016 were used to validate the model. In this work, different types of mother wavelets and different combinations of input data were evaluated based on the minimum air temperature, relative humidity and extraterrestrial solar radiation on a horizontal surface. The results demonstrated the effectiveness of the new hybrid W–GPR model compared with the classical GPR model in terms of root mean square error (RMSE), relative root mean square error (rRMSE), mean absolute error (MAE) and determination coefficient (R2).

Medical image denoising using optimal thresholding of wavelet coefficients with selection of the best decomposition level and mother wavelet

AbstractMedical images have become omnipresent in diagnosis and therapy. However, they can be affected by various types of noise that reduce image quality and make the final diagnostic decision difficult. The main objective of this research is to effectively remove the noise while preserving the important image characteristics. This paper proposes a novel approach for image denoising based on discrete wavelet transform (DWT) with the selection of the best decomposition level and mother wavelet. Then, the thresholding function is carried out in the detail coefficients. Optimal thresholding is done using new optimization techniques such as the crow search algorithm and social spider optimization techniques. Finally, the inverse of DWT is applied to reconstruct the denoised image. The proposed method is evaluated using peak signal to noise ratio, mean square error, and the structural similarity index measure. The experimental results show the efficiency of the optimization‐based denoising method over standard methods. Interesting results are obtained with all kinds of noise, and improvements about 30 dB can be reached with the Rician noise.

An investigation on deep learning and wavelet transform to nowcast wind power and wind power ramp: A case study in Brazil and Uruguay

Large variations in wind energy production over a period of minutes to hours is a challenge for electricity balancing authorities. The use of reliable tools for the prediction of wind power and wind power ramp events is essential for the operator of the electrical system. The main objective of this work is to analyze the wind power and wind power ramp forecasting at Brazil and Uruguay. To achieve this goal the wavelet decomposition applying 48 different mother wavelet functions and deep learning techniques are used. The recurrent neural network was trained to perform the forecasting of 1 h ahead, and then, using it, the trained network was applied to recursively infer the forecasting for the next hours of the wind speed. After this computational procedure, the wind power and the wind power ramp were predicted. The results showed good accuracy and can be used as a tool to help national grid operators for the energy supply. The wavelet discrete Meyer family (dmey) demonstrates greater precision in the decomposition of the wind speed signals. Therefore, it is proven that the wavelet dmey is the most accurate in the decomposition of temporal wind signals, whether using signals from tropical or subtropical regions.

Source Localization of EEG Brainwaves Activities via Mother Wavelets Families for SWT Decomposition.

A Brain-Computer Interface (BCI) is a system used to communicate with an external world through the brain activity. The brain activity is measured by electroencephalography (EEG) signal and then processed by a BCI system. EEG source reconstruction could be a way to improve the accuracy of EEG classification in EEG based brain-computer interface (BCI). The source localization of the human brain activities can be an important resource for the recognition of the cognitive state, medical disorders, and a better understanding of the brain in general. In this study, we have compared 51 mother wavelets taken from 7 different wavelet families, which are applied to a Stationary Wavelet Transform (SWT) decomposition of an EEG signal. This process includes Haar, Symlets, Daubechies, Coiflets, Discrete Meyer, Biorthogonal, and reverse Biorthogonal wavelet families in extracting five different brainwave subbands for source localization. For this process, we used the Independent Component Analysis (ICA) for feature extraction followed by the Boundary Element Model (BEM) and the Equivalent Current Dipole (ECD) for the forward and inverse problem solutions. The evaluation results in investigating the optimal mother wavelet for source localization eventually identified the sym20 mother wavelet as the best choice followed by bior6.8 and coif5.

