Abstract: Gross domestic product (GDP) is an important indicator for determining a country's or region's economic status and development level, and it is closely linked to inflation, unemployment, and economic growth rates. These basic indicators can comprehensively and effectively reflect a country's or region's future economic development. The center of radial basis function neural network and smoothing factor to take a uniform distribution of the random radial basis function artificial neural network will be the focus of this study. This stochastic learning method is a useful addition to the existing methods for determining the center and smoothing factors of radial basis function neural networks, and it can also help the network more efficiently train. GDP forecasting is aided by the genetic algorithm radial basis neural network, which allows the government to make timely and effective macrocontrol plans based on the forecast trend of GDP in the region. This study uses the genetic algorithm radial basis, neural network model, to make judgments on the relationships contained in this sequence and compare and analyze the prediction effect and generalization ability of the model to verify the applicability of the genetic algorithm radial basis, neural network model, based on the modeling of historical data, which may contain linear and nonlinear relationships by itself, so this study uses the genetic algorithm radial basis, neural network model, to make, compare, and analyze judgments on the relationships contained in this sequence.

Abstract: We propose a differential radial basis function (RBF) network termed RBF-DiffNet—whose hidden layer blocks are partial differential equations (PDEs) linear in terms of the RBF—to make the baseline RBF network robust to noise in sequential data. Assuming that the sequential data derives from the discretisation of the solution to an underlying PDE, the differential RBF network learns constant linear coefficients of the PDE, consequently regularising the RBF network by following modified backward-Euler updates. We experimentally validate the differential RBF network on the logistic map chaotic timeseries as well as on 30 real-world timeseries provided by Walmart in the M5 forecasting competition. The proposed model is compared with the normalised and unnormalised RBF networks, ARIMA, and ensembles of multilayer perceptrons (MLPs) and recurrent networks with long short-term memory (LSTM) blocks. From the experimental results, RBF-DiffNet consistently shows a marked reduction in the prediction error over the baseline RBF network (e.g., 41% reduction in the root mean squared scaled error on the M5 dataset, and 53% reduction in the mean absolute error on the logistic map); RBF-DiffNet also shows a comparable performance to the LSTM ensemble but requires 99% less computational time. Our proposed network consequently enables more accurate predictions—in the presence of observational noise—in sequence modelling tasks such as timeseries forecasting that leverage the model interpretability, fast training, and function approximation properties of the RBF network.

Abstract: We present a novel numerical method for solving ordinary differential equations using radial basis function (RBF) network with extreme learning machine algorithm. A single-layer RBF link neural network model has been developed for the proposed method. The weight from the hidden layer to the output layer can be calculated efficiently by extreme learning machine algorithm. The experimental comparison of various methods proves that the proposed method shows better performance than the existing methods.

Abstract: In this paper, a radial basis function neural network (RBFN) model has been trained by canonical particle swarm optimisation (PSO) and improved particle swarm optimisation (IMPSO) algorithms to efficiently predict the exchange rate of Indian rupees against the exchange rate of G-7 countries for future days. We have used two variants of PSO such as canonical PSO and IMPSO for optimising the parameters of radial basis function neural network through learning from the past data of exchange rate prediction. Here, we have considered 43 countries' exchange rates to predict the Indian rupees against the G-7 countries. Forty-three exchange rates have been collected and based on their correlation analysis a dataset has been prepared to validate the proposed model. In addition, a fair comparison has been carried out between IMPSO tuned RBFN and canonical PSO tuned RBFN with respect to the results obtained by varying the number of iterations for future days' prediction. From the experimental results, it is observed that the predictive performance of IMPSO tuned RBFN modelling the case of higher number of iterations is promising vis-à-vis canonical PSO tuned RBFNs model.

Abstract: This paper gives idea about design method for adaptive neural controller is proposed and it is applied to the non-linear system Continuous stirred tank reactor CSTR. The investigating controller used in this paper is designed in tuned with adaptive process. To analyze the performance of effect of foot print of uncertainty on the controllers’ performance two various types of algorithms namely state feedback control and observer based control are used Radial basis function Neural network is utilized for approximation of the nonlinear function . Software validation result of suggested method is discussed below.

Abstract: The determination of The Radial Basis Function Network centers is an open problem. This work determines the cluster centers by a proposed gradient algorithm, using the information forces acting on each data point. These centers are applied to a Radial Basis Function Network for data classification. A threshold is established based on Information Potential to classify the outliers. The proposed algorithms are analysed based on databases considering the number of clusters, overlap of clusters, noise, and unbalance of cluster sizes. Combined, the threshold, and the centers determined by information forces, show good results in comparison to a similar Network with a k-means clustering algorithm.

