Mother Wavelet Function Research Articles

Fault signature extraction of rolling bearings under variable speed via time–frequency overlap group sparse representation

The high-fidelity extraction of the nonperiodic fault transients of rolling bearings under variable speed is of significant importance, while still a challenge for early-stage fault diagnosis of major equipment such as aero engines and wind turbines. A method termed continuous symmetric Laplace wavelet transform (CSLWT) enhanced time–frequency overlap group sparse (OGS) representation is proposed in this paper. A symmetric Laplace mother wavelet function is proposed which could satisfy the admissibility condition of wavelet decomposition and reconstruction, upon which the CSLWT is fabricated and adopted as the sparse representation dictionary to match the nonperiodic fault transients. Since the decomposition coefficients of nonperiodic fault impulses via the CSLWT exhibit group sparsity on the time–frequency plane with unknown intervals, the time–frequency OGS model is adopted and then solved for extraction of the nonperiodic fault transients. Moreover, a data driven, multi-objective optimization strategy is presented for determining the hyper-parameters of the sparse model. The correlated kurtosis of angular envelope signal (CK-AE) and harmonic-to-noise energy ratio of the order spectrum (HNR-OS) are introduced as the optimization objectives, and the Pareto front is solved based on the NSGA-II algorithm, upon which the acceptable solutions set is chosen from the Pareto front, and the proper hyper-parameters are further determined via proposed normalized solutions distance density sorting of the acceptable solutions set. The performance of the proposed method is validated via processing both simulated and experimental vibration signals, as well as compared with some tradition fault diagnosis methods.

Artificial neural network and discrete wavelet transform for inter-turn short circuit and broken rotor bars faults diagnosis under various operating conditions

Introduction. This work presents a methodology for detecting inter-turn short circuit (ITSC) and broken rotor bars (BRB) fault in variable speed induction machine controlled by field oriented control. If any of these faults are not detected at an early stage, it may cause an unexpected shutdown of the industrial processes and significant financial losses. Purpose. For these reasons, it is important to develop a new diagnostic system to detect in a precautionary way the ITSC and BRB at various load condition. We propose the application of discrete wavelet transform to overcome the limitation of traditional technique for no-stationary signals. The novelty of the work consists in developing a diagnosis system that combines the advantages of both the discrete wavelet transform (DWT) and artificial neural network (ANN) to identify and diagnose defects, related to both ITSC and BRB faults. Methods. The suggested method involves analyzing the electromagnetic torque signal using DWT to calculate the stored energy at each level of decomposition. Then, this energy is applied to train neural network classifier. The accuracy of ANN based on DWT, was improved by testing different orthogonal wavelet functions on simulated signal. The selection process identified 5 pertinent wavelet energies, concluding that, Daubechies44 (db44) is the best suitable mother wavelet function for effectively detecting and classifying failures in machines. Results. We applied numerical simulations by MATLAB/Simulink software to demonstrate the validity of the suggested techniques in a closed loop induction motor drive. The obtained results prove that this method can identify and classify these types of faults under various loads of the machine. References 31, table 1, figures 9.

Evaluation of the Efficiency of Mother Wavelet Functions for Simulating Endurance Time Excitations

Evaluation of the Efficiency of Mother Wavelet Functions for Simulating Endurance Time Excitations

Quantitative Analysis of Mother Wavelet Function Selection for Wearable Sensors-Based Human Activity Recognition.

Recent advancements in the Internet of Things (IoT) wearable devices such as wearable inertial sensors have increased the demand for precise human activity recognition (HAR) with minimal computational resources. The wavelet transform, which offers excellent time-frequency localization characteristics, is well suited for HAR recognition systems. Selecting a mother wavelet function in wavelet analysis is critical, as optimal selection improves the recognition performance. The activity time signals data have different periodic patterns that can discriminate activities from each other. Therefore, selecting a mother wavelet function that closely resembles the shape of the recognized activity's sensor (inertial) signals significantly impacts recognition performance. This study uses an optimal mother wavelet selection method that combines wavelet packet transform with the energy-to-Shannon-entropy ratio and two classification algorithms: decision tree (DT) and support vector machines (SVM). We examined six different mother wavelet families with different numbers of vanishing points. Our experiments were performed on eight publicly available ADL datasets: MHEALTH, WISDM Activity Prediction, HARTH, HARsense, DaLiAc, PAMAP2, REALDISP, and HAR70+. The analysis demonstrated in this paper can be used as a guideline for optimal mother wavelet selection for human activity recognition.

