Radial Basis Function Neural Network Research Articles

Radial Basis Function Neural Networks Towards Electronic Trust Quantification

Radial Basis Function Neural Networks Towards Electronic Trust Quantification

Approximation-based adaptive two-bit-triggered bipartite tracking control for nonlinear networked MASs subject to periodic disturbances

Purpose This paper aims to investigate the problem of adaptive bipartite tracking control in nonlinear networked multi-agent systems (MASs) under the influence of periodic disturbances. It considers both cooperative and competitive relationships among agents within the MASs. Design/methodology/approach In response to the inherent limitations of practical systems regarding transmission resources, this paper introduces a novel approach. It addresses both control signal transmission and triggering conditions, presenting a two-bit-triggered control method aimed at conserving system transmission resources. Additionally, a command filter is incorporated to address the problem of complexity explosion. Furthermore, to model the uncertain nonlinear dynamics affected by time-varying periodic disturbances, this paper combines Fourier series expansion and radial basis function neural networks. Finally, the effectiveness of the proposed methodology is demonstrated through simulation results. Findings Based on neural networks and command filter control method, an adaptive two-bit-triggered bipartite control strategy for nonlinear networked MASs is proposed. Originality/value The proposed control strategy effectively addresses the challenges of limited transmission resources, nonlinear dynamics and periodic disturbances in networked MASs. It guarantees the boundedness of all signals within the closed-loop system while also ensuring effective bipartite tracking performance.

Surface Mechanical Property Prediction and Process Optimization of 18CrNiMo7-6 Carburized Steel Stator Guide Based on Radial Basis Function Neural Network and NSGA-II Algorithm

The carburizing process is a key technology that affects the mechanical properties of the surface of the hydraulic motor stator guide rail, and the related process parameters have an important influence on surface hardness, the thickness of the carburized layer, and the deformation of the guide rail. However, at present, the relationship between the carburizing process parameters and the surface mechanical properties of the target is not clear. This paper proposes a “hardness prediction and process parameter optimization” method. Firstly, a finite element model is established, with carburizing time, temperature, and carbon potential as the three input factors; the optimal Latin hypercubic experimental design and sensitivity analysis are applied. Secondly, surface hardness, carburized layer thickness, and deformation are taken as the output values, and an RBF neural network is used to construct the prediction model. The results show that the RBF neural network can be accurately used for the prediction of surface hardness, the thickness of the carburized layer, and deformation, and for the optimization of process parameters. The optimized parameters of surface hardness and the thickness of the carburized layer were increased by 4.2% and 5.1%, respectively, and the deformation amount was reduced to 0.31 mm, achieving the goal of optimal design.

Spatial analysis and soft computational modeling for hazard assessment of potential toxic elements in potable groundwater

Swiftly increasing population and industrial developments of urban areas has accelerated the worsening of the water quality in recent years. Groundwater samples from different locations of the Doon valley, Garhwal Himalaya were analyzed to measure concentrations of six potential toxic elements (PTEs) viz. chromium (Cr), nickel (Ni), arsenic (As), molybdenum (Mo), cadmium (Cd), and lead (Pb) using Inductively Coupled Plasma Mass Spectrometer (ICP-MS) with the aim to study the spatial distribution and associated hazards. In addition, machine learning algorithms have been used for prediction of water quality and identification of influencing PTEs. The results inferred that the mean values (in the units of µg L−1) of analyzed PTEs were observed in the order of Mo (1.066) > Ni (0.744) > Pb (0.337) > As (0.186) > Cr (0.180) > Cd (0.026). The levels and computed risks of PTEs were found below the safe limits. The radial basis function neural network (RBF-NN) algorithms showed high level of accuracy in the predictions of heavy metal pollution index (HPI), heavy metal evaluation index (HEI), non-carcinogenic (N-CR) and carcinogenic (CR) parameters with determination coefficient values ranged from 0.912 to 0.976. However, the modified heavy metal pollution index (m-HPI) and contamination index (CI) predictions showed comparatively lower coefficient values as 0.753 and 0.657, respectively. The multilayer perceptron neural network (MLP-NN) demonstrated fluctuation in precision with determination coefficient between 0.167 and 0.954 for the prediction of computed indices (HPI, HEI, CI, m-HPI). In contrast, the proficiency in forecasting of non-carcinogenic and carcinogenic hazards for both sub-groups showcased coefficient values ranged from 0.887 to 0.995. As compared to each other, the radial basis function (RBF) model indicated closer alignments between predicted and actual values for pollution indices, while multilayer perceptron (MLP) model portrayed greater precision in prediction of health risk indices.

