Radial Basis Function Research Articles

Comparison of vibration values of rotating discs with variable parameters obtained by finite element analysis modeling with different machine learning algorithms

PurposeRotating functionally graded (FG) disks of variable thickness generates vibration. This study aims to analyze the vibration generated by the rotating disks using a finite element program and compare the results obtained with the regression methods.Design/methodology/approachTransverse vibration values of rotating FG disks with variable thickness were modeled using different regression methods. The accuracies of the obtained models are compared. In the context of comparing regression methods, multiple linear regression (MLR), extreme learning machine (ELM), artificial neural networks (ANNs) and radial basis function (RBF) were used in this study. The error graph between the observed value and the predicted value of each regression method was obtained. The error values of the regression methods used with scientific error measures were calculated.FindingsThe analysis of the transverse vibration of rotating FG disks with the finite element program is consistent with the studies in the literature. When the variables and vibration value determined on the disk are modeled with ELM, MLR, ANN and RBF regression methods, it is concluded that the most accurate model order is RBF, ANN, MLR and ELM.Originality/valueThere are studies on the vibration value of rotating discs in the literature, but there are very few studies on modeling. This study shows that ELM, MLR, ANN and RBF, which are machine learning methods, can be used in modeling the vibration value of rotating discs.

A Neural Network-Based State-Constrained Control Strategy for Underactuated Aerial Transportation Systems Within Narrow Workspace

The aerial transportation system belongs to a symmetrical system and has recently garnered increasing attention from researchers due to its broad application range and convenient operation. The control difficulty of the aerial transportation system lies in the fact that the load is not directly actuated, posing a significant challenge for state-constrained control. Taking the motion of an unmanned aerial vehicle (UAV) suspension transportation system within complex pipelines as an example, this paper employs the the swept volume signed distance field (SVSDF) method to search for state boundaries, which is an aspect not considered or elaborated in many state-constrained control approaches. Furthermore, adaptive state-constrained control based on the radial basis function (RBF) neural network is utilized for the case of experiencing unknown air resistance. The convergence of the proposed method for underactuated and actuated state variables is theoretically demonstrated based on the Lyapunov technique. Compared with existing methods, the error integral index demonstrates that the proposed method displays better convergence capability in the simulation section when considering state constraints under disturbance and air resistance.

A computational study of fractional variable-order nonlinear Newton–Leipnik chaotic system with radial basis function network

A computational study of fractional variable-order nonlinear Newton–Leipnik chaotic system with radial basis function network

Prescribed Performance Control for PEM Fuel Cell Air Supply System Based on Fully Actuated Approach With Fixed Regulation Time

ABSTRACTThe problem of air feed system control with guaranteed prescribed performance and fixed time control is investigated for proton exchange membrane fuel cell (PEMFC). First of all, the original model of PEMFC air feed system is converted to fully actuated system using higher order fully actuated system (HOFAS) approach. A fixed time extended state observer (ESO) is employed to approximate the cathode pressure. The parameter uncertainty is compensated by an adaptive radial basis function neural network (RBFNN). Then a prescribed performance sliding mode controller is designed with fixed convergence time. The proposed control law could guarantee the prescribed transient response for oxygen excess ratio (OER) error under stack current changing and bounded uncertainty. Lyapunov approach is utilized to proof fixed‐time stability of proposed controller. Simulation results of the study tests illustrate that the presented controller is efficient under constant OER tracking control, constant OER tracking control with parameter perturbation, and variable OER tracking control, respectively.

