Hybrid Radial Basis Research Articles

A novel meshless method for solving long-term evolution problem on irregular domain

In the context of method of approximate particular solutions (MAPS), we propose a novel meshless computational scheme based on hybrid radial basis function (RBF)-polynomial bases to solve both parabolic and hyperbolic partial differential equations over a large terminal time interval on irregular spatial domain. By using space–time approach, the original time-dependent problem is firstly reformulated into an elliptic boundary value problem. Integrated polyharmonic splines (PS)-type RBF kernels in conjunction with multivariate polynomials are then employed to construct the approximate solution space. This superior combination enables us to stably achieve highly accurate solution. Due to the adoption of the polyharmonic splines, the difficulty of determining a suitable shape parameter of RBF is alleviated. Moreover, employing the recently developed ghost point method, the precision and stability of the approximation can be further enhanced. For numerical verification, four examples are investigated to demonstrate the robustness of the proposed methodology in terms of the aforementioned advantages.

Numerical investigation of high-dimensional option pricing PDEs by utilizing a hybrid radial basis function - finite difference procedure

The target of this research is to resolve high-dimensional partial differential equations (PDEs) for multi-asset options, modeled as parabolic time-dependent PDEs. We present a hybrid radial basis function - finite difference (RBF-FD) solver, which combines the advantages of Gaussian and multiquadric functions. Additionally, we employ the Krylov subspace method on the resulting system of ordinary differential equations, reducing the computation load for finding the numerical solution. Computational tests, up to seven dimensions, and comparisons support the superiority of our hybrid solver.

A hybrid radial basis function—Finite difference method for modelling two-dimensional thermo-elasto-plasticity, Part 2. Application to cooling of hot-rolled steel bars on a cooling bed

This paper represents Part 2 of the parallel paper Part 1, where the strong form hybrid RBF-FD method was developed for solving thermo-elasto-plastic problems. It addresses the industrial application of this novel meshless method to steel bars cooling on a cooling bed (CB) where the formation of residual stress is of primary interest. The study investigates the impact of the distance between the bars and the distance to the heat shield above the CB on radiative heat fluxes and, consequently, on thermo-mechanical response. The thermal model is solved on bars cross-section with a RBF-FD method where augmented polyharmonic splines are used for the local approximation. View factors, computed with a Monte-Carlo method, are included in radiative heat fluxes. The thermal solution is incrementally applied on a mechanical model that assumes a generalised plane strain state and captures bars bending. The study employs a hybrid RBF-FD method to resolve a nonlinear discontinuous mechanical problem successfully. The simulation of the process shows how different process parameters influence the thermo-mechanical response of the bars.

Classification of cancer types based on microRNA expression using a hybrid radial basis function and particle swarm optimization algorithm.

The diagnosis and treatment of cancer is one of the most challenging aspects of the medical profession, despite advances in disease diagnosis. MicroRNAs are small noncoding RNA molecules involved in regulating gene expression and are associated with several cancer types. Therefore, the analysis of microRNA data has become one of the most important areas of cancer research in recent years. This paper presents an improved method for cancer-type classification based on microRNA expression data using a hybrid radial basis function (RBF) and particle swarm optimization (PSO) algorithm. Two datasets containing microRNA information were used, and preprocessing and normalization operations were performed on the raw data. Feature selection was carried out by using the PSO algorithm, which can identify the most relevant and informative features in the data along with helping to prioritize them. Using a PSO algorithm for feature selection is an effective approach to microRNA analysis. This enhances the accuracy and reliability of cancer-type classifications based on microRNA expression data. In the proposed method, we, respectively, achieved an accuracy of 0.95% and 0.91% on both datasets, with an average of 0.93%, using an improved RBF neural network classifier. These results demonstrate that the proposed method outperforms previous works. RESEARCH HIGHLIGHTS: To enhance the accuracy of cancer-type classifications based on microRNA expression data. We present a minimal feature selection method using particle swarm optimization to reduce computational load & radial basis function to improve accuracy.

