Search Results (18)

This paper presents a novel B-spline wavelet-based scheme for solving multi-term time–space variable-order fractional nonlinear diffusion-wave equations. By combining semi-orthogonal B-spline wavelets with a collocation approach and a quasilinearization technique, we transform the original problem into a system of algebraic equations. To enhance the computational efficiency, we derive the operational matrix formulation of the proposed scheme. We provide a rigorous convergence analysis of the method and demonstrate its accuracy and effectiveness through numerical experiments. The results confirm the robustness and computational advantages of our approach for solving this class of fractional differential equations. Full article

The effective management of spatiotemporal Earth observation data is a significant challenge due to their growing size and scale, geometric distortion, temporal gaps, and restricted access. In this article, we introduce a novel methodology utilizing a Discrete Global Grid System (DGGS) to address a set of challenges related to spatiotemporal data storage with a live updating mechanism, the multiresolution processing of an arbitrary region of interest (ROI) in real time, and the approximation of missing data in a smooth, continuous manner. We use reverse Chaikin subdivision and B-spline curve fitting to handle temporal data gaps, allowing for real-time updates. Additionally, our work presents a triangular wavelet scheme to incorporate a flexible, tensor-based multiresolution storage scheme for spatiotemporal raster data. The case study we present uses data from the RADARSAT Constellation Mission (RCM) of the Canadian Space Agency (CSA). Our system enables the dynamic retrieval and visualization of time-varying data for a user-defined ROI. The obtained results demonstrate that our method ensures high data fidelity while making spatiotemporal data more accessible across various practical applications in Earth observation. Full article

This paper addresses the critical need for advanced real-time vehicle detection methodologies in Vehicle Intelligence Systems (VIS), especially in the context of using Unmanned Aerial Vehicles (UAVs) for data acquisition in severe weather conditions, such as heavy snowfall typical of the Nordic region. Traditional vehicle detection techniques, which often rely on custom-engineered features and deterministic algorithms, fall short in adapting to diverse environmental challenges, leading to a demand for more precise and sophisticated methods. The limitations of current architectures, particularly when deployed in real-time on edge devices with restricted computational capabilities, are highlighted as significant hurdles in the development of efficient vehicle detection systems. To bridge this gap, our research focuses on the formulation of an innovative approach that combines the fractional B-spline wavelet transform with a tailored U-Net architecture, operational on a Raspberry Pi 4. This method aims to enhance vehicle detection and localization by leveraging the unique attributes of the NVD dataset, which comprises drone-captured imagery under the harsh winter conditions of northern Sweden. The dataset, featuring 8450 annotated frames with 26,313 vehicles, serves as the foundation for evaluating the proposed technique. The comparative analysis of the proposed method against state-of-the-art detectors, such as YOLO and Faster RCNN, in both accuracy and efficiency on constrained devices, emphasizes the capability of our method to balance the trade-off between speed and accuracy, thereby broadening its utility across various domains. Full article

A low-power long-term ambulatory ECG monitor was developed for the acquisition, storage and processing of three simultaneous leads DI, aVF and V2 with a beat-to-beat heart rate measurement in real time. It provides long-term continuous ECG recordings until 84 h. The monitor uses a QRS complex detection algorithm based on the continuous wavelet transform with splines, which automatically selects the scale for the analysis of ECG records with different sampling frequencies. It includes a lead-off detection to continuously monitor the electrode connections and a real-time system of visual and acoustic alarms to alert users of abnormal conditions in its operation. The monitor presented is based in an ADS1294 analogue front end with four channels, 24-bit analog-to-digital converters and programmable gain amplifiers, a low-power dual-core ESP32 microcontroller, a microSD memory for data storage in a range of 4 GB to 32 GB and a 1.4 in thin-film transistor liquid crystal display (LCD) variant with a resolution of 128 × 128 pixels. It has programmable sampling rates of 250, 500 and 1000 Hz; a bandwidth of 0 Hz to 50% of the selected sampling rate; a CMRR of −105 dB; an input margin of ±2.4 V; a resolution of 286 nV; and a current consumption of 50 mA for an average battery life of 84 h. The ambulatory ECG monitor was evaluated with the commercial data-acquisition system BIOPAC MP36 and its module for ECG LABEL SS2LB, simultaneously comparing the morphologies of two ECG records and obtaining a correlation of 91.78%. For the QRS detection in real time, the implemented algorithm had an error less than 5%. The developed ambulatory ECG monitor can be used for the analysis of the dynamics of the heart rate variability in long-term ECG records and for the development of one’s own databases of ECG recordings of normal subjects and patients with cardiovascular and noncardiovascular diseases. Full article

