Abstract: The classification of protein structures is essential for their function determination in bioinformatics. At present, a reasonably high rate of prediction accuracy has been achieved in classifying proteins into four classes in the SCOP database according to their primary amino acid sequences. However, for further classification into fine-grained folding categories, especially when the number of possible folding patterns as those defined in the SCOP database is large, it is still quite a challenge. In our previous work, we have proposed a two-level classification strategy called hierarchical learning architecture (HLA) using neural networks and two indirect coding features to differentiate proteins according to their classes and folding patterns, which achieved an accuracy rate of 65.5%. In this paper, we use a combinatorial fusion technique to facilitate feature selection and combination for improving predictive accuracy in protein structure classification. When applying various criteria in combinatorial fusion to the protein fold prediction approach using neural networks with HLA and the radial basis function network (RBFN), the resulting classification has an overall prediction accuracy rate of 87% for four classes and 69.6% for 27 folding categories. These rates are significantly higher than the accuracy rate of 56.5% previously obtained by Ding and Dubchak. Our results demonstrate that data fusion is a viable method for feature selection and combination in the prediction and classification of protein structure.

Abstract: An intelligent sliding-mode control system using a radial basis function network (SMCRBFN) is proposed to control the position of a levitated object of a magnetic levitation system to compensate the uncertainties including the friction force in this study. First, the dynamic model of the magnetic levitation system is derived. Then, a sliding-mode approach is proposed to compensate the uncertainties that occurred in the magnetic levitation system. Moreover, to relax the requirement of uncertainty bound in the design of a traditional sliding-mode control system and further increase the robustness of the magnetic levitation system, a radial basis function network estimator is proposed to estimate the uncertainties of the system dynamics online. The effectiveness of the proposed control scheme is verified by some experimental results. With the proposed SMCRBFN system, the position of the levitated object of the magnetic levitation system possesses the advantages of good transient control performance and robustness to uncertainties for tracking periodic trajectories

Abstract: Function approximation, which finds the underlying relationship from a given finite input-output data is the fundamental problem in a vast majority of real world applications, such as prediction, pattern recognition, data mining and classification. Various methods have been developed to address this problem, where one of them is by using artificial neural networks. In this paper, the radial basis function network and the wavelet neural network are applied in estimating periodic, exponential and piecewise continuous functions. Different types of basis functions are used as the activation function in the hidden nodes of the radial basis function network and the wavelet neural network. The performance is compared by using the normalized square root mean square error function as the indicator of the accuracy of these neural network models.

Abstract: This paper presents a fuzzy hybrid learning algorithm (FHLA) for the radial basis function neural network (RBFNN). The method determines the number of hidden neurons in the RBFNN structure by using cluster validity indices with majority rule while the characteristics of the hidden neurons are initialized based on advanced fuzzy clustering. The FHLA combines the gradient method and the linear least-squared method for adjusting the RBF parameters and the neural network connection weights. The RBFNN with the proposed FHLA is used as a classifier in a face recognition system. The inputs to the RBFNN are the feature vectors obtained by combining shape information and principal component analysis. The designed RBFNN with the proposed FHLA, while providing a faster convergence in the training phase, requires a hidden layer with fewer neurons and less sensitivity to the training and testing patterns. The efficiency of the proposed method is demonstrated on the ORL and Yale face databases, and comparison with other algorithms indicates that the FHLA yields excellent recognition rate in human face recognition.

Abstract: This paper proposes a novel technique that combines orthogonal least-squares (OLS) and enhanced particle swarm optimization (EPSO) algorithms to construct the radial basis function (RBF) network for real-time power dispatch (RTPD). The goals considered are fuel cost, power wheeling cost, and NOx/CO2 emissions. The RBF network is composed of three-layer structures, which contain the input, hidden, and output layer. To simplify the network, the OLS algorithm is used first to determine the number of centers in the hidden layer. With an appropriate network structure, the EPSO algorithm is then used to tune the parameters in the network, including the dilation and translation of RBF centers and the weights between the hidden and output layer. The proposed approach has been tested on the IEEE 30-bus six-generator and practical Taiwan Power Company (Taipower) systems. Testing results indicate that the proposed approach can make a quick response and yield accurate RTPD solutions as soon as the inputs are given. Comparisons of learning performance are made to the existing artificial neural network (ANN), conventional RBF network, and basic particle swarm optimization (PSO) methods

