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Feng, Hsuan Ming, Ching Chang Wong, and Ji Hwei Horng. "RBFNs Nonlinear Control System Design through BFPSO Algorithm." Applied Mechanics and Materials 764-765 (May 2015): 619–23. http://dx.doi.org/10.4028/www.scientific.net/amm.764-765.619.
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All parameters are automatically extracted by the bacterial foraging particle swarm optimization (BFPSO) algorithm to approach the desired control system. Three parameterize basis function neural networks (RBFNs) model to solve the car-pole system problem. Several free parameters of radial basis functions can be automatically tuned by the direct of the specified fitness function. In additional, the proper number of radial basis functions (RBFs) of the constructed RBFNs can be chosen by the defined fitness function which takes this factor into account. The desired multiple objectives of the RBFNs control system are proposed to simultaneously approach the smaller errors with a fewer RBFs number. Simulations show that the developed RBFNs control systems efficiently achieve the desired the setting lot as soon as possible.
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Alqezweeni, Mohie Mortadha, Vladimir Ivanovich Gorbachenko, Maxim Valerievich Zhukov, and Mustafa Sadeq Jaafar. "Efficient Solving of Boundary Value Problems Using Radial Basis Function Networks Learned by Trust Region Method." International Journal of Mathematics and Mathematical Sciences 2018 (June 3, 2018): 1–4. http://dx.doi.org/10.1155/2018/9457578.
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A method using radial basis function networks (RBFNs) to solve boundary value problems of mathematical physics is presented in this paper. The main advantages of mesh-free methods based on RBFN are explained here. To learn RBFNs, the Trust Region Method (TRM) is proposed, which simplifies the process of network structure selection and reduces time expenses to adjust their parameters. Application of the proposed algorithm is illustrated by solving two-dimensional Poisson equation.
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Holden, Sean B., and Mahesan Niranjan. "Average-Case Learning Curves for Radial Basis Function Networks." Neural Computation 9, no. 2 (February 1, 1997): 441–60. http://dx.doi.org/10.1162/neco.1997.9.2.441.
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The application of statistical physics to the study of the learning curves of feedforward connectionist networks has to date been concerned mostly with perceptron-like networks. Recent work has extended the theory to networks such as committee machines and parity machines, and an important direction for current and future research is the extension of this body of theory to further connectionist networks. In this article, we use this formalism to investigate the learning curves of gaussian radial basis function networks (RBFNs) having fixed basis functions. (These networks have also been called generalized linear regression models.) We address the problem of learning linear and nonlinear, realizable and unrealizable, target rules from noise-free training examples using a stochastic training algorithm. Expressions for the generalization error, defined as the expected error for a network with a given set of parameters, are derived for general gaussian RBFNs, for which all parameters, including centers and spread parameters, are adaptable. Specializing to the case of RBFNs with fixed basis functions (basis functions having parameters chosen without reference to the training examples), we then study the learning curves for these networks in the limit of high temperature.
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HUANG, DE-SHUANG. "RADIAL BASIS PROBABILISTIC NEURAL NETWORKS: MODEL AND APPLICATION." International Journal of Pattern Recognition and Artificial Intelligence 13, no. 07 (November 1999): 1083–101. http://dx.doi.org/10.1142/s0218001499000604.
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This paper investigates the capabilities of radial basis function networks (RBFN) and kernel neural networks (KNN), i.e. a specific probabilistic neural networks (PNN), and studies their similarities and differences. In order to avoid the huge amount of hidden units of the KNNs (or PNNs) and reduce the training time for the RBFNs, this paper proposes a new feedforward neural network model referred to as radial basis probabilistic neural network (RBPNN). This new network model inherits the merits of the two old odels to a great extent, and avoids their defects in some ways. Finally, we apply this new RBPNN to the recognition of one-dimensional cross-images of radar targets (five kinds of aircrafts), and the experimental results are given and discussed.
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Gil Pita, R., R. Vicen, M. Rosa, M. P. Jarabo, P. Vera, and J. Curpian. "Ultrasonic flaw detection using radial basis function networks (RBFNs)." Ultrasonics 42, no. 1-9 (April 2004): 361–65. http://dx.doi.org/10.1016/j.ultras.2003.11.018.