A Novel Fault Distance Estimation Method for Voltage Source Converter-Based HVDC Transmission Lines

In this work, a digital fault locator has been designed using Arduino for bipolar VSC–HVDC transmission lines based on the ratio of voltage to current signals from source end. Current and voltage signals of only rectifier end have been processed with discrete wavelet transform using DB-4 as the mother wavelet. After the signals are decomposed using wavelet up to level 4, approximate coefficients are taken. Standard deviation is then calculated and given as input to the fault locator designed in Arduino. Fault location logic has been designed in Arduino using the input features. Various fault cases are tested using proposed fault locator to check the effectiveness of the method. Percentage error in fault location estimation is within 1%. Some of the advantages of the proposed digital fault locator are no requirement of communication link, reaches setting is up to 99.8% of line length, percentage error is within 1%, and lower implementation cost. Hence the proposed digital fault locator can be implemented is a real power system effectively.

Fractional spline wavelets within the surface texture analysis

The article describes the possibilities of applying fractional spline wavelets for diagnosing the surface texture of machine parts. The research was conducted on the surface profiles of samples prepared using additive technology and face milling. The surface profiles were analysed using fractional spline wavelets for various scaling function order values. The obtained results were compared with filtration results acquired using a one-dimensional wavelet transform, for various groups of mother wavelets. In order to better illustrate the spline wavelet application-wise possibilities, the analysis was conducted at several decomposition levels. The executed tests indicated the advantages and disadvantages of an approach towards surface texture using fractional spline wavelets, which can be directly translated to better surface diagnostics of manufactured machine parts.

MR Image Compression Based on Selection of Mother Wavelet and Lifting Based Wavelet

MR Image Compression Based on Selection of Mother Wavelet and Lifting Based Wavelet

Performance of Genetic Algorithm and Levenberg Marquardt Method on Multi-Mother Wavelet Neural Network Training for 3D Huge Meshes Deformation: A Comparative Study

We propose, in this paper, a novel technique for large Laplacian boundary deformations using estimated rotations. The introduced method is used in the domain of Region of Interest (ROI) to align features of mesh based on Multi Mother Wavelet Neural Network (MMWNN) structure found in several mother wavelet families. The wavelet network allows the alignment of the characteristic points of the original mesh towards the target mesh. The key component of our correspondence scheme is a deformation energy that penalizes geometric distortion, encourages structure preservation and simultaneously allows mesh topology changes. To ensure the design of wavelet neural network architecture, an optimization algorithm should be applied to estimate and optimize the network parameters. Therefore, we compare our approach of 3d mesh deformation using MMWNN architecture based on genetic algorithm and our approach relying on Levenberg-Marquardt Method. We also discuss the existing comparison metrics for static and deformed triangle meshes employing the two mentioned approaches. Besides, we enumerate their strengths, weaknesses and relative performance.

Monitoramento da Integridade Estrutural de uma laje de concreto utilizando transformadas de wavelet

A presente contribuição utiliza uma metodologia para localizar danos em um sistema estrutural do tipo laje de concreto empregando transformadas de Wavelet. Esse sistema estrutural é modelado numericamente empregando o Método dos Elementos Finitos (MEF). O sinal da deflexão vertical da laje danificada é utilizado na localização da posição do dano empregando a transformada discreta de wavelet (TDW). As wavelets mães estudadas foram a: Daubechies, Symlets e ReverseBior. O tipo de dano implementado é dado sob a forma de perda localizada da rigidez do concreto da laje utilizando uma variável escalar de dano D. O sinal da deflexão, obtido na análise estática da laje, é interpolado e depois ampliado empregando a regularização de Tikhonov antes de ser transformado. O elemento finito utilizado na modelagem da laje apresenta quatro nós e seis graus de liberdade por nó, sendo três translações e três rotações. A calibração dos parâmetros bj da regularização de Tikhonov mostrou-se fundamental para amplificar e suavizar as perturbações nos gráficos dos coeficientes de wavelet. Além disso, todas as wavelets mães avaliadas foram capazes de identificar o dano proposto. Entretanto, quando a variável escalar de dano é maior ou igual a 0,20, somente o sinal da estrutura na condição danificada foi necessário para detectar a posição do dano. Já, para valores de dano menores que 0,20, foi necessário o emprego do sinal da diferença, obtido entre as condições da estrutura sem e com dano.

