Abstract: This paper presents a novel algorithm for training radial basis function (RBF) networks, in order to produce models with increased accuracy and parsimony. The proposed methodology is based on a nonsymmetric variant of the fuzzy means (FM) algorithm, which has the ability to determine the number and locations of the hidden-node RBF centers, whereas the synaptic weights are calculated using linear regression. Taking advantage of the short computational times required by the FM algorithm, we wrap a particle swarm optimization (PSO) based engine around it, designed to optimize the fuzzy partition. The result is an integrated framework for fully determining all the parameters of an RBF network. The proposed approach is evaluated through its application on 12 real-world and synthetic benchmark datasets and is also compared with other neural network training techniques. The results show that the RBF network models produced by the PSO-based nonsymmetric FM algorithm outperform the models produced by the other techniques, exhibiting higher prediction accuracies in shorter computational times, accompanied by simpler network structures.

Abstract: In this paper, an adaptive dynamic sliding-mode control system (ADSMCS) with recurrent radial basis function network (RRBFN) for indirect field-orientation control induction motor (IM) drive is proposed. The ADSMCS comprises a dynamic sliding-mode controller (DSMC), an RRBFN uncertainty observer and a robust controller. The DSMC is proposed to reduce the chattering phenomenon. However, due to the uncertainty bound being unknown of the switching function for the DSMC, an ADSMCS is proposed to increase the robustness and improve the control performance of IM drive. In the ADSMCS, an RRBFN uncertainty observer is used to estimate an unknown nonlinear time-varying function of lumped parameter uncertainty online. Moreover, the adaptive learning algorithms for the RRBFN are derived using the Lyapunov stability theorem to train the parameters of the RRBFN online. Furthermore, a robust controller is proposed to confront the uncertainties including approximation error, optimal parameter vector and higher order term in Taylor series. A computer simulation and an experimental system are developed to validate the effectiveness of the proposed ADSMCS. All control algorithms are implemented in a TMS320C31 DSP-based control computer. The simulation and experimental results confirm that the ADSMCS grants robust performance and precise response regardless of load disturbances and IM uncertainties.

Abstract: 'Meta-cognitive Radial Basis Function Network' (McRBFN) and its 'Projection Based Learning' (PBL) algorithm for classification problems in sequential framework is proposed in this paper and is referred to as PBL-McRBFN. McRBFN is inspired by human meta-cognitive learning principles. McRBFN has two components, namely the cognitive component and the meta-cognitive component. The cognitive component is a single hidden layer radial basis function network with evolving architecture. In the cognitive component, the PBL algorithm computes the optimal output weights with least computational effort by finding analytical minima of the nonlinear energy function. The meta-cognitive component controls the learning process in the cognitive component by choosing the best learning strategy for the current sample and adapts the learning strategies by implementing self-regulation. In addition, sample overlapping conditions are considered for proper initialization of new hidden neurons, thus minimizes the misclassification. The interaction of cognitive component and meta-cognitive component address the what-to-learn, when-to-learn and how-to-learn human learning principles efficiently. The performance of the PBL-McRBFN is evaluated using a set of benchmark classification problems from UCI machine learning repository and two practical problems, viz., the acoustic emission signal classification and the mammogram for cancer classification. The statistical performance evaluation on these problems has proven the superior performance of PBL-McRBFN classifier over results reported in the literature.

Abstract: In this paper, we present a sequential projection-based metacognitive learning algorithm in a radial basis function network (PBL-McRBFN) for classification problems. The algorithm is inspired by human metacognitive learning principles and has two components: a cognitive component and a metacognitive component. The cognitive component is a single-hidden-layer radial basis function network with evolving architecture. The metacognitive component controls the learning process in the cognitive component by choosing the best learning strategy for the current sample and adapts the learning strategies by implementing self-regulation. In addition, sample overlapping conditions and past knowledge of the samples in the form of pseudosamples are used for proper initialization of new hidden neurons to minimize the misclassification. The parameter update strategy uses projection-based direct minimization of hinge loss error. The interaction of the cognitive component and the metacognitive component addresses the what-to-learn, when-to-learn, and how-to-learn human learning principles efficiently. The performance of the PBL-McRBFN is evaluated using a set of benchmark classification problems from the University of California Irvine machine learning repository. The statistical performance evaluation on these problems proves the superior performance of the PBL-McRBFN classifier over results reported in the literature. Also, we evaluate the performance of the proposed algorithm on a practical Alzheimer's disease detection problem. The performance results on open access series of imaging studies and Alzheimer's disease neuroimaging initiative datasets, which are obtained from different demographic regions, clearly show that PBL-McRBFN can handle a problem with change in distribution.

