Abstract: This paper introduces a three-step framework for classifying multiclass radiography images The first step utilizes a de-noising technique based on wavelet transform (WT) and the statistical Kolmogorov Smirnov (KS) test to remove noise and insignificant features of the images An unsupervised deep belief network (DBN) is designed for learning the unlabelled features in the second step Although small-scale DBNs have demonstrated significant potential, the computational cost of training the restricted Boltzmann machine is a major issue when scaling to large networks Moreover, noise in radiography images can cause a significant corruption of information that hinders the performance of DBNs The combination of WT and KS test in the first step helps improve performance of DBNs Discriminative feature subsets obtained in the first two steps serve as inputs into classifiers in the third step for evaluations Five frequently used classifiers including naive Bayes, radial basis function network, random forest, sequential minimal optimization, and support vector machine and four different case studies are implemented for experiments using the Image Retrieval in Medical Application data set The experimental results show that the three-step framework has significantly reduced computational cost and yielded a great performance for multiclass radiography image classification Along with effective applications in image processing in other fields published in the literature, deep learning network in this paper has again demonstrated its robustness in handling a complex set of medical images This implies that the proposed approach can be implemented in real practice for analysing noisy radiography images, which have many useful medical applications such as diagnosis of diseases related to lung, breast, musculoskeletal or pediatric studies

Abstract: The chamber pressure modeling of the industrial coke furnace is difficult due to the flame instability in the fuel burner and various disturbances. To deal with this issue, a new optimization method using radial basis function (RBF) neural network is proposed to improve the modeling accuracy and simplify the modeling structure. An improved multi-objective evolutionary algorithm (MOEA) is proposed to optimize the input layer, the hidden layer, and the parameters of the basis functions of the RBF neural network. The structure/parameter encoding and local search, prolong and pruning operators are designed to make MOEA suitable for optimization of the RBF neural network. Once a group of Pareto optimal solutions is derived, the RBF neural network with good generalization capability can be chosen succinctly in terms of root-mean-square error of a selected unused dataset. It shows that only a little prior knowledge of the plant is required and the approach has efficiently compromised between the generalization capability, approximation performance, and structure simplification of the RBF neural network when tested on a nonlinear dynamic function and the industrial chamber pressure.

Abstract: We propose a novel nearest-neighbors approach to organize and curb the growth of radial basis function network in kernel adaptive filtering (KAF). The nearest-instance-centroid-estimation (NICE) kernel least-mean-square (KLMS) algorithm provides an appropriate time-space tradeoff with good performance. Its centers in the input/feature space are organized by quasi-orthogonal regions for greatly simplified filter evaluation. Instead of using all centers to evaluate/update the function approximation at every new point, a linear search among the iteratively-updated centroids determines the partial function to be used, naturally forming locally-supported partial functionals. Under this framework, partial functionals that compose the adaptive filter are quickly stored/retrieved based on input, each corresponding to a specialized “spatial-band” subfilter. The filter evaluation becomes the update of one of the subfilters, creating a content addressable filter bank (CAFB). This CAFB is incrementally updated for new signal applications with mild constraints, always using the past-learned partial filter sums, opening the door for transfer learning and significant efficiency for new data scenarios, avoiding training from scratch as have been done since the invention of adaptive filtering. Using energy conservation relation, we show the sufficient condition for mean square convergence of the NICE-KLMS algorithm and establish the upper and lower bounds of steady-state excess-mean-square-error (EMSE). Simulations on chaotic time-series prediction demonstrate similar levels of accuracy as existing methods, but with much faster computation involving fewer input samples. Simulations on transfer learning using both synthetic and real-world data demonstrate that NICE CAFB can leverage previously learned knowledge to related task or domain.

Abstract: An adaptive robust control system is considered for dual-arm manipulators (DAM) using the combination of second-order sliding mode control (SOSMC) and neural networks. The SOSMC deals with the system robustness when faced with external disturbances and parametric uncertainties. Meanwhile, the radial basis function network (RBFN) is to constitute an adaptation mechanism for approximating the unknown dynamic model of DAM. The stability of model estimator-integrated controller is analyzed using Lyapuov theory. To show the effectiveness of proposed controller, a four DOFs-DAM is applied as an illustrating example. The results reveal that the controller works well, excellently adapt to no information of robot modeling.