Enhancing power transformer health assessment through dimensional reduction and ensemble approaches in Dissolved Gas Analysis

AbstractTransformer health analysis using Dissolved Gas Analysis is crucial for diagnosing power transformer faults. This paper proposes an innovative approach to diagnose power transformer faults by integrating machine learning algorithms with Ensemble techniques. The method involves fusing reduced dimensional input features through Principal Component Analysis with Ensemble techniques such as Bagging, Decorate, and Boosting. Various machine learning algorithms, including Decision Tree (DT), K‐Nearest Neighbours, Radial Basis Function Network, and Support Vector Machine, are employed in conjunction with Ensemble techniques. The long short‐term memory algorithm was used to create synthetic data to solve the issue of data imbalance. A dataset of 683 samples is used in the study for training, testing, validation, and comparison with current techniques. The results highlight the effectiveness of Ensemble techniques, particularly Boosting, which demonstrates superior performance across all classification algorithms. The Boosting with DT algorithm achieves an impressive accuracy of 98.32%, surpassing alternative methods. In validation, the proposed Boosting Ensemble technique outperforms various approaches, showcasing its diagnostic accuracy and superiority over alternative methods. The research emphasises the model's effectiveness in smoothing input vectors, enhancing harmony with ensemble techniques, and overcoming limitations in prior methods.

Research on Pose Error Modeling and Compensation of Posture Adjustment Mechanism Based on WOA-RBF Neural Network

This paper is aimed to address the issue of decreased accuracy in the ship block docking caused by the structural errors of posture adjustment mechanism. First, inverse kinematic analysis is performed to investigate the sources of static errors in the mechanism. Subsequently, based on the closed-loop vector method, a pose error model for the moving platform is established, which includes eight categories of error terms. The impact of various structural errors on the pose accuracy of the moving platform is then compared and analyzed under both single-limb and multi-limb configurations. Therefore, a compensation method based on the whale optimization algorithm optimized radial basis function neural network is proposed. By transforming pose errors into actuator length errors, it establishes a predictive model between the theoretical pose of the dynamic platform and actuator length errors. After optimizing the network parameters, it yields the actuator length compensation to correct the actual pose of the dynamic platform. Simulation and experimental results validate the effectiveness of this method in enhancing the motion accuracy of the parallel mechanism. The mean pose accuracy of the moving platform is improved by 85.07%, demonstrating a significant compensation effect.

Adaptive Neural Delay Feedback Control of a Typical Robot on a Slope

ABSTRACTIn this article, an adaptive neural delay feedback control strategy is proposed for the motion control of a two‐wheel self‐balancing robot (TWSBR) on a slope with an input delay. Based on the Lagrange equation, the dynamic model of the robot is derived. Given a target trajectory vector, the corresponding error system is obtained. An input delay and uncertainties are considered. First, the system with an input delay is transformed into a delay‐free one. Second, a quadratic performance optimization criterion is defined, and a linear quadratic regulator (LQR) controller is designed to minimize the error between the system's state vector and the target vector. Thirdly, an integral sliding mode controller is added to the LQR controller to enhance the system's robustness. To reduce the “chattering” phenomenon, an adaptive neural delay feedback control scheme is developed based on the adaptive learning of the uncertainties' upper bound by a radial basis function neural network (RBFNN). It is demonstrated that a relaxation process exists at the beginning of the upslope motion. As the input delay increases, the swing range of the center of gravity of the pendulum expands. The angle can converge to the steady state more quickly, but the relaxation time is still 0.031 s which has nothing to do with the input delay. An example of the back‐and‐forth motion of a TWSBR on a slope can verify an excellent agreement between theoretical analysis and numerical results.

RBFNN based fixed time sliding mode control for PEMFC air supply system with input delay

Ensuring rapid regulation of the oxygen excess ratio (OER) in proton exchange membrane fuel cells (PEMFC) during load changes is an important challenge. In this paper, fixed time sliding mode control of a PEMFC with input delay has been investigated. First, a simplified fourth-order nonlinear dynamical model with input disturbance and input delay is considered and a cascade structure is selected for the control design. A radial basis function neural network (RBFNN) is designed to estimate the input disturbance. To achieve precise estimation, a Cuckoo Search Algorithm is utilized to calculate the parameters of the RBFNN. Then, a new sliding mode controller is proposed for trajectory tracking within a fixed time. To ensure the effectiveness of the proposed controller, the fixed time convergence of both sliding and reaching phases is investigated and proven. Finally, a robust prediction based sliding mode control is designed for the PEMFC system that by incorporating the disturbance estimation, can eliminate the effect of input delay. The effectiveness and robustness of the proposed controller are validated via comparative simulations. It is noteworthy that this is the first study to propose predictor based control for input delay PEMFCs.

