Floating wind turbines (FWTs) are now recognized as one of the most effective and affordable renewable energy sources. However, their performance is strongly influenced by dynamic environmental conditions, particularly sea waves under significant oscillatory conditions. Ocean wave and wind disturbance affect turbine positioning, underscoring the critical essential for adaptive and robust control mechanisms to manage the unpredictable external inputs. In this context, we present an innovative method based on federated deep learning for training capsule networks to detect disturbances and enable adaptive robust control of FWTs among the environmental uncertainty. Through the proposed technique, a unique mixture of sliding mode control and deep reinforcement learning (DRL) yields in the extraction of wide features and modeling of spatial relationships between sensor data in the capsule networks framework. Furthermore, by employing federated learning, the capsule-net model is trained in a distributed manner across multiple wind turbines. Therefore, enhanced accuracy and effectiveness of disturbance detection are guaranteed. Simulation results reveal effective identification of disturbances which in turn improves the performance and stability of FWTs under the coarse environmental situation. The global Lyapunov stability analysis proves the FWTs’ closed-loop stability. Performance of the superior DRL is evaluated in comparison with a radial basis function neural network (RBFNN) estimation. The innovative DRL method represents a significant advancement in the control of FWTs as a high potential of development for intelligent management of similar systems. As a final aim, this research work finds out the reliability and efficiency of FWTs in variable weather conditions (short-term) and erratic ocean environments (long-term). Moreover, the control system makes a substantial impact on the sustainable development of the wind and renewable energy sector.

Floating wind turbines (FWTs) are now recognized as one of the most effective and affordable renewable energy sources. However, their performance is strongly influenced by dynamic environmental conditions, particularly sea waves under significant oscillatory conditions. Ocean wave and wind disturbance affect turbine positioning, underscoring the critical essential for adaptive and robust control mechanisms to manage the unpredictable external inputs. In this context, we present an innovative method based on federated deep learning for training capsule networks to detect disturbances and enable adaptive robust control of FWTs among the environmental uncertainty. Through the proposed technique, a unique mixture of sliding mode control and deep reinforcement learning (DRL) yields in the extraction of wide features and modeling of spatial relationships between sensor data in the capsule networks framework. Furthermore, by employing federated learning, the capsule-net model is trained in a distributed manner across multiple wind turbines. Therefore, enhanced accuracy and effectiveness of disturbance detection are guaranteed. Simulation results reveal effective identification of disturbances which in turn improves the performance and stability of FWTs under the coarse environmental situation. The global Lyapunov stability analysis proves the FWTs' closed-loop stability. Performance of the superior DRL is evaluated in comparison with a radial basis function neural network (RBFNN) estimation. The innovative DRL method represents a significant advancement in the control of FWTs as a high potential of development for intelligent management of similar systems. As a final aim, this research work finds out the reliability and efficiency of FWTs in variable weather conditions (short-term) and erratic ocean environments (long-term). Moreover, the control system makes a substantial impact on the sustainable development of the wind and renewable energy sector.

ABSTRACT The radial basis functions (RBF) network is popularly used in many machine learning applications. Semantic segmentation of remotely sensed image which can be addressed via a clustering task, is essential in land cover applications. In this study, a novel semi-supervised spectral clustering method, referred to as SLIC-RBF-CCA, is introduced for land cover multi-band image segmentation. The proposed SLIC-RBF-CCA approach is composed of two steps: i) a Simple Linear Iterative Clustering (SLIC) algorithm is initially applied to a set of pseudo-RGB images obtained from the singular vectors of a flattened matrix of a multi-band image; ii) a novel superpixel-based Radial Basis Function Canonical Correlation Analysis (RBF-CCA) generates canonical variables which are used to achieve final image segmentation. Specifically, a superpixel-based radial basis function is defined as the first variable in the framework of Canonical Correlation Analysis, in which the RBF centres are obtained as the local mean from superpixel regions. The second variable of SLIC-RBF-CCA is based on a few labelled pixels. The associated canonical variables, related to the pixels of a full image, are then applied by a k -means clustering algorithm. The proposed approach can be interpreted as an example of multi-view machine learning with attention mechanism. Finally, the effectiveness of the proposed algorithm has been validated using experiments on several remotely sensed multi-band images, including two patches from TopoSys GmbH and three patches from City of Potsdam from the ISPRS, showing excellent performance with segmentation accuracy > 85 % .