Abstract: Fast and accurate contingency selection and ranking method has become a key issue to ensure the secure operation of power systems. In this paper multi-layer feed forward artificial neural network (MLFFN) and radial basis function network (RBFN) are proposed to implement the online module for power system static security assessment. The security classification, contingency selection and ranking are done based on the composite security index which is capable of accurately differentiating the secure and non-secure cases. For each contingency case as well as for base case condition, the composite security index is computed using the full Newton Raphson load flow analysis. The proposed artificial neural network (ANN) models take loading condition and the probable contingencies as the input and assess the system security by screening the credible contingencies and ranking them in the order of severity based on composite security index. The numerical results of applying the proposed approach to IEEE 118-bus test system demonstrate its effectiveness for online power system static security assessment. The comparison of the ANN models with the model based on Newton Raphson load flow analysis in terms of accuracy and computational speed indicate that the proposed model is effective and reliable in the fast evaluation of the security level of power systems. The proposed online static security assessment (OSSA) module realized using the ANN models are found to be suited for online application.

Abstract: An artificial neural network is a technique of artificial intelligence that has the ability to learn from experiences, improving its performance by adapting to the changes in the environment. The main advantages of neural networks are: the possibility of efficient manipulation of large amounts of data and its ability to generalize results. Considering the great potential of this technique, this paper aims to establish a comparison between Multilayer Feedforward - a Multilayer Perceptron network (MLP) with feedforward learning - and a Radial Basis Function Network (RBF). The RBF and MLP networks are usually employed in the same kind of applications (nonlinear mapping approximation and pattern recognition), however their internal calculation structures are different. A comparison was made by using experimental data from a microphone installed inside a galvanized iron pipeline of 60 m length, under various operating conditions. The signal from the microphone coupled to a data acquisition board in a microcomputer was decomposed in different frequency noises. The dynamics of these noises in time were used as inputs to the neural models to locate and determine the magnitude of the leaks (model outputs). The results obtained from the test sets, with leaks caused intentionally, showed that the two neural structures were able to detect and locate leaks in pipes. Nevertheless, the Multilayer Perceptron network showed a slightly better performance.

Abstract: We analyze globally convergent, derivative-free trust-region algorithms relying on radial basis function interpolation models. Our results extend the recent work of Conn, Scheinberg, and Vicente [SIAM J. Optim., 20 (2009), pp. 387--415] to fully linear models that have a nonlinear term. We characterize the types of radial basis functions that fit in our analysis and thus show global convergence to first-order critical points for the ORBIT algorithm of Wild, Regis, and Shoemaker [SIAM J. Sci. Comput., 30 (2008), pp. 3197--3219]. Using ORBIT, we present numerical results for different types of radial basis functions on a series of test problems. We also demonstrate the use of ORBIT in finding local minima on a computationally expensive environmental engineering problem involving remediation of contaminated groundwater.

Abstract: In this work we illustrate how approximate dynamic programing can be utilized to address problems of stochastic reachability in infinite state and control spaces. In particular we focus on the reach-avoid problem and approximate the value function on a linear combination of radial basis functions. In this way we get significant computational advantages with which we obtain tractable solutions to problems that cannot be solved via generic space gridding due to the curse of dimensionality. Numerical simulations indicate that control policies coming as a result of approximating the value function of stochastic reachability problems achieve close to optimal performance.