Using Multi-Sensor Data Fusion Techniques and Machine Learning Algorithms for Improving UAV-Based Yield Prediction of Oilseed Rape

Accurate and timely prediction of oilseed rape yield is crucial in precision agriculture and field remote sensing. We explored the feasibility and potential for predicting oilseed rape yield through the utilization of a UAV-based platform equipped with RGB and multispectral cameras. Genetic algorithm–partial least square was employed and evaluated for effective wavelength (EW) or vegetation index (VI) selection. Additionally, different machine learning algorithms, i.e., multiple linear regression (MLR), partial least squares regression (PLSR), least squares support vector machine (LS-SVM), back propagation neural network (BPNN), extreme learning machine (ELM), and radial basis function neural network (RBFNN), were developed and compared. With multi-source data fusion by combining vegetation indices (color and narrow-band VIs), robust prediction models of yield in oilseed rape were built. The performance of prediction models using the combination of VIs (RBFNN: Rpre = 0.8143, RMSEP = 171.9 kg/hm2) from multiple sensors manifested better results than those using only narrow-band VIs (BPNN: Rpre = 0.7655, RMSEP = 188.3 kg/hm2) from a multispectral camera. The best models for yield prediction were found by applying BPNN (Rpre = 0.8114, RMSEP = 172.6 kg/hm2) built from optimal EWs and ELM (Rpre = 0.8118, RMSEP = 170.9 kg/hm2) using optimal VIs. Taken together, the findings conclusively illustrate the potential of UAV-based RGB and multispectral images for the timely and non-invasive prediction of oilseed rape yield. This study also highlights that a lightweight UAV equipped with dual-image-frame snapshot cameras holds promise as a valuable tool for high-throughput plant phenotyping and advanced breeding programs within the realm of precision agriculture.

Evolving Transparent Credit Risk Models: A Symbolic Regression Approach Using Genetic Programming

Credit scoring is a cornerstone of financial risk management, enabling financial institutions to assess the likelihood of loan default. However, widely recognized contemporary credit risk metrics, like FICO (Fair Isaac Corporation) or Vantage scores, remain proprietary and inaccessible to the public. This study aims to devise an alternative credit scoring metric that mirrors the FICO score, using an extensive dataset from Lending Club. The challenge lies in the limited available insights into both the precise analytical formula and the comprehensive suite of credit-specific attributes integral to the FICO score’s calculation. Our proposed metric leverages basic information provided by potential borrowers, eliminating the need for extensive historical credit data. We aim to articulate this credit risk metric in a closed analytical form with variable complexity. To achieve this, we employ a symbolic regression method anchored in genetic programming (GP). Here, the Occam’s razor principle guides evolutionary bias toward simpler, more interpretable models. To ascertain our method’s efficacy, we juxtapose the approximation capabilities of GP-based symbolic regression with established machine learning regression models, such as Gaussian Support Vector Machines (GSVMs), Multilayer Perceptrons (MLPs), Regression Trees, and Radial Basis Function Networks (RBFNs). Our experiments indicate that GP-based symbolic regression offers accuracy comparable to these benchmark methodologies. Moreover, the resultant analytical model offers invaluable insights into credit risk evaluation mechanisms, enabling stakeholders to make informed credit risk assessments. This study contributes to the growing demand for transparent machine learning models by demonstrating the value of interpretable, data-driven credit scoring models.

