Search Results (31)

The combination of fractional derivatives (due to their global behavior) and the challenges related to hyperbolic PDEs pose formidable obstacles in solving fractional hyperbolic equations. Due to the importance and applications of the fractional telegraph equation, solving it and presenting accurate solutions via a novel and effective method can be useful. This work introduces and implements a method based on the spectral element method (SEM) that relies on interpolating scaling functions (ISFs). Through the use of an orthonormal projection, the method maps the equation to scaling spaces raised from multi-resolution analysis (MRA). To achieve this, the Caputo fractional derivative (CFD) is represented by ISFs as a square matrix. Remarkable efficiency, ease of implementation, and precision are the distinguishing features of the presented method. An analysis is provided to demonstrate the convergence of the scheme, and illustrative examples validate our method. Full article

This study investigated the impact of the June 2015 geomagnetic storms on the Brazilian equatorial and low-latitude ionosphere by analyzing various data sources, including solar wind parameters from the advanced compositional explorer satellite (ACE), global positioning satellite vertical total electron content (GPS-VTEC), geomagnetic data, and validation of the SAMI2 model-VTEC with GPS-VTEC. The effect of geomagnetic disturbances on the Brazilian longitudinal sector was examined by applying multiresolution analysis (MRA) of the maximum overlap discrete wavelet transform (MODWT) to isolate the diurnal component of the disturbance dynamo (Ddyn), DP2 current fluctuations from the ionospheric electric current disturbance (Diono), and semblance cross-correlation wavelet analysis for local phase comparison between the Sq and Diono currents. Our findings revealed that the significant fluctuations in DP2 at the Brazilian equatorial stations (Belem, dip lat: −0.47° and Alta Floresta, dip lat: −3.75°) were influenced by IMF Bz oscillations; the equatorial electrojet also fluctuated in tandem with the DP2 currents, and dayside reconnection generated the field-aligned current that drove the DP2 current system. The short-lived positive ionospheric storm during the main phase on 22 June in the Southern Hemisphere in the Brazilian sector was caused by the interplay between the eastward prompt penetration of the magnetospheric convection electric field and the westward disturbance dynamo electric field. The negative ionospheric storms that occurred during the recovery phase from 23 to 29 June 2015, were attributed to the westward disturbance dynamo electric field, which caused the downward E × B drift of the plasma to a lower height with a high recombination rate. The comparison between the SAMI2 model-VTEC and GPS-VTEC indicates that the SAMI2 model underestimated the VTEC within magnetic latitudes of −9° to −24° in the Brazilian longitudinal sector from 6 to 17 June 2015. However, it demonstrated satisfactory agreement with the GPS-VTEC within magnetic latitudes of −9° to 10° from 8 to 15 June 2015. Conversely, the SAMI2 model overestimated the VTEC between ±10° magnetic latitudes from 16 to 28 June 2015. The most substantial root mean square error (RMSE) values, notably 10.30 and 5.48 TECU, were recorded on 22 and 23 June 2015, coinciding with periods of intense geomagnetic disturbance. Full article

Battery state-of-health (SOH) estimation is an effective approach to evaluate battery reliability and reduce maintenance costs for battery-based backup power supply systems. This paper proposes a novel SOH estimation method for batteries, which only uses the response characteristics of load surges and is, therefore, non-destructive to the estimated battery and its system. The discrete wavelet transform (DWT) method based on multi-resolution analysis (MRA) is used for wavelet energy features extraction, and the fuzzy cerebellar model neural network (FCMNN) is introduced to design the battery SOH estimator. The response voltage signals to load surges are used in the training and detection process of the FCMNN. Compared to conventional methods, the proposed method only exploits characteristics of online response signals to the inrush currents rather than injecting interference signals into the battery. The effectiveness of the proposed method is validated by detailed simulation analysis and experiments. Full article

The multi-resolution analysis (MRA) associated with quadratic phase Fourier transform (QPFT) serves as a tool to construct orthogonal bases of the L2(R). Consequently, it assumes a pivotal role in facilitating potential applications of QPFT. Inspired by the sampling theorem applicable to band-limited signals in the QPFT domain, this paper formulates the development of the MRA linked with QPFT. Subsequently, we develop a method for constructing orthogonal bases for L2(R), followed by some examples. Full article

