Basis Functions Research Articles

A Hybrid Fuzzy Predictive DVR Model for Voltage Estimation Using Intelligent Learning

A self-constructing intelligence-based learning law is proposed for the prediction of power quality mitigation through a dynamic voltage restorer (DVR). To tackle voltage-based power quality concerns in the distribution network, a fuzzy neural-based hybridization control approach using an evolving Takagi–Sugeno–Kang (e-TSK) and radial basis function (RBFN) is developed. The estimated value of fundamental weight components is achieved by the eTSK predictive model. The evaluated weight values are used to update the parameters for the generation of the reference load voltage components. The RBFN is used to achieve the desired task of dc and ac link voltage regulation. The self-tuned control algorithm is developed based on an intelligence technique that avoids the trapping of local optima, and early convergence, and reduces the voltage oscillation to obtain an optimal solution. A meta-heuristic optimization approach of grey wolf optimization (GWO) and grey wolf-cuckoo search (GWOCS) is selected to optimize the parameters of eTKS and RBFN to find the best-fitted predictive model under the dynamic state. The hybridization of the model with GWO and GWOCS is implemented for improving the training and generalization capability. The performance of VSC-based DVR is validated using the d-SPACE Micro lab box under the various power quality scenario.

Compressive Sensing Enhanced Multilevel Characteristic Basis Function Method for Analyzing Electrically Large Scattering Problems

Compressive Sensing Enhanced Multilevel Characteristic Basis Function Method for Analyzing Electrically Large Scattering Problems

Tchebichef Transform Domain-Based Deep Learning Architecture for Image Super-Resolution.

Recent advances in the area of artificial intelligence and deep learning have motivated researchers to apply this knowledge to solve multipurpose applications in the area of computer vision and image processing. Super-resolution (SR), in the past few years, has produced remarkable results using deep learning methods. The ability of deep learning methods to learn the nonlinear mapping from low-resolution (LR) images to their corresponding high-resolution (HR) images leads to compelling results for SR in diverse areas of research. In this article, we propose a deep learning-based image SR architecture in the Tchebichef transform domain. This is achieved by integrating a transform layer into the proposed architecture through a customized Tchebichef convolutional layer (TCL). The role of TCL is to convert the LR image from the spatial domain to the orthogonal transform domain using Tchebichef basis functions. The inversion of the transform mentioned earlier is achieved using another layer known as the inverse TCL (ITCL), which converts back the LR images from the transform domain to the spatial domain. It has been observed that using the Tchebichef transform domain for the task of SR takes the advantage of high and low- frequency representation of images that makes the task of SR simplified. Furthermore, a transfer learning-based approach is adopted to enhance the quality of images by considering Covid19 medical images as an additional experiment. It is shown that our architecture enhances the quality of X-ray and CT images of COVID-19, providing a better image quality that may help in clinical diagnosis. Experimental results obtained using the proposed Tchebichef transform domain SR (TTDSR) architecture provides competitive results when compared with most of the deep learning methods employed using a fewer number of trainable parameters.

A Radial Basis Function-Based Graph Attention Network With Squeeze Loss Optimization for Link Prediction

Graph attention networks is a popular method to deal with link prediction tasks, but the weight assigned to each sample is not focusing on the sample's own performance in training. Moreover, since the number of links is much larger than nodes in a graph, mapping functions are usually used to map the learned node features to link features, whose expression of node similarity determines the quality of link feature learning. To tackle the above issues, a new model graph attention networks based on Radial Basis Function (RBF) with squeeze loss is proposed, including two improvements. Firstly, RBF function with extended parameters is used to transform the node features output by attention layer into link features. The result of link feature embedding can be improved by shortening the distance of nodes with links and enlarging the distance of nodes without links in vector space. Secondly, squeeze loss is designed to adjust the loss according to the performance of samples in training and change the proportion of sample loss in the loss function to allocate training resources reasonably. The link prediction task performed on datasets shows that the performance of proposed method is better than baselines.