This study focuses on identifying damage in reinforced concrete (RC) beams using time-domain modal testing and wavelet analysis. A numerical model of an RC beam was used to generate various damage scenarios with different severities and locations. Acceleration time histories were recorded for both damaged and undamaged structures. Two damage indices, DI_MW and DI_SW, derived from the wavelet analysis, were employed to determine the location and severity of the damage. The results showed that different wavelet families and specific mother wavelets had varying effectiveness in detecting damage. The Daubechies wavelet family (db2, db6, and db9) detected damage at the center and sides of the RC beams due to good time and frequency localization. The Biorthogonal wavelet family (bior2.8 and bior3.1) provided improved time–frequency resolution. The Symlets wavelet family (sym2 and sym7) offered a balanced trade-off between time and frequency localization. The Shannon wavelet family (shan1-0.5 and shan1-0.1) exhibited good time localization, while the Frequency B-Spline wavelet family (fbsp2-1-0.1) excelled in frequency localization. Certain combinations of mother wavelets, such as shan1-0.5 with the DI_SW index, were highly effective in detecting damage. The DI_SW index outperformed DI_MW across different numerical models. Selecting appropriate wavelet analysis techniques, particularly utilizing shan1-0.5 in the DI_SW, proved effective for detecting damage in RC beams. Full article

A fundamental notion in building engineering is the equal displacement rule, which posits that the peak inelastic displacement of a system subjected to a ground motion excitation is approximately equal to the displacement of the same system responding elastically. The purpose of this study is to determine if the equal displacement rule can additionally be applied to wind excitations. To achieve this purpose, bilinear single-degree-of-freedom systems were subjected to B-spline wavelet excitations, Fejér–Korovkin wavelet excitations, and wind excitations derived from wind tunnel tests. The results showed the equal displacement rule generally held for excitations with neutral polarity. The frequency content of the excitation had a significant effect on the response because it shifted the location of the displacement-controlled region of the response spectrum. Duration had a mild effect for excitations with neutral polarity. The effect of stiffness and strength degradation due to gravity loads on the response was more pronounced for short-period structures. For regularly shaped buildings subjected to wind forces, the findings suggest that the equal displacement rule applies in the cross-wind direction however not in the along-wind direction. Full article

The stability of a hybrid AC-DC microgrid depends mainly upon the bidirectional interlinking converter (BIC), which is responsible for power transfer, power balance, voltage solidity, frequency and transients sanity. The varying generation from renewable resources, fluctuating loads, and bidirectional power flow from the utility grid, charging station, super-capacitor, and batteries produce various stability issues on hybrid microgrids, like net active-reactive power flow on the AC-bus, frequency oscillations, total harmonic distortion (THD), and voltage variations. Therefore, the control of BIC between AC and DC buses in grid-connected hybrid microgrid power systems is of great importance for the quality/smooth operation of power flow, power sharing and stability of the whole power system. In literature, various control schemes are suggested, like conventional droop control, communication-based control, model predictive control, etc., each addressing different stability issues of hybrid AC-DC microgrids. However, model dependence, single-point-failure (SPF), communication vulnerability, complex computations, and complicated multilayer structures motivated the authors to develop online adaptive neural network (NN) Q-learning-based full recurrent adaptive neurofuzzy nonlinear control paradigms for BIC in a grid-connected hybrid AC-DC microgrid. The proposed strategies successfully ensure the following: (i) frequency stabilization, (ii) THD reduction, (iii) voltage normalization and (iv) negligible net active-reactive power flow on the AC-bus. Three novel adaptive NN Q-learning-based full recurrent adaptive neurofuzzy nonlinear control paradigms are proposed for PQ-control of BIC in a grid-connected hybrid AC-DC microgrid. The control schemes are based on NN Q-learning and full recurrent adaptive neurofuzzy identifiers. Hybrid adaptive full recurrent Legendre wavelet-based Neural Network Q-learning-based full recurrent adaptive NeuroFuzzy control, Hybrid adaptive full recurrent Mexican hat wavelet-based Neural Network Q-learning-based full recurrent adaptive NeuroFuzzy control, and Hybrid adaptive full recurrent Morlet wavelet-based Neural Network Q-learning-based full recurrent adaptive NeuroFuzzy control are modeled and tested for the control of BIC. The controllers differ from each other, based on variants used in the antecedent part (Gaussian membership function and B-Spline membership function), and consequent part (Legendre wavelet, Mexican hat wavelet, and Morlet wavelet) of the full recurrent adaptive neurofuzzy identifiers. The performance of the proposed control schemes was validated for various quality and stability parameters, using a simulation testbench in MATLAB/Simulink. The simulation results were bench-marked against an aPID controller, and each proposed control scheme, for a simulation time of a complete solar day. Full article