Abstract: Purpose – The purpose of this paper is to propose a novel contribution to adaptive sampling strategies for non‐intrusive reduced order models based on Proper Orthogonal Decomposition (POD). These strategies aim at reducing the cost of optimization by improving the efficiency and accuracy of POD data‐fitting surrogate models to be used in an online surrogate‐assisted optimization framework for industrial design.Design/methodology/approach – The effect of the strategies on the model accuracy is investigated considering the snapshot scaling, the design of experiment size and the truncation level of the POD basis and compared to a state‐of‐the‐art radial basis function network surrogate model on objectives and constraints. The selected test case is a Mach number and angle of attack domain exploration of the well‐known RAE2822 airfoil. Preliminary airfoil shape optimization results are also shown.Findings – The numerical results demonstrate the potential of the capture/recapture schemes proposed for adequately...

Abstract: In industrial design optimization, objectives and constraints are generally given as implicit form of the design variables, and are evaluated through computationally intensive numerical simulation. Under this situation, response surface methodology is one of helpful approaches to design optimization. One of these approaches, known as sequential approximate optimization (SAO), has gained its popularity in recent years. In SAO, the sampling strategy for obtaining a highly accurate global minimum remains a critical issue. In this paper, we propose a new sampling strategy using sequential approximate multi-objective optimization (SAMOO) in radial basis function (RBF) network. To identify a part of the pareto-optimal solutions with a small number of function evaluations, our proposed sampling strategy consists of three phases: (1) a pareto-optimal solution of the response surfaces is taken as a new sampling point; (2) new points are added in and around the unexplored region; and (3) other parts of the pareto-optimal solutions are identified using a new function called the pareto-fitness function. The optimal solution of this pareto-fitness function is then taken as a new sampling point. The upshot of this approach is that phases (2) and (3) add sampling points without solving the multi-objective optimization problem. The detailed procedure to construct the pareto-fitness function with the RBF network is described. Through numerical examples, the validity of the proposed sampling strategy is discussed.

Abstract: In wireless sensor network, the exact positions of the sensor nodes is necessary for location-aware services. Traditional approaches are not producing satisfactory results. In this paper we propose the use of Time Difference of Arrival (TDOA) information with Neural network for accurate node localization. We use two artificial neural network models-Back Propagation Network (BPN) and Radial Basis Function (RBF) Network model for Wireless Sensor Network's node localization problem. Time Difference of Arrival (TDOA) data is used to calculate the distance information from anchor nodes to sensor nodes. This distance information was used to train the neural networks' models. Simulation results show the superiority of Radial Basis Function Network over Back Propagation Network in terms of root mean square error when training data density is high.

Abstract: This paper proposes a novel self-constructing least-Wilcoxon generalized Radial Basis Function Neural-Fuzzy System (LW-GRBFNFS) and its applications to non-linear function approximation and chaos time sequence prediction. In general, the hidden layer parameters of the antecedent part of most traditional RBFNFS are decided in advance and the output weights of the consequent part are evaluated by least square estimation. The hidden layer structure of the RBFNFS is lack of flexibility because the structure is fixed and cannot be adjusted effectively according to the dynamic behavior of the system. Furthermore, the resultant performance of using least square estimation for output weights is often weakened by the noise and outliers. This paper creates a self-constructing scenario for generating antecedent part of RBFNFS with particle swarm optimizer (PSO). For training the consequent part of RBFNFS, instead of traditional least square (LS) estimation, least-Wilcoxon (LW) norm is employed in the proposed approach to do the estimation. As is well known in statistics, the resulting linear function by using the rank-based LW norm approximation to linear function problems is usually robust against (or insensitive to) noises and outliers and therefore increases the accuracy of the output weights of RBFNFS. Several nonlinear functions approximation and chaotic time series prediction problems are used to verify the efficiency of self-constructing LW-GRBFNIS proposed in this paper. The experimental results show that the proposed method not only creates optimal hidden nodes but also effectively mitigates the noise and outliers problems.

