Radial Basis Function Research Articles

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

Numerical investigation of the mesh-free collocation approach for solving third kind VIEs with nonlinear vanishing delays

The principal purpose of this investigation is to present an approximate algorithm for solving third-kind Volterra integral equation with nonlinear vanishing delays using mesh-free techniques based on a radial basis function collocation scheme. This technique does not require background approximation cells, and the algorithm is efficient, has good stability and does not require much computer memory. A description of the approach for the proposed equations is provided. The error estimation of the proposed approach is also provided. The accuracy and reliability of the new scheme are demonstrated through numerical examples. Some of these examples have been compared with analytical solutions and moving least squares methods. The numerical results validate their agreement with theoretical error estimates.

측정오차 공변량을 고려한 포아송 소지역 모델의 준모수적 계층적 베이즈 추정

In the sample survey, it is impossible to obtain sufficient samples in relatively small areas, which makes it difficult to estimate accurate statistics for small areas. For this reason, various studies on small area estimation are constantly being conducted, and in particular, the Fay-Herriot (1979) model has been expanded to various forms as one of the most widely used small area estimation models. In this study, we developed a semiparametric regression model based on a radial basis function that can consider nonlinear relationships between the resulting variables and covariates, extended from the model considering the measurement error of the covariate in the Poisson distribution proposed by Nam, Hwang(2021). Also, parameter estimation and model fit were performed through hierarchical Bayesian estimation using Gibbs sampling and Metropolis-Hastings algorithm among Markov chain Monte Carlo techniques. Simulations were conducted under various conditions to confirm the suitability of the model developed in this study, and the excellence of the developed model was further verified through empirical analysis using data from the 8th Korean longitudinal study of aging.

Enhancing pilot vigilance assessment: The role of flight data and continuous performance test in detecting random attention loss in short IFR flights

Situational awareness (SA) and fatigue management are crucial aspects of aviation safety, particularly during demanding flight phases. This study introduces an innovative approach employing flight data, machine learning, and Continuous Performance Test (CPT) metrics to predict pilot performance and SA during instrument approaches under Instrument Meteorological Conditions (IMC). Data were collected from over 10 pilots across more than 40 flights in a high-fidelity Cessna 172 analog flight simulator.Significant correlations were observed between dynamic cognitive performance parameters and the exceedance shape factor, a novel measure of pilot sustained attention introduced in this research. Key variables identified through correlation analysis included variability, interstimulus change, and reaction time standard deviation.Importantly, commission scores and reaction time standard deviation emerged as key predictors in the machine learning model, specifically the Optimizable Gaussian Process Regression (GPR) model with a radial basis function kernel. The model achieved a validation R-squared of 0.90 and a test R-squared of 0.70. These systems could incorporate additional data sources, such as eye-tracking and scan pattern analysis, for a better assessment of pilot SA and fatigue levels. While post-flight measurements are inherently reactive, they are effective for monitoring the degradation of pilot CPT scores after each leg of high-frequency, short-duration flights.Notable limitations include the need to understand individual cognitive differences among pilots, such as age, experience, and cognitive style. The predictive model also requires validation in actual flight conditions to determine its ecological validity. Future research should aim to address these limitations, generalize the findings, and integrate CPT data with other sensor inputs to provide a more comprehensive understanding of pilot performance.

Automatic recognition system for concrete cracks with support vector machine based on crack features

Cracks are a common problem in concrete surfaces. With the continuous optimization of machine vision-based inspection systems, effective crack detection and recognition is the core of the entire system. In this study, support vector machine (SVM) was used to distinguish cracks from other regions. To complete the recognition system of the SVM, a framework consisting of an image processing and recognition model was proposed. An algorithm combining the Prewitt operator with the Otsu threshold was proposed for image segmentation. The binary image processed by the new algorithm combined with mathematical morphology can result in a more complete crack zone and fewer interference regions. After the initial parameter extraction, most of the impurity areas were screened by preliminary discrimination, removing 99% of the impurities. This processing step ensured the balance and effectiveness of the samples. To establish an automatic identification model based on SVM with a radial basis function, compactness, occupancy rate, and length–width ratio were selected as input parameters after comparing these three features with all six features of the crack. The recognition accuracy of this system reaches 97.14%, demonstrating that the proposed method is effective and satisfies practical requirements.