Analyzing network traffic activities is imperative in network security to detect attack patterns. Due to the complex nature of network traffic event activities caused by continuously changing computing environments and software applications, identifying the patterns is one of the challenging research topics. This study focuses on analyzing the effectiveness of integrating Multi-Resolution Analysis (MRA) and visualization in identifying the attack patterns of network traffic activities. In detail, a Discrete Wavelet Transform (DWT) is utilized to extract features from network traffic data and investigate their capability of identifying attacks. For extracting features, various sliding windows and step sizes are tested. Then, visualizations are generated to help users conduct interactive visual analyses to identify abnormal network traffic events. To determine optimal solutions for generating visualizations, an extensive evaluation with multiple intrusion detection datasets has been performed. In addition, classification analysis with three different classification algorithms is managed to understand the effectiveness of using the MRA with visualization. From the study, we generated multiple visualizations associated with various window and step sizes to emphasize the effectiveness of the proposed approach in differentiating normal and attack events by forming distinctive clusters. We also found that utilizing MRA with visualization advances network intrusion detection by generating clearly separated visual clusters. Full article

Spatial and spectral information are essential sources of information in remote sensing applications, and the fusion of panchromatic and multispectral images effectively combines the advantages of both. Due to the existence of two main classes of fusion methods—component substitution (CS) and multi-resolution analysis (MRA), which have different advantages—mixed approaches are possible. This paper proposes a fusion algorithm that combines the advantages of generalized intensity–hue–saturation (GIHS) and non-subsampled shearlet transform (NSST) with principal component analysis (PCA) technology to extract more spatial information. Therefore, compared with the traditional algorithms, the algorithm in this paper uses PCA transformation to obtain spatial structure components from PAN and MS, which can effectively inject spatial information while maintaining spectral information with high fidelity. First, PCA is applied to each band of low-resolution multispectral (MS) images and panchromatic (PAN) images to obtain the first principal component and to calculate the intensity of MS. Then, the PAN image is fused with the first principal component using NSST, and the fused image is used to replace the original intensity component. Finally, a fused image is obtained using the GIHS algorithm. Using the urban, plants and water, farmland, and desert images from GeoEye-1, WorldView-4, GaoFen-7 (GF-7), and Gaofen Multi-Mode (GFDM) as experimental data, this fusion method was tested using the evaluation mode with references and the evaluation mode without references and was compared with five other classic fusion algorithms. The results showed that the algorithms in this paper had better fusion performances in both spectral preservation and spatial information incorporation. Full article

Thermal infrared imagery plays an important role in a variety of fields, such as surface temperature inversion and urban heat island effect analysis, but the spatial resolution has severely restricted the potential for further applications. Data fusion is defined as data combination using multiple sensors, and fused information often has better results than when the sensors are used alone. Since multi-resolution analysis is considered an effective method of image fusion, we propose an MTF-GLP-TAM model to combine thermal infrared (30 m) and multispectral (10 m) information of SDGSAT-1. Firstly, the most relevant multispectral bands to the thermal infrared bands are found. Secondly, to obtain better performance, the high-resolution multispectral bands are histogram-matched with each thermal infrared band. Finally, the spatial details of the multispectral bands are injected into the thermal infrared bands with an MTF Gaussian filter and an additive injection model. Despite the lack of spectral overlap between thermal infrared and multispectral bands, the fused image improves the spatial resolution while maintaining the thermal infrared spectral properties as shown by subjective and objective experimental analyses. Full article

Identifying the impacts of climatic factors on runoff change has become a central topic in climate and hydrology research. This issue, however, has received minimal attention in karst watersheds worldwide. Multi-resolution analysis (MRA), continuous wavelet transform (CWT), cross wavelet transform (XWT) and wavelet transform coherence (WTC) are used to study the teleconnection in time and frequency between climate change and hydrological processes in a typical karst watershed at different time scales. The main results are: (1) All climatic factors exhibit a main cycle at 12-month time scales with runoff changes, but the main periodic bandwidth of rainfall on runoff changes is much wider than that of temperature and evaporation, indicating that rainfall is the main factor affecting runoff changes. (2) In other cycles, the impact of rainfall on runoff changes is the interlacing phenomena with positive and negative, but the impact of temperature and evaporation on runoff change is mainly negative. (3) The response of runoff to rainfall is in time in the high-energy region and the low-energy significant-correlation region and has shown a positive correlation with a smaller phase angle, but it is slightly lagged at 16-month time scales. Moreover, the runoff change lags behind temperature and evaporation for 1–2 months in those regions. (4) It has been found that there is a strong effect of rainfall over runoff, but a lesser effect of temperature and evaporation over runoff. The study sheds light on the main teleconnections between rainfall, evapotranspiration and surface runoff, which in turn might help to attain the better management of water resources in typical karst watersheds. Full article

