Radial Basis Function Research Articles

Multiquadric Collocations for Nonlinear Vibration of Functionally Graded Plates of Ti–6Al–4V Metal

While Finite Element Method (FEM) has proven reliable for analyzing linear or nonlinear stresses in materials, structures, and fluid flows, its reliance on mesh generation can escalate project simulation costs. In contrast, mesh- free techniques offer an alternative by directly generating system algebraic equations for the entire issue domain, bypassing the need for a preset mesh. This study focuses on investigating the nonlinear free vibration response of shear-deformable Functionally Graded Material (FGM) plates. These plates are expected to exhibit varying material properties, following a power-law distribution linked to the volume fractions of constituent materials as plate thickness increases. Utilizing shear deformation theories and von Karman nonlinear kinematics, the study seeks a mathematical solution for the real physical issues encountered in these plates. To address these challenges, a meshless method employing the Multi Quadric Radial Basis Function (MQRBF) is employed for evaluation. The computed results reveal insights into how different material properties and amplitudes influence the nonlinear free vibration response of composite plates. Comparing these outcomes to prior research demonstrates promising progress in this area.

Uncertain seismic response and robustness analysis of isolated continuous girder bridges

When calculating the seismic response of structures, conventional methods often neglect uncertainty and suffer from excessive computation. Although robustness metrics have been effective in evaluating structural safety, they are not suitable for isolated continuous girder bridges (ICGB). To address this issue, this paper introduces an uncertain seismic response and robustness assessment method tailored to ICGB: Firstly, the method considers uncertainty in material parameters and ground motion by constructing a data set using Monte Carlo simulation. Secondly, a genetic algorithm for parallel optimisation of radial basis function neural network (GAPO-RBFNN) is trained to predict the seismic responses of the bridges. Thirdly, a robustness metric specifically designed for bridges is derived and applied to bridge. Finally, the proposed robustness metric is validated on lead rubber bearing (LRB) and shape memory alloy-lead rubber bearing (SMA-LRB) bridges. Results indicate that the GAPO-RBFNN model accurately approximates the mapping relationship between structural parameters and seismic response, with an average error of only 0.32% and a 70% reduction in computation time compared with traditional methods. Moreover, the new robustness metric overcomes the limitations of the dismantled member method and is applicable to bridge. The robustness of the SMA-LRB-ICGB, strengthened by SMA, is improved, providing evidence of the effectiveness of the proposed robustness metric.

Comparative study of adaptive trajectory tracking controller for four-wheel mobile robot with prescribed-prediction performance

The nonlinear external disturbances and unmodeled dynamics characteristics have crucial impacts on trajectory tracking control accuracy of a four-wheel mobile robot (FWMR) under complicated working conditions. In this work, an adaptive trajectory tracking controller is designed for the FWMR to achieve the prescribed-prediction performance. On the basis of establishing the FWMR’s dynamics equations, an enhanced prescribed performance function (EPPF) is constructed to restrain the tracking errors of the FWMR within a certain range without requiring the exact initial conditions, thus guaranteeing the transient performance of the control system. Then, an optimal-predictive control (OPC) approach is presented to fulfill the asymptotic stability of the tracking errors of the FWMR. Specifically, the radial basis function neural network (RBFNN) incorporating a minimum parameter learning approach that are implanted into the expected controller is designed to attenuate the nonlinear external disturbances and the unmodeled dynamics of the FWMR. Lastly, comparative simulation investigations are carried out to illustrate the superiority of the proposed EPPF-OPC controller, and moreover, the comparative experiments are further performed to validate the practical effectiveness of the EPPF-OPC controller based on a self-established robot operating system (ROS) test platform of the FWMR.

