Abstract: In this paper, an efficient mesh deformation technique for hybrid-unstructured grids, based on radial basis functions, has been developed. The principle procedure adopted for this scheme can be divided into two steps. First, a series of radial basis functions are constructed by an interpolation method according to the displacements of moving boundary points. Later, the displacements of all points in the computation domain are determined by the aforementioned radial basis function series. To improve the efficiency, data reduction should be introduced into the interpolation process. Consequently, a multilevel subspace radial basis function interpolation method based on a “double-edged” greedy algorithm is presented to create an approximate interpolation for all moving boundary points. This method is computationally efficient, preserves orthogonality, and has no dependency on the type of flow solver. Typical deformation problems of a LANN wing, DLR-F6 wing–body–nacelle–pylon configuration and DLR-F11 high-li...

Abstract: Drought forecasting with proper accuracy, notably helps the drought management, and therefore, reduces the damages caused by drought. The aim of this study is to forecast the drought at short-, mid-, and long-term time scales. To this aim, the Standard Precipitation Index (SPI) was calculated on 3, 6, 9, 12, and 24-month time scales based on monthly precipitation data over a 35-year period from 1972 to 2006 in Gorganroud basin. After monitoring the drought, according to the SPI time series and applying six approaches of neural networks, drought forecasting was provided. In the present study, utilized neural networks were Recursive Multi-Step Multi-Layer Perceptron (RMSMLP), Direct Multi-Step Multi-Layer Perceptron (DMSMLP), Recursive Multi-Step Radial Basis Function (RMSRBF), Direct Multi-Step Radial Basis Function (DMSRBF), Recursive Multi-Step Generalized Regression Neural Network (RMSGRNN), and Direct Multi-Step Generalized Regression Neural Network (DMSGRNN). MLP was used in previous studies, in this study this network is applied as a basis for comparing the performance of statistical neural networks (RBF and GRNN). The results based on R2, RMSE, and MAE, showed the forecasting accuracy decreased by increasing lead time of forecasting and increased while SPI time-scale increased. Moreover, recursive models reflected better performance at smaller time scales of SPI, whereas direct models showed better accuracy at longer time scales of SPI. According to the results of drought class forecasting, recursive models performed better than direct models. Generally, the results showed that RBF and GRNN had the best performance in forecasting the drought index and drought class, respectively.

Abstract: Daily Weather forecasting is used for multiple reasons in multiple areas like agriculture, energy supply, transportations, etc. Accuracy of weather conditions shown in forecast reports is very necessary. In this paper, the review is conducted to investigate a better approach for forecasting which compares many techniques such as Artificial Neural Network, Ensemble Neural Network, Backpropagation Network, Radial Basis Function Network, General Regression Neural Network, Genetic Algorithm, Multilayer Perceptron, Fuzzy clustering, etc. which are used for different types of forecasting. Among which neural network with the backpropagation algorithm performs prediction with minimal error. Neural network is a complex network which is self-adaptive in nature. It learns by itself using the training data and generates some intelligent patterns which are useful for forecasting the weather. This paper reviews various techniques and focuses mainly on neural network with back propagation technique for daily weather forecasting. The technique uses 28 input parameters to forecast the daily weather in terms of temperature, rainfall, humidity, cloud condition, and weather of the day.

Abstract: In this paper a new technique is presented for transforming the domain integral related to the source term that characterizes the Poisson Equation, within the scope of the boundary element method, for two-dimensional problems. Similarly to the Dual Reciprocity Technique, the proposed scheme avoids domain discretization using primitive radial basis functions; however, it transforms the domain integral into a single boundary integral directly. The proposed procedure is simpler, more versatile and some useful and modern techniques related to radial basis function theory can be applied. Numerical tests show the accuracy of the proposed technique for a simple class of complete radial interpolation functions, pointing out the importance of internal poles and the potential of applying fitting interpolation schemes to minimize the computational storage, particularly considering more complex future approaches, in which a mass matrix may be generated. For the analysis of the accuracy and convergence of the proposed method, results are compared with those obtained using Dual Reciprocity, using known analytical solutions for reference.

Abstract: This paper studies the generalization performance of radial basis function (RBF) networks using local Rademacher complexities. We propose a general result on controlling local Rademacher complexities with the L-1-metric capacity. We then apply this result to estimate the RBF networks' complexities, based on which a novel estimation error bound is obtained. An effective approximation error bound is also derived by carefully investigating the Holder continuity of the l(p) loss function's derivative. Furthermore, it is demonstrated that the RBF network minimizing an appropriately constructed structural risk admits a significantly better learning rate when compared with the existing results. An empirical study is also performed to justify the application of our structural risk in model selection.