Data-driven control of wind turbine under online power strategy via deep learning and reinforcement learning

This study proposes a data-driven wind turbine (WT) model predictive control (MPC) enhanced by a deep-learning (DL) radial basis function network (RBFN) and a reinforcement-learning (RL) deep Q-learning network (DQN). The RBFN provides comprehensive aerodynamic predictions, including thrust, torque, and power. Besides, the MPC linearization relies on the RBFN prediction to estimate force sensitivities. The DQN achieves an online power strategy (OPS) that solves the 2-degree-of-freedom (2-DOF) optimization of rotor speed and pitch angle, which can actively adjust power capture to meet different power requirements. The DQN adopts a novel bisection algorithm with a first-in-first-out (FIFO) queue for high-precision 2-DOF results. The MPC coordinates the permanent magnet synchronous generator (PMSG) and pitch servo, considering shaft rotation and tower movement. Compared with the maximum power point tracking (MPPT) and power reference point tracking (PRPT) based controls, the proposed RBFN-DQN-MPC reduces power fluctuation and ensures constant output. This study also compares the DQN with the categorical DQN (C51), which indicates that the DQN is more effective in the 2-DOF optimization. Hence, WTs enhanced by the DL-RL-MPC are intelligent and reliable for flexible wind generation.

Radial Basis Function Neural Networks (RBFNN) for Secure Intrusion Detection in the Internet of Drones (IoD)

With the rapid rise of the Internet of Things (IoT), drones are being used in various applications such as surveillance and delivery services. Despite this, there are serious security threats as well. This study proposes an innovative secure intrusion detection platform for the Internet of Drones (IoD) framework in order to address this problem. We use Radial Basis Function Neural Networks (RBFNN) and Non-Linear Partial Differential Equations (NL-PDEs) technique to enhance the intrusion detection capabilities. In addition the incorporation of block-chain technology fortifies the security and transparency of the system, ensuring the integrity of captured intrusion data. The proposed technique has been rigorously tested and evaluated to determine its accuracy in identifying malicious attacks and unauthorized access scenarios. Through this methodology, the Internet of Drones (IoD) security framework is strengthened, thereby mitigating potential risks derived from their widespread use. The main objective of this study is to make it easier for drone technology to be adopted and used safely and securely in a variety of contexts and industries.

Using collocation with radial basis functions in a pseudospectral framework to the analysis of laminated plates by the Reissner’s mixed variational theorem

Abstract In order to predict the static deformations and free vibration behaviour of thin and thick cross-ply laminated plates, we integrate Carrera’s unified formulation with a radial basis function collocation technique on a pseudospectral framework, using Reissner’s mixed variational theorem. Numerical examples illustrate the precision and effectiveness of this collocation technique for static and vibration problems.

Composite adaptive neural control for automatic carrier landing system with input saturation and output constraints

This paper investigates the automatic carrier landing control problem in the presence of model uncertainty, airwake disturbances, input saturation, and output constraints. Considering the performance requirements of the carrier-based aircraft, a composite adaptive neural controller is proposed based on the time-varying barrier Lyapunov function and backstepping control techniques. The radial basis function neural network is used to approximate the model uncertainty, where the neural network weight update law incorporating prediction and tracking errors further improves the convergence rate of the neural network and mitigates high-frequency oscillations. Furthermore, an adaptive disturbance compensation model is established to mitigate the adverse effects of airwake disturbances and estimation errors in the neural network. Based on the Lyapunov stability theory, it is proven that the proposed controller maintains the aircraft trajectory within the prescribed constraints and also ensures that all signals in the closed-loop control system are semiglobally uniformly ultimately bounded. Finally, comparative simulations are performed to demonstrate the effectiveness and superiority of the proposed composite adaptive neural control method.

Investigating the missing-wedge problem in small-angle X-ray scattering tensor tomography across real and reciprocal space.

Small-angle-scattering tensor tomography is a technique for studying anisotropic nanostructures of millimetre-sized samples in a volume-resolved manner. It requires the acquisition of data through repeated tomographic rotations about an axis which is subjected to a series of tilts. The tilt that can be achieved with a typical setup is geometrically constrained, which leads to limits in the set of directions from which the different parts of the reciprocal space map can be probed. Here, we characterize the impact of this limitation on reconstructions in terms of the missing wedge problem of tomography, by treating the problem of tensor tomography as the reconstruction of a three-dimensional field of functions on the unit sphere, represented by a grid of Gaussian radial basis functions. We then devise an acquisition scheme to obtain complete data by remounting the sample, which we apply to a sample of human trabecular bone. Performing tensor tomographic reconstructions of limited data sets as well as the complete data set, we further investigate and validate the missing wedge problem by investigating reconstruction errors due to data incompleteness across both real and reciprocal space. Finally, we carry out an analysis of orientations and derived scalar quantities, to quantify the impact of this missing wedge problem on a typical tensor tomographic analysis. We conclude that the effects of data incompleteness are consistent with the predicted impact of the missing wedge problem, and that the impact on tensor tomographic analysis is appreciable but limited, especially if precautions are taken. In particular, there is only limited impact on the means and relative anisotropies of the reconstructed reciprocal space maps.