A linear canonical S transform (LCST) is considered a generalization of the Stockwell transform (ST). It analyzes signals and has multi-angle, multi-scale, multiresolution, and temporal localization abilities. The LCST is mostly suitable to deal with chirp-like signals. It aims to possess the characteristics lacking in a classical transform. Our aim in this paper was to derive the sampling theorem for the LCST with the help of a multiresolution analysis (MRA) approach. Moreover, we discuss the truncation and aliasing errors for the proposed sampling theory. These types of sampling results, as well as methodologies for solving them, have applications in a wide range of fields where symmetry is crucial. Full article

This paper proposes a fault-detection system for faulty induction motors (bearing faults, interturn shorts, and broken rotor bars) based on multiresolution analysis (MRA), correlation and fitness values-based feature selection (CFFS), and artificial neural network (ANN). First, this study compares two feature-extraction methods: the MRA and the Hilbert Huang transform (HHT) for induction-motor-current signature analysis. Furthermore, feature-selection methods are compared to reduce the number of features and maintain the best accuracy of the detection system to lower operating costs. Finally, the proposed detection system is tested with additive white Gaussian noise, and the signal-processing method and feature-selection method with good performance are selected to establish the best detection system. According to the results, features extracted from MRA can achieve better performance than HHT using CFFS and ANN. In the proposed detection system, CFFS significantly reduces the operation cost (95% of the number of features) and maintains 93% accuracy using ANN. Full article

Wavelet transform is an important tool in the computational signal processing of terahertz time-domain spectroscopy (THz-TDS) measurements. Despite its prevalence, the effects of using different forms of wavelet transforms in THz-TDS studies have not been investigated. In this paper, we explore the implications of using the maximal overlap discrete wavelet transform (MODWT) versus the well-known discrete wavelet transform (DWT). We demonstrate that the spectroscopic features extracted using DWT can vary over different overlapping frequency ranges. On the contrary, MODWT is translation-invariant and results in identical features, regardless of the spectral range used for its implementation.We also demonstrate that the details coefficients obtained by the multiresolution analysis (MRA) using MODWT are associated with zero-phase filters. In contrast, DWT details coefficients suffer from misalignments originated from the down- and upsampling operations in DWT pyramid algorithm. Such misalignments have adverse effects when it is critical to retain the exact location of the absorption lines. We study the differences of DWT and MODWT both analytically and experimentally, using reflection THz-TDS measurements of α-lactose monohydrate. This manuscript can guide the researchers to select the right wavelet analysis tool for their specific application of the THz spectroscopy. Full article

The main objective of this study is to analyze the spatial and temporal variability of gross and net primary production (GPP and NPP) in Peninsular Spain across 15 years (2004–2018) and determine the relationship of those carbon fluxes with precipitation and air temperature. A time series study of daily GPP, NPP, mean air temperature, and monthly standardized precipitation index (SPI) at 1 km spatial resolution is conducted to analyze the ecosystem status and adaptation to changing environmental conditions. Spatial variability is analyzed for vegetation and specific forest types. Temporal dynamics are examined from a multiresolution analysis based on the wavelet transform (MRA-WT). The Mann–Kendall nonparametric test and the Theil–Sen slope are applied to quantify the magnitude and direction of trends (increasing or decreasing) within the time series. The use of MRA-WT to extract the annual component from daily series increased the number of statistically significant pixels. At pixel level, larger significant GPP and NPP negative changes (p-value < 0.1) are observed, especially in southeastern Spain, eastern Mediterranean coastland, and central Spain. At annual temporal scale, forests and irrigated crops are estimated to have twice the GPP of rainfed crops, shrublands, grasslands, and sparse vegetation. Within forest types, deciduous broadleaved trees exhibited the greatest annual NPP, followed by evergreen broadleaved and evergreen needle-leaved tree species. Carbon fluxes trends were correlated with precipitation. The temporal analysis based on daily TS demonstrated an increase of accuracy in the trend estimates since more significant pixels were obtained as compared to annual resolution studies (72% as to only 17%). Full article