Abstract: In this article, a new multivariate radial basis functions neural network model is proposed to predict the complex chaotic time series. To realize the reconstruction of phase space, we apply the mutual information method and false nearest-neighbor method to obtain the crucial parameters time delay and embedding dimension, respectively, and then expand into the multivariate situation. We also proposed two the objective evaluations, mean absolute error and prediction mean square error, to evaluate the prediction accuracy. To illustrate the prediction model, we use two coupled Rossler systems as examples to do simultaneously single-step prediction and multistep prediction, and find that the evaluation performances and prediction accuracy can achieve an excellent magnitude. © 2013 Wiley Periodicals, Inc. Complexity, 2013.

Abstract: This paper proposes the application of a Fully Complex-Valued Radial Basis Function network (FC-RBF), Meta-Cognitive Fully Complex-Valued Radial Basis Function network (Mc-FCRBF) and Extreme Learning Machine (ELM) for the prediction of Parkinson's disease. With the help of Unified Parkinson's Disease Rating Scale (UPDRS), the severity of the Parkinson's disease is predicted and for untreated patients, the UPDRS scale spans the range (0–176). The FC-RBF network uses a fully complex valued activation function sech, which maps cn → c. The performance of the complex RBF network depends on the number of neurons and initialization of network parameters. The implementation of the self-regulatory learning mechanism in the FC-RBF network results in Mc-FCRBF network. It has two components: a cognitive component and a meta-cognitive component. The meta-cognitive component decides how to learn, what to learn and when to learn based on the knowledge acquired by the FC-RBF network. Extreme learning mechanism uses sigmoid activation function and it works with fast speed. In ELM network, the real valued inputs and targets are applied to the network. The result indicates that the Mc-FCRBF network has good prediction accuracy than ELM and FC-RBF network.

Abstract: A tensor is used to describe head-related transfer functions (HRTFs) dependent on frequencies, sound directions and anthropometric parameters. It can represent the multi-dimensional structure of measured HRTFs. To construct a personalization model, high-order singular value decomposition (HOSVD) is firstly applied to extract individual core tensor as the outputs of the model. Some important anthropometric parameters are selected by Laplacian score and correlation analysis between all measured parameters and the individual core tensor. They act as the inputs of the personalization model. Then a nonlinear model is constructed based on radial basis function (RBF) neural network to predict individual HRTFs according to the measured anthropometric parameters. Compared with back-propagation (BP) neural network method, simulation results demonstrate the better performance for predicting individual HRTFs in the midsaggital plane at high elevations.

Abstract: Global gravity field solutions are commonly modelled in spherical harmonic basis functions. Additionally, radial basis functions on the sphere with quasi-local support are used to model regional refinements of gravity fields. However, these functions are usually not orthogonal on a sphere, which makes the modelling process more complex. In this paper we study and compare different radial basis functions and their performance in regional gravity field modelling on the sphere by making use of simulated data. In addition to the type of radial basis function also the size of the study area on the sphere, the point grid, the margins and the method which is used to solve the singular system have to be taken into account. The synthetic signal, which we use in our simulation, is a residual signal in a bandwidth which corresponds to the bandwidth of GOCE satellite gravity observations.

Abstract: Model performance and convergence rate are two key measures for assessing the methods used in nonlinear system identification using Radial Basis Function neural networks. A new extension of the Newton algorithm is proposed to further improve these two aspects by extending the results of recently proposed continuous forward algorithm (CFA) and hybrid forward algorithm (HFA). Computational complexity analysis confirms its efficiency, and numerical examples show that it converges faster and potentially outperforms CFA and HFA.

Abstract: Neural network applications in adaptive multiuser detection (MUD) schemes are suggested here in the context of space division multiple access–orthogonal frequency division multiplexing system. In this paper, various neural network (NN) models like feed forward network (FFN), recurrent neural network (RNN) and radial basis function network (RBFN) are adopted for MUD. MUD using NN models outperforms other existing schemes like genetic algorithm--assisted minimum bit error rate (MBER) and minimum mean square error MUDs in terms of BER performance and convergence speed. Among these NN models, the FNN MUD performs efficiently as RNN in full load scenario, where the number of users is equal to number of receiving antennas. In overload scenario, where the number of users is more than the number of receiving antennas, the FNN MUD performs better than RNN MUD. Further, the RBFN MUD provides a significant enhancement in performance over FNN and RNN MUDs under both overload and full load scenarios because of its better classification ability due to Gaussian nonlinearity. Extensive simulation analysis considering Stanford University Interim channel models applied for fixed wireless applications shows improvement in convergence speed and BER performance of the proposed NN-based MUD algorithms.