Purpose This paper aims to achieve precise motion control of linear push rods, and the radial basis function (RBF) neural network to adjust parameters of the Proportional Integral Derivative (PID) controller is introduced in this paper. The proposed RBF-PID control strategy is used for the motion control of linear push rods, and the validation experiments are carried out. Design/methodology/approach First, the structure and working principle of the linear push rods were analyzed, and the hardware system of the control system was designed based on the pulse width modulation principle. Subsequently, based on the discrete PID algorithm, an RBF-PID control scheme for linear push rods was proposed by combining RBF neural networks. Finally, the effectiveness of the proposed scheme was verified by comparing the motion control experiments of sine wave and composite waveform. Findings The experimental results show that the accuracy of linear push rod trajectory tracking control using the RBF-PID control method is higher than that of traditional PID control, and it has good anti-interference and robustness. Compared with the traditional PID controller, the RBF-PID controller reduces the maximum error (MAX), root-mean-square error (RMSE) and mean absolute error (MAE) by 11.73%, 11.5% and 13.57%, respectively, when tracking sine signals; when tracking composite wave signals, the RBF-PID controller reduced MAX, RMSE and MAE by 31.44%, 3.99% and 13.67%, respectively. Originality/value This paper proposes a novel RBF-PID control approach for the motion control of linear push rods, and the experimental results have demonstrated the effectiveness of this method, which can further extend the application of linear push rods.

In this work, [Bmim][PF6] ionic liquid (i.e., 1-N-butyl-3-methylimidazolium hexafluorophosphate) is utilized for CO2 capture. Since the experimental studies have their difficulty, we tried to develop multi-layer perceptron (MLP) and radial basis function (RBF) neural network models for estimating CO2 mole fraction in [Bmim][PF6]. The MLP with 11 hidden neurons, tangent and logarithm sigmoid activation functions in the secret and output layers, trained by the Levenberg-Marquardt algorithm, is selected as the most accurate neural network model. In the first layer, the weight matrix of temperature and pressure has been determined at 23.1182 and 2.9099, respectively. The bias vector is calculated at 15.544 in the first layer. In the second layer, the values of the weight vector and bias were determined at -1.2246 and -24.1089, respectively. It is worth noting that the MLP model provides the relative deviation of 0.0859%, 8.74%, and 30.88% for temperatures of 283.15, 298.15, and 323.15K, respectively. The results confirmed that the MLP neural network presents higher inaccuracy for predicting CO2 solubility at higher temperatures.

For fully actuated marine surface vessels (MSVs) with model uncertainties, unknown external disturbance, and unmeasurable velocity, this paper proposes an adaptive non-singular fast terminal sliding mode (NFTSM) finite-time trajectory tracking control scheme based on an improved nonlinear disturbance observer (INDO) and radial basis function neural networks (RBFNN). Firstly, this paper proposes a novel form of second-order nonlinear tracking differentiator (NTD) to generate more accurate virtual position and velocity signals. Then, this paper designs an INDO for more accurate estimation and compensation of unknown external disturbance problems. By combining the NTD-based virtual signals with desired signals, an NFTSM surface is constructed to accelerate system convergence and improve tracking accuracy. In addition, this paper designs RBFNN to approximate model uncertainties with added estimation velocity error. Furthermore, an improved adaptive law is used to estimate the upper bound of neural networks approximation error and INDO error to enhance the system’s adaptability to complex uncertainties and improve the robustness of the system. Lyapunov stability analysis shows that all system signals remain globally bounded in finite time. Finally, the comparative simulation verifies the accuracy and superiority of the proposed scheme (INDO-RBFNN-ANFTSMC).

To address the issue of reduced tracking accuracy caused by time-varying characteristic parameters during the path-tracking process of intelligent electric vehicles, this paper proposes a control strategy that integrates an adaptive linear quadratic regulator (IALQR) with a radial basis function neural network (RBFNN)-based adaptive feedforward control, effectively mitigating the impact of time-varying parameter variations. Based on linear quadratic regulator (LQR) theory, an adaptive linear quadratic regulator (ALQR) is designed, which employs an adaptive sliding mode observer (ASMO) to estimate tire lateral forces and incorporates the forgetting factor recursive least squares (FFRLS) method to dynamically adjust tire cornering stiffness. Furthermore, considering road curvature and changes in lateral tracking error, an adaptive feedforward controller based on an RBFNN is developed to generate the feedforward steering angle. Finally, a co-simulation platform is established using CarSim/Simulink. Under double-lane-change conditions, the proposed strategy demonstrates a 38.8% improvement in tracking accuracy compared with ALQR alone and an 83.9% enhancement over conventional LQR, validating the feasibility of this integrated control approach.