Abstract: In this paper, the use of radial basis function network (RBFN) for simultaneous online identification and indirect adaptive control of nonlinear dynamical systems is demonstrated. The motivation of using RBFN comes from the simplicity of its structure and simpler mathematical formulation, which gives it an advantage over multi-layer feed-forward neural network (MLFFNN). Since most processes are nonlinear, the use of conventional proportional-integral-derivative controller is not useful. Most of the time plant’s dynamics information is not available. This creates another limitation on the use of conventional control techniques, which works only if plant’s dynamics information is available. The proposed controller is tested for parameter variations and disturbance effects. Simulation results showed that RBFN is able to capture the unknown dynamics as well as simultaneously able to adaptively control the plant. It is also found to compensate the effects of parameter variations and disturbances. The comparative analysis is also done with MLFFNN in each simulation example, and it is found that performance of RBFN is better than that of MLFFNN.

Abstract: We present in this paper comparisons on the performances among five typical radial basis functions methods, namely radial basis collocation method (RBCM), radial basis Galerkin method (RBGM), compactly supported radial basis collocation method (CSRBCM), compactly supported radial basis Galerkin method (CSRBGM), and finite subdomain radial basis collocation method (FSRBCM), for solving problems arising from engineering industries and applied sciences. Numerical comparison results demonstrate that the RBCM and FSRBCM possess high accuracy and superior convergence rates in which the FSRBCM particularly attains higher accuracy for problems with large gradients. The FSRBCM, CSRBCM and RBCM are computationally efficient while the CSRBCM, CSRBGM and FSRBCM can greatly improve the ill-conditioning of the resultant matrix. In conclusion, its advantages on high accuracy; exponential convergence; well-conditioning; and effective computation make the FSRBCM a first-choice among the five radial basis functions methods.

Abstract: Many existing results on fault-tolerant algorithms focus on the single fault source situation, where a trained network is affected by one kind of weight failure. In fact, a trained network may be affected by multiple kinds of weight failure. This paper first studies how the open weight fault and the multiplicative weight noise degrade the performance of radial basis function (RBF) networks. Afterward, we define the objective function for training fault-tolerant RBF networks. Based on the objective function, we then develop two learning algorithms, one batch mode and one online mode. Besides, the convergent conditions of our online algorithm are investigated. Finally, we develop a formula to estimate the test set error of faulty networks trained from our approach. This formula helps us to optimize some tuning parameters, such as RBF width.

Abstract: Diabetes is one of the foremost causes for the increase in mortality among children and adults in recent years. Classification systems are being used by doctors to analyse and diagnose the medical data. Radial basis function neural networks are more attractive for classification of diseases, especially in diabetes classification, because of it’s non iterative nature. Radial basis function neural networks are four layer feed forward neural network with input layer, pattern layer, summation layer and the decision layer respectively. The size of the pattern layer increases on par with training data set size. Though various attempts have made to solve this issue by clustering input data using different clustering algorithms like k-means, k-medoids, and SOFM etc. However main difficulty of determining the optimal number of neurons in the pattern layer remain unsolved. In this paper, we present a new model based on cluster validity index with radial basis neural network for classification of diabetic patients data. We employ cluster validity index in class by class fashion for determining the optimal number of neurons in pattern layer. A new convex fitness function has also been designed for bat inspired optimization algorithm to identify the weights between summation layer and pattern layer. The proposed model for radial basis function neural network is tested on Pima Indians Diabetes data set and synthetic data sets. Experimental results proved that our approach performs better in terms of accuracy, sensitivity, specificity, classification time, training time, network complexity and computational time compared to conventional radial basis function neural network. It is also proved that proposed model performs better compared to familiar classifiers namely probabilistic neural network, feed forward neural network, cascade forward network, time delay network, artificial immuine system and GINI classifier.

Abstract: Soccer match attendance is an example of group behavior with noisy context that can only be approximated by a limited set of quantifiable factors. However, match attendance is representative of a wider spectrum of context-based behaviors for which only the aggregate effect of otherwise individual decisions is observable. Modeling of such behaviors is desirable from the perspective of economics, psychology, and other social studies with prospective use in simulators, games, product planning, and advertising. In this paper, we evaluate the efficiency of different neural network architectures as models of context in attendance behavior by comparing the achieved prediction accuracy of a multilayer perceptron (MLP), an Elman recurrent neural network (RNN), a time-lagged feedforward neural network (TLFN), and a radial basis function network (RBFN) against a multiple linear regression model, an autoregressive moving average model with exogenous inputs, and a naive cumulative mean model. We show that the MLP, TLFN, and RNN are superior to the RBFN and achieve comparable prediction accuracy on datasets of three teams from the English Football League Championship, which indicates weak importance of context transition modeled by the TLFN and the RNN. The experiments demonstrate that all neural network models outperform linear predictors by a significant margin. We show that neural models built on individual datasets achieve better performance than a generalized neural model constructed from pooled data. We analyze the input parameter influences extracted from trained networks and show that there is an agreement between nonlinear and linear measures about the most significant attributes.

