Radial Basis Function Research Articles

Data-Driven Smart Assessment for Enterprise Audit Risks Based on Radial Base Function Neural Network and Grey Correlation Analysis

In the era of big data, audit risk assessment is facing increasing business volume. Hence, it is important to develop automatic audit risk assessment methods for enterprises with the assistance of intelligent algorithms. As a consequence, this paper proposes data-driven smart assessment for enterprise audit risks-based radial basis function (RBF) neural networks and grey correlation analysis (GCA). First, evaluation data are collected and analyzed to understand the characteristics and influencing factors of enterprise audit risks. Secondly, RBF interpolation is introduced to establish the network structure for RBF neural networks. Then, GCA is integrated with RBF Interpolation (RBFNN) to formulate the automatic audit risk evaluation method, and the proposal is named RBF and GCA. Such a combined methodology can improve audit risk assessment efficiency. Finally, we make some experiments to evaluate the proposed TBF-GCA on a real-world dataset, and some evaluation indicators are specified based on the actual audit risk situation of the enterprises. The obtained results reveal that RBF–GCA has high accuracy in identity precision and can effectively identify audit risks for enterprises.

A Hybrid Algorithm for Multiple Disease Prediction: Radial Basis Function and Logistic Regression

Disease prediction is an important aspect of modern medicine, which aims to diagnose disease early and provide appropriate treatment to patients. This research uses a hybrid approach that combines the RBF (Radial Basis Function) kernel algorithm with logistic regression to predict various diseases in medical datasets. This method is intended to improve prediction performance by exploiting the advantages of each algorithm. This research uses a dataset containing medical information about several diseases collected from the Kaggle dataset. First, the RBF kernel is applied to transform the data features into a more informative, non-linear representation. Then, the logistic regression model is used to make predictions based on the features that have been processed by the RBF kernel. In this research, the hybrid RBF (Radial Basis Function) method was proven to be superior in predicting multiple diseases. This method shows the highest accuracy of 0.9460, as well as excellent precision, recall, and F1-score values of 0.8680, 0.8097, and 0.8294, respectively. The advantage of the hybrid RBF method lies in its ability to capture complex patterns in data that other methods often cannot identify, as well as its ability to handle non-linear decision boundaries, which are a common characteristic in medical datasets. Keywords: Disease prediction, Hybrid approach, RBF kernel algorithm, Logistic regression, medical datasets

An Optimization Study of Circumferential Groove Casing Treatment in a High-Speed Axial Flow Compressor

In this paper, a numerical optimization study of single-groove casing treatment was conducted on a high-speed axial compressor. One of the aims is to find the optimal structure of a single groove that can improve compressor stability with minimal loss in efficiency. Another aim is to explore suitable parameters for rapidly evaluating the compressor stall margin. A design optimization platform has been constructed in this paper, which utilizes NSGA-II and a Radial Basis Function (RBF) neural net model to carry out the optimization. The stall margin of the compressor with A single groove was accurately determined by calculating its entire overall performance line. A Pareto front is obtained through optimization, and the optimal design can be selected from the Pareto front. By considering both stall margin and efficiency loss, one of the optimal designs was found to achieve a 7.49% improvement in stall margin with a 0.24% improvement in peak efficiency. Based on the database, the effect of design parameters of a single groove on compressor stability and performance is analyzed. A series of evaluation parameters of stall margin were compared to their degree of correlation with the real stall margin calculated by the entire overall performance line. As a result, tip blockage and momentum ratio can be used as efficient parameters for quickly evaluating the compressor stall margin without the need to calculate the entire performance curve of the compressor.

Adaptive Decentralized Control for Constrained Strong Interconnected Nonlinear Systems and Its Application to Inverted Pendulum.

This work is dedicated to adaptive decentralized tracking control for a class of strong interconnected nonlinear systems with asymmetric constraints. Currently, there are few related studies on unknown strongly interconnected nonlinear systems with asymmetric time-varying constraints. To deal with the assumptions of the interconnection terms in the design process, which include upper functions and structural restrictions, the properties of Gaussian function in radial basis function (RBF) neural networks are applied to overcome this difficulty. By constructing the nonlinear state-dependent function (NSDF) and using a new coordinate transformation, the conservative step that the original state constraint converts into a new boundary of the tracking error is removed. Meanwhile, the virtual controller's feasibility condition is removed. It is proven that all the signals are bounded, especially the original tracking error and the new tracking error, which are both bounded. In the end, simulation studies are carried out to verify the effectiveness and benefits of the proposed control scheme.