Radial Basis Function (RBF) and Multilayer Perceptron (MLP) Comparative Analysis on Building Renovation Cost Estimation: The Case of Greece

Renovation of buildings has become a major area of development for the construction industry. In the building construction sector, generating a precise and trustworthy cost estimate before building begins is the greatest challenge. Emphasizing the value of using ANN models to forecast the total cost of a building renovation project is the ultimate objective. As a result, building firms may be able to avoid financial losses as long as there is as little discrepancy between projected and actual costs for remodeling works in progress. To address the gap in the research, Greek contractors specializing in building renovations provided a sizable dataset of real project cost data. To build cost prediction ANNs, the collected data had to be organized, assessed, and appropriately encoded. The network was developed, trained, and tested using IBM SPSS Statistics software 28.0.0.0. The dependent variable is the final cost. The independent variables are initial cost, estimated completion time, actual completion time, delay time, initial and final demolition-drainage costs, cost of expenses, initial and final plumbing costs, initial and final heating costs, initial and final electrical costs, initial and final masonry costs, initial and final construction costs of plasterboard construction, initial and final cost of bathrooms, initial and final cost of flooring, initial and final cost of frames, initial and final cost of doors, initial and final cost of paint, and initial and final cost of kitchen construction. The first procedure that was employed was the radial basis function (RBF). The efficiency of the RBFNN model was evaluated and analyzed during training and testing, with up to 6% sum of squares error and nearly 0% relative error in the training sample, which accounted for roughly 70% of the total sample. The second procedure implemented was the method called the multi-layer perceptron (MLP). The efficiency of the MLPNN model was assessed and examined during training and testing; the training sample, which made up around 70% of the overall sample, had a relative error of 0–7% and a sum of squares error ranging from 1% to 5%, confirming specifically the efficacy of RBFNN in calculating the overall cost of renovations.

Maximum Local Density-Driven Non-overlapping Radial Basis Function Support Kernel Neural Network

The learning and optimization of kernels in the radial basis function neural network (RBFNN) are crucial. However, in existing methods, there are issues of overfitting when learning kernel parameters. The learned kernels are also sensitive to outliers. This paper proposes a general kernel learning strategy for RBFNN called non-overlapping maximum local density support kernel learning (MLD-SKL), which contains two modules, the non-overlapping maximum local density (MLD) kernel learning module and support kernel learning (SKL) module. In the MLD kernel learning stage, the candidate set of kernels is incrementally determined based on the local density of samples. Meanwhile, it is required that the coverage ranges of kernels from different classes do not overlap with each other. This module is effective in reducing the impact of outliers. In the SKL stage, kernel importance indicator is defined to measure the importance of kernels. The learned support kernels are utilized to construct a maximum local density-driven non-overlapping radial basis function support kernel neural network (MLD-RBFSKNN). The RBFNN constructed through MLD-SKL exhibits a more compact structure. The experiments demonstrate that the proposed MLD-RBFSKNN improves accuracy in recognition task. Furthermore, while achieving superior recognition performance, the final constructed network also has the minimum number of kernels.

A Hierarchical Control Method for Trajectory Tracking of Aerial Manipulators Arms

To address the control challenges of an aerial manipulator arm (AMA) mounted on a drone under conditions of model inaccuracy and strong disturbances, this paper proposes a hierarchical control architecture. In the upper-level control, Bézier curves are first used to generate smooth and continuous desired trajectory points, and the theory of singular trajectory lines along with a Radial Basis Function Neural Network (RBFNN) is introduced to construct a highly accurate multi-configuration inverse kinematic solver. This solver not only effectively avoids singular solutions but also enhances its precision online through data-driven methods, ensuring the accurate calculation of joint angles. The lower-level control focuses on optimizing the dynamic model of the manipulator. Using a Model Predictive Control (MPC) strategy, the dynamic behavior of the manipulator is predicted, and a rolling optimization process is executed to solve for the optimal control sequence. To enhance system robustness, an RBFNN is specifically introduced to compensate for external disturbances, ensuring that the manipulator maintains stable performance in dynamic environments and computes the optimal control commands. Physical prototype testing results show that this control strategy achieves a root mean square (RMS) error of 0.035, demonstrating the adaptability and disturbance rejection capabilities of the proposed method.

Super-Resolving and Denoising 4D flow MRI of Neurofluids Using Physics-Guided Neural Networks.