A Novel Interpolation Method for Soil Parameters Combining RBF Neural Network and IDW in the Pearl River Delta

Soil fertility is a critical factor in agricultural production, directly impacting crop growth, yield, and quality. To achieve precise agricultural management, accurate spatial interpolation of soil parameters is essential. This study developed a new interpolation prediction framework that combines Radial Basis Function (RBF) neural networks with Inverse Distance Weighting (IDW), termed the IDW-RBFNN. This framework initially uses the IDW method to apply preliminary weights based on distance to the data points, which are then used as input for the RBF neural network to form a training dataset. Subsequently, the RBF neural network further trains on these data to refine the interpolation results, achieving more precise spatial data interpolation. We compared the interpolation prediction accuracy of the IDW-RBFNN framework with ordinary Kriging (OK) and RBF methods under three different parameter settings. Ultimately, the IDW-RBFNN demonstrated lower error rates in terms of RMSE and MRE compared to direct RBF interpolation methods when adjusting settings based on different power values, even with a fixed number of data samples. As the sample size decreases, the interpolation accuracy of OK and RBF methods is significantly affected, while the error of IDW-RBFNN remains relatively low. Considering both interpolation accuracy and resource limitations, we recommend using the IDW-RBFNN method (p = 2) with at least 60 samples as the minimum sampling density to ensure high interpolation accuracy under resource constraints. Our method overcomes limitations of existing approaches that use fixed steady-state distance decay parameters, providing an effective tool for soil fertility monitoring in delta regions.

Dual-Arm Space Robot On-Orbit Operation of Auxiliary Docking Prescribed Performance Impedance Control

The impedance control of a dual-arm space robot in orbit auxiliary docking operation is studied. First, for the closed-chain hybrid system formed by the dual-arm space robot after capture operation, the dynamic equation of position uncontrolled and attitude controlled is established. The second-order linear impedance model and second-order approximate environment model are established for the problem of simultaneous output force/pose control of the end of the manipulator. Then, aiming at the transient performance control requirements of the dual-arm space robot auxiliary docking operation in orbit, a sliding mode controller with equivalent replacement of tracking errors is designed by introducing Prescribed Performance Control (PPC) theory. Next, Radial Basis Function Neural Networks (RBFNN) are used to accurately compensate for the modeling uncertainties of the system. Finally, the stability of the system is verified by Lyapunov stability determination. The simulation results show that the attitude control accuracy is better than 0.5°, the position control accuracy is better than 10−3 m, and the output force control accuracy is better than 0.5 N when it reaches 30 N. It also indicated that the proposed control algorithm can limit the transient performance of the controlled system within the preset range and achieve high-precision force/pose control, which ensures a more stable on-orbit auxiliary docking operation of the dual-arm space robot.