Abstract: A new scheme to estimate the moment of inertia in the servo motor drive system in very low speed is proposed in this paper. The speed estimation scheme in most servo drive systems for low-speed operation is sensitive to the variation of machine parameter, especially the moment of inertia. To estimate the motor inertia value, the observer using the Radial Basis Function Network (RBFN) is applied. A control law for stabilizing the system and adaptive laws for updating both of the weights in the RBFN and a bounding constant are established so that the whole closed-loop system is stable in the sense of Lyapunov. The effectiveness of the proposed inertia estimation is verified by simulations and experiments

Abstract: Purpose – The purpose of this paper is to investigate an alternative approach that can predict non‐linear relations.Design/methodology/approach – An engineered approach to fabric development is described in which a radial basis function network is trained with worsted fabric constructional parameters to predict functional and aesthetic properties of fabrics. An objective method of fabric appearance evaluation with the help of digital image processing is introduced. The prediction of fabric properties by the network with changing basic fibre characteristics and fabric constructional parameters is found to have good correlation with the experimental values of fabric functional and aesthetic properties.Findings – The radial basis function network can successfully predict the fabric functional and aesthetic properties from basic fibre characteristics and fabric constructional parameters with considerable accuracy. The network prediction is in good correlation with the actual experimental data. There is some e...

Abstract: The support vector machine (SVM) has been receiving increasing interest in an area of QSAR study for its ability in function approximation and remarkable generalization performance However, selection of support vectors and intensive optimization of kernel width of a nonlinear SVM are inclined to get trapped into local optima, leading to an increased risk of underfitting or overfitting To overcome these problems, a new nonlinear SVM algorithm is proposed using adaptive kernel transform based on a radial basis function network (RBFN) as optimized by particle swarm optimization (PSO) The new algorithm incorporates a nonlinear transform of the original variables to feature space via a RBFN with one input and one hidden layer Such a transform intrinsically yields a kernel transform of the original variables A synergetic optimization of all parameters including kernel centers and kernel widths as well as SVM model coefficients using PSO enables the determination of a flexible kernel transform according to the performance of the total model The implementation of PSO demonstrates a relatively high efficiency in convergence to a desired optimum Applications of the proposed algorithm to QSAR studies of binding affinity of HIV-1 reverse transcriptase inhibitors and activity of 1-phenylbenzimidazoles reveal that the new algorithm provides superior performance to the backpropagation neural network and a conventional nonlinear SVM, indicating that this algorithm holds great promise in nonlinear SVM learning

Abstract: This paper presents neural-network-based recognition system for automatic light emitting diode (LED) inspection. Two types of neural-networks, back-propagation neural-network (BPNN) and radial basis function network (RBFN), are proposed and tested. The current-voltage (I-V) data from the LED inspection process is used for the network training and testing. This study adopts 300 random picking as network training and employs 100 samples as network testing. The experimental results show that if the classification work is done well, the accuracy of recognition is 100% for BPNN and 96% for RBFN, and the testing speed of the proposed approach is almost one half faster than the traditional inspection system does. The proposed neural-network approach is successfully demonstrated by real data sets and can be effectively developed as a system for a practical application purpose.

Abstract: In this paper, an evolutionary algorithm with spatially distributed surrogates (EASDS) for multiobjective optimization is presented. The algorithm performs actual analysis for the initial population and periodically every few generations. An external archive of the unique solutions evaluated using the actual analysis is maintained to train the surrogate models. The data points in the archive are split into multiple partitions using k-Means clustering. A Radial Basis Function (RBF) network surrogate model is built for each partition using a fraction of the points in that partition. The rest of the points in the partition are used as a validation data to decide the prediction accuracy of the surrogate model. Prediction of a new candidate solution is done by the surrogate model with the least prediction error in the neighborhood of that point. Five multiobjective test problems are presented in this study and a comparison with Nondominated Sorting Genetic Algorithm II (NSGA-II) is included to highlight the benefits offered by our approach. EASDS algorithm consistently reported better nondominated solutions for all the test cases for the same number of actual evaluations as compared to a single global surrogate model and NSGA-II.