In this article, a novel and efficient collocation method based on Fibonacci wavelets is proposed for the numerical solution of the non-linear Hunter–Saxton equation. Firstly, the operational matrices of integration associated with the Fibonacci wavelets are constructed by following the strategy of Chen and Hsiao. The operational matrices merged with the collocation method are used to convert the given problem into a system of algebraic equations that can be solved by any classical method, such as Newton’s method. Moreover, the non-linearity arising in the Hunter–Saxton equation is handled by invoking the quasi-linearization technique. To show the efficiency and accuracy of the Fibonacci-wavelet-based numerical technique, the approximate solutions of the non-linear Hunter–Saxton equation with other numerical methods including the Haar wavelet, trigonometric B-spline, and Laguerre wavelet methods are compared. The numerical outcomes demonstrate that the proposed method yields a much more stable solution and a better approximation than the existing ones. Full article

In this paper, two new families of non-stationary subdivision schemes are introduced. The schemes are constructed from uniform generalized B-splines with multiple knots of orders 3 and 4, respectively. Then, we construct a third-order reverse subdivision framework. For that, we derive a generalized multi-resolution mask based on their third-order subdivision filters. For the reverse of the fourth-order scheme, two methods are used; the first one is based on least-squares formulation and the second one is based on solving a linear optimization problem. Numerical examples are given to show the performance of the new schemes in reproducing different shapes of initial control polygons. Full article

This paper deals with polynomial Hermite splines. In the first part, we provide a simple and fast procedure to compute the refinement mask of the Hermite B-splines of any order and in the case of a general scaling factor. Our procedure is solely derived from the polynomial reproduction properties satisfied by Hermite splines and it does not require the explicit construction or evaluation of the basis functions. The second part of the paper discusses the factorization properties of the Hermite B-spline masks in terms of the augmented Taylor operator, which is shown to be the minimal annihilator for the space of discrete monomial Hermite sequences of a fixed degree. All our results can be of use, in particular, in the context of Hermite subdivision schemes and multi-wavelets. Full article

We present a wavelet finite-element method (WFEM) based on B-spline wavelets on the interval (BSWI) for three-dimensional (3D) frequency-domain airborne EM modeling using a secondary coupled-potential formulation. The BSWI, which is constructed on the interval (0, 1) by joining piecewise B-spline polynomials between nodes together, has proved to have excellent numerical properties of multiresolution and sparsity and thus is utilized as the basis function in our WFEM. Compared to conventional basis functions, the BSWI is able to provide higher interpolating accuracy and boundary stability. Furthermore, due to the sparsity of the wavelet, the coefficient matrix obtained by BSWI-based WFEM is sparser than that formed by general FEM, which can lead to shorter solution time for the linear equations system. To verify the accuracy and efficiency of our proposed method, we ran numerical experiments on a half-space model and a layered model and compared the results with one-dimensional (1D) semi-analytic solutions and those obtained from conventional FEM. We then studied a synthetic 3D model using different meshes and BSWI basis at different scales. The results show that our method depends less on the mesh, and the accuracy can be improved by both mesh refinement and scale enhancement. Full article

This paper focuses on a method to construct wavelet Riesz bases with homogeneous boundary condition and use them to a kind of second-order elliptic equation. First, we construct the splines on the interval $[0,1]$ and consider their approximation properties. Then we define the wavelet bases and illustrate the condition numbers of stiffness matrices are small and bounded. Finally, several numerical examples show that our approach performs efficiently. Full article

In the present article, we implement a new numerical scheme, the quasilinearized semi-orthogonal B-spline wavelet method, combining the semi-orthogonal B-spline wavelet collocation method with the quasilinearization method, for a class of multi-term non-linear fractional order equations that contain both the Riemann–Liouville fractional integral operator and the Caputo fractional differential operator. The quasilinearization method is utilized to convert the multi-term non-linear fractional order equation into a multi-term linear fractional order equation which, subsequently, is solved by means of semi-orthogonal B-spline wavelets. Herein, we investigate the operational matrix and the convergence of the proposed scheme. Several numerical results are delivered to confirm the accuracy and efficiency of our scheme. Full article

In this paper, we present a new computational method for solving linear Fredholm integral equations of the second kind, which is based on the use of B-spline quasi-affine tight framelet systems generated by the unitary and oblique extension principles. We convert the integral equation to a system of linear equations. We provide an example of the construction of quasi-affine tight framelet systems. We also give some numerical evidence to illustrate our method. The numerical results confirm that the method is efficient, very effective and accurate. Full article

A wavelet-based finite element method (WFEM) is developed to calculate the elastic band structures of two-dimensional phononic crystals (2DPCs), which are composed of square lattices of solid cuboids in a solid matrix. In a unit cell, a new model of band-gap calculation of 2DPCs is constructed using plane elastomechanical elements based on a B-spline wavelet on the interval (BSWI). Substituting the periodic boundary conditions (BCs) and interface conditions, a linear eigenvalue problem dependent on the Bloch wave vector is derived. Numerical examples show that the proposed method performs well for band structure problems when compared with those calculated by traditional FEM. This study also illustrates that filling fractions, material parameters, and incline angles of a 2DPC structure can cause band-gap width and location changes. Full article