Abstract: The majority of cities are rapidly growing. This makes the monitoring and modeling of urban change’s spatial patterns critical to urban planners, decision makers, and environment protection activists. Although a wide range of methods exists for modeling and simulating urban growth, machine learning ML techniques have received less attention despite their potential for producing highly accurate predictions of future urban extents. The aim of this study is to investigate two ML techniques, namely radial basis function network RBFN and multi-layer perceptron MLP networks, for modeling urban change. By predicting urban change for 2010, the models’ performance is evaluated by comparing results with a reference map and by using a set of pertinent statistical measures, such as average spatial distance deviation and figure of merit. The application of these techniques employs the case study area of Mumbai, India. The results show that both models, which were tested using the same explanatory variables, produced promising results in terms of predicting the size and extent of future urban areas. Although a close match between RBFN and MLP is observed, RBFN demonstrates higher spatial accuracy of prediction. Accordingly, RBFN was utilized to simulate urban change for 2020 and 2030. Overall, the study provides evidence that RBFN is a robust and efficient ML technique and can therefore be recommended for land use change modeling.

Abstract: The paper proposes a learning method for an evolving Radial Basis Neural Network that makes it possible in an online mode to adjust not only synaptic weights but also parameters of the radial basis functions and the network architecture. A special feature of architecture learning is that a number of neurons in the network can both increase and decrease with a sequential stream of information at the system input. The implementation of the proposed algorithms has low computational complexity. The proposed evolving neural network can process data in an online mode.

Abstract: The aim of this study is to evaluate the influence of temperature, moisture and frequency on nine honeys from viscoelastic (complex viscosity, η ∗ , loss modulus, G ″, and storage modulus, G ′) point of view using artificial neural networks (ANN) and adaptive neuro-fuzzy inference system (ANFIS). The temperature has ranged between 5 and 40 °C, the moisture content 16.04 and 17.82% and the frequency 0.1 and 10 Hz. Artificial neural networks (Multilayer perceptron – MLP, Probabilistic neural network – PNN, Radial basis function network – RBF and Recurrent network – RN) have been used to evaluate their model of prediction usefulness. Keeping into account the statistical parameters values, it seems that the ANNs methodology predicts better the evolution of viscoelastic parameters of honey in function of temperature, frequency and moisture content than ANFIS.

Abstract: In this paper, a local meshless method is presented, and this method is based on the linear combination of moving least squares and local radial basis functions in the same compact support domain, by changing the coefficient of the linear combination, the new method possesses the properties of moving least squares approximation and local radial basis functions, because of the local property of this method, it gives us the convenience of computing and it is suitable for practical problems. Numerical experiments are given to demonstrate the accuracy, effectiveness and feasibility of this method.

Abstract: This paper presents a method for the prediction of NO x emissions in a biomass combustion process through the combination of flame radical imaging, contourlet transform and Zernike moment (CTZM), and least squares support vector regression (LS-SVR) modeling. A novel feature extraction technique based on the CTZM algorithm is developed. The contourlet transform provides the multiscale decomposition for flame radical images and the selected operator based on Zernike moments is designed to provide the well-defined structure for the images. The resulted image features are a variable structure, which is originated from the CTZM. Finally, the variable features of the images of four flame radicals (OH*, CN*, CH*, and $\text{C}^{\ast }_{2}$ ) are defined. The relationship between the variable features of radical images and NO x emissions is established through radial basis function network modeling, SVR modeling, and the LS-SVR modeling. A comparison between the three modeling approaches shows that the LS-SVR model outperforms the other two methods in terms of root-mean-square error and mean relative error criteria. In addition, the structure of the image features has a significant impact on the performance of the prediction models. The test results obtained on a biomass-gas fired test rig show the effectiveness of the proposed technical approach for the prediction of NO x emissions.

Abstract: In this paper, Radial Basis Function (RBF) neural Network has been implemented on eight directional values of gradient features for handwritten Hindi character recognition. The character recognition system was trained by using different samples in different handwritings collected of various people of different age groups. The Radial Basis Function network with one input and one output layer has been used for the training of RBF Network. Experiment has been performed to study the recognition accuracy, training time and classification time of RBF neural network. The recognition accuracy, training time and classification time achieved by implementing the RBF network have been compared with the result achieved in previous related work i.e. Back propagation Neural Network. Comparative result shows that the RBF with directional feature provides slightly less recognition accuracy, reduced training and classification time.

Abstract: In this paper, a new constrained error variable similar to sliding mode surface (SMC) is pro- posed to ensure a prescribed position tracking performance of a robot manipulator. A decentralized controller using this constrained error variable and a radial basis function network (RBF) is designed. The proposed decentralized and constrained control system ensures a prescribed transient and steady- state time positioning performance of the decentralized manipulator components without violation of the prescribed performance. The effectiveness of the proposed decentralized and robust control scheme was determined by comparing the results of simulated and experimental evaluation with the conven- tional SMC and finite-time terminal SMC methods.