To obtain high-resolution velocity fields of cerebrospinal fluid (CSF) and cerebral blood flow by applying a physics-guided neural network (div-mDCSRN-Flow) to 4D flow MRI. The div-mDCSRN-Flow network was developed to improve spatial resolution and denoise 4D flow MRI. The network was trained with patches of paired high-resolution and low-resolution synthetic 4D flow MRI data derived from computational fluid dynamic simulations of CSF flow within the cerebral ventricles of five healthy cases and five Alzheimer's disease cases. The loss function combined mean squared error with a binary cross-entropy term for segmentation and a divergence-based regularization term for the conservation of mass. Performance was assessed using synthetic 4D flow MRI in one healthy and one Alzheimer' disease cases, an in vitro study of healthy cerebral ventricles, and in vivo 4D flow imaging of CSF as well as flow in arterial and venous blood vessels. Comparison was performed to trilinear interpolation, divergence-free radial basis functions, divergence-free wavelets, 4DFlowNet, and our network without divergence constraints. The proposed network div-mDCSRN-Flow outperformed other methods in reconstructing high-resolution velocity fields from synthetic 4D flow MRI in healthy and AD cases. The div-mDCSRN-Flow network reduced error by 22.5% relative to linear interpolation for in vitro core voxels and by 49.5% in edge voxels. The results demonstrate generalizability of our 4D flow MRI super-resolution and denoising approach due to network training using flow patches and physics-based constraints. The mDCSRN-Flow network can facilitate MRI studies involving CSF flow measurements in cerebral ventricles and association of MRI-based flow metrics with cerebrovascular health.

Recognizing Signatures Using Normalized Generalization Neural Network

One of the most prevalent behavioral biometrics is the signature. In this paper, signatures are utilized in the case of recognition. Multiple contributions are provided here. Firstly, statistical analysis of efficiency is taken into consideration for the feature extraction. Secondly, a novel classifier is suggested. It is employed to recognize the signatures and it is called the Normalized Generalization Neural Network (NGNN). In terms of error rates, comparisons are established between different neural networks in the literature and the novel NGNN. The proposed NGNN consists of the input layer, normalization layer, Radial Basis Function (RBF) layer, and output layer. It can be considered as an enhanced or developed version of the Generalized Regression Neural Network (GRNN). A large number of signatures' attributes from the Biometric Ideal Test (BIT) database is utilized. That is, 1750 patterns of attributes are exploited. A significant improvement in the error rates over previous networks is achieved when using the novel NGNN. The Mean Absolute Error (MAE) has reached 0.028 and the Mean Square Error (MSE) has obtained 0.014. In addition, further experimental results on the BIT database showed better Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE) of 0.002 and 0.119, respectively.

Machine learning approaches for assessing stability in acid-crude oil emulsions: application to mitigate formation damage

The stability of acid-crude oil emulsion poses manifold issues in the oil industry. Experimentally evaluating this phenomenon may be costly and time-consuming. In contrast, machine learning models have proven effective in predicting and evaluating various phenomena. This research is the first of its kind to assess the stability of acid-crude oil emulsion, employing various classification machine learning models. For this purpose, a data set consisting of 249 experimental data points belonging to 11 different crude oil samples was collected. Three tree-based models, namely decision tree (DT), random forest (RF), and categorical boosting (CatBoost), as well as three artificial neural network models, namely radial basis function (RBF), multi-layer perceptron (MLP) and convolutional neural network (CNN), were developed based on the properties of crude oil, acid, and protective additive. The CatBoost model obtained the highest accuracy with 0.9687, followed closely by the CNN model with 0.9673. In addition, confusion matrix findings showed the superiority of the CatBoost model. Finally, by applying the SHapley Additive exPlanations (SHAP) method to analyze the impact of input parameters, it was found that the crude oil viscosity has the most significant effect on the model's output with the mean absolute SHAP value of 0.88.

Distributed Adaptive Output Feedback Consensus for Nonlinear Stochastic Multiagent Systems by Reference Generator Approach.