An efficient method for solving high-dimension stationary FPK equation of strongly nonlinear systems under additive and/or multiplicative white noise

Engineering structures may suffer from drastic nonlinear random vibrations in harsh environments. Random vibration has been extensively studied since 1960s, but is still an open problem for large-scale strongly nonlinear systems. In this paper, a random vibration analysis method based on the Neural Networks for large-scale strongly nonlinear systems under additive and/or multiplicative Gaussian white noise (GWN) excitations is proposed. In the proposed method, the high-dimensional steady-state Fokker–Planck-Kolmogorov (FPK) equation governing the state’s probability density function (PDF) is firstly reduced to low-dimensional FPK equation involving only the interested state variables, generally one or two dimensions. The equivalent drift coefficients (EDCs) and diffusion coefficients (EDFs) in the low-dimensional FPK equation are proven to be the conditional mean of the coefficients given the interested variables. Furthermore, it is shown that the conditional mean can be optimally estimated by regression. Subsequently, the EDCs and EDFs, as functions of the retained variables, are approximated by the semi-analytical Radial Basis Functions Neural Networks trained with samples generated by a few deterministic analyses. Finally, the Physics Informed Neural Network is employed to solve the reduced steady-state FPK equation, and the PDF of the system responses is obtained. Four typical examples under additive and/or multiplicative GWN excitations are used to examine the accuracy and efficiency of the proposed method by comparing its results with the exact solution (if available) or Monte Carlo simulations. The proposed method also exhibits greater accuracy than the globally-evolving-based generalized density evolution equation scheme, a similar method of its kind, especially for strongly nonlinear systems. Notably, even though steady-state systems are applied in this paper, there is no obstacle to extending the proposed framework to transient systems.

Method of Radial Basis Functions for Solving the Partial Integro-Differential Equation of Diffusion with Nonlocal Effects

Method of Radial Basis Functions for Solving the Partial Integro-Differential Equation of Diffusion with Nonlocal Effects

Research on ride comfort optimization of the vehicle considering the subframe.

When the vehicle is in motion, the elastic deformation of the flexible subframe significantly influences ride comfort. Therefore, it is crucial to investigate the impact of flexible subframes on vehicle ride comfort. In order to enhance the reliability and optimization efficiency of our research, this paper incorporates the concept of elastic deformation in the flexible subframe into the investigation of vehicle ride comfort, and proposes a multi-objective optimization approach to enhance the overall vehicle ride comfort. The vibration mathematical model elucidates how flexible subframes affect vehicle ride comfort and establishes a rigid-flexible coupling model for a specific vehicle with a flexible subframe to analyze the impact of its elastic deformation on vehicle ride comfort through simulation experiments. Subsequently, a radial basis function approximation model is established, and the multi-objective particle swarm optimization and non-dominated sorting genetic algorithm II algorithms are employed to conduct multi-objective optimization of the stiffness of the subframe bushing with the aim of enhancing vehicle ride comfort. The findings indicate that the flexible subframe has a significant impact on vehicle ride comfort. Specifically, on bump roads, peak values of vertical and longitudinal seat accelerations decrease while lateral seat acceleration increases. On random roads, peak values of longitudinal and lateral seat accelerations increase while vertical acceleration decreases. Furthermore, the stiffness of the subframe bushing optimized by the non-dominated sorting genetic algorithm II algorithm further enhances vehicle ride comfort and aligns more closely with the optimization requirements in this study.

A local meshless method for the numerical solution of multi-term time-fractional generalized Oldroyd-B fluid model

This work presents an accurate and efficient method, for solving a two dimensional time-fractional Oldroyd-B fluid model. The proposed method couples the Laplace transform (LT) with a radial basis functions based local meshless method (LRBFM). The suggested numerical scheme first uses the LT which transform the given equation to an elliptic equation in LT space, and then it utilizes the LRBFM to solve transformed equation in LT space, and then the solution is converted back into the time domain via the improved Talbot's scheme. The local meshless methods are widely recognized for scattered data interpolation and for solving PDEs in complex shaped domains. The adaptability, simplicity, and ease of use are features that have led to the popularity of local meshless methods. The local meshless methods are easy and straightforward, they only requires to solve linear system of equations. The main objective of using the LT is to avoid the computation of costly convolution integral in time-fractional derivative and the effect of time stepping on accuracy and stability of numerical solution. The stability and the convergence of the proposed numerical scheme are discussed. Further, the Ulam-Hyers (UH) stability of the proposed model is discussed. The accuracy and efficiency of the suggested numerical approach have been demonstrated using numerical experiments on five different domains with regular nodes distribution.