Multi-Frequency Ultrasound Imaging Fusion Method Based on Wavelet Transform for Guided Screw Insertion.

Intraosseous ultrasound imaging can serve as a guiding tool for the placement of pedicle screws during spinal fusion surgery; thus far, there has been limited scholarly exploration of methods for intraosseous multifrequency ultrasound imaging, which can achieve simultaneous high resolution and deep penetration. The proposed method introduced a dynamic fusion strategy grounded in wavelet transformation for multifrequency image decomposition. This strategy accomplished the effective amalgamation of high-frequency ultrasound images and low-frequency ultrasound images, enabling the obtaining of fused images with enhanced details and better overall image quality. A novel near-field effect elimination method was also proposed to improve the quality of ultrasound imaging in the near-field region. Experimental evaluations were conducted on isolated bovine circle bone and sheep spine with pedicle screw tracks. The fusion images are capable of effectively detecting areas within the pedicle screw track that have either ruptured or are in close proximity to rupture, even measuring the size of breaches. Evaluation criteria, including information entropy (IE), spatial frequency (SF), average gradient (AG), mutual information (MI), structural similarity index (SSIM), and edge information-based image fusion quality metric (QAB/F), were employed to assess the fusion performance; moreover, the influence of mother wavelet function selection and decomposition levels on computational complexity and fusion image quality was thoroughly discussed. The proposed method exhibited promising potential for intraosseous imaging navigation, which can aid in accurate diagnosis, treatment planning, and monitoring in fields such as orthopedics, surgery, and interventional procedures.

Improving Rock Classification with 1D Discrete Wavelet Transform Based on Laboratory Reflectance Spectra and Gaofen-5 Hyperspectral Data

The high intra-class variability of rock spectra is an important factor affecting classification accuracy. The discrete wavelet transform (DWT) can capture abrupt changes in the signal and obtain subtle differences between the spectra of different rocks. Taking laboratory spectra and hyperspectral data as examples, high-frequency features after DWT were used to improve the discrimination accuracy of rocks. Various decomposition levels, mother wavelet functions, and reconstruction methods were used to compare the accuracy. The intra-class variability was measured using the intra-class Spectral Angle Mapper (SAM). Our results show that the high-frequency features could improve the discrimination accuracy of laboratory spectra by 13.4% (from 46.5% to 59.9%), compared to the original spectral features. The accuracy of image spectra in two study areas increased by 8.6% (from 68.3% to 76.9%) and 7.2% (from 81.3% to 88.5%), respectively. Haar wavelets highlighted the spectral differences between different rocks. After DWT, intra-class SAM reduced and intra-class variability of rocks decreased. The Pearson correlation coefficient indicated a negative correlation between intra-class variability and overall accuracy. It suggested that improving classification accuracy by reducing intra-class variability was feasible. Though the result of lithological mapping still leaves room for improvement, this study provides a new approach to reduce intra-class variability, whether using laboratory spectra or hyperspectral data.

Enhancing Electroretinogram Classification with Multi-Wavelet Analysis and Visual Transformer

The electroretinogram (ERG) is a clinical test that records the retina’s electrical response to light. Analysis of the ERG signal offers a promising way to study different retinal diseases and disorders. Machine learning-based methods are expected to play a pivotal role in achieving the goals of retinal diagnostics and treatment control. This study aims to improve the classification accuracy of the previous work using the combination of three optimal mother wavelet functions. We apply Continuous Wavelet Transform (CWT) on a dataset of mixed pediatric and adult ERG signals and show the possibility of simultaneous analysis of the signals. The modern Visual Transformer-based architectures are tested on a time-frequency representation of the signals. The method provides 88% classification accuracy for Maximum 2.0 ERG, 85% for Scotopic 2.0, and 91% for Photopic 2.0 protocols, which on average improves the result by 7.6% compared to previous work.