This article investigates the distributed leader-following consensus for a class of nonlinear stochastic multiagent systems (MASs) under directed communication topology. In order to estimate unmeasured system states, a dynamic gain filter is designed for each control input with reduced filtering variables. Then, a novel reference generator is proposed, which plays a key role in relaxing the restriction on communication topology. Based on the reference generators and filters, a distributed output feedback consensus protocol is proposed by a recursive control design approach, which incorporates adaptive radial basis function (RBF) neural networks to approximate the unknown parameters and functions. Compared with existing works on stochastic MASs, the proposed approach can significantly reduce the number of dynamic variables in filters. Furthermore, the agents considered in this article are quite general with multiple uncertain/unmatched inputs and stochastic disturbance. Finally, a simulation example is given to demonstrate the effectiveness of our results.

Dynamic Neural Network Predictive Compensation-Based Point-to-Point Iterative Learning Control With Nonuniform Batch Length.

This article discusses the problem of nonuniform running length in incomplete tracking control, which often occurs in industrial processes due to artificial or environmental changes, such as chemical engineering. It affects the design and application of iterative learning control (ILC) that relies on the strictly repetitive property. Therefore, a dynamic neural network (NN) predictive compensation strategy is proposed under the point-to-point ILC framework. To handle the difficulty of establishing an accurate mechanism model for real process control, the data-driven approach is also introduced. First, applying the iterative dynamic linearization (IDL) technique and radial basis function NN (RBFNN) to construct the iterative dynamic predictive data model (IDPDM) relies on input-output (I/O) signal, and the extended variable is defined by a predictive model to compensate for the incomplete operation length. Then, a learning algorithm based on multiple iteration errors is proposed using an objective function. This learning gain is constantly updated through the NN to adapt to changes in the system. In addition, the composite energy function (CEF) and compression mapping prove that the system is convergent. Finally, two numerical simulation examples are given.

An Improved Type-1 Fuzzy Regression Function for COVID-19 Cases Prediction

The deficiency in data collection and reporting has led to the emergence of uncertainty in the data in the pandemic process. These matters cause that traditional statistical and mathematical models have been functionless and unreliable in this issue. In this respect, this study presents an ensemble prediction model with innovative and contemporary properties to model COVID-19 cases in the UK and USA inclusively throughout the whole pandemic process. The proposed ensemble prediction model is composed of an assembly of Type-1 fuzzy regression functions with elastic net regularization (E-T1FRF) and radial basis function neural networks (RBFNNs). Thus, the proposed ensemble model can successfully model the uncertainty in the data with the fuzzy modelling perspective of T1FRF and also thoroughly adapt to the patterns in the data thanks to the flexible modelling ability of RBFNN based on data. With the proposed ensemble prediction model, the cases in the entire pandemic process from the beginning of March 2020 to the end of June 2022 were modelled and predicted for 23 different periods in one-month prediction steps. The proposed model produced predictions with MAPE values below 3% in all but periods except for three periods. Also, the average MAPE values for all periods were obtained at around 2% for the UK and only 1.5% for the US. These results, at a reasonable level of error, demonstrated the practicality of the usage of the proposed community model for other countries and provided valuable information for future action.

Machine Learning Methods for Evaluation of Technical Factors of Spraying in Permanent Plantations