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Joug, Shian Ming, Hsuan Ming Feng, and Dong Hui Guo. "Self-Tuning RBFNs Mobile Robot Systems through Bacterial Foraging Particle Swarm Optimization Learning Algorithm." Applied Mechanics and Materials 284-287 (January 2013): 2128–36. http://dx.doi.org/10.4028/www.scientific.net/amm.284-287.2128.
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A radial basis function neural networks (RBFNs) mobile robot control system is automatically developed with the image processing and learned by the bacterial foraging particle swarm optimization (BFPSO) algorithm in this paper. The image-based architecture of robot model is self-generated to travel the routing path in the dynamical and complicated environments. The visible omni-directional image sensors capture the surrounding environment to represent the behavior model of the mobile robot system. Three parameterize RBFNs model with the centers and spreads of each radial basis function, and the connection weights to solve the mobile robot path traveling and routing problems. Several free parameters of radial basis functions can be automatically tuned by the direct of the specified fitness function. In additional, the proper number of radial basis functions of the constructed RBFNs can be chosen by the defined fitness function which takes this factor into account. The desired multiple objectives of the RBFNs control system are proposed to simultaneously approach the shorter path and avoid the unexpected obstacles. Evaluations of PSO and BFPSO show that the developed RBFNs robot systems skip the obstacles and efficiently achieve the desired targets as soon as possible.
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Dash, Ch Sanjeev Kumar, Ajit Kumar Behera, Satchidananda Dehuri, and Sung-Bae Cho. "Radial basis function neural networks: a topical state-of-the-art survey." Open Computer Science 6, no. 1 (May 2, 2016): 33–63. http://dx.doi.org/10.1515/comp-2016-0005.
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AbstractRadial basis function networks (RBFNs) have gained widespread appeal amongst researchers and have shown good performance in a variety of application domains. They have potential for hybridization and demonstrate some interesting emergent behaviors. This paper aims to offer a compendious and sensible survey on RBF networks. The advantages they offer, such as fast training and global approximation capability with local responses, are attracting many researchers to use them in diversified fields. The overall algorithmic development of RBF networks by giving special focus on their learning methods, novel kernels, and fine tuning of kernel parameters have been discussed. In addition, we have considered the recent research work on optimization of multi-criterions in RBF networks and a range of indicative application areas along with some open source RBFN tools.
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MAYORGA, RENÉ V., and JONATHAN CARRERA. "A RADIAL BASIS FUNCTION NETWORK APPROACH FOR THE COMPUTATION OF INVERSE CONTINUOUS TIME VARIANT FUNCTIONS." International Journal of Neural Systems 17, no. 03 (June 2007): 149–60. http://dx.doi.org/10.1142/s0129065707001020.
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This Paper presents an efficient approach for the fast computation of inverse continuous time variant functions with the proper use of Radial Basis Function Networks (RBFNs). The approach is based on implementing RBFNs for computing inverse continuous time variant functions via an overall damped least squares solution that includes a novel null space vector for singularities prevention. The singularities avoidance null space vector is derived from developing a sufficiency condition for singularities prevention that conduces to establish some characterizing matrices and an associated performance index.
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HUANG, DE-SHUANG. "APPLICATION OF GENERALIZED RADIAL BASIS FUNCTION NETWORKS TO RECOGNITION OF RADAR TARGETS." International Journal of Pattern Recognition and Artificial Intelligence 13, no. 06 (September 1999): 945–62. http://dx.doi.org/10.1142/s0218001499000525.
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This paper extends general radial basis function networks (RBFN) with Gaussian kernel functions to generalized radial basis function networks (GRBFN) with Parzen window functions, and discusses applying the GRBFNs to recognition of radar targets. The equivalence between the RBFN classifiers (RBFNC) with outer-supervised signals of 0 or 1 and the estimate of Parzen windowed probabilistic density is proved. It is pointed out that the I/O functions of the hidden units in the RBFNC can be extended to general Parzen window functions (or called as potential functions). We present using recursive least square-backpropagation (RLS–BP) learning algorithm to train the GRBFNCs to classify five types of radar targets by means of their one-dimensional cross profiles. The concepts about the rate of recognition and confidence in the process of testing classification performance of the GRBFNCs are introduced. Six generalized kernel functions such as Gaussian, Double-Exponential, Triangle, Hyperbolic, Sinc and Cauchy, are used as the hidden I/O functions of the RBFNCs, and the classification performance of corresponding GRBFNCs for classifying one-dimensional cross profiles of radar targets is discussed.