Traffic complexity assessment on the malacca strait with traffic zone matrix based on AIS data

This study proposes a novel and feasible framework for assessing maritime traffic complexity, utilising historical Automatic Identification System data to extract dynamic traffic characteristics of sea waters and quantify the corresponding maritime traffic complexity. The processed historical statistics are initially segmented into subsets according to different geographic traffic cells based on traffic zones. Subsequently, a Radial Basis Function regression model with a Gaussian kernel is employed to extract dynamic traffic parameters at the central coordinates of each geographic traffic zone based on subsets. The dynamic parameters derived from nonlinear regression and complexity sub-models are ultimately applied in maritime traffic complexity identification. The effectiveness of the proposed framework is validated through complexity assessments in selected areas of Malacca Strait. Empirical results are significant for maritime shipping research on data-driven traffic complexity monitoring and digitalised decision support.

Evaluation of green development of energy consumption in the Pearl River Delta urban agglomeration based on radial basis function neural network

AbstractThe study utilizes the RBF neural network model to evaluate the green development of the Pearl River Delta urban agglomeration, revealing a consistent increase in development levels from 2005 to 2020 despite notable inter‐city variations. The model adeptly handles complex interactions within urban green development, offering insights into comprehensive impacts and aiding in policy evaluation and optimization. It provides urban planners and decision‐makers with data‐driven support, enhancing the scientific basis and stability of policy‐making.

Using Key Predictors in an SVM Model for Differentiating Spinal Fractures and Herniated Intervertebral Discs in Preoperative Anesthesia Evaluation

Background/Objectives: Spinal conditions, such as fractures and herniated intervertebral discs (HIVDs), are often challenging to diagnose due to overlapping clinical symptoms and the difficulty in assessing their functional impact. Accurate differentiation between these conditions is crucial for effective treatment, particularly in the context of preoperative anesthesia evaluation, where understanding the underlying condition can influence anesthesia planning and pain management. Methods and Materials: This study presents a Support Vector Machine (SVM) model designed to distinguish between spinal fractures and HIVDs using key clinical predictors, including age, gender, preoperative Visual Analog Scale (VAS) pain scores, and the number of spinal fractures. A retrospective analysis was conducted on a dataset of 199 patients diagnosed with these conditions. The SVM model, using a radial basis function (RBF) kernel, classified the conditions based on the selected predictors. Model performance was evaluated using precision, recall, accuracy, and the Kappa index, with Leave-One-Out (LOO) cross-validation applied to ensure robust results. Results: The SVM model achieved a precision of 92.1% for fracture cases and 91.2% for HIVDs, with recall rates of 98.1% for fractures and 70.5% for HIVDs. The overall accuracy was 92%, and the Kappa index was 0.76, indicating substantial agreement. The analysis revealed that age and VAS pain scores were the most critical predictors for accurately diagnosing these conditions. Conclusions: These results highlight the potential of the SVM model with an RBF kernel to reliably differentiate between spinal fractures and HIVDs using routine clinical data. Future work could enhance model performance by incorporating additional clinical parameters relevant to preoperative anesthesia evaluation.

Using Collocation with Radial Basis Functions in a Pseudospectral Framework for a New Layerwise Shallow Shell Theory

Using Collocation with Radial Basis Functions in a Pseudospectral Framework for a New Layerwise Shallow Shell Theory

A neuromorphic radial-basis-function net using magnetic bits for time series prediction

Magnetic tunnel junctions (MTJs) are considered strong candidates for constructing neuromorphic systems owing to their low power consumption and high integrability. However, research on MTJ-based local approximation network is still lacking. In this work, we propose an MTJ-based radial basis function (RBF) network and numerically investigate its time-series prediction capability. The results demonstrate that the MTJ-based RBF network can enhance its prediction performance by utilizing increased environmental temperatures, achieving performance better than traditional software artificial neural networks.

