Radial Basis Function Research Articles

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.

Modeling of the discharge coefcient of diferential pressure fowmeters: approximation by using radial-basis function neural networks

The discharge coefficient of flow transducers of liquids and gases of differential pressure flowmeters plays an important role in flow rate measurement. The problem of modeling and calculating the discharge coefficient of differential pressure flowmeters directly affects the accuracy of flow rate measurement of these devices. The results of modeling the discharge coefficient of the differential pressure flowmeter in the form of radial-basis neural networks are presented. The described structure of the neural network calculates the values of the discharge coefficient with an angular pressure tapping method. The article evaluates the error of approximation of the discharge coefficient by radial-basis function networks and provides recommendations for building such networks to solve problems of modeling the characteristics of differential pressure flowmeters. The article discusses the main advantages and disadvantages of using such networks as discharge coefficients of the differential pressure flowmeters. The research showed that the use of such networks is justified by their properties to approximate the discharge coefficient and their efficiency in measuring gas and liquid flow rates.

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.

Advanced classification of hot subdwarf binaries using artificial intelligence techniques and Gaia DR3 data

Context. Hot subdwarf stars are compact blue evolved objects, burning helium in their cores surrounded by a tiny hydrogen envelope. In the Hertzsprung-Russell Diagram they are located by the blue end of the Horizontal Branch. Most models agree on a quite probable common envelope binary evolution scenario in the Red Giant phase. However, the current binarity rate for these objects is yet unsolved, but key, question in this field. Aims. This study aims to develop a novel classification method for identifying hot subdwarf binaries within large datasets using Artificial Intelligence techniques and data from the third Gaia data release (GDR3). The results will be compared with those obtained previously using Virtual Observatory techniques on coincident samples. Methods. The methods used for hot subdwarf binary classification include supervised and unsupervised machine learning techniques. Specifically, we have used Support Vector Machines (SVM) to classify 3084 hot subdwarf stars based on their colour-magnitude properties. Among these, 2815 objects have Gaia DR3 BP/RP spectra, which were classified using Self-Organizing Maps (SOM) and Convolutional Neural Networks (CNN). In order to ensure spectral quality, previously to SOM and CNN classification, our 2815 BP/RP set were pre-analysed with two different approaches: the cosine similarity technique and the Uniform Manifold Approximation and Projection (UMAP) technique. Additional analysis onto a golden sample of 88 well-defined objects, is also presented. Results. The findings demonstrate a high agreement level (∼70–90%) with the classifications from the Virtual Observatory Sed Analyzer (VOSA) tool. This shows that the SVM, SOM, and CNN methods effectively classify sources with an accuracy comparable to human inspection or non-AI techniques. Notably, SVM in a radial basis function achieves 70.97% reproducibility for binary targets using photometry, and CNN reaches 84.94% for binary detection using spectroscopy. We also found that the single–binary differences are especially observable on the infrared flux in our Gaia DR3 BP/BR spectra, at wavelengths larger than ∼700 nm. Conclusions. We find that all the methods used are in fairly good agreement and are particularly effective to discern between single and binary systems. The agreement is also consistent with the results previously obtained with VOSA. In global terms, considering all quality metrics, CNN is the method that provides the best accuracy. The methods also appear effective for detecting peculiarities in the spectra. While promising, challenges in dealing with uncertain compositions highlight the need for caution, suggesting further research is needed to refine techniques and enhance automated classification reliability, particularly for large-scale surveys.

Performance analysis of air conditioner system integrated with thermal energy storage using enhanced machine learning modelling coupled with fire hawk optimizer

Integrating air conditioning (AC) systems with thermal energy storage (TES) offers a promising solution for managing large buildings' peak load demands and energy efficiency. Predicting the performance of the AC-TES is a significant index in ensuring optimal cooling load and energy consumption. However, conventional approaches encounter challenges in achieving high levels of accuracy, reliability, and scalability. Therefore, this study introduces leveraging machine learning techniques and in-situ measurements for precise predicting the energy performance of AC-TES system in a semi-arid climate building. The study proposes a hybrid prediction strategy leveraging the benefits of machine learning and meta-heuristic optimization algorithms. The proposed approach integrates a Radial Basis Function Neural Network (RBFNN) with the Fire Hawk Optimizer (FHO) for predicting the performance parameters of the AC-TES system; including, energy consumption, cooling load, air room temperature and performance coefficient (COP). The RBFNN framework in the developed strategy is trained to identify intricate patterns and correlations within the data, while the FHO is utilized to explore the optimal hyperparameters of the RBFNN for maximizing the prediction accuracy. The proposed strategy was modelled in MATLAB software and validated using a publicly available measurements for the AC-TES system. The system maintained improved cooling performance in which the average daily values of energy consumption, cooling load, air room temperature and COP are 1100 kWh/hr, 1.30 kW, 23.97 oC, and 3.12, respectively. The statistical outcomes depict that the developed RBFNN-FHO strategy achieved an impressive prediction accuracy of 95.81% accuracy, a 0.94 correlation coefficient, a 0.4193 mean absolute error (MAE), and a 0.5200 root mean square error (RMSE), respectively. Furthermore, the performance of the proposed RBFNN-FHO is model, is compared with the existing machine-learning approaches utilized for predicting the dynamic performances of HVAC systems. The comparative analysis with existing techniques highlights the robustness and effectiveness of the proposed RBFNN-FHO strategy in predicting AC-TES performances.

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.