Evaluating the performance of different mother wavelet functions for down-sampling of earthquake records

Application of discrete wavelet transform for down-sampling earthquake records has been started since 2002. Although the mother wavelet function plays an important role in the accuracy of wavelet transform, there is no study to investigate the effect of this function on dynamic analysis error. In addition, most studies have used a limited number of earthquake records for down-sampling application of wavelet transform. Therefore, in this paper, a comprehensive study is performed on 36 different mother wavelet functions and 100 earthquake records. The linear and nonlinear response spectra of the main records and their down-sampled ones have been used to evaluate the performance of different mother wavelet functions. Approximate waves are obtained for three levels using wavelet transform. Also, dynamic analyses are done for 101 single-degree-of-freedom systems (with a period between 0 and 5 s) and 5 behavior coefficients consisting of more than 7 million analyses. Results show that the Daubechies family of wavelet functions used in previous studies for down-sampling earthquake records often cause errors greater than 15%. But the Biorthogonal wavelet functions which have not been used for down-sampling before, have an error of less than 2.5% and are the best wavelet functions for down-sampling earthquake records. In addition, a method called wavelet functions combination is presented to ensure minimum errors at different levels of down-sampling. In the next step, to evaluate the effect of the wavelet function on the accuracy of dynamic analysis of real structures, 3, 9, and 20 story structures are analyzed using the IDA method and finally, an irregular structure is also analyzed. The results obtained from the nonlinear analysis of these structures show that Biorthogonal wavelet functions can reduce the wavelet error from 27% to 6%.

High-order Synchrosqueezing Superlets Transform and its application to mechanical fault diagnosis

Under the condition of variable speed, the vibration signal of mechanical transmission components present the typical non-stationary characteristics. Nevertheless, some problems, such as insufficient time–frequency energy concentration and frequent noise disturbance, exist in the current signal processing methods during the extraction of time-varying fault characteristics. Different from the frequently-used time–frequency analysis (TFA) methods such as Continuous Wavelet Transform (CWT) and Synchrosqueezing Transform (SST), High-order Synchrosqueezing Superlets Transform (HSSLT) is proposed in this paper in order to obtain a clearer and more centralized time–frequency representation (TFR). Firstly, multiple groups of wavelets with increased bandwidth are combined into a super wavelet set, and then the Superlets Transform (SLT) is proposed. The single wavelet mother function in the traditional CWT is replaced by this superlets set, which has better wavelet diversity and analytical ability for complex multi-component signals. On this basis, in order to further improve the accuracy of instantaneous frequency (IF) estimation and the energy concentration of TFA, the superlets coefficients calculated by SLT are used for the high-order IF estimation and time–frequency energy rearrangement, thereby HSSLT is presented in this paper. It has obvious advantages of high-resolution TFR and strong noise robustness. Finally, through the rolling bearing fault diagnosis of test bench and the 850 kW offshore wind turbine, the good application potential of the proposed HSSLT in the mechanical fault diagnosis under variable speed conditions is verified.

An accurate automated speaker counting architecture based on James Webb Pattern

Speaker counting is an important research area in sound forensics. There are limited speaker counting papers in the literature, as it is challenging to collect datasets. This work aims to collect a new overlapping speech signal dataset for speaker counting and propose a novel feature engineering model. In this work, textural feature extraction is based on the iconic James Webb space telescope; hence, this pattern is named James Webb Pattern (JWPat). A new speaker counting speech dataset comprising 3,121 speeches divided into 32 classes (the class number corresponded to the number of speakers) was collected. A new framework that mimics the deep learning model has been proposed to classify the collected speech classes. The proposed feature engineering model is self-organized and uses various mother wavelet functions to generate features at both low and high levels. We have obtained the best classification accuracy of 86.74% using the symlet4 mother wavelet function. Using our proposed framework, eight classification results have been calculated with accuracy ranging from 75.94% to 86.74%. This range is over 10% accuracy, and it demonstrates the effect of the mother wavelet function on the classification performance. Moreover, the feature extraction capability of the mirror of the James Webb telescope has been demonstrated. Our proposed method yielded 86.74% accuracy on a large dataset and indicated the success of our proposed model.

Wavelet-based Hybrid Learning Framework for Motor Imagery Classification

Due to their vital applications in many real-world situations, researchers are still presenting bunches of methods for better analysis of motor imagery (MI) electroencephalograph (EEG) signals. However, in general, EEG signals are complex because of their nonstationary and high-dimensionality properties. Therefore, high consideration needs to be taken in both feature extraction and classification. In this paper, several hybrid classification models are built and their performance is compared. Three famous wavelet mother functions are used for generating scalograms from the raw signals. The scalograms are used for transfer learning of the well-known VGG-16 deep network. Then, one of six classifiers is used to determine the class of the input signal. The performance of different combinations of mother functions and classifiers are compared on two MI EEG datasets. Several evaluation metrics show that a model of VGG-16 feature extractor with a neural network classifier using the Amor mother wavelet function has outperformed the results of state-of-the-art studies.