Abstract: In this paper, we propose a novel adaptive kernel for the radial basis function neural networks. The proposed kernel adaptively fuses the Euclidean and cosine distance measures to exploit the reciprocating properties of the two. The proposed framework dynamically adapts the weights of the participating kernels using the gradient descent method, thereby alleviating the need for predetermined weights. The proposed method is shown to outperform the manual fusion of the kernels on three major problems of estimation, namely nonlinear system identification, patter classification and function approximation.

Abstract: This brief presents a novel learning scheme for categorical data based on radial basis function (RBF) networks. The proposed approach replaces the numerical vectors known as RBF centers with categorical tuple centers, and employs specially designed measures for calculating the distance between the center and the input tuples. Furthermore, a fast noniterative categorical clustering algorithm is proposed to accomplish the first stage of RBF training involving categorical center selection, whereas the weights are calculated through linear regression. The method is applied on 22 categorical data sets and compared with several different learning schemes, including neural networks, support vector machines, naive Bayes classifier, and decision trees. Results show that the proposed method is very competitive, outperforming its rivals in terms of predictive capabilities in the majority of the tested cases.

Abstract: In the last decade, a wide range of machine learning approaches were proposed and experimented to model highly nonlinear manufacturing processes. However, improving the performance of such models is challenging due to the complexity and high dimensionality of the manufacturing processes in general. In this paper, we propose bidirectional echo state reservoir networks (Bi-ESNs) trained using support vector machine privileged information method (SVM $$+$$ ) to model a winding machine process. The proposed model will be applied, tested and compared to reported models in the literature such as classical ESN with linear regression, ESN with a linear SVM readout, genetic programming, feedfoward neural network with backpropagation, radial basis function network, adaptive neural fuzzy inference system and local linear wavelet neural network. The developed results show that Bi-ESNs trained with SVM $$+$$ are promising. It was able to provide better generalization performance compared to other models.

Abstract: An adaptive backstepping control (ABSC) using a functional link radial basis function network (FLRBFN) uncertainty observer is proposed in this study to construct a high-performance six-phase permanent magnet synchronous motor (PMSM) position servo drive system. The dynamic model of a field-oriented six-phase PMSM position servo drive is described first. Then, a backstepping control (BSC) system is designed for the tracking of the position reference. Since the lumped uncertainty of the six-phase PMSM position servo drive system is difficult to obtain in advance, it is very difficult to design an effective BSC for practical applications. Therefore, an ABSC system is designed using an adaptive law to estimate the required lumped uncertainty in the BSC system. To further increase the robustness of the six-phase PMSM position servo drive, an FLRBFN uncertainty observer is proposed to estimate the lumped uncertainty of the position servo drive. In addition, an online learning algorithm is derived using Lyapunov stability theorem to learn the parameters of the FLRBFN online. Finally, the proposed position control system is implemented in a 32-bit floating-point DSP, TMS320F28335. The effectiveness and robustness of the proposed intelligent ABSC system are verified by some experimental results.

Abstract: In this paper, the spectral meshless radial point interpolation (SMRPI) technique is applied to the inverse time-dependent force function in the wave equation on regular and irregular domains. The SMRPI is developed for identifying the force function which satisfies in the wave equation subject to the integral overspecification over a portion of the spatial domain or to the overspecification at a point in the spatial domain. This method is based on erudite combination of meshless methods and spectral collocation techniques. The point interpolation method with the help of radial basis functions is used to construct shape functions which play as basis functions in the frame of SMRPI. Since the problem is known to be ill-posed, Thikhonov regularization strategy is employed to solve effectively the discrete ill-posed resultant linear system. Three numerical examples are tested to show that numerical results are accurate for exact data and stable with noisy data.