Research on fixed-time time-varying formation of heterogeneous multi-agent systems based on tracking error observer under DoS attacks

In this paper, the fixed-time time-varying formation of heterogeneous multi-agent systems (MASs) based on tracking error observer under denial-of-service (DoS) attacks is investigated. Firstly, the dynamic pinning strategy is used to reconstruct the communication channel for the system that suffers from DoS attacks to prevent the discontinuous transmission information of the communication network from affecting MASs formation. Then, considering that the leader state is not available to each follower under DoS attacks, a fixed-time distributed observer without velocity information is constructed to estimate the tracking error between followers and the leader. Finally, adaptive radial basis function neural network (RBFNN) is used to approximate the unknown ensemble disturbances in the system, and the fixed-time time-varying formation scheme is designed with the constructed observer. The effectiveness of the proposed control algorithm is demonstrated by the numerical simulation.

Event-Based Nonsingular Fixed-Time Tracking Control of an Uncertain Manipulator System Subject to Full-State Static Constraints.

This article centers around investigating the event-triggered nonsingular fixed-time tracking issue for an n -link rigid robot manipulator with full-state constraints, external disturbances, and model uncertainties. We propose the definition of the constrainedly practically fixed-time stability (CPFTS) and provide a sufficient condition for CPFTS. A novel auxiliary function is developed to address the singularity issue caused by repeated differentiation in achieving the fixed-time tracking control. The uncertain parameters are approximated using the radial basis function neural network (RBFNN). This study proposes the model-based and the neutral network-based tracking control approaches, designed using the scaling function technique and the barrier Lyapunov function, respectively, to ensure that the tracking error systems are CPFTS and the full-state constraints comply. Moreover, the communication transmission load is reduced using the relative threshold event-triggered control strategy. Simulation results demonstrate the effectiveness of the proposed tracking control algorithms.

Efficient Numerical Solution of the Sharma-Tasso-Olver Equation Using Radial Basis Function-Pseudo Spectral Method with Comparative Analysis

In this study, we will solve the Sharma-Tasso-Olver equation by utilizing the radial basis function-pseudo spectral approach. Pseudo spectral techniques are renowned for their exceptional precision but have constraints regarding their ability to handle geometric variations. The integration of Radial Basis Functions (RBF) with pseudo spectral methods offers a solution to surmount this particular limitation. To estimate the differentials with respect to the variable , we will use the radial basis functions, including commonly used ones like multiquadric, inverse multiquadric, and inverse quadric, have been employed. Furthermore, the problem has transformed into the ordinary differential equation (ODE), and the solution to this ODE system has been acquired through the application of the fourth-order Runge-Kutta method. Additionally, a comparative analysis has been conducted between the solutions obtained through the suggested technique and the exact solutions.

MODELLING DOMESTIC WATER DEMAND IN MALAYSIA TO IDENTIFY INFLUENCING FACTORS: A COMPARATIVE ANALYSIS

Water crises are often experienced by many developing countries worldwide. Predicting future domestic water demand and identifying the influential factors are vital to managing water supply effectively. This study aims to determine the best predictive models among Multiple Linear Regression (MLR), Multi-layer Perceptron (MLP), and Radial Basis Function (RBF) Neural Networks as well as to identify the significant influential factors towards domestic water demand. Based on the yearly records from 2000 to 2018 obtained from the Malaysian Water Association, the Department of Environment, and the Department of Statistics Malaysia the analysis results indicate an increasing pattern of domestic water in Malaysia with the demand for non-domestic water twice lower than domestic water. Based on RMSE and R-squared, Multi-layer Perceptron is the best model for predicting domestic water demand. The MLR model shows that the two most significant influential factors towards domestic water demand are price and design capacity, with negative and positive relationships. The results describe that an increase in price affects a decrease in water demand, while an increase in design capacity will reduce the water demand. The findings suggest that the water utilities in Malaysia should focus more on these identified factors.