Automated accurate detection of depression using twin Pascal’s triangles lattice pattern with EEG Signals

Electroencephalogram (EEG)-based major depressive disorder (MDD) machine learning detection models can objectively differentiate MDD from healthy controls but are limited by high complexities or low accuracies. This work presents a self-organized computationally lightweight handcrafted classification model for accurate MDD detection using a reference subject-based validation strategy. We used the public Multimodal Open Dataset for Mental Disorder Analysis (MODMA) comprising 128-channel EEG signals from 24 MDD and 29 healthy control (HC) subjects. The input EEG was decomposed using multilevel discrete wavelet transform with Daubechies 4 mother wavelet function into eight low- and high-level wavelet bands. We used a novel Twin Pascal’s Triangles Lattice Pattern(TPTLP) comprising an array of 25 values to extract local textural features from the raw EEG signal and subbands. For each overlapping signal block of length 25, two walking paths that traced the maximum and minimum L1-norm distances from v1 to v25 of the TPTLP were dynamically generated to extract features. Forty statistical features were also extracted in parallel per run. We employed neighborhood component analysis for feature selection, a k-nearest neighbor classifier to obtain 128 channel-wise prediction vectors, iterative hard majority voting to generate 126 voted vectors, and a greedy algorithm to determine the best overall model result. Our generated model attained the best channel-wise and overall model accuracies. The generated system attained an accuracy of 76.08% (for Channel 1) and 83.96% (voted from the top 13 channels) using leave-one-subject-out(LOSO) cross-validation (CV) and 100% using 10-fold CV strategies, which outperformed other published models developed using same (MODMA) dataset.

Improvement of Lithological Mapping Using Discrete Wavelet Transformation from Sentinel-1 SAR Data

Lithological mapping using dual-polarization synthetic aperture radar (SAR) data is limited by the low classification accuracy. In this study, we extract ten parameters (backscatter coefficients and polarization decomposition parameters) from the Sentinel-1 dual-pol SAR data. Using 94 mother wavelet functions (MF), a one-level two-dimensional discrete wavelet transform (DWT) is applied to all the parameters, and the suitable MF is screened by comparing the overall accuracy and F1 score. Finally, the lithological mapping of the study area is performed. According to the cross-validation results, DWT can improve the overall accuracy for all MF. Db13 improved the overall accuracy by 6.1% (from 49.5% to 55.6%). The F1 score of granitoids improved by 0.223. Among the five rock units, Grantoids and Quaternary alluvium and sediment with finer gravel can be better differentiated than the other three rock units. The overall accuracy of effusive rocks (marine basic volcanic rocks) is not improved by DWT, but this study confirms the great potential of DWT in lithology classification.

A Comparative Analysis of the Choice of Mother Wavelet Functions Affecting the Accuracy of Forecasts of Daily Balances in the Treasury Single Account

Improving the accuracy of cash flow forecasting in the TSA is key to fulfilling government payment obligations, minimizing the cost of maintaining the cash reserve, providing the absence of outstanding debt accumulation and ensuring investment in financial instruments to obtain additional income. This study aims to improve the accuracy of traditional methods of forecasting the time series compiled from the daily remaining balances in the TSAbased on prior decomposition using a discrete wavelet transform. The paper compares the influence of selecting a mother wavelet out of 570 mother wavelet functions belonging to 10 wavelet families (Haar;Dabeshies; Symlet; Coiflet; Biorthogonal Spline; Reverse Biorthogonal Spline; Meyer; Shannon; Battle-Lemarie; and Cohen–Daubechies–Feauveau) and the decomposition level (from 1 to 8) on the forecast accuracy of time series compiled from the daily remaining balances in the TSA in comparison with the traditional forecasting method without prior timeseries decomposition. The model with prior time series decomposition based on the Reverse Biorthogonal Spline Wavelet [5.5] mother wavelet function, upon the eighth iteration, features the highest accuracy, significantly higher than that of the traditional forecasting models. The choice of the mother wavelet and the decomposition level play an important role in increasing the accuracy of forecasting the daily remaining balances in the TSA.