Abstract: Direction-dependent scaling, shaping, and rotation of Gaussian basis functions are introduced for maximal trend sensing with minimal parameter representations for input output approximation. It is shown that shaping and rotation of the radial basis functions helps in reducing the total number of function units required to approximate any given input-output data, while improving accuracy. Several alternate formulations that enforce minimal parameterization of the most general radial basis functions are presented. A novel "directed graph" based algorithm is introduced to facilitate intelligent direction based learning and adaptation of the parameters appearing in the radial basis function network. Further, a parameter estimation algorithm is incorporated to establish starting estimates for the model parameters using multiple windows of the input-output data. The efficacy of direction-dependent shaping and rotation in function approximation is evaluated by modifying the minimal resource allocating network and considering different test examples. The examples are drawn from recent literature to benchmark the new algorithm versus existing methods

Abstract: Technical analysis of stocks mainly focuses on the study of irregularities, which is a non-trivial task. Because one time scale alone cannot be applied to all analytical processes, the identification of typical patterns on a stock requires considerable knowledge and experience of the stock market. It is also important for predicting stock market trends and turns. The last two decades has seen attempts to solve such non-linear financial forecasting problems using AI technologies such as neural networks, fuzzy logic, genetic algorithms and expert systems but these, although promising, lack explanatory power or are dependent on domain experts. This paper presents an algorithm, PXtract to automate the recognition process of possible irregularities underlying the time series of stock data. It makes dynamic use of different time windows, and exploits the potential of wavelet multi-resolution analysis and radial basis function neural networks for the matching and identification of these irregularities. The study provides rooms for case establishment and interpretation, which are both important in investment decision making.

Abstract: Radial Basis Function Neural Networks (RBFN) have been recently studied due to their qualification as an universal function approximation. This paper investigates the use of RBF neural networks for software cost estimation. The focus of this study is on the design of these networks, especially their middle layer composed of receptive fields, using two clustering techniques: the C-means and the APC-III algorithms. A comparison between a RBFN using C-means and a RBFN using APC-III, in terms of estimates accuracy, is hence presented. This study uses the COCOMO'81 dataset and data on Web applications from the Tukutuku database.

Abstract: An algorithm is disclosed for constructing nonlinear models from high-dimensional scattered data. The algorithm progresses iteratively adding a new basis function at each step to refine the model. The placement of the basis functions is driven by a statistical hypothesis test that reveals geometric structure when it fails. At each step the added function is fit to data contained in a spatio-temporally defined local region to determine the parameters, in particular, the scale of the local model. The proposed method requires no ad hoc parameters. Thus, the number of basis functions required for an accurate fit is determined automatically by the algorithm. The approach may be applied to problems including modeling data on manifolds and the prediction of financial time-series. The algorithm is presented in the context of radial basis functions but in principle can be employed with other methods for function approximation such as multi-layer perceptrons.

Abstract: This work suggests recurrent neurofuzzy networks as a means to model the thermal condition of power transformers. Experimental results with actual data reported in the literature show that neurofuzzy modeling requires less computational effort, and is more robust and efficient than multilayer feedforward networks, a radial basis function network, and classic deterministic modeling approaches

Abstract: The application of artificial neural network to compressor performance map prediction is investigated. Different types of artificial neural network such as multilayer perceptron network, radial basis function network, general regression neural network, and a rotated general regression neural network proposed by the authors are considered. Two different models are utilized in simulating the performance map. The results indicate that while the rotated general regression neural network has the least mean error and best agreement to the experimental data, it is however limited to curve fitting application. On the other hand, if one considers a tool for curve fitting as well as for interpolation and extrapolation applications, multilayer perceptron network technique is the most powerful candidate. Further, the compressor efficiency based on the multilayer perceptron network technique is determined. Excellent agreement between the predictions and the experimental data is obtained.Copyright © 2007 by ASME

Abstract: Improving the efficiency of ship optimization is crucial for modern ship design. Compared with traditional methods, multidisciplinary design optimization (MDO) is a more promising approach. For this reason, Collaborative Optimization (CO) is discussed and analyzed in this paper. As one of the most frequently applied MDO methods, CO promotes autonomy of disciplines while providing a coordinating mechanism guaranteeing progress toward an optimum and maintaining interdisciplinary compatibility. However, there are some difficulties in applying the conventional CO method, such as difficulties in choosing an initial point and tremendous computational requirements. For the purpose of overcoming these problems, optimal Latin hypercube design and Radial basis function network were applied to CO. Optimal Latin hypercube design is a modified Latin Hypercube design. Radial basis function network approximates the optimization model, and is updated during the optimization process to improve accuracy. It is shown by examples that the computing efficiency and robustness of this CO method are higher than with the conventional CO method.

