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The purpose of this paper is to provide an effective and simple technique to structural damage identification, particularly to identify a crack in a structure. Artificial neural networks approach is an alternative to identify the extent and location of the damage over the classical methods. Radial basis function (RBF) networks are good at function mapping and generalization ability among the various neural network approaches. RBF neural networks are chosen for the present study of crack identification.

Analyzing the vibration response of a structure is an effective way to monitor its health and even to detect the damage. A novel two‐stage improved radial basis function (IRBF) neural network methodology with conventional RBF in the first stage and a reduced search space moving technique in the second stage is proposed to identify the crack in a cantilever beam structure in the frequency domain. Latin hypercube sampling (LHS) technique is used in both stages to sample the frequency modal patterns to train the proposed network. Study is also conducted with and without addition of 5% white noise to the input patterns to simulate the experimental errors.

The results show a significant improvement in identifying the location and magnitude of a crack by the proposed IRBF method, in comparison with conventional RBF method and other classical methods. In case of crack location in a beam, the average identification error over 12 test cases was 0.69 per cent by IRBF network compared to 4.88 per cent by conventional RBF. Similar improvements are reported when compared to hybrid CPN BPN networks. It also requires much less computational effort as compared to other hybrid neural network approaches and classical methods.

The proposed novel IRBF crack identification technique is unique in originality and not reported elsewhere. It can identify the crack location and crack depth with very good accuracy, less computational effort and ease of implementation.

The Motz problem can be considered as a benchmark problem for testing the performance of numerical methods in the solution of elliptic problems with boundary singularities. The purpose of this paper is to address the solution of the Motz problem using the radial basis function (RBF) method, which is a truly meshfree scheme.

Both the global RBF collocation method (also known as Kansa's method) and the recently proposed local RBF‐based differential quadrature (LRBFDQ) method are considered. In both cases, it is shown that the accuracy of the solution can be significantly increased by using special functions which capture the behavior of the singularity. In the case of global collocation, the functional space spanned by the RBF is enlarged by adding singular functions which capture the behavior of the local singular solution. In the case of local collocation, the problem is modified appropriately in order to eliminate the singularities from the formulation.

The paper shows that the exponential convergence both with increasing resolution and increasing shape parameter, which is typical of the RBF method, is lost in problems containing singularities. The accuracy of the solution can be increased by collocation of the partial differential equation (PDE) at boundary nodes. However, in order to restore the exponential convergence of the RBF method, it is necessary to use special functions which capture the behavior of the solution near the discontinuity.

The paper uses Motz's problem as a prototype for problems described by elliptic partial differential equations with boundary singularities. However, the results obtained in the paper are applicable to a wide range of problems containing boundaries with conditions which change from Dirichlet to Neumann, thus leading to singularities in the first derivatives.

The paper shows that both the global RBF collocation method and the LRBFDQ method, are truly meshless methods which can be very useful for the solution of elliptic problems with boundary singularities. In particular, when complemented with special functions that capture the behavior of the solution near the discontinuity, the method exhibits exponential convergence both with resolution and with shape parameter.

In the new era of highly developed Internet information, the prediction of the development trend of network public opinion has a very important reference significance for monitoring and control of public opinion by relevant government departments.

Aiming at the complex and nonlinear characteristics of the network public opinion, considering the accuracy and stability of the applicable model, a network public opinion prediction model based on the bald eagle algorithm optimized radial basis function neural network (BES-RBF) is proposed. Empirical research is conducted with Baidu indexes such as “COVID-19”, “Winter Olympic Games”, “The 100th Anniversary of the Founding of the Party” and “Aerospace” as samples of network public opinion.

The experimental results show that the model proposed in this paper can better describe the development trend of different network public opinion information, has good stability in predictive performance and can provide a good decision-making reference for government public opinion control departments.

A method for optimizing the central value, weight, width and other parameters of the radial basis function neural network with the bald eagle algorithm is given, and it is applied to network public opinion trend prediction. The example verifies that the prediction algorithm has higher accuracy and better stability.

Machine learning methods have recently gained attention in business applications. We will explore the suitability of machine learning methods, particularly support vector regression (SVR) and radial basis function (RBF) approximation, in forecasting company sales. We compare the one-step-ahead forecast accuracy of these machine learning methods with traditional statistical forecasting techniques such as moving average (MA), exponential smoothing, and linear and quadratic trend regression on quarterly sales data of 43 Fortune 500 companies. Moreover, we implement an additive seasonal adjustment procedure on the quarterly sales data of 28 of the Fortune 500 companies whose time series exhibited seasonality, referred to as the seasonal group. Furthermore, we prove a mathematical property of this seasonal adjustment procedure that is useful in interpreting the resulting time series model. Our results show that the Gaussian form of a moving RBF model, with or without seasonal adjustment, is a promising method for forecasting company sales. In particular, the moving RBF-Gaussian model with seasonal adjustment yields generally better mean absolute percentage error (MAPE) values than the other methods on the sales data of 28 companies in the seasonal group. In addition, it is competitive with single exponential smoothing and better than the other methods on the sales data of the other 15 companies in the non-seasonal group.

The purpose of this research paper is to investigate and model the fused deposition modelling (FDM) process to predict the mechanical attributes of 3D printed specimens.

By exploiting the main effect plots, a Taguchi L18 orthogonal array is used to investigate the effects of such parameters on three mechanical attributes of the 3D printed specimens. A radial-based integrated network is then developed to map the eight FDM parameters to the three mechanical attributes for both PEEK and PEKK. Such an integrated network maps and predicts the mechanical attributes through two consecutive phases that consist of several radial basis functions (RBFs).