A Wavelet Neural Network-Based NARMA-L2 Feedforward Controller Using Genetic Algorithms to Control Nonlinear Systems

As a powerful nonlinear control design strategy, feedback linearization provides viable design tools for a wide range of nonlinear systems. This paper presents an intelligent feedback linearization design using the inverse feedforward control (IFC) scheme to control nonlinear dynamical systems. Particularly, the nonlinear autoregressive moving average (NARMA-L2) network is trained to reproduce the controlled system's forward dynamics. Consequently, the trained NARMA-L2 network can be directly employed in the IFC structure. To enhance the approximation ability of the NARMA-L2 structure, two wavelet neural networks (WNNs) are utilized to constitute the NARMA-L2 controller. Moreover, the RASP1 function was utilized as the mother wavelet function instead of the commonly employed Mexican hat function. To avoid the limitations of the gradient descent (GD) methods, the genetic algorithm has been used as the training method to optimize the NARMA-L2 inverse controller parameters. The simulation results showed that the proposed controller was effective in terms of precise control and robustness against external disturbances. Furthermore, a comparison study with other control structures revealed that the control results of the proposed WNN-based NARMA-L2 controller with the RASP1 function are superior to those of the WNN-based NARMA-L2 with the Mexican hat function, the multilayer perceptron (MLP)-based NARMA-L2 controller, and the PID controller.

An Intelligent Feedforward Controller Utilizing a Modified Gorilla Troops Optimization for Nonlinear Systems

This paper presents an intelligent feedforward controller based on the feedback linearization approach to control nonlinear systems. In particular, the nonlinear autoregressive moving average (NARMA-L2) network is trained to reproduce the forward dynamics of the controlled system. Consequently, the trained NARMA-L2 network can be immediately integrated into the inverse feedforward control (IFC) structure. In order to improve the NARMA-L2 structure's ability to approximate nonlinear systems, the NARMA-L2 controller is comprised of two wavelet neural networks (WNNs). In addition, the RASP1 function was used as the mother wavelet function in the structure of the WNN rather than the more common Mexican Hat, Gaussian, and Morlet functions. To prevent the limitations of gradient descent (GD) methods, an artificial gorilla troops optimization (GTO) algorithm is used to determine the optimal settings for the NARMA-L2 inverse controller parameters. In particular, a modified version of the GTO algorithm, which is called the Modified GTO (MGTO) algorithm, is proposed in this work for training the NARMA-L2 inverse controller. This algorithm has demonstrated superior optimization outcomes in comparison to other methods. The effectiveness of the proposed control strategy is demonstrated using two nonlinear dynamical systems. Specifically, several evaluation tests are used to assess the effectiveness of the WNN-based NARMA-L2 in terms of control accuracy and robustness against external disturbances in each of the systems under consideration. These tests clearly demonstrated the effectiveness of the control system. Finally, a comparison study showed that the proposed WNN-based NARMA-L2 controller achieved better control results compared to the multilayer perceptron (MLP) and the radial basis function (RBF)-based NARMA-L2 controllers.

Investigating the Effect of Flickering Frequency Pair and Mother Wavelet Selection in Steady-State Visually-Evoked Potentials on Two-Command Brain-Computer Interfaces