Reproduction and generalization of robot trajectory tracking control method using reinforcement learning and neural network techniques

Abstract. This paper introduces a method for controlling the trajectory of a manipulator robot with uncertainty, using reinforcement learning. The control is designed to work even when there are limitations on the inputs to the system. Reinforcement learning and neural networks are employed alongside standard robust control techniques to enhance the fixed-time convergence of the system state. A novel algorithm is proposed to develop a reinforcement learning-based approach. This approach utilizes radial basis function neural networks and nonsingular fast terminal sliding mode control to ensure error convergence within a predetermined time. This paper presents the task of monitoring the intended path followed by robotic arms in the presence of uncertain and unfamiliar disruptions. The experimental results validate that the suggested approach substantially improves both the stability and accuracy of trajectory tracking, making it more feasible for real-world applications in robotic systems.

Radial Basis Function Neural Networks Towards Electronic Trust Quantification

Radial Basis Function Neural Networks Towards Electronic Trust Quantification

A Two-Stage Feature Selection Method to Enhance Prediction of Daily PM2.5 Concentration Air Pollution

In recent decades, air pollution has negatively affected human health and the environment. One of the important features contributing to air pollution is called PM2.5. However, daily prediction of PM2.5 is still lacking, especially using feature selection infused into the model. Hence, the main objective of this research is to utilize the feature selection procedures by proposing two stages feature selection methods namely adjusted correlation sharing t-test (adjcorT) and radial basis function neural network (RBFNN) in identifying the important features. This consequently also helps enhance the prediction of daily PM2.5 concentrations. Secondary data were obtained from the Department of Environment Malaysia (DOE) from 2018 until 2022 that consists of 5 years of air pollutant daily data. The results found that adjcorT-RBFNN identified the NO2, PM2.5, PM10, CO, O3, wind speed and SO2 as important features. The finding revealed that the accuracy, sensitivity, specificity, precision, F1 score and AUROC value, for a day-ahead prediction in Shah Alam are 0.756, 0.801, 0.717, 0.717, 0.757, and 0.758 respectively. Additionally, the predicted model may serve as an instrument for an early warning system, providing local authorities with information on air quality for formulation of strategies of air quality improvement.

Trajectory Tracking Control of a Morphing UAV using Radial Basis Function Artificial Neural Network Based Fast Terminal Sliding Mode: Theory and Experimental

Lately, Morphing Aerial Systems (MASs) have seen a surge in demand due to their exceptional maneuverability, flexibility, and agility in navigating complex environments. Unlike conventional drones, MASs boast the ability to adapt and alter their morphology during flight. However, managing the control and stability of these innovative and unconventional vehicles poses a significant challenge, particularly during the aerial transformation phases. To solve this problem, this manuscript proposes a Radial Basis Function Artificial Neural Network-Based Fast Terminal Sliding Mode Control (RBFANN-FTSMC) method. This approach is designed to effectively manage morphology changes, ensure precise trajectory tracking, and mitigate the impact of external disturbances and parameter uncertainties. Accordingly, the RBFANN-FTSMC will be evaluated against Proportional Integral Derivative (PID), Sliding Mode (SM), and Fast Terminal Sliding Mode (FTSM) controllers through two flight simulation scenarios to validate its effectiveness. Additionally, the control parameters will be optimized using a recent metaheuristic algorithm known as the Whale Optimization Algorithm (WOA). A novel hardware control diagram is explained. Finally, the ability to alter morphologies and the results of experimental tests are discussed to highlight the performance and limitations of the mechanical structure and the implemented RBFANN-FTSMC.

A Linear Quadratic Regulation Controller Based on Radial Basis Function Network Approximation

This paper proposes a linear quadratic regulation (LQR) tracking control method based on a radial basis function (RBF) that successfully compensates for the shortcomings of the LQR method. The LQR method depends on the linearity of a model. Specifically, an RBF neural network is used to approximate and compensate for the nonlinear part of a controlled object in the PID type-I, type-II and type-III control loops to improve the performance of the system. Through the simulation of different industrial systems, such as underdamped, overdamped and critically damped systems, the method significantly improves the dynamic response performance indices, such as the rise time and settling time, of the system.