Introduction: Plasmonic photothermal therapy (PPTT) with noble metal nanoparticles (NPs) have gained great relevance as less invasive platforms in the treatment of adenocarcinoma-type cancer tumors. The PPTT uses laser radiation to generate plasmonic effects in NPs that are distributed in the cancerous tissue, producing hyperthermia and cell death by apoptosis. Objective: To obtain two-dimensional temperature distributions and the associated cell damage distributions in tumoral tissue subjected to PPTT. Method: A numerical methodology based on Radial Basis Functions (RBFs) is implemented for solving the Pennes or bioheat equation and the Arrhenius and Three-state models for cellular damage estimation. The developed, validated and applied numerical methodology is based on the method of approximate particular solutions in local formulation (LMAPS). Results: The capability to solve problems with variable sources, multiple regions and different types of boundary conditions is shown by the comparison with OpenFOAM computational tool based on finite volume method and numerical results reported in the literature. This is performed by solving hypothetical situations of heat transfer in tissues including 1D and 2D domains with metabolic sources, perfusion term and radiation thermal conversion. Conclusions: The developed methodology is applied to a situation of PPTT in superficial tissue, from laser energy distribution description to the local percentage of cellular damage. This numerical methodology is the basis of the analysis, optimization and design of PPTT application processes in clinical environments considering its potential to solve complex geometries, time-varying boundary conditions and parameters and domains with multiple regions.

In this paper, the effect of viscous dissipation on the two-dimensional, steady Cu-water nanofluid bioconvection containing oxytactic bacteria of oxytactic bacteria is numerically and statistically investigated. The importance of this study lies in addressing viscous dissipation, a significant factor for thermal and solutal transport in nanoparticle suspensions in nanofluid bioconvection systems. The main aim is to examine how the Eckert number, representing viscous dissipation, modifies flow behavior, convective heat transfer, and bacterial distribution in a square cavity. The governing non-dimensional equations are solved by the radial basis function (RBF) collocation method. It is found that viscous dissipation weakens heat transfer along the hot wall while enhancing bacterial density and mass transfer, and that variations in thermal and bioconvective Rayleigh numbers along-side Peclet and Lewis numbers strongly influence the thermal and microbial transport. In the statistical analysis, both curve and surface fittings are carried out involving the Eckert number. Furthermore, neural network modeling is employed to predict the average Nusselt, Sherwood number, and bacterial density along the side walls. All models are constructed on the basis of numerical data generated from the simulations. For varying values of the Eckert number, both quadratic and cubic polynomial approximations yield satisfactory agreement when evaluated using the mean squared error criterion. Moreover, the neural network model reliably captures the average quantities of interest, showing strong consistency with the data. The results highlight both the physical significance of viscous dissipation and the usefulness of data-driven modeling in complex nanofluid problems.

Research on a rapid prediction method for magnetic anomaly responses in the penetration process based on an improved proper orthogonal decomposition (POD)-radial basis function (RBF) neural network

Enhanced phase compensation in digital holographic microscopic imaging flow cytometry using radial basis function neural networks

Analysis of the band structure of elastic waves in 3D nano phononic crystals based on the local radial basis function collocation method

Improved fast non-singular adaptive super-twisting sliding mode control based on radial basis function neural network approximation for robot joint module.

In coastal pumping stations, the intake sump geometry strongly affects flow uniformity, hydraulic loss, and vortex formation. This study establishes an Isight-based automated simulation and optimization framework for an axial-flow pump with a closed-type intake to clarify the influence of bellmouth diameter and clearance height on sump hydraulics. A Radial Basis Function surrogate model combined with the NonLinear Programming by Quadratic Lagrangian (NLPQL) was employed to minimize hydraulic loss and improve flow uniformity. The results show that hydraulic loss first decreases and then increases with bellmouth diameter, whereas velocity uniformity and the mean inflow angle exhibit nonlinear variations with clearance height. The optimal configuration increases efficiency by 3.82% and the velocity uniformity by 1.62% compared with the baseline. Helicity density and the Ω-criterion were used to identify vortex structures, revealing that small clearances intensify bottom and wall-attached vortices, whereas larger clearances promote symmetric inflow. An improved tangential-velocity method based on iso-vorticity contours effectively captured near-wall vortex dynamics. These findings provide theoretical support for achieving low head loss, stable inflow, and controlled vortex behavior in axial-flow pump intake systems.

Abstract Against the backdrop of worsening global energy shortages and environmental pollution, the automotive industry is accelerating its shift toward electrification. However, the energy management strategies of hybrid vehicles still suffer from issues such as response lag and insufficient fuel economy optimization. Therefore, this study employs digital signal processing technology to establish a mathematical model of the power system for plug-in hybrid electric vehicles. Based on forward modeling methods, it also simulates the vehicle’s dynamic response under different driving conditions. Experiments have shown that under urban road cycling conditions, the initial value of the state of charge was 0.7, which decreased to 0.3 after 90 minutes, while fuel consumption reached 0.7 kilograms. As the testing time increased by 4 times, the lowest state of charge dropped to 0.25 and fuel consumption increased to 1.8 kilograms. This study used radial basis function neural network for working condition prediction, and when the data volume reached 320, the prediction accuracy improved to 0.89 and the RMSE decreased to 0.10. Research findings indicate that the proposed method outperforms comparative approaches in computation time, classification accuracy, and fuel economy optimization. The integration of digital signal processing technology and driving condition prediction can effectively enhance the energy management efficiency of plug-in hybrid electric vehicles, providing technical support for subsequent power system optimization.