Application of deep learning reduced-order modeling for single-phase flow in faulted porous media

AbstractOur research is positioned within the framework of subsurface resource utilization for sustainable economies. We concentrate on modeling the underground single-phase fluid flow affected by geological faults using numerical simulations. The study of such flows is characterized by strong uncertainites in the data defing the problem due to the difficulty of taking precise measurements in the subsoil. We aim to demonstrate the feasibility of a reduced order model that is both reliable and computationally efficient, thereby facilitating the incorporation of uncertainties. We account for the uncertainities of the properties of the rock and the geometry of the fault. The latter is achieved by using a radial basis function mesh deformation method. This approach benefits from a mixed-dimensional framework to model the rock matrix and faults as n and $${n-1}$$ n - 1 dimensional domains, allowing for non-conforming meshes. Our primary focus is on a reduced-order model capable of reproducing flow variables across the entire domain. We utilize the Deep Learning Reduced Order Model (DL-ROM), a nonintrusive neural network-based technique, and we compare it against the traditional Proper Orthogonal Decomposition (POD) method across various scenarios. The most relevant contributions of this work are: the proof of concept of the use of neural network for reduced order models for subsoil flow, dealing with non-affine problems and mixed dimensional domain. Additionally, we generalize an existing mesh deformation method for discontinuous deformation maps. Our analysis highlights the capability of reduced order model, highlighting DL-ROM’s capacity to expedite complex analyses with promising accuracy and efficiency, making multi-query analyses with various quantities of interest affordable.

A CAD-oriented parallel-computing design framework for shape and topology optimization of arbitrary structures using parametric level set

Recently, the high-resolution topology optimization to promote engineering applicability has gained much more attentions. However, an accurate and highly-efficient design framework for implementing shape and topology optimization of engineering structures with integration of CAD model is still in demand. In the current work, the critical intention is to develop a CAD-oriented parallel-computing design framework for arbitrary structures, where the Parametric Level Set Method (PLSM) is employed for shape and topology optimization. Firstly, an implicit identification model is constructed for generating a signed distance field using the vertex and normal information from the ‘STL’ file of engineering structures. The signed distance field is combined with the compactly supported radial basis functions (CSRBFs) to solve the initial level set function with a parametrization. This method is applied to present all domains, including design domains, Neumann boundary domains, Dirichlet boundary domains, and non-design domains. Secondly, the CPU parallel strategy is considered for allocating partitions of structural stiffness matrix in finite element analysis to different CPU cores for the parallel-computing to save computation costs. Thirdly, a parallel-computing design formulation is developed for performing shape and topology optimization of arbitrary structures, in which the partitioned terms of all design variables and stiffness matrix are concurrently computed on each CPU core. Finally, several classic benchmarks and the critical engineering structure of Virtual Reality (VR) glass part with extremely complex geometries, are discussed to demonstrate the effectiveness and efficiency of the proposed design framework.

Practical time‐varying formation cooperative control for high‐order nonlinear multi‐agent systems avoiding spatial resource conflict via safety constraints

AbstractThe operation of multi‐agent systems (MAS) in space necessitates considerations for obstacle avoidance, collision prevention, and connectivity among agents. This coupling conflict, stemming from spatial resource utilization, poses a significant and non‐negligible threat to the safe operation of MAS. This article proposes a consensus control scheme for the time‐varying formation of MAS, incorporating functions for maintaining connectivity, collision avoidance, and obstacle dodging. This scheme effectively constrains the time‐varying formation tracking error within an arbitrarily small range. The considered system model takes a high‐order nonlinear form, with uncertainties and disturbances present in each order. This grants the control scheme with high generality and practicability. By employing barrier Lyapunov function to delineate the safe operational space of MAS, conflicts in spatial resource utilization are avoided. This approach simultaneously fulfills the requirements for connectivity maintenance, collision avoidance, and obstacle dodging in the safe operation of MAS. An additional rotation operator is integrated into the controller to smoothly address the “minima” problem, eliminating the need for external intervention. Gaussian radial basis function is used to estimate the nonlinear terms, uncertainties, and unknown perturbation online in the system. The stability of the MAS under the proposed control scheme is analyzed through Lyapunov function. Finally, numerical simulation results are demonstrated to explain the effectiveness of the control scheme.