Broadband RCS Acquisition by Finite Periodic Arrays Using the Characteristic Basis Function and Asymptotic Waveform Evaluation

Broadband RCS Acquisition by Finite Periodic Arrays Using the Characteristic Basis Function and Asymptotic Waveform Evaluation

An alternative numerical solution for the Orr–Sommerfeld problem

A simple tutorial for the numerical solution of the Orr–Sommerfeld problem is presented. The aim is the determination of the neutral stability threshold to the linear instability for the Poiseuille flow within a plane parallel channel. Such an instability is hydrodynamic in nature as it is driven by the advection term in the local momentum balance equation. The numerical solution is achieved by a spectral method. The basis functions are chosen as Chebyshev polynomials multiplied by a suitable overall factor meant to allow the fulfilment of the boundary conditions. The details of the numerical code implemented via the Mathematica software environment are also provided. A comparison with other numerical solutions of the same problem implemented via the tau-method is presented.

Comparison of machine learning models for the estimation of solar power generation in Australia

Solar power is a renewable energy source that contributes a lot to improving the environmental sustainability of energy production. In Australia, rooftop solar panel systems are installed for power generation. By seeking the optimal installation strategy, people could develop more efficient technologies and systems. In this work, data related to power generation was gathered between January 1 and December 31, 2022. This article only analyzes qualitative data in the dataset. Firstly, the support vector machine (SVM) model is used to compare the results obtained by removing only one qualitative feature at a time with the results obtained by including all features. It is concluded that the shading condition feature has a significant impact on power generation, and then. By comparing the accuracy of K-nearest neighbor (KNN), Logistic Regression, SVM with Radial Basis Function (RBF) kernel, and Decision Tree, it was found that SVM with RBF kernel is the most suitable classification method for the feature of the shading condition.

Transient elastodynamic responses of the concrete ceiling reinforced with nano-materials: A new strategy to improve the efficiency of building construction

Concrete is a durable and resilient material that can withstand substantial damage and decay. The durability of a concrete ceiling is often extensive, requiring little maintenance or repairs. Concrete has the capacity to be molded and reshaped into a wide variety of shapes, allowing architects and designers the liberty to create unique and attractive ceiling designs. This research provides practical suggestions for improving the effectiveness and durability of transient elastodynamics in concrete ceilings that are reinforced with nano-materials. Nano-materials are often used in building construction because of their many benefits. To accurately model the concrete structure reinforced by nanocomposites, a new mathematical simulation is introduced in this study. The simulation utilizes the Halpin-Tsai method, stress-strain relation in linear poroelasticity for the composite layer, considers the function of mixing, and incorporates Hamilton’s principle. The objective is to achieve an accurate representation of the concrete structure. The governing equations of the time-dependent mathematical simulation are solved using Newmark’s time integration method, an isogeometric approach (IGA), and NURBS functions as the basis functions. The current study’s results compared to the published article in the literature showcase the accuracy of the mathematical simulation and solution approach. Incorporating nanoparticles into the concrete ceiling may ultimately improve the efficiency of this kind of construction, especially when exposed to high external transient stresses.

Prediction of artificial neural network for sulfate removal from wastewater and application analysis of key factors in anaerobic biological system

Prediction and application of the SO42- removal performance of an anaerobic biological system was conducted through the integration of artificial neural networks (ANNs). The present investigation involved the utilization of Radial Basis Function Neural Networks (RBFNN) and Multilayer Perceptron Neural Networks (MLPNN) for more rigorous prediction of SO42- removal rates. The findings of the study demonstrated that reducing the chemical oxygen demand (COD) to sulfate ratio (COD/SO42-) led to a consequent decline in the removal of SO42-. In the context of predicting SO42- reduction under conditions characterized by low COD/SO42-, MLPNN exhibited superior suitability when compared to RBFNN. The sulfate removal process was primarily influenced by various operation parameters, with the COD/SO42- being particularly influential. The proposed sensitive MLPNN model contributed to the prediction of effluent quality and potential real-time adjustments of wastewater treatment operations. The predictive evaluation of effective sulfate (SO42-) removal from sulfate-rich wastewater under various operation parameters is a significant point of guideline.