Validated on a set of further experiments, the integrated network was successful in predicting the mechanical attributes of the 3D printed specimens. It also outperformed the well-known RBF network with an overall improvement of 24% in the coefficient of determination. The integrated network is also further validated by predicting the mechanical attributes of a medical-surgical implant (i.e. the MidFace Rim) as an application.

The main aim of this paper is to accurately predict the mechanical properties of parts produced using the FDM process. Such an aim requires modelling a highly dimensional space to represent highly nonlinear relationships. Therefore, a radial-based integrated network based on the combination of composition and superposition of radial functions is developed to model FDM using a limited number of data points.

The purpose of this paper is to present a novel algorithm for image inpainting, which has been widely used for removing unwanted objects from images or reconstructing damaged photographs.

An image piecewise inpainting technique based on radial basis function (RBF) is used to transform the 2D image inpainting problem into 3D implicit surface reconstruction problem. And a RBF center reduction method is proposed. By RBF resampling, the algorithm can nicely fix the damaged image or remove specific objects.

Experimental results show that the proposed algorithms can prevent the edge blur caused by the isotropic character of RBF, and effectively reduce the RBF centers without a loss in accuracy.

The proposed inpainting approach is interesting for its combination of RBF method and region segmentation that can handle the restoring of high‐variation areas.

The purpose of this paper is to develop a common remaining shelf life prediction model that is generally applicable for postharvest table grape using an optimized radial basis function (RBF) neural network to achieve more accurate prediction than the current shelf life (SL) prediction methods.

First, the final indicators (storage temperature, relative humidity, sensory average score, peel hardness, soluble solids content, weight loss rate, rotting rate, fragmentation rate and color difference) affecting SL were determined by the correlation and significance analysis. Then using the analytic hierarchy process (AHP) to calculate the weight of each indicator and determine the end of SL under different storage conditions. Subsequently, the structure of the RBF network redesigned was 9-11-1. Ultimately, the membership degree of Fuzzy clustering (fuzzy c-means) was adopted to optimize the center and width of the RBF network by using the training data.

The results show that this method has the highest prediction accuracy compared to the current the kinetic–Arrhenius model, back propagation (BP) network and RBF network. The maximum absolute error is 1.877, the maximum relative error (RE) is 0.184, and the adjusted R² is 0.911. The prediction accuracy of the kinetic–Arrhenius model is the worst. The RBF network has a better prediction accuracy than the BP network. For robustness, the adjusted R² are 0.853 and 0.886 of Italian grape and Red Globe grape, respectively, and the fitting degree are the highest among all methods, which proves that the optimized method is applicable for accurate SL prediction of different table grape varieties.

This study not only provides a new way for the prediction of SL of different grape varieties, but also provides a reference for the quality and safety management of table grape during storage. Maybe it has a further research significance for the application of RBF neural network in the SL prediction of other fresh foods.

The performance measure approach (PMA) is widely adopted for reliability analysis and reliability-based design optimization because of its robustness and efficiency compared to reliability index approach. However, it has been reported that PMA involves repeat evaluations of probabilistic constraints therefore it is prohibitively expensive for many large-scale applications. In order to overcome these disadvantages, the purpose of this paper is to propose an efficient PMA-based reliability analysis technique using radial basis function (RBF).

The RBF is adopted to approximate the implicit limit state functions in combination with latin hypercube sampling (LHS) strategy. The advanced mean value method is applied to obtain the most probable point (MPP) with the prescribed target reliability and corresponding probabilistic performance measure to improve analysis accuracy. A sequential framework is proposed to relocate the sampling center to the obtained MPP and reconstruct RBF until a criteria is satisfied.

The method is shown to be better in the computation time to the PMA based on the actual model. The analysis results of probabilistic performance measure are accurately close to the reference solution. Five numerical examples are presented to demonstrate the effectiveness of the proposed method.

The main contribution of this paper is to propose a new reliability analysis technique using reconstructed RBF approximate model. The originalities of this paper may lie in: investigating the PMA using metamodel techniques, using RBF instead of the other types of metamodels to deal with the low efficiency problem.

The present paper aims to address the description of a numerical optimization procedure, based on mesh morphing, and its application for the improvement of the aerodynamic performance of an industrial glider which suffers of a large separation occurring in the wing–fuselage junction region at high incidence angles.

Shape variations were applied to the baseline configuration through a mesh morphing technique founded on the mathematical framework of radial basis functions (RBF). The aerodynamic solutions were obtained coupling an RANS code with the mesh morphing tool RBF Morph™. Two shape modifiers were set up to generate a parametric numerical model. An optimization procedure, based on a design of experiment sampling, was set up implementing the fully automated workflow within a high performance computing (HPC) environment. The optimal candidates maximizing the aerodynamic efficiency were identified by means of a cubic RBF response surface approach.

The separation was significantly reduced, modifying the local geometry of fuselage and fairing and maintaining the wing aerofoil unchanged. A relevant aerodynamic efficiency improvement was finally gained.

The developed procedure proved to be a very powerful and efficient tool in facing aerodynamic design problems. However, it might be computationally very expensive if a large number of design variables are adopted and, in those cases, the method can be suitably used only within the HPC environment.

Such an optimization study is part of an explorative set of analyses that focused on better addressing the numerical strategies to be used in the development of the EU FP7 Project RBF4AERO.

This paper compares three different radial basis function neural networks, as well as the diffuse element method, according to their ability of approximation. This is very useful for the optimization of electromagnetic devices. Tests are done on several analytical functions and on the TEAM workshop problem 25.