Abstract: There are many methods can be used to calculate ship's magnetic field such as harmonic wave analysis, finite element method, integral equation method, boundary element method and so on. But these methods generally have disadvantage of complex calculation and poor universality. In this paper, we have built a predicted model based on improved Radial Basis Function (RBF) neural network to study the relationship between ship's important parameters and magnetic field directly. Generally, the parameters of RBF are set by experience. In order to get the best result, we have chosen the spread parameter according to Particle Swarm Optimization (PSO) algorithm and verified the effect of network by an example.

Abstract: The objective of the image restoration process is to improve the high-quality visual resolution from degraded images using various techniques in Artificial Intelligence., utilizing a normalization method, a method of centers and weights that has been adapted from the Radial Basis Function Network (RBFN) is initiated to the Stochastic Normalizations method as a Bayesian Learning algorithm. The normalized form of the RBFN-SB algorithm is derived, and the RBFN input data vector is from a damaged image array raised using Taylor's expansion. Following the dynamics of the normalized technique appeared to be tactful in comparison with the RBFN-SB. The test performance comparable to BN and, concomitantly, better validation losses suitable for ensuring results unpredictability estimation through approximate Bayesian posterior are procured. To test the outcome of the proposed system gave speed up the learning process, with minimum mean squared error (MSE) and produced better results of restoration images from damaged images. In the same form, the normalization accuracy can also be improved notably by the Bayesian learning algorithm.

Abstract: Predicting the mechanical behavior of metallic materials, such as stress-strain curves, is important for studying the plastic behavior of materials. This paper intends to investigate machine learning methods’ capacity to predict the aluminum alloy’s stress-strain curves under different temperature levels. Specifically, three machine learning methods (Gaussian process regression (GPR), neural network (NN), and boosted trees (BT) were employed to predict the stress-strain response of Al6061- T6 at different temperatures, including 25°C, 100°C, 200°C, and 300°C. The performance of the studied machine learning methods has been verified using actual strain-stress measurements collected using uniaxial tensile testing on Al6061-T6. Four statistical scores have been adopted to evaluate the prediction accuracy. Results revealed the potential of machine learning methods in predicting strain-stress measurements. Furthermore, results showed that the NN model dominates the other models by providing a prediction with an averaged mean absolute error percentage of 0.213.

Abstract: This paper describes a new approach for approximating the inverse kinematics of a manipulator using an Ant Colony Optimization (ACO) based RBFN (Radial Basis Function Network). In this paper, a training solution using the ACO and the LMS (Least Mean Square) algorithm is presented in a two-phase training procedure. To settle the problem that the cluster results of k-mean clustering Radial Basis Function (RBF) are easy to be influenced by the selection of initial characters and converge to a local minimum, Ant Colony Optimization (ACO) for the RBF neural networks which will optimize the center of RBF neural networks and reduce the number of the hidden layer neurons nodes is presented. The result demonstrates that the accuracy of Ant Colony Optimization for the Radial Basis Function (RBF) neural networks is higher, and the extent of fitting has been improved.

Abstract: This paper uses a radial basis function (RBF) neural network for star identification. A feature vector consisting of distance and angle cosine values is constructed as a library of recognition feature stars and input to the neural network. Then, the network’s output is the number of the corresponding primary star. Comparing the training efficiency and robustness of the grid algorithm with the BP neural network and radial basis function neural network for star identification, the experimental results show that the radial basis function neural network has a strong anti-interference ability against noise and pseudo-star interference. The following conclusions are drawn from the simulation tests: the sample recognition rate of radial basis function neural network algorithm can reach 96% for star position and star addition noise; when the proportion of pseudo-star reaches 20%, the sample recognition rate of radial basis function neural network algorithm is still higher than grid algorithm and BP neural network, which indicates that the radial basis function neural network algorithm has the solid anti-interference ability to both noise and pseudo-star. Therefore, the radial basis function neural network algorithm based on star Identification has specific application prospects.

Abstract: This paper presents a methodology that uses the central composite design and the radial basis function neural networks in type-1 or in interval type-2 model to generate a network that evaluates quality features in an industrial image processing. The methodology includes a couple of radial basis functions as Huygen’s tractrix and triangular membership functions as complementary contributions that have not been reported in literature as radial basis functions. The advantage of using this proposal is that the training is not required to get an accurate result, also the generation of the IT2 RBFNN fuzzy rule base for evaluating quality characteristics is simplified by using the central composite design method and statistical indicators extracted from the product specification data. Experimental results show an error reduction of 90% when the interval type-2 Mandami Radial basis function neural network was compared against its type-1 counterpart using the Gaussian membership functions onto a radial basis function network. On the other hand, the implementation of the Huygen’s tractrix, found a reduction error of 50% in comparison to the Gaussian function.