A second-order exponential integration constraint energy minimizing generalized multiscale method for parabolic problems

This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial discretization of the model problem using constraint energy minimizing generalized multiscale finite element method (CEM-GMsFEM). This approach consists of two stages. First, the auxiliary space is constructed by solving local spectral problems, where the basis functions corresponding to small eigenvalues are captured. The multiscale basis functions are obtained in the second stage using the auxiliary space by solving local energy minimization problems over the oversampling domains. The basis functions have exponential decay outside the corresponding local oversampling regions. We shall consider the first and second-order explicit exponential Runge-Kutta approach for temporal discretization and to build a fully discrete numerical solution. The exponential integration strategy for the time variable allows us to take full advantage of the CEM-GMsFEM as it enables larger time steps due to its stability properties. We derive the error estimates in the energy norm under the regularity assumption. Finally, we will provide some numerical experiments to sustain the efficiency of the proposed method.

Cognitive reserve, depressive symptoms, obesity, and change in employment status predict mental processing speed and executive function after COVID-19.

The risk factors for post-COVID-19 cognitive impairment have been poorly described. This study aimed to identify the sociodemographic, clinical, and lifestyle characteristics that characterize a group of post-COVID-19 condition (PCC) participants with neuropsychological impairment. The study sample included 426 participants with PCC who underwent a neurobehavioral evaluation. We selected seven mental speed processing and executive function variables to obtain a data-driven partition. Clustering algorithms were applied, including K-means, bisecting K-means, and Gaussian mixture models. Different machine learning algorithms were then used to obtain a classifier able to separate the two clusters according to the demographic, clinical, emotional, and lifestyle variables, including logistic regression with least absolute shrinkage and selection operator (LASSO) (L1) and Ridge (L2) regularization, support vector machines (linear/quadratic/radial basis function kernels), and decision tree ensembles (random forest/gradient boosting trees). All clustering quality measures were in agreement in detecting only two clusters in the data based solely on cognitive performance. A model with four variables (cognitive reserve, depressive symptoms, obesity, and change in work situation) obtained with logistic regression with LASSO regularization was able to classify between good and poor cognitive performers with an accuracy and a weighted averaged precision of 72%, a recall of 73%, and an area under the curve of 0.72. PCC individuals with a lower cognitive reserve, more depressive symptoms, obesity, and a change in employment status were at greater risk for poor performance on tasks requiring mentalprocessing speedand executive function. Study registration: www.ClinicalTrials.gov , identifier NCT05307575.

Study on the space field reconstruction method of the radial basis function of electromagnetic radiation under optimal parameters

ABSTRACT Electromagnetic radiation (EM) pollution has a certain impact on human life and health, and the reconstruction of the EM space field in this paper is of great practical significance for EM analysis and research. The radial basis function (RBF) sufficiently considers the influence of each sampling point and is more suitable for reconstructing the EM space field than other spatial interpolation methods. Currently, when RBF is used to reconstruct the EM space field, the optimal determination of the basis function and shape parameter (SP) is rarely considered. This ultimately leads to low reconstruction accuracy of the EM space field. Therefore, in this paper, the particle swarm optimization (PSO) is used to calculate the optimal SP of the RBF. On this basis, reliable EM space field reconstruction is performed, which helps people understand the EM distribution characteristics in actual situations from a visual perspective. The EM sampling data of a region on the Yunnan Normal University campus are used as the data source, and the RBF under the optimal parameters is used for EM reconstruction. The accuracy of its interpolation results is evaluated and compared and analyzed with inverse distance weighting (IDW) after distance index optimization. The results show that the RBF under optimal parameters reconstructs the EM space field with high accuracy and good effect, which can truly reflect the actual distribution of EM.