Numerical Simulation of Droplet Coalescence Using Meshless Radial Basis Function and Domain Decomposition Method

The present investigation of the dynamic two-binary droplet interactions has gained attention since its use to expand and improve several numerical methods. Generally, its interactions are classified into coalescence, bouncing, reflective, and stretching separation. This study simulated droplet coalescence using the meshless radial basis function (RBF) method. These methods are used to solve the Navier-Stokes equations combined with the Cahn-Hilliard equations to track the interface between two fluids. This work uses the fractional step method to calculate the pressure-velocity coupling in the Navier-Stokes equations. The numerical results were compared with the available data in the literature to validate the proposed method. Based on the validation, the proposed method conforms well with the literature. To identify further coalescence characteristics, the model considered different values in viscosity (2, 4, and 8 cP), collision velocity (1.5 m/s and 3 m/s), and surface tension (0.014, 0.028, and 0.056 N/m) parameters. The increasing viscosity was linearly proportional to the collision time, whereas increased surface tension and collision velocity shortened the collision time.

Inverse feedforward control of piezoelectric actuators using optimized composite neural network-based Hammerstein model

This paper utilizes the optimized composite neural network (OCNN)-Hammerstein model to directly identify the dynamic inverse hysteresis effect, employing it as a feedforward controller to compensate for the rate-dependent and amplitude-dependent dynamic hysteresis of the piezoelectric actuator. The OCNN-Hammerstein model consists of an optimized composite neural network and an auto-regressive exogenous model in series. The OCNN comprises convolutional neural network layer and radial basis function neural network layer, with its hyperparameters optimized using a modified grey wolf optimizer algorithm. Compared to the existing dynamic Prandtl-Ishlinskii-Hammerstein and dynamic Bouc-Wen-Hammerstein models in the literature, the feedforward controller based on the proposed model in this paper demonstrates superior performance, with an RSME below 0.45 μm and a 74.5% reduction in relative hysteresis at the condition of 300 Hz and maximum amplitude. The feedforward controller exhibits universality across all amplitude ranges and within the 50–300 Hz frequency range, while also providing predictive compensation for dynamic hysteresis at 300–400 Hz. The feedforward controller based on the OCNN-Hammerstein model in this paper provides a crucial methodology for open-loop control of piezoelectric actuators.

Relative Radiometric Normalization for the PlanetScope Nanosatellite Constellation Based on Sentinel-2 Images

Detecting and characterizing continuous changes on Earth’s surface has become critical for planning and development. Since 2016, Planet Labs has launched hundreds of nanosatellites, known as Doves. Despite the advantages of their high spatial and temporal resolution, these nanosatellites’ images still present inconsistencies in radiometric resolution, limiting their broader usability. To address this issue, a model for radiometric normalization of PlanetScope (PS) images was developed using Multispectral Instrument/Sentinel-2 (MSI/S2) sensor images as a reference. An extensive database was compiled, including images from all available versions of the PS sensor (e.g., PS2, PSB.SD, and PS2.SD) from 2017 to 2022, along with data from various weather stations. The sampling process was carried out for each band using two methods: Conditioned Latin Hypercube Sampling (cLHS) and statistical visualization. Five machine learning algorithms were then applied, incorporating both linear and nonlinear models based on rules and decision trees: Multiple Linear Regression (MLR), Model Averaged Neural Network (avNNet), Random Forest (RF), k-Nearest Neighbors (KKNN), and Support Vector Machine with Radial Basis Function (SVM-RBF). A rigorous covariate selection process was performed for model application, and the models’ performance was evaluated using the following statistical indices: Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Lin’s Concordance Correlation Coefficient (CCC), and Coefficient of Determination (R2). Additionally, Kruskal–Wallis and Dunn tests were applied during model selection to identify the best-performing model. The results indicated that the RF model provided the best fit across all PS sensor bands, with more accurate results in the longer wavelength bands (Band 3 and Band 4). The models achieved RMSE reflectance values of approximately 0.02 and 0.03 in these bands, with R2 and CCC ranging from 0.77 to 0.90 and 0.87 to 0.94, respectively. In summary, this study makes a significant contribution to optimizing the use of PS sensor images for various applications by offering a detailed and robust approach to radiometric normalization. These findings have important implications for the efficient monitoring of surface changes on Earth, potentially enhancing the practical and scientific use of these datasets.

Integrated metaheuristic approaches for estimation of fracture porosity derived from fullbore formation micro-imager logs: Reaping the benefits of stand-alone and ensemble machine learning models

Fracture porosity is one of the most effective parameters for reservoir productivity and recovery efficiency. This study aims to predict and improve the accuracy of fracture porosity estimation through the application of advanced machine learning (ML) algorithms. A novel approach was introduced for the first time to estimate fracture porosity by reaping the benefits of petrophysical and fullbore formation micro-imager (FMI) data based on employing various stand-alone, ensemble, optimisation and multi-variable linear regression (MVLR) algorithms. This study proposes a ground-breaking two-step committee machine (CM) model. Petrophysical data containing compressional sonic-log travel time, deep resistivity, neutron porosity and bulk density (inputs), along with FMI-derived fracture porosity values (outputs), were employed. Nine stand-alone ML algorithms, including back-propagation neural network, Takagi and Sugeno fuzzy system, adaptive neuro-fuzzy inference system, decision tree, radial basis function, extreme gradient boosting, least-squares boosting, least squares support vector regression and k-nearest neighbours, were trained for initial estimation. To improve the efficacy of stand-alone algorithms, their outputs were combined in CM structures using optimisation algorithms. This integration was applied through five optimisation algorithms, including genetic algorithm, ant colony, particle swarm, covariance matrix adaptation evolution strategy (CMA-ES) and Coyote optimisation algorithm. Considering the lowest error, the CM with CMA-ES showed superior performance. Subsequently, MVLR was employed to improve the CMs further. Employing MVLR to combine the CMs yielded a 57.85% decline in mean squared error and a 4.502% improvement in the correlation coefficient compared to the stand-alone algorithms. The results of the benchmark analysis validated the efficacy of this approach.