Abstract: The air transport industry crucially depends on traffic forecasting for supporting management decisions. In this study, a singular spectrum analysis (SSA)-based ensemble forecasting modeling approach is proposed. The original air passenger time series is first decomposed into three components: trend, seasonal oscillations, and irregular component. The trend is predicted by generalized regression neural network (GRNN), whereas seasonal oscillations are predicted by radial basis function networks (RNFNs). The empirical results of Hong Kong (HK) air passenger data show a significant improvement of the proposed ensemble method in comparison to other results of competing models.

Abstract: It is known that interpolation with radial basis functions of the same shape can guarantee a nonsingular interpolation matrix, whereas little was known when one uses various shapes. In this paper, we prove that functions from a class of compactly supported radial basis functions are convex on a certain region; based on this local convexity and other local geometrical properties of the interpolation points, we construct a sufficient condition which guarantees diagonally dominant interpolation matrices for radial basis functions interpolation with different shapes. The proof is constructive and can be used to design algorithms directly. Numerical examples show that the scheme has a low accuracy but can be implemented efficiently. It can be used for inaccurate models where efficiency is more desirable. Large scale 3D implicit surface reconstruction problems are used to demonstrate the utility and reasonable results can be obtained efficiently.

Abstract: Visualizing high dimensional data by projecting them into two or three dimensional space is one of the most effective ways to intuitively understand the data's underlying characteristics, for example their class neighborhood structure. While data visualization in low dimensional space can be efficient for revealing the data's underlying characteristics, classifying a new sample in the reduced-dimensional space is not always beneficial because of the loss of information in expressing the data. It is possible to classify the data in the high dimensional space, while visualizing them in the low dimensional space, but in this case, the visualization is often meaningless because it fails to illustrate the underlying characteristics that are crucial for the classification process. In this paper, the performance-preserving property of the previously proposed Restricted Radial Basis Function Network in reducing the dimension of labeled data is explained. Here, it is argued through empirical experiments that the internal representation of the Restricted Radial Basis Function Network, which during the supervised learning process organizes a visualizable two dimensional map, does not only preserve the topographical structure of high dimensional data but also captures their class neighborhood structures that are important for classifying them. Hence, unlike many of the existing dimension reduction methods, the Restricted Radial Basis Function Network offers two dimensional visualization that is strongly correlated with the classification process.

Abstract: This paper's purpose is to provide a numerical scheme to approximate solutions of the nonlinear Klein-Gordon equation by applying the multiquadric quasi-interpolation scheme and the integrated radial basis function network scheme. Our scheme uses θ-weighted scheme for discretization of the temporal derivative and the integrated form of the multiquadric quasi-interpolation scheme for approximation of the unknown function and its spatial derivative. To confirm the accuracy and ability of the presented scheme, this scheme is applied on some test experiments and the numerical results have been compared with the exact solutions. Furthermore, it should be emphasized that with the presently available computing power, it has become possible to develop realistic mathematical models for the complicated problems in science and engineering. The mathematical description of various processes such as the nonlinear Klein-Gordon equation occurring in mathematical physics leads to a nonlinear partial differential equation. However, the mathematical model is only the first step towards the solution of the problem under consideration. The development of the well-documented, robust and reliable numerical tech- nique for handing the mathematical model under consideration is the next step in the solution of the problem. This second step is at least as important as the first one. Therefore, the robustness, the efficiency and the reliability of the numerical technique have to be checked carefully.

Abstract: Self-organizing map (SOM) is a powerful paradigm that is extensively applied for clustering and visualization purpose. It is also used for regression learning, especially in robotics, thanks to its ability to provide a topological projection of high dimensional non linear data. In this case, data extracted from the SOM are usually restricted to the best matching unit (BMU), which is the usual way to use SOM for classification , where class labels are attached to individual neurons. In this article, we investigate the influence of considering more information from the SOM than just the BMU when performing regression. For this purpose , we quantitatively study several output functions for the SOM, when using these data as input of a linear regression, and find that the use of additional activities to the BMU can strongly improve regression performance. Thus, we propose an unified and generic framework that embraces a large spectrum of models from the traditional way to use SOM, with the best matching unit as output, to models related to the radial basis function network paradigm, when using local receptive field as output.