Aerodynamic stability analysis of the concrete ceiling reinforced with advanced functionally graded nano-materials: A sustainable approach for construction materials

Proper consideration should be given to the stability of new concrete in order to assure the quality of building engineering, while also demanding its excellent flowability. The inadequate initial state stability negatively impacts the long-term durability of reinforced concrete structures, although this issue has not been well addressed. This work focuses on assessing the aerodynamic response of concrete ceilings reinforced with advanced functionally graded nano-materials. As the reinforcement of the current concrete structure, graphene oxide powders (GOPs) are used with improved material properties than other types of reinforcement. For mathematical modeling of the current structure, Reddy’s Higher-order Shear Deformation Theory is used to model the current work’s displacement fields. Also, the perturbation aerodynamic force is mathematically described using the Bernoulli equation for potential flow. After that using a method that involves separating variables, we may get the answer for the aerodynamic pressure in its ultimate form. Haber-Schaim foundation made of auxetic material in the Cartesian coordinate system is used to model the foundation of the current work with high accuracy. After obtaining the governing equations and associated boundary conditions, a meshless approach with weighted orthogonal basis and Kronecker delta-based shape functions are used to solve the equations. Finally, some suggestions for improving the aerodynamics and flutter velocity of airflow of the presented concrete plate reinforced by GOPs are presented for related aerodynamics industries.

Adaptive robust control of nonaffine nonlinear systems via an improved event‐triggered mechanism

AbstractThis paper aims to address the problem of event‐based adaptive robust control for a class of nonaffine nonlinear systems against actuator faults and unknown deception attacks. Firstly, different from the widely used relative threshold triggering mechanism, an improved event‐triggered mechanism with the time‐varying function threshold is devised for effectively saving more communication costs between controller and actuator. Then, based on a class of modified filter‐based coordinate transformations and the improved event‐triggered mechanism, the intermediate virtual control laws are devised to construct actual controllers, which not only guarantees robust stabilization of the system but also relaxes the universal assumptions on control coefficients and attack weights. Besides, the design challenges resulting from the presence of coupling terms in the nonaffine nonlinear system are successfully overcome by virtue of mean value theorem and the property of fuzzy basis function. Theoretical analysis proves that all signals of the closed‐loop system are semiglobally uniformly ultimately bounded (SUUB) and the Zeno behavior can be averted. Finally, the effectiveness of the proposed strategy is verified via comprehensive simulation results.

Adaptive anti‐windup output feedback control for nonlinear systems and its stability analysis

SummaryIn the practical application of adaptive control methods, a windup phenomenon for the systems with input saturation may occur because there exists an input restriction such as saturation of actuator in most actual systems due to physical reasons. In this paper, to alleviate the influence of the windup phenomenon by input saturation, we propose an output feedback exponentially passive (OFEP)‐based adaptive model recovery anti‐windup (AMRAW) control strategy for the stable nonlinear systems with input saturation. Moreover, in order to realize an augmented OFEP system for non‐OFEP nonlinear systems that do not satisfy the OFEP properties, a parallel feedforward compensator (PFC) is introduced, and a radial basis function (RBF) neural network (NN)‐based adaptive feedforward input is designed to attain accurate tracking performance for systems with the PFC. Furthermore, the detailed stability analysis of the proposed AMRAW control system is provided, and the performance of the proposed method is validated through appropriate numerical simulations.

Properties of Positive Linear Operators Connected with Squared Fundamental Functions

The aim of this article is to present a general class of positive linear operators of discrete type related to squared fundamental basis functions. If these operators are expressed by a series, we propose to truncate them by a finite sum while still keeping the property of converging towards the identity operator in a weighted space. A relation between the local smoothness of functions and the local approximation is obtained. In the variant in which the operators are described by a finite sum, we establish the limit of their iterates.

Fractional-Order Sliding-Mode Control and Radial Basis Function Neural Network Adaptive Damping Passivity-Based Control with Application to Modular Multilevel Converters

This paper proposes a hybrid control scheme that combines fractional-order sliding-mode control (FOSMC) with radial basis function neural network adaptive damping passivity-based control (RBFPBC) for modular multilevel converters (MMC) under non-ideal operating conditions. According to the passive control theory, we establish the Euler–Lagrange (EL) models of positive and negative sequences based on the unbalanced grid. A passivity-based controller that satisfies the energy dissipation law is designed. To enable rapid convergence of the system energy storage function, a radial basis function neural network (RBFNN) is introduced to adjust the injection damping adaptively. Additionally, a fractional-order sliding-mode controller (FOSMC) is designed. The fractional-order sliding mode surface used can improve tracking performance, and effectively suppressed the undesirable chattering phenomenon compared to the traditional sliding-mode control (SMC). Finally, combining the two control methods can effectively solve the issue of passivity-based control (PBC) being too dependent on parameters. The proposed hybrid control scheme enhances the ability of the system to resist disturbances, and improves its overall robustness. Simulation results demonstrate the feasibility and effectiveness of this control method.