Abstract: It is difficult to estimate the relationship between the motion of joint and the motion of image features, making the Calibration-free visual servoing control challenging. In traditional methods, the hand-eye relationship is usually approximated in purely online or offline ways. A practical scheme for robot arm manipulation with both online and offline learning is proposed in this paper. The hand-eye relationship is formulated in a local linear format with Jacobian matrix, which is approximated by radial-basis function network (RBFN). Primitively, the RBFN is trained offline to form a relatively appropriate estimation of the Jacobian matrix, which is the beginning of the online step. Then, an online modification of the RBFN is executed, compensating the error caused by changes of camera's position and pose or insufficient training. The simulation experiments show that the proposed scheme can provide a reliable offline trained model and can adapt well to the changes of camera's position and pose due to the online update law.

Abstract: WANG Jianqiang, HUANG Kaiqi, and SU Jianhua 1) School of Electrical Engineering and Automation, Jiangxi University of Science and Technology, Ganzhou 341000, Jiangxi Province, P. R. China 2) The State Key Laboratory for Management and Control of Complex System, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, P. R. China Abstract: In this paper, we propose a motion estimation method based on a feed-forward radial basis network for grasping arbitrary moving objects. We first employ a kernel correlation filtering (KCF) algorithm to track the target position in real-time and establish the motion model of the target. Using the feed-forward radial base network, we then adjust the sampling time of the Kalman filter (KF) to predict the motion parameters of the target. Since that, we can reduce the computing time and improve the accuracy of the estimation of the motion parameters. Compared with the feed-forward perceptron network, the proposed method shortens the required time for grasping by 20%, which can avoid a failure grasp due to the arbitrary movement of the object in grasping.

Abstract: AI-based treatments have shown promise in a variety of fields, particularly those directly connected to human health. Some AI processors are used to categorize and distinguish groupings and patterns, while others are used to forecast future values based on data from previous study and the environment in which that data was employed. An artificial neural network that employs radial basis functions as activation functions is known as a radial basis function network. The radial basis functions input and the neural parameters are combined linearly to produce the network output. There are several applications for radial-based functional networks, such as function approximation, classification, time series prediction, and system control. In this paper, the RBF network will be used in two phases: the data training phase, where the data is trained with the inputs and outputs to obtain new values for the outputs and compare them with the original outputs, and the testing phase, where only the inputs are entered without the outputs and the outputs are evaluated using the RMSE calculation, where it reached a performance of RMSE of 0.018. In the training phase of utilizing the system, the mistake rate was 0.04 and the success rate was 96%; in the testing phase, the error rate was 0.05 and the success rate was 95%.

Abstract: Fast and accurate diagnosis of the diseases consider one of the major challenges in giving proper treatment. Different techniques have their own limitations in terms of accuracy and time. Neural network technique used as a powerful discriminating classifier for tasks in medical diagnosis for early detection of diseases. It had already been applied in diagnose many diseases, like chronic kidney disease (CKD) which is one of the leading causes of death contributed by other illnesses such as diabetes, hypertension, lupus, anemia or weak bones that lead to bone fractures. In this paper, a deep learning method to perform a both feature extraction and the classification for CKD detection using Radial Basis Function Network as activation function . This network has great ability of accurate and speed diagnosing, so it is useful to use it in medicine to give the doctors or medical team the right diagnoses. Better performance in terms of accuracy, specificity and sensitivity will be selected as classification model. To test the performance of RBF model, a CDK dataset is employed which contains the clinical manifestations of six diseases as a sample. After applying training method, the network will match these manifestations with the manifestations obtained from sample patients to decide right disease which was entered to the program, the result, shows good performance, low error ratio, high accuracy.

Abstract: Three radial basis functions (RBFs): Gaussian RBF, multiquadric RBF, and inverse multiquadric RBF, are compared for the radial basis function network (RBFN) as sparse reconstruction of a non-intrusive reduced order model (ROM) based on proper orthogonal decomposition (POD). Steady-state temperature distributions of an industrial-scale gas boiler by computational fluid dynamic (CFD) simulations are applied as training dataset for the ROM. The optimal number of training samples and truncated eigenmodes are selected by adaptive sampling and projection error, respectively. Sparse data of 16 sensors located in the inner wall of the boiler was applied as an input for the RBFNs of this study for the consideration of realistic application. Parameter study was performed for the shape factor on each RBF and reconstruction error are analyzed as the performance of each RBFN. The RBFN with Gaussian RBF showed the best predictability upon the optimal shape factor. Gaussian RBF is recommended for RBFN as sparse reconstruction under the premise of prior search for optimal shape factor.