Background Non-mass breast cancer, presenting with calcifications, asymmetric dense shadows, and architectural distortions, is challenging to distinguish from non-puerperal mastitis (NPM) due to radiological similarities on mammography. Purpose This study aims to develop a mammographic-based radiomics model to differentiate NPM from non-mass breast cancer, addressing the limitations of subjective BI-RADS assessments that risk misdiagnosis or delayed treatment. Methods Mammographic images from 104 patients (44 NPM, 60 non-mass breast cancer), collected from January 2018 to June 2023, were retrospectively analyzed. Two senior breast radiologists independently reviewed images, with disagreements resolved by a more senior radiologist. Regions of interest (ROIs) were manually delineated using 3DSlicer, and 576 radiomic features (shape, first-order, texture) were extracted using PyRadiomics. The Least Absolute Shrinkage and Selection Operator (LASSO) algorithm with 10-fold nested cross-validation selected 6 predictive features, and a support vector machine (SVM) model with a Radial Basis Function kernel was constructed. Performance was evaluated using nested cross-validation, calculating the area under the curve (AUC), accuracy, sensitivity, specificity, positive predictive value (PPV), and negative predictive value (NPV). Results Calcification type and asymmetric dense shadows differed significantly between NPM and non-mass breast cancer (P < 0.05). The radiomics model achieved an AUC of 0.844 (95% CI: 0.787–0.904), accuracy of 0.769 (95% CI: 0.735–0.803), sensitivity of 0.883 (95% CI: 0.792–0.974), specificity of 0.678 (95% CI: 0.576–0.779), PPV of 0.784 (95% CI: 0.749–0.819), and NPV of 0.778 (95% CI: 0.662–0.896), compared with radiologists’ BI-RADS assessment (AUC: 0.860, 95% CI: 0.790–0.930; accuracy: 0.856, 95% CI: 0.787–0.923; sensitivity: 0.833, 95% CI: 0.736–0.926; specificity: 0.886, 95% CI: 0.791–0.979; PPV: 0.909, 95% CI: 0.832–0.984; NPV: 0.796, 95% CI: 0.679–0.907). Conclusions Radiomics using PyRadiomics-extracted features, LASSO, and SVM provides a robust quantitative tool to differentiate NPM from non-mass breast cancer, enhancing diagnostic precision and clinical decision-making.

ABSTRACT In this article, a novel mathematical model of a quadrotor UAV (Unmanned Aerial Vehicle) suffering from one type of structural fault, angle deflection in a motor and the corresponding mechanical link, has been derived. Such faults add additional nonlinear terms to the differential equations of motion and change the 3D configuration of the UAV. These nonlinear terms rely significantly on the unknown fault angles, which are estimated via a Radial Basis Function Neural Network (RBFNN). Moreover, a Non‐singular Fast Terminal Sliding Mode Control (NFTSMC) scheme optimized by a Genetic Algorithm (GANFTSMC) has been designed for trajectory tracking and reduction of control effort. Simulation results for the entire closed‐loop system, using three different types of reference signals and fault angles, demonstrate the significant performance of the proposed controller in the presence of structural faults and external disturbances. Furthermore, the settling time of error dynamics of the system states to the origin has been finite, and the superior performance of our proposed control strategy has been validated via comparison with other robust nonlinear control techniques implemented in the literature.

A physics-informed framework based on radial basis functions for forward and inverse heat conduction problems in anisotropic materials

Abstract This paper investigates the disturbance‐observer‐based finite‐time fault‐tolerant control problem for an output‐constrained permanent magnet linear motor system characterized by unknown dead‐zone inputs and uncertain control coefficients. To address this challenge, a set of novel parameter functions, along with corresponding adaptive control laws, are developed as the primary means to estimate the unknown dynamic effects. Furthermore, a radial basis function neural algorithm is used to approximate the nonlinear composite friction where a proportional‐differential‐based gradient descent accelerator is embedded to fasten the convergence speed of the neural network weight . Additionally, uncertain disturbances are mitigated using a modified disturbance observer equipped with an adaptive compensation law, which effectively eliminates compensation deviation. In conclusion, we present rigorous proof procedures, supported by extensive simulation experiments, to validate the effectiveness and feasibility of the proposed theory.

An active learning method for high-dimensional and small failure probability problems combining matrix-operation radial basis function model with matrix-operation hybrid optimization algorithm