A hybrid radial basis function-finite difference method for modelling two-dimensional thermo-elasto-plasticity, Part 1: Method formulation and testing

A hybrid version of the strong form meshless Radial Basis Function-Finite Difference (RBF-FD) method is introduced for solving thermo-mechanics. The thermal model is spatially discretised with RBF-FD, where trial functions are polyharmonic splines augmented with polynomials. For time discretisation, the explicit Euler method is employed. An extension of RBF-FD, the hybrid RBF-FD, is introduced for solving mechanical problems. The model is one-way coupled, where temperature affects displacements. The thermo-elastoplastic material response is considered where the stress field is generally non-smooth. The hybrid RBF-FD, where the finite difference method is used to discretise the divergence operator from the balance equation, is shown to be successful when dealing with such problems. The mechanical model is introduced in a plane strain and in a generalised plane strain (GPS) assumption. For the first time, this work presents a strong form RBF-FD for GPS problems subjected to integral form constraints. The proposed method is assessed regarding h-convergence and accuracy on the benchmark with heating an elastoplastic square. It is proven to be successful at solving one-way coupled thermo-elastoplastic problems. The proposed novel meshless approach is efficient, accurate, and robust. Its use in an industrial situation is provided in Part 2 of this paper.

An improved local radial basis function method for solving small-strain elasto-plasticity

Strong-form meshless methods received much attention in recent years and are being extensively researched and applied to a wide range of problems in science and engineering. However, the solution of elasto-plastic problems has proven to be elusive because of often non-smooth constitutive relations between stress and strain. The novelty in tackling them is the introduction of virtual finite difference stencils to formulate a hybrid radial basis function generated finite difference (RBF-FD) method, which is used to solve small-strain von Mises elasto-plasticity for the first time by this original approach. The paper further contrasts the new method to two alternative legacy RBF-FD approaches, which fail when applied to this class of problems. The three approaches differ in the discretization of the divergence operator found in the balance equation that acts on the non-smooth stress field. Additionally, an innovative stabilization technique is employed to stabilize boundary conditions and is shown to be essential for any of the approaches to converge successfully. Approaches are assessed on elastic and elasto-plastic benchmarks where admissible ranges of newly introduced free parameters are studied regarding stability, accuracy, and convergence rate.

An Efficient Reliability Analysis Method Based on the Improved Radial Basis Function Neural Network

Abstract This paper develops an efficient reliability analysis method based on the improved radial basis function neural network (RBFNN) to increase the accuracy and efficiency of structural reliability analysis. To solve the problems of low computational accuracy and efficiency of the RBFNN, an improved RBFNN method is developed by transferring the sampling center of Latin hypercube sampling (LHS) from the mean values of random variables to the most probable point (MPP) in the sampling step. Then, the particle swarm optimization algorithm is adopted to optimize the shape parameters of RBFNN, and the RBFNN model is assessed by the cross-validation method for subsequent reliability analysis using Monte Carlo simulation (MCS). Four numerical examples are investigated to demonstrate the correctness and effectiveness of the proposed method. To compare the computational accuracy and efficiency of the proposed method, the traditional radial basis function method, hybrid radial basis neural network method, first-order reliability method (FORM), second-order reliability method (SORM), and MCS method are applied to solve each example. All the results demonstrate that the proposed method has higher accuracy and efficiency for structural reliability analysis. Importantly, one practical example of an industrial robot is provided here, which demonstrates that the developed method also has good applicability and effectiveness for complex engineering problems.

Hybrid Surrogate Model-Based Multi-Objective Lightweight Optimization of Spherical Fuel Element Canister

A number of canisters need to be lightweight designed to store the spherical fuel elements (SFE) used in high-temperature gas-cooled reactors (HTGR). The main challenge for engineering is pursuing high-accuracy and high-efficiency optimization simultaneously. Accordingly, a hybrid surrogate model-based multi-objective optimization method with the numerical method for the lightweight and safe design of the SFE canister is proposed. To be specific, the drop analysis model of the SFE canister is firstly established where the finite element method—discrete element method (FEM–DEM) coupled method is integrated to simulate the interaction force between the SFE and canister. Through simulation, the design variables, optimization objectives, and constraints are identified. Then the hybrid radial basis function—response surface method (RBF–RSM) surrogate method is carried out to approximate and simplify the accurate numerical model. A non-dominated sorting genetic algorithm (NSGA-II) is used for resolving this multi-objective model. Optimal design is validated using comprehensive comparison, and the reduction of weight and maximum strain can be up to 2.46% and 44.65%, respectively. High-accuracy simulation with high-efficiency optimization is successfully demonstrated to perform the lightweight design on nuclear facilities.