Neural learning control for sampled‐data nonlinear systems based on Euler approximation and first‐order filter

AbstractThe primary focus of this research paper is to explore the realm of dynamic learning in sampled‐data strict‐feedback nonlinear systems (SFNSs) by leveraging the capabilities of radial basis function (RBF) neural networks (NNs) under the framework of adaptive control. First, the exact discrete‐time model of the continuous‐time system is expressed as an Euler strict‐feedback model with a sampling approximation error. We provide the consistency condition that establishes the relationship between the exact model and the Euler model with meticulous detail. Meanwhile, a novel lemma is derived to show the stability condition of a digital first‐order filter. To address the non‐causality issues of SFNSs with sampling approximation error and the input data dimension explosion of NNs, the auxiliary digital first‐order filter and backstepping technology are combined to propose an adaptive neural dynamic surface control (ANDSC) scheme. Such a scheme avoids the ‐step time delays associated with the existing NN updating laws derived by the common ‐step predictor technology. A rigorous recursion method is employed to provide a comprehensive verification of the stability, guaranteeing its overall performance and dependability. Following that, the NN weight error systems are systematically decomposed into a sequence of linear time‐varying subsystems, allowing for a more detailed analysis and understanding. In order to ensure the recurrent nature of the input variables, a recursive design is employed, thereby satisfying the partial persistent excitation condition specifically designed for the RBF NNs. Meanwhile, it can verify that the NN estimated weights converge to their ideal values. Compared with the common ‐step predictor technology, there is no need to redesign the learning rules due to the designed NN weight updating laws without time delays. Subsequently, after capturing and storing the convergence weights, a novel neural learning dynamic surface control (NLDSC) scheme is specifically formulated by leveraging the acquired knowledge. The introduced methodology reduces computational complexity and facilitates practical implementation. Finally, empirical evidence obtained from simulation experiments validates the efficacy and viability of the proposed methodology.

Spatial and temporal heterogeneity of soil salinity and ionic coupling relationship under the water-saving renovation of a typical irrigation district in arid and semi-arid areas

Soil salinization is a global environmental problem. To investigate the spatiotemporal heterogeneity of soil salinity and the coupling relationship of soil salinity ions under water-saving renovation conditions, we chose Shenwu Irrigation Area, where water-saving renovation projects are being conducted comprehensively. Specifically, for our field experiments, we chose 46 soil sampling points. Specifically, we used different spatial interpolation methods and coupling coordination models were applied to study the spatial and temporal distribution of soil salinity and soil salt-based ion coupling relationship changes during different water-saving periods in the irrigation area between 2015 and 2022. The results showed that (1) the emergence of soil salinity extremes after water-saving renovation project led to an increase in the variability of soil salinity. (2) Compared with the Inverse Distance Weighted, Radial Basis Function, and Universal Kriging interpolations, the Mean Absolute Error of the Ordinary Kriging interpolation was reduced by 12.68 %, 43.96 %, and 38.77 %, the Root Mean Square Error was reduced by 14.34 %, 60.85 %, and 36.53 %, reflective of a significant improvement in accuracy, and thus confirming this method to be optimal for elucidating soil salinity. (3) Compared with pre-water-saving renovation project, the average soil desalination rates in the 0–50 cm soil layer during and after project implementation were 5.71 % and 35.67 %. The impact of the water-saving renovation project was highest in channelside areas, followed by croplands, and lowest in lakeside areas. (4) The growth rates of soil salt-based ion coupling degree and coupling coordination degree after project implementation, compared with before implementation, were 17.07 % and 10.81 %. The implementation of water-saving renovation project improved soil quality. This study provides scientific support for the prevention and control of soil salinization in irrigation areas.

Analysis of effective area and mass transfer in a structure packing column using machine learning and response surface methodology

The study examined mass transfer coefficients in a structured CO2 absorption column using machine learning (ML) and response surface methodology (RSM). Three correlations for the fractional effective area (af), gas phase mass transfer coefficient (kG), and liquid phase mass transfer coefficient (kL) were derived with coefficient of determination (R2) values of 0.9717, 0.9907 and 0.9323, respectively. To develop these correlations, four characteristics of structured packings, including packing surface area (ap), packing corrugation angle (θ), packing channel base (B), and packing crimp height (h), were used. ML used five models, represented as random forest (RF), radial basis function neural network (RBF), multilayer perceptron (MLP), XGB Regressor, and Extra Trees Regressor (ETR), with the best models being radial basis function neural network (RBF) for af (R2 = 0.9813, MSE = 0.00088), RBF for kG (R2 = 0.9933, MSE = 0.00056), and multilayer perceptron (MLP) for kL (R2 = 0.9871, MSE = 0.00089). The channel base had the most impact on af and kL, while crimp height affected kG the most. Although the RSM method produced adequate equations for each output variable with good predictability, the ML method provides superior modeling capabilities.