Design of a robust intelligent controller based neural network for trajectory tracking of high-speed wheeled robots

The control design of wheeled mobile robots is often accomplished based on the robot’s kinematics which imposes critical challenges in the motion tracking control of such systems. In the related literature, most works designed dynamic controllers based on the terms of voltage or torque; however, the velocity is often utilized in industrial and commercial applications. To address this issue, this paper focuses on the design of a velocity-based control for the trajectory-tracking problem of mobile robots in practical applications including measurement acquisition. The control design of the mobile robot is realized in two separate parts using kinematic control and dynamic control. The design of kinematic control is carried out based on the robot’s kinematics where the motion is described without considering the forces and torques. A radial basis function (RBF) neural network (NN) based on the model-free controller is designed for the dynamic controller of mobile robots without relying on the system dynamics. In the proposed dynamic control, a time-delay estimation is adopted to estimate the disturbances and noises in the mobile robot and remove them from the feedback loop control. Several typical scenarios of mobile robots with high-speed movements are conducted to assess the feasibility of the proposed NN controller-based time-delay estimation under noises and disturbances. To show the supremacy of the suggested controller, the dynamic responses of the mobile robot test system are compared with the prevalent controllers. The extensive simulation and real-time examinations reveal the capability of the proposed NN controller-based time-delay estimation to control high-speed mobile robots under high-level noises and disturbances.

Evaluation of asphalt mixtures modified with low-density polyethylene and high-density polyethylene using experimental results and machine learning models

The widespread use of low-density polyethylene (LDPE) and high-density polyethylene (HDPE) plastics has resulted in a large amount of waste plastic that requires appropriate disposal or reuse. One potential solution is to use them in the modification of asphalt concrete (AC) mixtures for more sustainable highways. To study this possibility, permanent deformation and dynamic modulus (DM) of the LDPE and HDPE modified AC mixtures was investigated by conducting flow number (FN), flow time (FT) and DM tests on Superpave gyratory compacted specimens. Machine learning models; multi-layer perceptron (MLP), radial basis function neural network (RBFNN), generalized regression neural network (GRNN) and support vector machine (SVM) were used to predict the DM on the basis of frequency and temperature parameters. The model’s performance was gauged by analyzing the root mean square error, mean relative error, and coefficient of determination. The study findings revealed that the LDPE and HDPE modified AC mixtures provide 2.07 times and 1.27 times better resistance to permanent deformation, respectively, than their counterpart. It was also found that the LDPE and HDPE modified AC mixtures have 2.1 times and 1.4 times higher DM values, respectively, than the Control AC mixtures. Among the machine learning models, MLP (R2 = 0.98) showed best accuracy in predicting DM and thus is recommended to be used in similar studies due to its robustness. Additionally, the feature importance analysis revealed that frequency has the highest impact on DM predictions, followed by temperature and the inclusion of the LDPE.

Global Stochastic Comprehensive Sensitivity Analysis Based on Robustness Grouping and Improved Pelican Algorithm-Optimized Radial Basis Function Neural Network

Abstract Modeling analysis is one of the important means to analyze practical engineering, and as technology continues to evolve, various models are getting closer and closer to reality, while at the same time, there are more and more parameters in the models. It is important to analyse the impact of these parameters on the project to assist engineers in making plans or decisions. Sensitivity analysis (SA) can describe the effect of changes in these parameters on the model. However, complex models often have dozens or even hundreds of parameters, and most current SA methods struggle to deal reliably and effectively with these high-dimensional problems. In addition, it is difficult to obtain the sensitivity of continuous points in the parameter space with traditional SA methods. Therefore, this paper proposes a method that combines adaptive grouping and an Improved Pelican Optimization Algorithm for an optimal radial basis function (IPOA-RBF) agent model to solve these problems. Firstly, a clustering grouping method considering grouping robustness is established to obtain objective and stable parameter grouping results in high-dimensional sensitivity analysis. Secondly, a proxy model based on radial basis function neural network and an improved Pelican optimization algorithm are proposed to capture the logic of the proxy model to obtain the parameter sensitivity of continuous points in the parameter space. Finally, the superiority and applicability of this method is verified using an arch dam simulation model.