A Modified RBF Collocation Method for Solving the Convection-Diffusion Problems

The main purposes of this study are to propose the modified radial basis function (RBF) collocation method using a hybrid radial basis function to solve the convection-diffusion problems numerically and to choose the optimal shape parameter of radial basis functions. The modified numerical scheme is tested on a benchmark problem with varying shape parameters. The root mean square error and maximum error are used to validate the accuracy and efficiency of the method. The proposed method can be a good alternative to the radial basis function collocation method to improve accuracy and results.

Joint Random Forest and Particle Swarm Optimization for Predictive Pathloss Modeling of Wireless Signals from Cellular Networks

The accurate and reliable predictive estimation of signal attenuation loss is of prime importance in radio resource management. During wireless network design and planning, a reliable path loss model is required for optimal predictive estimation of the received signal strength, coverage, quality, and signal interference-to-noise ratio. A set of trees (100) on the target measured data was employed to determine the most informative and important subset of features, which were in turn employed as input data to the Particle Swarm (PS) model for predictive path loss analysis. The proposed Random Forest (RF-PS) based model exhibited optimal precision performance in the real-time prognostic analysis of measured path loss over operational 4G LTE networks in Nigeria. The relative performance of the proposed RF-PS model was compared to the standard PS and hybrid radial basis function-particle swarm optimization (RBF-PS) algorithm for benchmarking. Generally, results indicate that the proposed RF-PS model gave better prediction accuracy than the standard PS and RBF-PS models across the investigated environments. The projected hybrid model would find useful applications in path loss modeling in related wireless propagation environments.

Modeling the pile settlement using the Integrated Radial Basis Function (RBF) neural network by Novel Optimization algorithms: HRBF-AOA and HRBF-BBO

The Pile movement is one of the most crucial matters in designing piles and foundations that need to be estimated for any project failure. Over the variables used in forecasting Pile Settlement, many methods have been introduced to appraise it. However, existing a wide range of theoretical strategies to investigate the pile subsidence, the soil-pile interactions are still ambiguous for academic researchers. Most studies have tried to work out the subsidence rate in piles after loading passing time by artificial intelligence methods. Generally, the Artificial Neural Network (ANN) has drawn attention to show the actual views of pile settlement over the loading phase vertically. This research aims to present the Hybrid Radial Basis Function neural network integrated with the Novel Arithmetic Optimization Algorithm and Biogeography-Based Optimization to calculate the optimal number of neurons embedded in hidden layers. The transportation network of Klang Valley, Mass Rapid Transit in Kuala Lumpur, Malaysia, was chosen to analyze the piles’ settlement and earth features using HRBF-AOA and HRBF-BBO scenarios. Over the prediction process, the R-values of HRBF-AOA and HRBF-BBO were obtained at 0.9825 and 0.9724, respectively. The MAE also shows a similar trend as 0.2837 and 0.323, respectively.

Prediction of the Nitrogen Content of Rice Leaf Using Multi-Spectral Images Based on Hybrid Radial Basis Function Neural Network and Partial Least-Squares Regression.

This paper's novel focus is predicting the leaf nitrogen content of rice during growing and maturing. A multispectral image processing-based prediction model of the Radial Basis Function Neural Network (RBFNN) model was proposed. Moreover, this paper depicted three primary points as the following: First, collect images of rice leaves (RL) from a controlled condition experimental laboratory and new shoot leaves in different stages in the visible light spectrum, and apply digital image processing technology to extract the color characteristics of RL and the morphological characteristics of the new shoot leaves. Secondly, the RBFNN model, the General Regression Model (GRL), and the General Regression Method (GRM) model were constructed based on the extracted image feature parameters and the nitrogen content of rice leaves. Third, the RBFNN is optimized by and Partial Least-Squares Regression (RBFNN-PLSR) model. Finally, the validation results show that the nitrogen content prediction models at growing and mature stages that the mean absolute error (MAE), the Mean Absolute Percentage Error (MAPE), and the Root Mean Square Error (RMSE) of the RFBNN model during the rice-growing stage and the mature stage are 0.6418 (%), 0.5399 (%), 0.0652 (%), and 0.3540 (%), 0.1566 (%), 0.0214 (%) respectively, the predicted value of the model fits well with the actual value. Finally, the model may be used to give the best foundation for achieving exact fertilization control by continuously monitoring the nitrogen nutrition status of rice. In addition, at the growing stage, the RBFNN model shows better results compared to both GRL and GRM, in which MAE is reduced by 0.2233% and 0.2785%, respectively.