Quantum chemical “Aufbau” principles: how to estimate the shape of highly flexible (bio-)polymers? A recursively extendable “chemion picture” of Euler-Hückel-type

An outline is given of how to split the n-dimensional space of torsion angles occurring in flexible (bio-)polymers (like alkanes, nucleic acids, or proteins, for instance) into n one-dimensional potential curves. Forthcoming applications will focus on the “protein folding problem,” beginning with polyglycine.ContextIn accordance with Euler’s topology rules, molecules are considered to be composed of “vertices” (atoms, ligands, bonding sites, functional groups, and bigger fragments). Following Hückel, each vertex is represented by only one basis function. Starting from the “monofocal” hydrids CH4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{CH}_4$$\\end{document}, NH3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{NH}_3$$\\end{document}, OH2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{OH}_2$$\\end{document}, FH, and SiH4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{SiH}_4$$\\end{document}, PH3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{PH}_3$$\\end{document}, SH2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ extrm{SH}_2$$\\end{document}, ClH as anchor units, “chemionic” Hamiltonians (of individual “chemion ensembles” and proportional nuclear charges) are constructed recursively, together with an appropriate basis set for the first five (normal) alkanes and some related oligomers like primary alcohols, alkyl amines, and alkyl chlorides.MethodsStandard methods (“Restricted Hartree-Fock RHF” and “Full Configuration Interaction FCI”) are used to solve the various stationary Schrödinger equations. Two software packages are indispensable: “SMILES” for integral evaluations over Slater-type orbitals (STO), and “Numerical Recipes” for matrix diagonalizations and inversions. While managing with only two-center repulsion integrals, “implicit multi-center integrations” lead us to the non-empirical fundament of Hoffmann’s “Extended-Hückel Theory.”

Adjustment of model misspecification in estimation of population total under ranked set sampling through balancing

In the model-based approach, researchers assume that the underlying structure, which generates the population of interest, is correctly specified. However, when the working model differs from the underlying true population model, the estimation process becomes quite unreliable due to misspecification bias. Selecting a sample by applying the balancing conditions on some functions of the covariates can reduce such bias. This study aims at suggesting an estimator of population total by applying the balancing conditions on the basis functions of the auxiliary character(s) for the situations where the working model is different from the underlying true model under a ranked set sampling without replacement scheme. Special cases of the misspecified basis function model, i.e. homogeneous, linear, and proportional, are considered and balancing conditions are introduced in each case. Both simulation and bootstrapped studies show that the total estimators under proposed sampling mechanism keep up the superiority over simple random sampling in terms of efficiency and maintaining robustness against model failure.

Gauss-like Logarithmic Kernel Function to improve the performance of kernel machines on the small datasets

Support vector machine is one of the most used machine learning algorithms with a comprehensive mathematical infrastructure. The power behind the algorithm is the kernel trick that enables the model to overcome non-linear data distributions by using functions that satisfy the Mercer condition. Undoubtedly, the radial basis function (RBF) is among the most widely used of these functions. The RBF kernel, which has a Gaussian curve, performs local boundary surfaces and supports the generalization capability of the model. In this study, a novel kernel function named Logarithmic Kernel Function (LKF), which has a Gaussian-like curve is presented. The crucial contribution of the LKF is that it can model the dataset better than other similarly shaped kernels in the case of a few training samples (10% and 30%). In the study, 6 classifications and 5 regression sets are handled to compare kernels. Instead of giving the hyperparameters needed by the models manually, they are estimated through the Tree Parzen Estimator, which is based on Sequential Modeling Optimization. This estimation process is repeated 10 times and the average results are obtained. The proposed LKF surpasses the most competitive kernels in various classification and regression tasks.