Model-based PD neural network control for pipe crack sealing manipulator

This study focuses on the control of a pipe crack sealing manipulator (PCSM) for concrete pipe crack sealing, with the capability to maneuver through horizontal and vertical pipes. This PCSM is a tree-type robot with five different branches. Observation and simulation studies indicate that only the fifth branch of the PCSM effectively executed the repair operation. However, in real application, the movement of these links is hindered by disturbances and uncertainties, preventing them from behaving as intended. Hence, a robust control scheme is essential to effectively manage the links of a pipe crack sealing manipulator. To address this need, this study introduces a Model-based PD neural network control (MBPDNNC) algorithm, which is then compared against modal-based PD (MBPD), Sliding mode control (SMC) with constant plus proportional rate reaching Law (CPPRL), and super twisting SMC (STSMC). The simulation study reveals that MBPDNN is characterized by greater accuracy and less chattering compared to the contrast control methods. The main contribution of this work is the compensation of disturbance by updating the weight by using the Radial basis function neural network (RBFNN). Through observation, it is evident that the neural network yields more promising results in the presence of disturbances and uncertainties.

Learning-based adaptive neural control for safer navigation of unmanned surface vehicle with variable mass

This paper presents a novel approach to the precise control of variable mass unmanned surface vehicles (USVs) during payload deployment, where both mass and draught undergo unpredictable changes. We propose a draught observation method and an adaptive control strategy that leverages the strong coupling between the USV's motion states, mass, and draught. Our method employs a radial basis function neural network (RBF-NN) for real-time draught observation, using an offline training strategy based on gradient descent, combined with an adaptive online training strategy to improve observation accuracy. An adaptive control strategy based on the Backstepping method is then developed, incorporating real-time draught data from the RBF-NN to address unknown variations in mass and draught. The stability of both the RBF-NN observer and the adaptive control algorithm is rigorously verified using the Lyapunov method. Simulation results demonstrate that the proposed draught observation method achieves up to 30% faster convergence compared to traditional methods, with a significant improvement in observation accuracy. Furthermore, the adaptive control strategy effectively manages real-time adjustments in dynamic scenarios, maintaining robust control performance even under significant mass changes, where conventional approaches fail.

A metaheuristic algorithm based on a radial basis function neural networks

A metaheuristic algorithm based on a radial basis function neural networks

Fixed‐Time State Observer‐Based Robust Adaptive Neural Fault‐Tolerant Control for a Quadrotor Unmanned Aerial Vehicle

ABSTRACTThis paper presents a fixed‐time state observer‐based robust adaptive neural fault‐tolerant control (RANFTC) for attitude and altitude tracking and control of quadrotor unmanned aerial vehicles (UAVs), considering multiple actuator faults, parametric uncertainty, and unknown external disturbances simultaneously. A novel fixed‐time state error estimation based on sliding mode observer is designed, which is independent of initial conditions. A proportional–integral–derivative (PID) based sliding mode control (SMC) is proposed to handle actuator faults and unknown disturbances in combination with the fixed‐time observer within the fault‐tolerant control (FTC) design scheme. The radial basis function neural network (RBFNN) is employed with the controller to approximate the uncertain parameters of the system. Furthermore, two new adaptive laws are designed to estimate the sudden actuator fault and the unknown upper bound of disturbances independently. Implementing these estimation schemes avoids overestimation, enhances the robustness of the presented controller, and substantially eliminates the control chattering problem. By applying the Lyapunov stability concept, the suggested control strategy guarantees that the states of the quadrotor UAV converge to the origin in a finite time. Finally, simulation studies are conducted to demonstrate the tracking performance and highlight the effectiveness of the proposed FTC design compared to the existing FTC methods.

Event-triggered finite-time adaptive neural network control for quadrotor UAV with input saturation and tracking error constraints

In this article, an event-triggered finite-time adaptive neural network control tracking strategy is proposed for quadrotor unmanned aerial vehicle (UAV) with input saturation and error constraints. Firstly, the radial basis function neural networks (RBFNNs) are adopted to identify the unknown uncertainty of quadrotor UAV model from the installation errors, gyroscope errors and so on. An auxiliary equation is constructed to deal with input physical saturation from the actuator motors. Additionally, by combining the performance function and error transformation, the issue of error constraint is solved. Based on the Lyapunov stability theory and event-triggered mechanisms, a finite-time adaptive neural network scheme is developed to ensure that the closed-loop quadrotor UAV system is semi-globally practically finite-time stable, and save the computation, resources, and transmission load. Finally, the simulation results illustrate the good tracking performance of quadrotor UAV by using the proposed control strategy.