A Hybrid RBF Collocation Method and Its Application in the Elastostatic Symmetric Problems

In this paper, a new hybrid radial basis function collocation method (HRBF-CM) is proposed to help resolve two-dimensional elastostatic symmetric problems. In the new approach, the hybrid radial basis function (HRBF) combines the infinitely smooth RBF and piecewise smooth RBF, containing two parameters (the shape parameter and the weight parameter). Discretization schemes are presented in detail. We use MATLAB to implement the HRBF-CM and produce numerical results which demonstrate the potential of this method. The new method’s accuracy is higher than that of the traditional methods, especially in the case of a more significant number of nodes. We discuss the new method’s effectiveness compared to the widely used traditional RBF and also investigate the effect of parameters on the method’s performance under the new method.

Dynamic System Modeling of a Hybrid Neural Network with Phase Space Reconstruction and a Stability Identification Strategy

Focusing on the identification of dynamic system stability, a hybrid neural network model is proposed in this research for the rotating stall phenomenon in an axial compressor. Based on the data fusion of the amplitude of the spatial mode, the nonlinear property is well characterized in the feature extraction of the rotating stall. This method of data processing can effectively avoid the inaccurate recognition of single or multiple measuring sensors only depending on pressure. With the analysis on the spatial mode, a chaotic characteristic was shown in the development of the amplitude with the first-order spatial mode. With the prerequisite of revealing the essence of this dynamic system, a hybrid radial basis function (RBF) neural network was adopted to represent the properties of the system by artificial intelligence learning. Combining the advantages of the methods of K-means and Gradient Descent (GD), the Chaos–K-means–GD–RBF fusion model was established based on the phase space reconstruction of the chaotic sequence. Compared with the two methods mentioned above, the calculation accuracy was significantly improved in the hybrid neural network model. By taking the strategy of global sample entropy and difference quotient criterion identification, a warning of inception can be suggested in advance of 12.3 revolutions (296 ms) with a multi-step prediction before the stall arrival.

Solving PDEs with a Hybrid Radial Basis Function: Power-Generalized Multiquadric Kernel

Solving PDEs with a Hybrid Radial Basis Function: Power-Generalized Multiquadric Kernel

Robust and general predictive models for condensation heat transfer inside conventional and mini/micro channel heat exchangers

To design, scale-up, and optimize the two-phase flow heat exchangers, accurate information about the heat transfer coefficient (HTC) is required. Here, an extensive database including 11,128 experimental data points from 80 sources, covering 37 condensing fluids over a wide range of operating conditions, were gathered for developing general and accurate models to forecast the HTC in mini/micro and conventional channel heat exchangers. The conventional intelligent approaches, namely, gaussian process regression (GPR), radial basis function (RBF), and hybrid radial basis function (HRBF) and also the least square fitting method (LSFM) were utilized for development of the new models. Firstly, the gathered data were used in evaluation of earlier two-phase HTC models, and these models showed average absolute relative error (AARE) values higher than 29%. Thus, more accurate models are necessary for these systems. Based on Pearson’s correlation analysis, eight dimensionless groups were selected as the most important input parameters. The GPR model showed the best results in estimation of Nu number for the test process with AARE of 4.50%. However, RBF and HRBF models estimated the HTC with AARE values 19.41% and 24.36% for testing data points, respectively. In addition, a general explicit correlation was developed by the least square fitting method (LSFM) for estimating the HTC, with acceptable results at an AARE of 23.40% for all analyzed data. The performance of the new general correlation, GPR and the previous models were assessed for different channel sizes, flow regimes, fluid types, and operating conditions. The new models and well-known earlier ones were examined with about 372 additional data samples from four new independent sources. The proposed models showed excellent results for prediction of HTC. Finally, a sensitivity analysis was studied based on the experimental data and the outcomes of the LSFM.