Abstract: A prediction method for chaotic time series, based on radial basis function (RBF) network, is proposed. First, two important parameters for reconstructing phase space, the time delay and the embedding dimension, are estimated by correlation integral method, and the embedding dimension is the number of input units. Second, RBF centers are optimized by means of the cross iterative fuzzy clustering algorithm (CIFCA) and the regularized orthogonal least squares algorithm (ROISA), and the selected RBF centers construct hidden units. The proposed method centralizes advantages of CIFCA and ROISA, and it can decrease network scale, improve generalization performance, accelerate network training speed and avoid ill-conditioning of learning problems. A case of known chaotic system, Rollser system, verifies validity of the proposed method.

Abstract: A new approach using a radial basis function network (RBFN) for pulse compression is proposed. In the study, networks using 13-element Barker code, 35-element Barker code and 21-bit optimal sequences have been implemented. In training these networks, the RBFN-based learning algorithm was used. Simulation results show that RBFN approach has significant improvement in error convergence speed (very low training error), superior signal-to-sidelobe ratios, good noise rejection performance, improved misalignment performance, good range resolution ability and improved Doppler shift performance compared to other neural network approaches such as back-propagation, extended Kalman filter and autocorrelation function based learning algorithms. The proposed neural network approach provides a robust mean for pulse radar tracking.

Abstract: Welding shrinkage and distortion affect the shape, dimensional accuracy and strength of the finished product. This work concerns the prediction of welding distortion in a pulsed metal inert gas welding (PMIGW) process. Six different types of radial basis function network (RBFN) models have been developed to predict the distortion of welded plates. Six process parameters, namely, pulse voltage, background voltage, pulse duty factor, pulse frequency, wire feed rate and the welding speed, along with the root mean square (RMS) values of two sensor signals, namely, the welding current and the voltage signals, are used as input variables of these models. The angular distortion and the transverse shrinkage of the welded plate are considered as the output variables. Inclusion of sensor signals in the models, as developed in this work, results in better output prediction.

Abstract: This paper proposes a new method for electricity price forecasting. The proposed method is based on the regression tree and NRBFN (Normalized Radial Basis Function Network) of ANN. The former is used to evaluate if-then rules and classify input data into some clusters. The latter is employed to calculate more accurate predicted values. The regression tree is one of data-mining techniques that extract if-then rules from database. NRBFN is an extension of RBFN (Radial Basis Function Network) that improves the generalization ability of RBFN. The effectiveness of the proposed method is demonstrated for real data of on-step ahead electricity price forecasting.

Abstract: This paper presents a new multiobjective cooperative–coevolutive hybrid algorithm for the design of a Radial Basis Function Network (RBFN). This approach codifies a population of Radial Basis Functions (RBFs) (hidden neurons), which evolve by means of cooperation and competition to obtain a compact and accurate RBFN. To evaluate the significance of a given RBF in the whole network, three factors have been proposed: the basis function’s contribution to the network’s output, the error produced in the basis function radius, and the overlapping among RBFs. To achieve an RBFN composed of RBFs with proper values for these quality factors our algorithm follows a multiobjective approach in the selection process. In the design process, a Fuzzy Rule Based System (FRBS) is used to determine the possibility of applying operators to a certain RBF. As the time required by our evolutionary algorithm to converge is relatively small, it is possible to get a further improvement of the solution found by using a local minimization algorithm (for example, the Levenberg–Marquardt method). In this paper the results of applying our methodology to function approximation and time series prediction problems are also presented and compared with other alternatives proposed in the bibliography.

Abstract: Based on radial basis functions approximation, we develop in this paper a new com-putational algorithm for numerical differentiation. Under an a priori and an a posteriori choice rules for the regularization parameter, we also give a proof on the convergence error estimate in reconstructing the unknown partial derivatives from scattered noisy data in multi-dimension. Numerical examples verify that the proposed regularization strategy with the a posteriori choice rule is effective and stable to solve the numerical differential problem.

Abstract: The distance calculation performed by a distance relay is incorrect due to ground fault resistance, prefault system conditions, mutual coupling effect and shunt capacitance influences. The problem ...