Adaptive neural network backstepping control for the magnetorheological semi-active air suspension system with uncertain mass and time-varying input delay

Aiming at rejecting external disturbance induced by the random road profile, this paper proposes an adaptive robust control strategy to address the control problem of semi-active air suspension system installed with magnetorheological dampers (MRD) for enhancing ride comfort and handling performance. To effectively depict the inherent nonlinear dynamics of the adjustable air spring, a radial basis function neural network (RBFNN) model is trained by the experimental data offline, and an adaptive learning algorithm is introduced to maintain the modeling accuracy. Moreover, to handle the prevalent sensitive parameter variation (such as sprung mass), a nonlinear estimator is designed to estimate the uncertain sprung mass. Furthermore, a delay compensator is integrated into the control law to mitigate the impact of the time-varying input delay caused by the actuator of MRD to restrain the chattering phenomena. Additionally, the stability of the closed-loop system is rigorously proven by employing a Lyapunov–Krasovskii functional, guaranteeing the boundedness of both tracking error and estimation error. Simulation results are displayed and analyzed, illustrating the feasibility and efficiency of the proposed control strategy in depressing the sprung mass acceleration and tire deflection, showing its significance in both control performance enhancement and chattering elimination.

Grain storage temperature prediction based on chaos and enhanced RBF neural network

Grain storage has very strict temperature requirements. Aiming at the problems of nonlinear characteristics and poor prediction accuracy of temperature parameters in grain storage, a combination of chaos theory and enhanced radial basis neural network is proposed as a temperature prediction model for grain storage (C-ERBF). The model first determines the embedding dimension and time delay of the grain storage temperature sequence using chaos theory. It then calculates the Lyapunov exponent to confirm its chaotic properties and reconstructs the sequence in the phase space to extract the hidden dynamic information and structure behind the sequence. Furthermore, the q-Normalized Least Mean Square Fourth (qXE-NLMF) algorithm is designed to enhance the radial basis function (RBF) neural network model for weight updating, to improve its prediction accuracy, and to accelerate the training speed of the model. As verified by the simulation experiments of Mackey–Glass chaotic time series prediction, the enhanced RBF (ERBF) network has faster convergence speed and lower steady-state error compared to the traditional RBF network. Finally, the optimized dataset from chaos theory is input into the model to achieve accurate predictions of grain storage temperature series. The experimental results show that the proposed C-ERBF model has higher prediction accuracy compared to other time series prediction methods. It can realize the grain pile temperature in advance, and take control measures in advance. This proactive approach significantly reduces the consumption of stored grain and prevents issues before they arise.

Comparison of Positioning Error Prediction Results of Industrial Robots Based on Three Different Types of Neural Networks

ABSTRACTWith the increasing development of industry, the market demand for manufacturing has shifted to large‐scale customized production. This poses new challenges to the production flexibility of industrial robots. The offline programming method can perfectly meet this challenge. But its disadvantage is that it relies heavily on the absolute positioning accuracy of industrial robots. In recent years, there has been an increasing number of studies using neural networks (NN) to predict the positioning errors of industrial robots to improve their absolute positioning accuracy. However, most of these studies only focus on the application of NNs, and do not compare the prediction results and performance of different kinds of NNs. This paper selects three typical network models: backpropagation neural network (BPNN), particle swarm algorithm optimization BPNN (PSO‐BPNN), and radial basis function neural network (RBFNN). Through in‐depth experiments and analysis of these networks, the purpose is to reveal their respective prediction effects and characteristics and to summarize their advantages and disadvantages. Experimental results show that BPNN performs poorly in predicting positioning errors. As an optimization method, the particle swarm algorithm can effectively improve the prediction performance of BPNN. In contrast, the RBFNN performs well, which makes it very suitable for predicting the positioning error of industrial robots.