Development of Intelligent Control Strategy for an Anesthesia System Based on Radial Basis Function Neural Network Like PID Controller

Development of Intelligent Control Strategy for an Anesthesia System Based on Radial Basis Function Neural Network Like PID Controller

Technology development of novel autogenous double pulse tungsten insert gas welding technique to evaluate the depth of penetration, micro segregation via machine learning and desirability function approach

The present research investigates the effect of process parameters on the microstructure, micro segregation, and material properties of the Autogenous Double Pulse Tungsten Inert Gas Welding (ADP-TIG) of Inconel 625. The optimization of the process parameter was evaluated by Response surface Methodology (RSM) Box Behnken method. In this article, the effects of the weld-bead geometry, weld centre (WC), weld interface (WI), and heat affected zone (HAZ) were evaluated through macro morphology, microstructure, SEM/EDAX, XRD, and micro hardness. The outcomes indicate that by employing a combination of high and low frequency pulsing in ADP-TIG, it is possible to regulate not only the dimensions of the weld-bead and penetration depth but also the HAZ. The ADP-TIG process has a low heat input, resulting in finer grains in the microstructure, reduced secondary phases, and a narrower HAZ. SEM images of alloy 625 confirms the depiction of fine equiaxed dendrites. The ADP-TIG process reduces secondary phase formation due to a reduction in Mo and Nb alloying elements. EDAX results also show that the micro segregation in the weld centre (WC) and weld interface (WI) is very less in the dendritic core region because of the lower heat Input. The XRD result confirms the presence of NbzNi, Cr₂Nb, Ni8Nb, Fe2Mo3 and FeNi phases. The maximum microhardness values in WC and WI are 290 HV and 280 HV, respectively. The impacts of ADP-TIG welding technique specifications on factors such as weld bead geometry, WC, WI, and HAZ have been thoroughly examined across a range of process parameters. Further the process parameters of ADP-TIG were optimized using a desirability function to achieve defect-free welds, followed by experimental validation. The desirability function results were then compared with a machine learning (ML) approach. The investigation aimed to assess ML algorithms' predictive capability for weldment outcomes. From the ML modelling results, Support Vector Machine (SVM) using the Radial Basis Function (RBF) kernel was identified as the superior strategy for accurately predicting Heat input, Mo segregation, and Nb segregation. Additionally, Gaussian process regression (GPR) with an RBF kernel was recommended for predicting the Width to Depth Ratio.

Interpretable Machine Learning for Chronic Kidney Disease Diagnosis: A Gaussian Processes Approach

Chronic Kidney Disease (CKD) is a global health issue impacting over 800 million people, characterized by a gradual loss of kidney function leading to severe complications. Traditional diagnostic methods, relying on laboratory tests and clinical assessments, have limitations in sensitivity and are prone to human error, particularly in the early stages of CKD. Recent advances in machine learning (ML) offer promising tools for disease diagnosis, but a lack of interpretability often hinders their adoption in clinical practice. Gaussian Processes (GP) provide a flexible ML model capable of delivering predictions and uncertainty estimates, essential for high-stakes medical applications. However, the integration of GP with interpretable methods remains underexplored. We developed an interpretable CKD classification model to address this knowledge gap by combining GP with Shapley Additive Explanations (SHAP). We assessed the model's performance using three GP kernels (Radial Basis Function, Matern, and Rational Quadratic). The results show that the Rational Quadratic kernel outperforms the other kernels, achieving an accuracy of 98.75%, precision of 100%, sensitivity of 97.87%, specificity of 100%, and an F1-score of 98.51%. SHAP values indicate that haemoglobin and specific gravity are the most influential features. The results demonstrate that the Rational Quadratic kernel enhances predictive accuracy and provides robust uncertainty estimates and interpretable explanations. This combination of accuracy and interpretability supports clinicians in making informed decisions and improving patient management and outcomes in CKD. Our study connects advanced ML techniques with practical medical applications, leading to more effective and reliable ML-driven healthcare solutions.

Fast Finite-Time Observer-Based Event-Triggered Consensus Control for Uncertain Nonlinear Multiagent Systems with Full-State Constraints.

This article studies a class of uncertain nonlinear multiagent systems (MASs) with state restrictions. RBFNNs, or radial basis function neural networks, are utilized to estimate the uncertainty of the system. To approximate the unknown states and disturbances, the state observer and disturbance observer are proposed to resolve those issues. Moreover, a fast finite-time consensus control technique is suggested in order to accomplish fast finite-time stability without going against the full-state requirements. It is demonstrated that every signal could be stable and boundless, and an event-triggered controller is considered for the saving of resources. Ultimately, the simulated example demonstrates the validity of the developed approach.