Automated Measurement of Cattle Dimensions Using Improved Keypoint Detection Combined with Unilateral Depth Imaging.

Traditional measurement methods often rely on manual operations, which are not only inefficient but also cause stress to cattle, affecting animal welfare. Currently, non-contact cattle dimension measurement usually involves the use of multi-view images combined with point cloud or 3D reconstruction technologies, which are costly and less flexible in actual farming environments. To address this, this study proposes an automated cattle dimension measurement method based on an improved keypoint detection model combined with unilateral depth imaging. Firstly, YOLOv8-Pose is selected as the keypoint detection model and SimSPPF replaces the original SPPF to optimize spatial pyramid pooling, reducing computational complexity. The CARAFE architecture, which enhances upsampling content-aware capabilities, is introduced at the neck. The improved YOLOv8-pose achieves a mAP of 94.4%, a 2% increase over the baseline model. Then, cattle keypoints are captured on RGB images and mapped to depth images, where keypoints are optimized using conditional filtering on the depth image. Finally, cattle dimension parameters are calculated using the cattle keypoints combined with Euclidean distance, the Moving Least Squares (MLS) method, Radial Basis Functions (RBFs), and Cubic B-Spline Interpolation (CB-SI). The average relative errors for the body height, lumbar height, body length, and chest girth of the 23 measured beef cattle were 1.28%, 3.02%, 6.47%, and 4.43%, respectively. The results show that the method proposed in this study has high accuracy and can provide a new approach to non-contact beef cattle dimension measurement.

Deep Koopman-operator-based model predictive control for free-floating space robots with disturbance observer

This paper investigates the optimal tracking control problem of free-floating space robots in the presence of non-ideal factors, such as model uncertainties and external disturbances. To address this issue, we first leverage the deep Koopman operator, facilitated with a deep neural network, to establish an offline formulation of a global linearization model for a micro-nano free-floating space robot. Based on the estimated linearization model, we then employ the model predictive control method for online optimization control, achieving a significantly reduced computational burden. Additionally, a decay factor is integrated into the model predictive control optimization objective function to balance the precision of joint angles tracking with the suppression of base satellite attitude disturbance. To further address the modeling inaccuracies and external disturbances, we incorporate a disturbance observer based on a radial basis function neural network for online compensation within the model predictive control framework. This augmentation enhances tracking precision and robustness. Several groups of simulation results are carried out to demonstrate the effectiveness of the proposed method, showing its capability of energy consumption, disturbance rejection and enhanced robustness. These highlight the potential of the proposed method to improve the control performance of free-floating space robots, even in the absence of a precise dynamic model.

Evaluating the Geoeffectiveness of Interplanetary Coronal Mass Ejections: Insights from a Support Vector Machine Approach with SHAP Value Analysis

In this study, we compiled a data set of 510 interplanetary coronal mass ejections (ICME) events from 1996–2023 and trained a radial basis function support vector machine (RBF-SVM) model to investigate the geoeffectiveness of ICMEs and its dependence on the solar wind conditions observed at 1 au. The model demonstrates high performance in classifying geomagnetic storm intensities at specific Disturbance Storm Time thresholds and evaluating the geoeffectiveness of ICMEs. The model’s output was assessed using precision, recall, F1 score, and true skill statistics (TSS), complemented by stratified k-folds cross-validation for robustness. At the −50 nT threshold, the model achieves precisions of 0.84 and 0.93, recalls of 0.94 and 0.82, and corresponding F1 scores of 0.89 and 0.87 for the categories separated by this threshold, respectively. Overall accuracy is noted at 0.88, with a TSS of 0.76. Despite challenges at the −100 nT threshold due to data set imbalance and limited samples, the model maintains an overall accuracy of 0.87, with a TSS of 0.69, demonstrating the model’s ability to effectively handle imbalanced data. Physical insights were gained through model explanation with a SHapley Additive exPlanations (SHAP) value analysis, pinpointing the role of the southward magnetic field component in triggering geomagnetic storms, as well as the critical impact of shock-ICME combinations in intensifying these storms. The effective application of an SVM model with SHAP value analysis offers a way to understand and predict the geoeffectiveness of ICMEs. It also underscores the capability of a relatively simple machine learning model in predicting space weather and revealing the underlying physical mechanisms.

Radial basis function neural network training using variable projection and fuzzy means

Radial basis function neural network training using variable projection and fuzzy means