IntroductionSteady-state visually evoked potentials (SSVEPs) have become popular in brain-computer interface (BCI) applications in addition to many other applications on clinical neuroscience (neurodegenerative disorders, schizophrenia, epilepsy, etc.), cognitive (visual attention, working memory, brain rhythms, etc.), and use of engineering researches. Among available methods to measure brain activities, SSVEPs have advantages like higher information transfer rate, simplicity in structure, and short training time. SSVEP-based BCIs use flickering stimuli at different frequencies to discriminate distinct commands in real life. Some features are extracted from the SSVEP signals before these commands are classified. The wavelet transform (WT) has attracted researchers among feature extraction methods since it utilizes the non-stationary signals well. In the WT, a sample function (named mother wavelet) represents the SSVEP signal in both time and frequency domains. Unfortunately, there is no universal mother wavelet function that fits all the signals. Therefore, choosing an appropriate mother wavelet function may be a challenge in WT-related studies. Although there are such studies in three- and seven-command SSVEP-based studies, there is no study for two-command systems in our knowledge. Materials and MethodsIn this study, two user commands flickered at the combinations of seven different frequencies were tested to determine which frequency pairs give the highest performance. For this purpose, three well-known wavelet features (energy, entropy, and variance) were calculated for each of derived EEG frequency bands from the discrete WT coefficients of SSVEP signals. The WT was repeated for six different mother wavelet functions (Haar, Db4, Sym4, Coif1, Bior3.5, and Rbior2.8). Then, four feature sets (every three features, and all together) were applied to seven commonly-used machine learning algorithms (Decision Tree, Discriminant Analysis, Logistic Regression, Naive Bayes, Support Vector Machines, Nearest Neighbors, and Ensemble Classifiers). Results and DiscussionWe achieved 100% accuracies among these 3,528 runs (7 classifiers x 4 feature sets x 6 mother wavelets x 21 flickering frequency pairs) using the mother wavelet function of Haar and the Ensemble Learner classifier. The highest classifier performances are 100% when two commands have the flickering frequency pairs of (6.0 and 10 Hz), (6.5 and 8.2 Hz), or (6.5 and 10.0 Hz). ConclusionWe obtained three main outcomes from this study. First, the most representative mother wavelet function was Haar, while the worst one was Symlet 4. Second, the Ensemble Learner classifier gave the maximum classifier performance in a two-command SSVEP-based BCI system. Besides, two user commands from SSVEP should be one of the frequency pairs of (6.0 and 10.0 Hz), (6.5 and 8.2 Hz), and (6.5 and 10.0 Hz) to achieve the maximum accuracy.

ANALYSIS OF MACHINE LEARNING BASED RENEWABLE ENERGY SYSTEMS

The present research focuses on the development and optimization of the particle swarm techniques inspired in nature to predict wind speed in renewable energies with real-time wind farm data structures, of unique machine learning architectures for neural networks alongside certain mathematical and stochastic populations. The research work in this article includes six modules, i.e., designing proposed architectures of the neural network with variants based on population stochastic particle swarm (SPS) optimization and developed mathematical parameters in place of hidden neuron numbers to effectively predict the speed of renewable energy systems that reach the set number of neurons. The wind farm data sets are used for training, testing and validation of the proposed model of wind speed predictors. The final prediction model proposed involves the applicability of a neural wavelet network for a predictive wind velocity and the mother wavelet function is used to allow the hidden neurons and to measure the wind speed output with the reduction of the set parameters.

Financial time series forecasting using optimized multistage wavelet regression approach.

This paper presents financial time series forecasting with multistage wavelet transform (WT). First, the time series data is processed through WT with different mother wavelet functions to extract high frequency and low frequency coefficients. Later, standard particle swarm optimization (PSO) algorithm is utilized to find optimal regression models in order to predict future samples. Mean square error (MSE) is opted as cost function for PSO to find optimal coefficients of the regression model. This study further extended to various mother wavelet functions and their decomposition levels to investigate their impacts on time series prediction. These investigations help to data scientists for selection of process parameters and variables. Further, the impact of control parameters of PSO is also discussed to show the importance in the search mechanism especially in regression problems.

An adaptive high-voltage direct current detection algorithm using cognitive wavelet transform

This paper proposes an algorithm that uses wavelet level adaptive decision-making for detecting high-voltage direct current (HVDC) discharge in wavelet transform cognitively. The identification and detection of HVDC discharge is an essential area of investigation, which contributes to ensuring pipeline safety and the optimal operation of an electrical power system. The proposed algorithm overcomes the wavelet packet transform’s disadvantage of needing to determine the level in advance. The decomposition level of wavelet packet transform is controlled by calculating relative wavelet energy change to decide its wavelet level. Our proposal extracts richer features of HVDC discharge by comparing other feature extraction algorithms. To select the best-suited mother wavelet function, we also design a selection method based on quantitative and qualitative approaches. An additional objective of this study is to detect the phenomenon of HVDC discharge using CP time-series data to assess the corrosion of energy pipelines. Moreover, a third primary discovery is that a wavelet-based application framework is designed to detect the HVDC discharge and further protect the energy pipeline. These discoveries can be valuably applied to the protection of power systems. They also provide brighter perspectives on future opportunities to expand on studies-to-date on the detection and classification of time-series data.