Detection of chlorophyll fluorescence parameters of potato leaves based on continuous wavelet transform and spectral analysis

The tuber development and nutrient transportation of potato crops are closely related to canopy photosynthesis dynamics. Chlorophyll fluorescence parameters of photosystem II, especially the maximum quantum yield of primary photochemistry (Fv/Fm), are intrinsic indicators for plant photosynthesis. Rapid detection of Fv/Fm of leaves by spectroscopy method instead of time-consuming pulse amplitude modulation technique could help to indicate potato development dynamics and guide field management. Accordingly, this study aims to extract fluorescence signals from hyperspectral reflectance to detect Fv/Fm. Hyperspectral imaging system and closed chlorophyll fluorescence imaging system were applied to collect the spectral data and values of Fv/Fm of 176 samples. The spectral data were decomposed by continuous wavelet transform (CWT) to obtain wavelet coefficients (WFs). Three mother wavelet functions including second derivative of Gaussian (gaus2), biorthogonal 3.3 (bior3.3) and reverse biorthogonal 3.3 (rbio3.3) were compared and the bior3.3 showed the best correlation with Fv/Fm. Two variable selection algorithms were used to select sensitive WFs of Fv/Fm including Monte Carlo uninformative variables elimination (MC-UVE) algorithm and random frog (RF) algorithm. Then the partial least squares (PLS) regression was used to establish detection models, which were labeled as bior3.3-MC-UVE-PLS and bior3.3-RF-PLS, respectively. The determination coefficients of prediction set of bior3.3-MC-UVE-PLS and bior3.3-RF-PLS were 0.8071 and 0.8218, respectively, and the root mean square errors of prediction set were 0.0181 and 0.0174, respectively. The bior3.3-RF-PLS had the best detection performance and the corresponding WFs were mainly distributed in the bands affected by fluorescence emission (650–800 nm), chlorophyll absorption and reflection. Overall, this study demonstrated the potential of CWT in fluorescence signals extraction and can serve as a guide in the quick detection of chlorophyll fluorescence parameters.

Modeling long-term rainfall-runoff time series through wavelet-weighted regularization extreme learning machine

As one of the most critical points of Iran, Lake Urmia has always been subjected to ecosystem changes due to severe water level drops. Many basins serve to feed the lake, e.g. the Shaharchay River basin, located west of the lake. In this paper, a new learning machine named “Weighted Regularization Extreme Learning Machine (WRELM)” is integrated with the Wavelet Transform (WT) (W-WRELM) to predict runoff-precipitation amounts of the Shaharchay River basin within an 18 year period from 2000 to 2017. Using the autocorrelation function, lags affecting runoff-precipitation time series are detected, then seven models are developed for both WRELM and W-ERELM by the mentioned lags. After that, all mother wavelets are testes and the best member of their family is identified. Also, the best models for the simulation of precipitation and runoff amounts are introduced through a sensitivity analysis. These models forecast target function values with acceptable exactness and high correlation. For example, the determination coefficient (R2) and Mean Absolute Error (MAE) for the best model of W-WRELM for the estimation of precipitation amounts are obtained to be 0.962 and 0.128, respectively. Moreover, the variance accounted for (VAF) and Scatter Index (SI) for the approximation of rainfall amounts are computed to 0.919 and 0.236, separately. Analyses showed that more than half of the precipitation amounts predicted by the W-WRELM 7 model have an error of more than 10%, but this value is about 64% for the predicted runoff. The lags (t-1), (t-2) and (t-12) are detected as the influencing lags in the simulation of the precipitation amounts of the Shaharchay River basin. Furthermore, the error and uncertainty analyses are conducted on the best models and it is concluded that the performance of W-WRELM in the prediction of precipitation amounts is underestimated, while its performance in the estimation of runoff values is overestimated.