Numerical analysis of uncertain frequency of rotating composites using NURBS-based isogeometric HSDT approach: Rim-driven configuration

This study delves into the impact of material and fabrication uncertainties on the natural frequencies of rim-driven rotating structures. Utilizing a higher-order shear deformation theory (HSDT), an isogeometric analysis (IGA) model predicts these frequencies. Sensitivity analysis via a radial basis function network (RBFN) model, validated with Monte Carlo simulation, highlights parameter influence. Parametric investigations unveil sensitivity patterns and influential parameters. Employing a stochastic approach, the study compares the effects of random material properties on the free vibration response of rotating and non-rotating plates. Additionally, the RBFN-based surrogate model assesses reliability parameters concerning resonance failure in rim-driven rotating composite structures.

Prediction of Vehicle–Live Animal Crashes in Britain: Contact and Noncontact Incidents

<div>Animal–vehicle collisions (AVCs) can result in devastating injuries to both humans and animals. Despite significant advances in crash prediction models, there is still a significant gap when it comes to injury severity prediction models in AVCs, especially concerning small animals. It is no secret that large mammals can pose a significant threat to road safety; however, researchers tend to overlook the impact of domestic and small animals wandering along the roads. In this study, STATS19 road safety data was used containing any type of live animal, and a radial basis function (RBF) model was used to predict different severities of injury regardless of whether the animal was hit, or not. As a means of better understanding the factors contributing to severities, regression trees were used to identify and retain only the most useful predictors, removing the less useful ones. A comparison was made between the performance of the trees across a range of severity classes, and the model-fitting results were discussed. Initially, the study was unable to generate satisfactory predictions, but the optimization of the key predictors and the combination of severity classes significantly improved their accuracy. Research findings revealed factors contributing to the severities, which were discussed accordingly. Particular attention was drawn to the pressing safety issue posed by animals crossing A-class single carriageways in rural site clusters. Animals being present on those carriageways without direct vehicular contact significantly contributed to the severity of the injuries sustained. Although the majority of contributing factors were related to human behavior, no evidence of road safety education, training, or publicity interventions specifically targeting AVCs was found in the literature.</div>

Improving the Efficiency of Electric Vehicles: Advancements in Hybrid Energy Storage Systems

Electric vehicles (EVs) encounter substantial obstacles in effectively managing energy, particularly when faced with varied driving circumstances and surrounding factors. This study aims to evaluate the performance of three different control systems in a fully operational hybrid energy storage system (HESS) installed in the Nissan Leaf. The objective is to improve the performance of EVs by focusing on optimising energy management in response to different global environmental and driving circumstances. This study utilises an analytical strategy by developing a distinct energy management system model using MATLAB/Simulink. This model is specifically designed for optimising the integration and control of batteries and supercapacitors (SCs) in a fully active HESS. This model mimics the performance of the controllers under three different driving cycles—Artemis rural, Artemis motorway, and US06. The findings demonstrate notable progress in managing the battery state of charge (SOC) and the system’s responsiveness, especially when employing the radial basis function (RBF) controller. This study emphasises the capacity of HESSs to enhance the effectiveness and durability of EVs, therefore promoting wider acceptance and progress in electric transportation technology.

Single-network based adaptive dynamic programming optimal control for robotic manipulator with joint limitation under input saturation

This paper proposes an optimal control method based on adaptive dynamic programming (ADP) for manipulators with joint limitation under input saturation. The asymmetric input saturation problem is solved by introducing a smooth function, by which the saturation and nonsmooth issues of the input caused by the actuators can be handled. Joint limitation of the manipulator is transformed through a transfer function, which is incorporated into the cost function of the whole robotic system, to guarantee the joint limitation will not be violated. Meanwhile, due to the difficulty in solving Hamilton-Jacobi-Bellman (HJB) equation, the critic network is constructed utilising radial basis function neural networks (RBFNNs) to approximate the cost function. This approach effectively overcomes the curse of dimensionality problem associated with dynamic programming. Subsequently, an ADP-based optimal controller is designed for the robotic system. Lyapunov synthesis is used in the stability analysis to prove all the signals are convergent and ultimately uniformly bounded (UUB). Simulations are conducted on a planar 3-DOF manipulator to validate the effectiveness of the proposed method. The results demonstrate the improved performance and feasibility of the developed ADP-based optimal control strategy in handling joint limitations and input saturation challenges in robotic systems.