Abstract: Abstract We present a novel numerical method for solving ordinary differential equations (ODEs) using Radial Basis Function (RBF) Network with Extreme Learning Machine Algorithm. A single layer Radial Basis Functional Link Neural Network (RBFNN) model has been developed for the proposed method. The weight from the hidden layer to the output layer can be calculated efficiently by Extreme Learning Machine algorithm. The experimental comparison of various methods proves that the proposed method shows better performance than the existing methods.

Abstract: Radial Basis Function networks accuracies mainly affected by its center selection from dataset. K-means (KM) clustering is a widely in numerous field for data classification and centers selection. However, initial centers selection poses high impact on KM clustering outcome. It suffers from its immense reliance on the initial centers selection algorithm from the dataset. KM algorithm has been enhanced for its performance from diverse perspectives over the years. Nonetheless, a good balance between quality and efficiency of the centers selected by the algorithm is not attained. To overcome this issue, this paper proposed an improvement on KM clustering algorithm in getting initial centers and reduce its sensitivity to initial centers. This paper introduce the use of improved K-means (KM) clustering that consider the each point distance as probability for selecting the initial centers with radial basis function network (RBFN) training algorithm. The proposed approach uses improved KM for centers selection in RBFN training algorithm shows accuracy improvement in predictions and with simpler network architecture compared to the conventional RBFN. The proposed network called IKM-RBFN was tested against the conventional RBFN, KM-RBFN, back-propagation neural network and long short-term memory neural network in FOREX EURUSD pair price predictions. The results are compared to proposed method on its root mean square error (RMSE) and mean absolute error (MAE) results. The proposed method shows promising results in improving RMSE accuracy over 20% in compared to other tested networks.

Abstract: The non-iterative structure of radial basis function neural networks makes them more appealing for classification tasks decade after decade. In line with the growth of the training data set, the pattern layer also grows. The unprecedented growth of data with no class labels is becoming a challenge for researchers who are working in data science, big data analysis, etc. Although there is literature witnessed for many algorithms to handle data with no class label. However, neural network-based algorithms with a special characteristic of radial basis neural networks for uncovering class labels are very rare. In this paper, we propose a novel class discovery algorithm that combines the best features of radial basis function neural networks (RBFN) and self-organizing feature map (SOFM). We have taken a few datasets with class label for our experimental work. In the training phase of the network, the training instances are used without class labels. In the test phase, they are validated by combining the predicted class labels with their actual class label. The result shows that the proposed algorithm can be treated as an alternative method for class discovery.

Abstract: Abstract For notifying the properties of special area with similar properties, clustering analysis is really helpful, and neural network methods have ability to create usable model. One of the best ways for clustering is fuzzy c-means, and fuzzy c-means by the basis of fuzzy method divides data set to different clusters. Radial basis function is neural network which is utilizing spread and this algorithm’s layers like input layer, hidden layer and output layer for creating effective neural network. This paper is introduced a novel method, in this method data points (longitude and latitude of main cities of Iran) by using fuzzy c-mean algorithm is divided to different clusters then for each cluster RBF neural networks is defined separately, and this method is FCM-RBF. The outcome of FCM-RBF build neural network for each cluster separately, and result of this study shows that radial basis function neural network can enhance the quality of analysis of outcomes of this kind of clustering and by applying this algorithms different clusters with same properties is calculated and create neural network separately for each cluster, and three clusters are proposed for this algorithms and data points of cluster2 and cluster3 has acceptable rate of adaptability with RBF neural network but data points of cluster1 can’t adapt themselves with neural network perfectly, and validity of outcomes of this clustering increase by using radial basis function neural network. In this algorithm data points of each clusters can separately analyze which is cause better comprehending of study area.

Abstract: Aiming at the problem of prediction accuracy in network situation awareness, a network security situation prediction method based on a generalized radial basis function (RBF) neural network is proposed. This method uses the K-means clustering algorithm to determine the data center and expansion function of the RBF and uses the least-mean-square algorithm to adjust the weights to obtain the nonlinear mapping relationship between the situation value before and after the situation and carry out the situation prediction. Simulation experiments show that this method can obtain situation prediction results more accurately and improve the active security protection of network security. Compared with the PSO-RBF model, AFSA-RBF model, and IAFSA-RBF model, the maximum relative error and minimum relative error of the IAFSA-PSO-RBF model are reduced by 14.27%, 8.91%, and 32.98%, respectively, and the minimum relative error is reduced by 1.69%, 12.97%, and 0.61%, respectively. This shows that the IAFSA-PSO-RBF model has reduced the prediction error interval, and the average relative error is 5%. Compared with the other three models, the accuracy rate is improved by more than 5%, and it has met the requirements for the prediction of the network security situation.