Considering the demand for the optimization of the technical factors of spraying for a greater area coverage and minimal drift, field tests were carried out to determine the interaction between the area coverage, number of droplets per cm2, droplet diameter, and drift. The studies were conducted with two different types of sprayers (axial and radial fan) in an apple orchard and a vineyard. The technical factors of the spraying interactions were nozzle type (ISO code 015, code 02, and code 03), working speed (6 and 8 km h−1), and spraying norm (250–400 L h−1). The airflow of both sprayers was adjusted to the plantation leaf mass and the working pressure was set for each repetition separately. A method using water-sensitive paper and a digital image analysis was used to collect data on coverage factors. The data from the field research were processed using four machine learning models: quantile random forest (QRF), support vector regression with radial basis function kernel (SVR), Bayesian Regularization for Feed-Forward Neural Networks (BRNN), and Ensemble Machine Learning (ENS). Nozzle type had the highest predictive value for the properties of number of droplets per cm2 (axial = 69.1%; radial = 66.0%), droplet diameter (axial = 30.6%; radial = 38.2%), and area coverage (axial = 24.6%; radial = 34.8%). Spraying norm had the greatest predictive value for area coverage (axial = 43.3%; radial = 26.9%) and drift (axial = 72.4%; radial = 62.3%). Greater coverage of the treated area and a greater number of droplets were achieved with the radial sprayer, as well as less drift. The accuracy of the machine learning model for the prediction of the treated surface showed a satisfactory accuracy for most properties (R2 = 0.694–0.984), except for the estimation of the droplet diameter for an axial sprayer (R2 = 0.437–0.503).

Adaptive Neural Cooperative Control of Multirobot Systems With Input Quantization.

This article develops the adaptive neural cooperative control scheme for a group of mobile robots with a limited sensing range in presence of input quantization by a dynamic surface control technique. First, to make the controller design feasible, the original robotic system is transformed into a new fully actuated system using a transverse function. Then, taking into consideration the effects of a hysteresis quantizer, an adaptive neural cooperative controller is developed based on the universal approximation property of the radial basis function neural networks and the connectivity preservation strategy. Furthermore, the proposed control scheme can guarantee that all closed-loop signals are semi-globally uniformly ultimately bounded. Meanwhile, desired constraints are not breached and tracking errors are within the predefined domains. Finally, several simulation results are carried out to testify the feasibility and efficiency of the theoretical findings revealed in this article.

Soil moisture inversion based on multiple drought indices and RBFNN: A case study of northern Hebei Province

Drought has a significant impact on crop growth and productivity, highlighting the critical need for precise and timely soil moisture estimation to mitigate agricultural losses. This study focuses on soil moisture retrieval in northern Hebei Province during July 2012, utilizing eight widely employed remote sensing drought indices derived from MODIS satellite data. These indices were cross-referenced with measured soil moisture levels for analysis. Based on their correlation coefficients, a composite remote sensing drought index set comprising six indices was identified. Furthermore, a radial basis function neural network (RBFNN) was employed to estimate soil relative humidity. The accuracy evaluation of the soil moisture estimation model, which integrates multiple remote sensing drought indices and the RBFNN, demonstrated clear superiority over models relying on single drought indices. The model achieved an average estimation accuracy of 87.54 % for soil relative humidity at a depth of 10 cm (SM10) and 87.36 % for a 20 cm depth (SM20). The root mean square errors (RMSE) for the test sets were 0.093 and 0.092, respectively. Validation results for July 2013 indicated that the inversion accurately reflected the actual soil moisture conditions, effectively capturing dynamic moisture changes. These results fully verify the reliability and practicability of the model. These findings introduce a novel approach to local agricultural soil moisture estimation, with significant implications for enhancing agricultural water resource management and decision-making processes.

Stability analysis and error estimates of implicit-explicit Runge-Kutta least squares RBF-FD method for time-dependent parabolic equation

In this paper, for the time-dependent parabolic equations defined on complex geometries domain, we develop and analyze the least-squares radial basis function finite difference method (RBF-FD) coupled with the implicit-explicit Runge-Kutta (IMEX-RK) time discretization up to third order accuracy, which improves stability and accuracy. We derive the absolute stability region and the optimal time-step constraint for four kinds of IMEX-RK schemes. Compared to the traditional explicit or implicit time discretization, these are not trivial. Under a wide time-step constraint, the stability and the error estimates in l2-norm are established. Finally, several numerical experiments on the regular domain and non-convex domain are performed to validate the theoretical analysis.