Stock movement prediction is important in the financial world because investors want to observe trends in stock prices before making investment decisions. However, given the non-linear non-stationary financial time series characteristics of stock prices, this remains an extremely challenging task. A wavelet is a mathematical function used to divide a given function or continuous-time signal into different scale components. Wavelet analysis has good time-frequency local characteristics and good zooming capability for non-stationary random signals. However, the application of the wavelet theory is generally limited to a small scale. The neural networks method is a powerful tool to deal with large-scale problems. Therefore, the combination of neural networks and wavelet analysis becomes more applicable for stock behavior prediction. To rebuild the signals in multiple scales, and filter the measurement noise, a forecasting model based on a stock price time series was provided, employing multiresolution analysis (MRA). Then, the deep learning in the neural network method was used to train and test the empirical data. To explain the fundamental concepts, a conceptual analysis of similar algorithms was performed. The data set for the experiment was chosen to capture a wide range of stock movements from 1 January 2009 to 31 December 2017. Comparison analyses between the algorithms and industries were conducted to show that the method is stable and reliable. This study focused on medium-term stock predictions to predict future stock behavior over 11 days of horizons. Our test results showed a 75% hit rate, on average, for all industries, in terms of US stocks on FORTUNE Global 500. We confirmed the effectiveness of our model and method based on the findings of the empirical research. This study’s primary contribution is to demonstrate the reconstruction model of the stock time series and to perform recurrent neural networks using the deep learning method. Our findings fill an academic research gap, by demonstrating that deep learning can be used to predict stock movement. Full article

This paper proposes a diagnosis method, combining signal analysis and classification models, to the rotor defect problems of motors. Two manufacture technologies, nonmagnetic high-temperature resistant ceramic adhesive and electrical discharge machining (EDM), are applied to make testing samples, including blowhole and perforation defects of rotor bars in this study. The typical multiresolution analysis (MRA) model is used to analyze acquired source current signals of motors. The features are extracted from the signals of each column of MRA-matrix, including maximum, mean, standard deviation, root-mean-square, and summation. The typical back-propagation neural network (BPNN) model is used to diagnose the rotor bar defects of motors, and then the various signal-to-noise ratio (SNR) of white Gaussian noise (WGN), 30, 25, and 20 dB, are added to the signals to verify the robustness of the proposed method. The results show the availability of the proposed method to diagnose the rotor bar defects of motors. Full article

Compared to using images in the visible and near-infrared (VNIR) wavelength range only, remotely sensed satellite imagery from the spectral wavelengths of both VNIR and shortwave infrared (SWIR), such as Sentinel-2A and Worldview-3, is more effective for analyzing various types of information for tasks such as land cover mapping, environmental monitoring and land use change detection. In this manuscript, a new sharpening technique to enhance the spatial resolution of Worldview-3 satellite imagery with various spatial and spectral resolutions is proposed. Selected and synthesized band schemes were used to produce optimal panchromatic images; then, sharpened images were generated by applying the Gram-Schmidt adaptive (GSA) and Gram-Schmidt 2 (GS2) techniques, which are component substitution (CS)- and multiresolution analysis (MRA)-based algorithms, respectively. In addition, to minimize the spectral distortion of the initial sharpened image, a postprocessing methodology for spectral distortion reduction was developed. Qualitative and quantitative evaluation of the sharpened images showed that the pansharpening performance using the GS2 technique based on the selected band scheme and spectral distortion reduction was the best. To confirm the usability of the SWIR band, supervised classification based on machine learning was performed on the pansharpened images obtained by applying the technique proposed in this study and on the pansharpened images obtained by the VNIR bands only. The classification accuracy of the results using SWIR bands was higher than that of VNIR bands only. In particular, it was confirmed that the accuracy of the classification of artificial facilities known to be effective for SWIR bands was greatly improved. Full article