Data-Driven Dynamic Security Partition Assessment of Power Systems Based on Symmetric Electrical Distance Matrix and Chebyshev Distance

A rapid dynamic security assessment (DSA) is crucial for online preventive and restoration decision-making. The deep learning-based DSA models have high efficiency and accuracy. However, the complex model structure and high training cost make them hard to update quickly. This paper proposes a dynamic security partition assessment method, aiming to develop accurate and incrementally updated DSA models with simple structures. Firstly, the power grid is self-adaptively partitioned into several local regions based on the mean shift algorithm. The input of the mean shift algorithm is a symmetric electrical distance matrix, and the distance metric is the Chebyshev distance. Secondly, high-level features of operating conditions are extracted based on the stacked denoising autoencoder. The symmetric electrical distance matrix is modified to represent fault locations in local regions. Finally, DSA models are constructed for fault locations in each region based on the radial basis function neural network (RBFNN) and Chebyshev distance. An online incremental updating strategy is designed to enhance the model adaptability. With the simulation software PSS/E 33.4.0, the proposed dynamic security partition assessment method is verified in a simplified provincial system and a large-scale practical system in China. Test results demonstrate that the Chebyshev distance can improve the partition quality of the mean shift algorithm by approximately 50%. The RBFNN-based partition assessment model achieves an accuracy of 98.96%, which is higher than the unified assessment with complex models. The proposed incremental updating strategy achieves an accuracy of over 98% and shortens the updating time to 30 s, which can meet the efficiency of online application.

RBFNN-PSO Intelligent Synchronisation Method for Sprott B Chaotic Systems with External Noise and Its Application in an Image Encryption System.

In the past two decades, research in the field of chaotic synchronization has attracted extensive attention from scholars, and at the same time, more synchronization methods, such as chaotic master-slave synchronization, projection synchronization, sliding film synchronization, fractional-order synchronization and so on, have been proposed and applied to chaotic secure communication. In this paper, based on radial basis function neural network theory and the particle swarm optimisation algorithm, the RBFNN-PSO synchronisation method is proposed for the Sprott B chaotic system with external noise. The RBFNN controller is constructed, and its parameters are used as the particle swarm particle optimisation parameters, and the optimal values of the controller parameters are obtained by the PSO training method, which overcomes the influence of external noise and achieves the synchronisation of the master-slave system. Then, it is shown by numerical simulation and analysis that the scheme has a good performance against external noise. Because the Sprott B system has multiple chaotic attractors with richer dynamics, the synchronization system based on Sprott B chaos is applied to the image encryption system. In particular, the Zigzag disambiguation method for top corner rotation and RGB channel selection is proposed, and the master-slave chaotic system synchronisation sequences are diffused to the disambiguated data streams, respectively. Therefore, the encryption and decryption of image transmission are implemented and the numerical simulation results are given, the random distribution characteristics of encrypted images are analysed using histogram and Shannon entropy methods, and the final results achieve the expected results.

Adaptive direct RBFNN consensus control for a class of unknown nonlinear underactuated systems

The consensus tracking control of a class of nonlinear underactuated multi-agent systems with uncertainties is studied in this paper. A radial basis function neural network (RBFNN)-based direct adaptive control algorithm is designed. Unlike many previous articles in which a neural network is employed to identify the unknown nonlinear functions in the system model or controller, this method directly approximates the ideal control law by a neural network, making the control law simpler. Based on the neural network direct control algorithm, a controller with a single-parameter learning scheme is designed. This new control method reduces the computational burden by reducing the amount of computational data. Finally, the closed-loop system is proved to be ultimately uniformly bounded stable; the application examples of the controllers are given by simulation.