Abstract: Application of Radial Basis Function Network (RBFN) to impact force identification.Application of Multilayer Perceptron (MLP) to the same task.Accuracy, success rate and error range comparison between RBFN and MLP.Estimation of accuracy improvement for using RBFN in place of MLP. Impact force identification from response sensors is important especially when force measurement using force sensor is not possible due to the installation or dynamic characteristic altering problems. For example, the bump-excited impact force acting on vehicle wheel or ship collision on an offshore structure. Among various existing impact identification approaches, neural network based force identification method has received great attention because one does not need to have a system model. Thus, it is less likely to be affected by ill-posed problem that often occurs during the inversion process. So far, previous studies focused on solving the impact force identification problem using only the conventional Multilayer Perceptron (MLP). Thus, there is a room for improvement to find an alternate algorithm that has great advantage over MLP. For this reason, this study proposes Radial Basis Function Network (RBFN) for possible further improvement in impact identification task. A comparative study between these two algorithms was conducted via experimental approach. Impact forces were made on a Perspex plate structure which was designed to produce similar dynamic behavior of a typical vehicle. Impact locations were fixed at four edges of the test rig to simulate impact events at a vehicle's wheels. Time-domain peak-to-peak and peak arrival time features were extracted from accelerometer data to use as network inputs. Few training data were taken in the way that they represent the entire range of magnitudes of all trial impacts made throughout the experiment. In overall, RBFN improved the impact localization and quantification accuracies by decreasing 32.98% and 40.91% error respectively compared to MLP. The improvement was mainly due to the RBFN's strong approximation ability and its superior tolerance to experimental noises/uncertainties.

Abstract: A neural network method for solving boundary value problems of mathematical physics is developed. In particular, based on the trust region method, a method for learning radial basis function networks is proposed that significantly reduces the time needed for tuning their parameters. A method for solving coefficient inverse problems that does not require the construction and solution of adjoint problems is proposed.

Abstract: Solar radiation is the basic energy source on planet earth. In order to estimate and forecast the solar radiation, it is vital to trace sun's orbit, climatic conditions and dissipation of rays. The function of solar photovoltaic systems is to convert solar energy into electric power. The output power relies on approaching radiation and few features of the intended solar panel. Currently, photovoltaic power is generated in larger amounts. It is necessary that the forecasted data could be efficiently used for controlling and running electricity gauze and to merchandise solar power. In this proposed method, ANNs are used to formulate the solar radiation prediction models. Two different datasets are gathered. The normalization, training and testing processes are done on the gathered historical data. The method used here is supervised learning. The implementation is done by Back Propagation algorithm and Radial basis function network and the results are compared. The prediction accuracy of this method has been studied by various error definitions. The result obtained has greater coincidence between the calculated and the estimated values.

Abstract: While pseudospectral (PS) methods can feature very high accuracy, they tend to be severely limited in terms of geometric flexibility. Application of global radial basis functions overcomes this, however at the expense of problematic conditioning (1) in their most accurate flat basis function regime, and (2) when problem sizes are scaled up to become of practical interest. The present study considers a strategy to improve on these two issues by means of using hybrid radial basis functions that combine cubic splines with Gaussian kernels. The parameters, controlling Gaussian and cubic kernels in the hybrid RBF, are selected using global particle swarm optimization. The proposed approach has been tested with radial basis-pseudospectral method for numerical approximation of Poisson, Helmholtz, and Transport equation. It was observed that the proposed approach significantly reduces the ill-conditioning problem in the RBF-PS method, at the same time, it preserves the stability and accuracy for very small shape parameters. The eigenvalue spectra of the coefficient matrices in the improved algorithm were found to be stable even at large degrees of freedom, which mimic those obtained in pseudospectral approach. Also, numerical experiments suggest that the hybrid kernel performs significantly better than both pure Gaussian and pure cubic kernels.