Prognosis of fatigue cracks in an aircraft wing using an adaptive tunable network and guided wave based structural health monitoring

Due to the stochastic behaviour of fatigue crack propagation resulting from the multifarious uncertainties such as aleatory uncertainty and epistemic uncertainty, a synthetic scheme integrating heterogeneous uncertainty resources is needed to make the prognosis of fatigue crack propagation be accurate. In this paper, an on-line updating strategy combining an adaptively tunable hybrid radial basis function (RBF) network and active Lamb waves based structural health monitoring is proposed for prognosis of fatigue cracks in an aircraft wing. A particle filter and Brownian motion with drift and proportionality coefficients are put forward to dynamically access a posteriori estimation of crack state and model parameters. Because of the advantages of flexibility, electrically stabilized and suitable for complex structure, the sensor layer with an embedded network of distributed piezoelectric transducers is utilized to collect Lamb wave signals describing crack states on-line. A hybrid spatial phase difference-based damage index (DI) is employed to capture the characteristics of Lamb wave signals to quantitatively determine the crack length. Furthermore, fatigue tests on the outboard wing of a real airplane are conducted to substantiate the proposed method. The experimental results demonstrate that the hybrid RBF model can timely trap the dynamic characteristics of sensor signals, and effectively predict the varying tendency of cracks growth. The uncertainties during the prognosis of fatigue cracking propagation can be effectively dealt with by combining the dynamic adjustability and the DIs-based on-line monitoring technique.

Hybrid radial basis function DEA and its applications to regression, segmentation and cluster analysis problems

This paper uses a radial basis function (RBF) transformation of data envelopment analysis (DEA) data to perform RBF-DEA. It is shown that the RBF-DEA frontier identifies cases that have average efficiency scores in traditional DEA. The formal identification of average efficiency cases allows decision-makers to use these cases and related information for regression, segmentation and cluster analysis. Additionally, negative inputs and outputs can be used in RBF-DEA and unique ranking of fully efficient cases in traditional DEA can be achieved by further evaluating these fully efficient cases against the average RBF-DEA regression frontier. When compared to traditional cluster analysis, RBF-DEA cluster analysis offers unique advantages in that number of clusters do not need to be mentioned and cluster labels are identified by the RBF-DEA technique. Furthermore, unlike the traditional techniques, RBF-DEA cluster memberships are not sensitive to any initial random starting points.

State of health estimation of lithium-ion battery based on an adaptive tunable hybrid radial basis function network

Accurate state of health (SOH) estimation is critical for the durability and safety of Lithium-ion batteries (LIBs). It is challenging to predict the SOH of LIBs due to the complex aging mechanism. In this paper, a novel adaptive tunable hybrid radial basis function network is proposed for accurate and robust SOH estimation. Firstly, two Kullback-Leibler distances are exploited to extract the dynamic and static characteristics of LIBs during the aging process. Secondly, the hybrid network is combined with the radial basis function network and the autoregressive model. A novel hybrid network state-space model is built to simulate the aging mechanism of LIBs. To increase the adaptive ability of the hybrid network, the structural parameters of the proposed hybrid network are adaptively modulated by Brownian motion modeling and particle filter. The Brownian motion with drift and scale coefficients is introduced in the state-space model to simulate the dynamic aging behavior of LIBs. The particle filter is used to update the structural parameters of the hybrid network in real-time. Furthermore, experiments are conducted on two datasets. The experimental results demonstrate that the proposed model has a high prediction accuracy. Moreover, the batteries with Gaussian white noise and dynamic discharging profiles are adopted to prove the reliability and robustness of the proposed model.

Hybrid radial basis function methods of lines for the numerical solution of viscous Burgers’ equation

An efficient and accurate hybrid radial basis function (HRBF) method is proposed to numerically solve the quasi-linear viscous Burgers’ equation. Two different RBFs are combined: an infinite smooth RBF defined by a shape parameter and a piecewise smooth RBF independent of the shape parameter. This combination formulates a family of HRBF methods, which is then used to approximate the spatial operator of the viscous Burgers equation. An efficient high-order solver is then used to integrate in time the resulting initial value problem. The developed numerical scheme is tested on some benchmark problems varying the Reynolds number. Accuracy and efficiency is validated using $$L_{\infty },~ L_{2}$$ and $$L_{\text {rms}}$$ error norms, as well as the number of nodes N over the domain of influence. A rigorous comparison is conducted against well-known numerical schemes to manifest improved accuracy of the proposed scheme. Eigenvalue stability analysis of the proposed technique is thoroughly discussed and confirmed by numerical examples. The proposed scheme is found a well-behaved alternative to RBF (Kansa) and RBF-PS methods with improved accuracy and good conditioning properties.