Abstract: In this paper, we present an approach for the diagnosis of Autism Spectrum Disorder (ASD) from Magnetic Resonance Imaging (MRI) scans with Voxel-Based Morphometry (VBM) detected features using Projection Based Learning (PBL) algorithm for a Meta-cognitive Radial Basis Function Network (McRBFN) classifier. McRBFN emulates human-like meta-cognitive learning principles. As each sample is presented to the network, the McRBFN uses the estimated class label, the maximum hinge error and class-wise significance to address the self-regulating principles of what-to-learn, when-to-learn and how-to-learn in a meta-cognitive framework. Initially, McRBFN begins with zero hidden neurons and adds required number of neurons to approximate the decision surface. When a neuron is added, its parameters are initialized based on the sample overlapping conditions. The output weights are updated using a PBL algorithm such that the network finds the minimum point of an energy function defined by the hinge-loss error. Moreover, as samples with similar information are deleted, over-training is avoided. The PBL algorithm helps to reduce the computational effort used in training. For simulation studies, we have used MR images from the Autism Brain Imaging Data Exchange (ABIDE) data set. The performance of the PBL-McRBFN classifier is evaluated on complete morphometric features set obtained from the VBM analysis. The performance evaluation study clearly indicates the superior performance of PBL-McRBFN classifier over other classification algorithms.

Abstract: This article uses the cluster dependent weighted fuzzy C-means based radial basis function neural network for comparing the different dimensionality reduction techniques for the fault diagnosis in the rolling element bearing. The vibration signals from normal bearing, bearing with defect on the inner race, and bearing with defect on the outer race were acquired under one radial load and two shaft speeds. These signals were subjected to the wavelet transform based denoising from which several time and frequency domain features were extracted. Dimensionality reduction techniques, namely, principal component analysis, Fisher’s criterion, and separation index, have been used to select the sensitive features. The selected features were used to train and test the radial basis function neural network, where the centers of the radial basis function units have been optimized by the cluster dependent weighted fuzzy C-means and the widths of the radial basis function units have been fixed by trial and error. Finally, a comparison of the dimensionality reduction techniques based on the radial basis function neural network performance is presented

Abstract: The mixed use of different shapes of radial basis functions (RBFs) in radial basis functions neural networks (RBFNNs) is investigated in this paper. For this purpose, we propose the use of a generalised version of the standard RBFNN, based on the generalised Gaussian distribution. The generalised radial basis function (GRBF) proposed in this paper is able to reproduce other different radial basis functions (RBFs) by changing a real parameter ?. In the proposed methodology, a hybrid evolutionary algorithm (HEA) is employed to estimate the number of hidden neuron, the centres, type and width of each RBF associated with each radial unit. In order to test the performance of the proposed methodology, an experimental study is presented with 20 datasets from the UCI repository. The GRBF neural network (GRBFNN) was compared to RBFNNs with Gaussian, Cauchy and inverse multiquadratic RBFs in the hidden layer and to other classifiers, including different RBFNN design methods, support vector machines (SVMs), a sparse probabilistic classifier (sparse multinominal logistic regression, SMLR) and other non-sparse (but regularised) probabilistic classifiers (regularised multinominal logistic regression, RMLR). The GRBFNN models were found to be better than the alternative RBFNNs for almost all datasets, producing the highest mean accuracy rank.

Abstract: Orthogonal frequency division multiplexing (OFDM) combined with multiple input multiple output (MIMO) antennas is one of the promising schemes for high rate data transmission and capacity improvement. However, in these systems, channel estimation task is critical for coherent detection and demodulation. In this study, we have proposed a channel estimator based on radial basis function neural network trained by gradient descent method for MIMO-OFDM systems. Simulation results show that the proposed estimator performs better than other considered channel estimation techniques.