An Improved Hilbert–Huang Transform for Vibration-Based Damage Detection of Utility Timber Poles

In this study, vibration based non-destructive testing (NDT) technique is adopted for assessing the condition of in-service timber pole. Timber is a natural material, and hence the captured broadband signal (induced from impact using modal hammer) is greatly affected by the uncertainty on wood properties, structure, and environment. Therefore, advanced signal processing technique is essential in order to extract features associated with the health condition of timber poles. In this study, Hilbert–Huang Transform (HHT) and Wavelet Packet Transform (WPT) are implemented to conduct time-frequency analysis on the acquired signal related to three in-service poles and three unserviceable poles. Firstly, mother wavelet is selected for WPT using maximum energy to Shannon entropy ratio. Then, the raw signal is divided into different frequency bands using WPT, followed by reconstructing the signal using wavelet coefficients in the dominant frequency bands. The reconstructed signal is then further decomposed into mono-component signals by Empirical Mode Decomposition (EMD), known as Intrinsic Mode Function (IMF). Dominant IMFs are selected using correlation coefficient method and instantaneous frequencies of those dominant IMFs are generated using HHT. Finally, the anomalies in the instantaneous frequency plots are efficiently utilised to determine vital features related to pole condition. The results of the study showed that HHT with WPT as pre-processor has a great potential for the condition assessment of utility timber poles.

Coupling the Xinanjiang model and wavelet-based random forests method for improved daily streamflow simulation

AbstractDaily streamflow modeling is an important tool for water resources management and flood mitigation. This study compared the performance of the Xinanjiang (XAJ) model and random forests (RF) method in a daily streamflow simulation, and proposed several hybrid models based on the XAJ model, wavelet analysis, and RF method (including XAJ-RF model, WRF model, and XAJ-WRF model). The proposed methods were applied to Shiquan station, located in the Upper Han River basin in China. Five performance measures (NSE, RMSE, PBIAS, MAE, and R) were adopted to evaluate the modeling accuracy. Results showed that XAJ-RF model had a relatively higher level of accuracy than that of the XAJ model and the RF model. Compared to the RF and XAJ-RF models, the performance statistics of WRF and XAJ-WRF were better. The results indicated that the coupled XAJ-RF model can be effectively applied and provide a useful alternative for daily streamflow modeling and the application of wavelet analysis contributed to the increasing accuracy of streamflow modeling. Moreover, 14 wavelet functions from various families were tested to analyze the impact of various mother wavelets on the XAJ-WRF model.

Analysis and visualization of meteorological extremes in humid subtropical regions

Understanding the variability in extreme meteorological events due to climate change and anthropogenic activities is crucial to ensure sustainable development. In this paper, the variation in precipitation and temperature in the Upper Narmada Basin (UNB), a humid subtropical region of central India, during 1901–2002, was analyzed using the Mann-Kendall (MK) test with the Sen’s slope (SS) estimator and innovative trend analysis (ITA). As a result, a significant negative trend in the annual precipitation occurred at two stations (12.5%) in the UNB, whereas no well-defined significant seasonal trends were detected. Moreover, in the annual mean temperature, a significant increasing trend occurred in the basin, with the highest and lowest rates of 0.470 °C/10 year and 0.287 °C/10 year, respectively. The seasonal temperature exhibited a significant increasing trend in the spring and autumn seasons. The trends in the extreme values were investigated using the ITA method. Furthermore, a quantitative study was carried out to measure the suitability of the ITA by comparing it with nonparametric methods (the MK test and SS estimator). The results endorse the reliability of the ITA method and show strong agreement between the trends and statistics of the parametric (ITA) and nonparametric approaches. To visualize the extreme events in meteorological series, a discrete wavelet transform (DWT) was employed with the Daubechies (db3) mother wavelet. In addition, change points were detected using the sequential Mann-Kendall (SQMK) and cumulative sum (CUSUM) tests. Significant change points in the annual precipitation were detected at nine stations (56.25%) during 1955–1958, while only three stations (18.75%) exhibited the annual mean temperature during 1960. The findings of this study could provide support to understand the variability in the meteorological trend over the basin and can help with water resource planning in future development.