Comparison of machine learning algorithms and multiple linear regression for live weight estimation of Akkaraman lambs

This study was designed to predict the post-weaning weights of Akkaraman lambs reared on different farms using multiple linear regression and machine learning algorithms. The effect of factors the age of the dam, gender, type of lambing, enterprise, type of flock, birth weight, and weaning weight was analyzed. The data was collected from a total of 25,316 Akkaraman lambs raised at multiple farms in the Çiftlik District of Niğde province. Comparative analysis was conducted by using multiple linear regression, Random Forest, Support Vector Machines (and Support Vector Regression), Extreme Gradient Boosting (XGBoost) (and Gradient Boosting), Bayesian Regularized Neural Network, Radial Basis Function Neural Network, Classification and Regression Trees, Exhaustive Chi-squared Automatic Interaction Detection (and Chi-squared Automatic Interaction Detection), and Multivariate Adaptive Regression Splines algorithms. In this study, the test dataset was divided into five layers using the K-fold cross-validation method. The performance of models was compared using performance criteria such as Adjusted R-squared (Adj-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}^{2}$$\\end{document}), Root Mean Square Error (RMSE), Mean Absolute Deviation (MAD), and Mean Absolute Percentage Error (MAPE) by utilizing test populations in the predicted models. Additionally, the presence of low standard deviations for these criteria indicates the absence of an overfitting problem. \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}^{2}$$\\end{document}The comparison results showed the Random Forest algorithm had the best predictive performance compared to other algorithms with Adj-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${R}^{2}$$\\end{document}, RMSE, MAD, and MAPE values of 0.75, 3.683, 2.876, and 10.112, respectively. In conclusion, the results obtained through Multiple Linear Regression for the live weights of Akkaraman lambs were less accurate than the results obtained through artificial neural network analysis.

A new modified Bessel‐type radial basis function for meshless methods: Utilized in the analysis of free vibration in 2D functionally graded Euler–Bernoulli beams

AbstractRadial basis functions (RBFs) are extensively employed in mesh‐free methods owing to their distinct properties. This study presents a novel RBF formulation based on a modified first‐kind Bessel function, introduced for the first time. The efficacy and precision of the proposed function are assessed through an examination of the free vibrations of Euler–Bernoulli beams composed of two‐directional functionally graded materials. Longitudinal and thickness property variations are modeled in polynomial and exponential forms, respectively. The performance of the novel RBF is scrutinized under various boundary conditions (clamped, simply supported, and free), and comparative analyses are conducted against similar investigations and an RBF based on the first‐kind Bessel function. Convergence analysis of the proposed modified first‐kind Bessel function‐based RBF reveals superior convergence rates compared to the first‐kind Bessel function‐based RBF. Moreover, a comparison between results obtained from modeling using the proposed RBF and exact solutions underscores the adequacy of this approach, with a maximum discrepancy of 4.933% observed under clamped‐free boundary conditions. In essence, the findings suggest that the proposed modified first‐kind Bessel function‐based RBF holds promise for analyzing the free vibrations of functionally graded Euler–Bernoulli beams. The primary aim of this research is to introduce and validate a new RBF based on a modified first‐kind Bessel function for the analysis of free vibrations in Euler–Bernoulli beams made of two‐directional functionally graded materials. The study focuses on evaluating the performance and accuracy of this novel RBF in comparison with existing RBFs and exact solutions. By addressing the limitations of conventional RBFs and proposing an innovative approach, this research aims to enhance the accuracy and efficiency of meshless methods in structural vibration analysis.

A GPU-accelerated Lagrangian method for solving the Liouville equation in random differential equation systems

This work presents and analyzes a numerical approach to efficiently solve the Liouville equation in the context of random ODEs using GPGPUs. Our method combines wavelet compression-based adaptive mesh refinement, Lagrangian particle methods, and radial basis function interpolation to create a versatile algorithm applicable in multiple dimensions. We discuss the advantages and limitations of this algorithm. To demonstrate its effectiveness, we compute the probability density function for various 2D and 3D random ODE systems with applications in physics and epidemiology.

A Study on Learning of Ensemble Classification Model Based on Radial Basis Function Neural Networks

A Study on Learning of Ensemble Classification Model Based on Radial Basis Function Neural Networks