Abstract: In this paper, a hybrid structure-adaptive radial basis function-extreme learning machine (HSARBF-ELM) network classifier is presented. HSARBF-ELM consists of a structure-adaptive radial basis function (SARBF) network and an extreme learning machine (ELM) network of cascade, where the output of the SARBF network hidden layer is used as the input layer of the ELM network. In the HSARBF-ELM network classifier, the SARBF network is utilized to achieve adaptively localizing kernel mapping of input vectors, after that step, the ELM network is utilized to implement global classification of mapping samples in the kernel space. HSARBF-ELM indicates the combination of localized kernel mapping learning and the global nonlinear classification, which combines the advantages of the SARBF network and the ELM network. The quantitative conditions for the separability enhancement and the corresponding theoretical explanation for the HSARBF-ELM network are given, which demonstrate that when input vectors go through the SARBF network, adaptively adjusting the RBF kernel parameters can boost the separability of the original sample space. Thus, the classification performance of the HSARBF-ELM network can be guaranteed theoretically. An appropriate learning algorithm for the HSARBF-ELM network is subsequently presented, which effectively combines the methods of density clustering with a potential function, center-oriented unidirectional repulsive force and the existing ELM algorithm, and the optimized complementary HSARBF-ELM network can be constructed. The experimental results show that the classification performance of the HSARBF-ELM network clearly outperforms the ELM network, and outperforms other classifiers on most classification problems.

Abstract: Radial Basis Function Neural Networks (RBF NNs) are one of the most applicable NNs in the classification of real targets. Despite the use of recursive methods and gradient descent for training RBF NNs, classification improper accuracy, failing to local minimum and low-convergence speed are defects of this type of network. In order to overcome these defects, heuristic and meta-heuristic algorithms have been conventional to training RBF network in the recent years. This study uses Stochastic Fractal Search Algorithm (SFSA) for training RBF NNs. The particles in the new algorithm explore the search space more efficiently by using the diffusion property, which is observed regularly in arbitrary fractals. To assess the performance of the proposed classifier, this network will be evaluated with the two benchmark datasets and a high-dimensional practical dataset (i.e., sonar). Results indicate that new classifier classifies sonar dataset six percent better than the best algorithm and its convergence speed is better than the other algorithms. Also has better performance than classic benchmark algorithms about all datasets.

Abstract: Estimation of individual phase flow rates in multiphase flow is of great significance to production optimization and reservoir management in oil and gas industry. This paper proposes radial basis function network to develop a virtual flow meter (VFM) that can estimate gas flow rate in multiphase flow production lines. The model is validated with actual well test measurements, and testing results reveal excellent performance and generalization capability of the developed VFM. The paper also discusses the significance of bottom-hole and choke valve measurements to attain accurate predictions. Proposed VFM model potentially offers an attractive and cost-effective solution to meet real-time production monitoring demands, and reduces operational and maintenance costs.

Abstract: In some approximation problems, sampling from the target function can be both expensive and time-consuming. It would be convenient to have a method for indicating where approximation quality is poor, so that generation of new data provides the user with greater accuracy where needed. In this paper, we propose a new adaptive algorithm for radial basis function (RBF) interpolation which aims to assess the local approximation quality, and add or remove points as required to improve the error in the specified region. For Gaussian and multiquadric approximation, we have the flexibility of a shape parameter which we can use to keep the condition number of interpolation matrix at a moderate size. Numerical results for test functions which appear in the literature are given for dimensions 1 and 2, to show that our method performs well. We also give a three-dimensional example from the finance world, since we would like to advertise RBF techniques as useful tools for approximation in the high-dimensional settings one often meets in finance.

Abstract: Since breast cancer is a common disease in society all over the world, early diagnosis is of vital importance in order to treat patients before it reaches an irreversible phase. Expert systems are being developed to make it easier to diagnose the disease. In this study, an ensemble of neural networks named radial basis function network (RBFN), generalized regression neural network (GRNN) and feed forward neural network (FFNN) is implemented to separate breast cancer data samples into benign/malignant classes. The utilities of these common methods and the proposed hybrid model which is a combination of these methods are explored and their performances are comparatively presented. The experimental results on Wisconsin Diagnostic Breast Cancer (WDBC) dataset have proven that the proposed method presents a promise for diagnosis of breast cancer. The proposed model can be used as a tool to assist medical specialists in making their decision on the disease.

Abstract: A novel radial basis function (RBF) neural network-based geometric error compensation method with displacement measurements only is proposed in this paper. The individual geometric error components are formulated mathematically based on laser interferometer calibration with displacement measurements only and modeled using RBF neural network for error compensation in motion controller. Only 4 and 15 displacement measurements are required to identify the error components for XY and XYZ table, respectively. The experiment results on two XY tables illustrate the effectiveness of the proposed method. The overall errors can be reduced significantly after compensation, and different data intervals can be selected to reduce calibration time but maintain a high level of accuracy. The proposed methodology can be extended to other types of precision machine and is more suitable for precision machines requiring a relative low level of accuracy, but fast calibration like those used for acceptance testing and periodic checking.