Abstract: This chapter presents a control approach for robotic manipulators based on a discrete-time sliding mode control which has received much less coverage in the literature with respect to continuous time sliding-mode strategies. This is due to its major drawback, consisting in the presence of a sector, of width depending on the available bound on system uncertainties, where robustness is lost because the sliding mode condition cannot be exactly imposed. For this reason, only ultimate boundedness of trajectories can be guaranteed, and the larger the uncertainties affecting the system are, the wider is the bound on trajectories which can be guaranteed. As a possible solution to this problem, in this chapter a discontinuous control law has been proposed, employing a controller inside the sector based on an estimation, as accurate as possible, of the overall effect of uncertainties affecting the system. Different solutions for obtaining this estimate have been considered and the achievable performances have be compared using experimental data. The first approach consists in estimating the uncertain terms by a well established method which is an adaptive on-line procedure for autoregressive modeling of non-stationary multivariable time series by means of a Kalman filtering. In the second solution, radial basis neural networks are used to perform the estimation of the uncertainties affecting the system. The proposed control system is evaluated on the ERICC robot arm. Experimental evidence shows satisfactory trajectory tracking performances and noticeable robustness in the presence of model inaccuracies and payload perturbations.

Abstract: Larger Electric Vehicles' penetration can change significantly load profiles in distribution grids. In order to protect the grid against peak demand caused by Electric Vehicles, cooperative techniques are developed, providing the ability to coordinate Electric Vehicles charging and thus shift power demand to off-peak periods. Therefore reliable prediction of future energy demand considering generation and profiles of other uncontrollable loads on distribution grid, can help better exploiting Electric Vehicle flexibility. This paper proposes a novel hybrid short-term load forecasting model coupling Singular Spectrum Analysis with Radial Basis Function network to improve electric power prediction accuracy regarding the existing radial basis function approach. These two techniques are compared and evaluated by absolute forecast errors and time span consistency. Then the hybrid model is exploited in a demand response strategy to optimize the charging timing of Electric Vehicles whereby the charging load is shifted and hence the overall peak demand reduced.

Abstract: For a single hidden layer feedforward artificial neural network to possess the universal approximation property, it is sufficient that the hidden layer nodes activation functions are continuous non-polynomial function It is not required that the activation function be a sigmoidal function In this paper a simple continuous, bounded, non-constant, differentiable, non-sigmoid and non-polynomial function is proposed, for usage as the activation function at hidden layer nodes The proposed activation function does require the computation of an exponential function, and thus is computationally less intensive as compared to either the log-sigmoid or the hyperbolic tangent function On a set of 10 function approximation tasks we demonstrate the efficiency and efficacy of the usage of the proposed activation functions The results obtained allow us to assert that, at least on the 10 function approximation tasks, the results demonstrate that in equal epochs of training, the networks using the proposed activation function reach deeper minima of the error functional and also generalize better in most of the cases, and statistically are as good as if not better than networks using the logistic function as the activation function at the hidden nodes

Abstract: In this chapter we presented different neural network methods for the solution of differential equations mainly Multilayer perceptron neural network, Radial basis function neural network, Multiquadric radial basis function network, Cellular neural network, Finite element neural network and Wavelet neural network. Recent development in all the above given methods has been also presented in this chapter to get better knowledge about the subject.

Abstract: Currently, there is a need in all disciplines for efficient and powerful machine learning (ML) algorithms for handling offline and real-time nonlinear data. Industrial applications abound from real-time control systems to modeling and simulation of complex systems and processes. Certain ML methods have become popular with researchers and engineers. Such techniques include fuzzy systems (FSs), artificial neural networks (ANNs), radial basis function (RBF) networks, and support vector regression (SVR) machines. Historically, polynomial-based learning machines (PLMs) based on the group method of data handling (GMDH) model have enjoyed usage similar to that of these other methods. However, unwieldy kernel functions in the form of large high-order polynomials, and relatively limited computer speed and capacity, have limited the use of PLMs to comparatively small problems with low dimensionality and simple functional relationships. Thus, true polynomial-based ML solutions have drifted out of vogue for at least two decades. This work attempts to reinvigorate the interest in PLMs by introducing a novel practical implementation called PolyNet. It will be shown that once certain algorithms are applied to the generation, training, and functional operation of PLMs, they can compete on par with or better than methods currently in use.

Abstract: Emotion play an important role at several activities in the present world. Human decision making, cognitive process and interaction between human & machine all the activities depends on human emotions. Facial expression, musical activities and several approaches used to find the human emotions. In this paper EEG is used to find the accurate emotion. Emotion classification is the huge task. Classification of the human emotion is a process that merges the feature selection and provides the class labels for the data. The proposed work has four stages which include preprocessing, feature extraction, feature selection and classification. This paper uses a Radial Basis Function Network with trained by Evolution algorithm and particle Swarm Optimization is used to select the particular features in the feature selection process. The result of the network will classify the human emotions into arousal and valence emotion. Based on the classification, different emotion level accuracy has to be validated.