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Dash, Ch Sanjeev Kumar, Ajit Kumar Behera, Satchidananda Dehuri, and Sung-Bae Cho. "Differential Evolution-Based Optimization of Kernel Parameters in Radial Basis Function Networks for Classification." International Journal of Applied Evolutionary Computation 4, no. 1 (January 2013): 56–80. http://dx.doi.org/10.4018/jaec.2013010104.
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In this paper a two phases learning algorithm with a modified kernel for radial basis function neural networks is proposed for classification. In phase one a new meta-heuristic approach differential evolution is used to reveal the parameters of the modified kernel. The second phase focuses on optimization of weights for learning the networks. Further, a predefined set of basis functions is taken for empirical analysis of which basis function is better for which kind of domain. The simulation result shows that the proposed learning mechanism is evidently producing better classification accuracy vis-à-vis radial basis function neural networks (RBFNs) and genetic algorithm-radial basis function (GA-RBF) neural networks.
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Wu, Yunfeng, Xin Luo, Fang Zheng, Shanshan Yang, Suxian Cai, and Sin Chun Ng. "Adaptive Linear and Normalized Combination of Radial Basis Function Networks for Function Approximation and Regression." Mathematical Problems in Engineering 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/913897.
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This paper presents a novel adaptive linear and normalized combination (ALNC) method that can be used to combine the component radial basis function networks (RBFNs) to implement better function approximation and regression tasks. The optimization of the fusion weights is obtained by solving a constrained quadratic programming problem. According to the instantaneous errors generated by the component RBFNs, the ALNC is able to perform the selective ensemble of multiple leaners by adaptively adjusting the fusion weights from one instance to another. The results of the experiments on eight synthetic function approximation and six benchmark regression data sets show that the ALNC method can effectively help the ensemble system achieve a higher accuracy (measured in terms of mean-squared error) and the better fidelity (characterized by normalized correlation coefficient) of approximation, in relation to the popular simple average, weighted average, and the Bagging methods.
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Dash, Ch Sanjeev Kumar, Ajit Kumar Behera, Satchidananda Dehuri, and Sung-Bae Cho. "A Novel Radial Basis Function Networks Locally Tuned with Differential Evolution for Classification." International Journal of Systems Biology and Biomedical Technologies 2, no. 2 (April 2013): 33–57. http://dx.doi.org/10.4018/ijsbbt.2013040103.
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The classification of diseases appears as one of the fundamental problems for a medical practitioner, which might be substantially improved by intelligent systems. The present work is aimed at designing in what way an intelligent system supporting medical decision can be developed by hybridizing radial basis function neural networks (RBFNs) and differential evolution (DE). To this extent, a two phases learning algorithm with a modified kernel for radial basis function neural networks is proposed for classification. In phase one, differential evolution is used to reveal the parameters of the modified kernel. The second phase focus on optimization of weights for learning the networks. The proposed method is validated using five medical datasets such as bupa liver disorders, pima Indians diabetes, new thyroid, stalog (heart), and hepatitis. In addition, a predefined set of basis functions are considered to gain insight into, which basis function is better for what kind of domain through an empirical analysis. The experiment results indicate that the proposed method classification accuracy with 95% and 98% confidence interval is better than the base line classifier (i.e., simple RBFNs) in all aforementioned datasets. In the case of imbalanced dataset like new thyroid, the authors have noted that with 98% confidence level the classification accuracy of the proposed method based on the multi-quadratic kernel is better than other kernels; however, in the case of hepatitis, the proposed method based on cubic kernel is promising.
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Ding, Shuo, and Xiao Heng Chang. "A MATLAB-Based Study on the Realization and Approximation Performance of RBF Neural Networks." Applied Mechanics and Materials 325-326 (June 2013): 1746–49. http://dx.doi.org/10.4028/www.scientific.net/amm.325-326.1746.
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BP neural network is a kind of widely used feed-forward network. However its innate shortcomings are gradually giving rise to the study of other networks. Currently one of the research focuses in the area of feed-forward networks is radial basis function neural network. To test the radial basis function neural network for nonlinear function approximation capability, this paper first introduces the theories of RBF networks, as well as the structure, function approximation and learning algorithm of radial basis function neural network. Then a simulation test is carried out to compare BPNN and RBFNN. The simulation results indicate that RBFNN is simpler in structure, faster in speed and better in approximation performance. That is to say RBFNN is superior to BPNN in many aspects. But when solving the same problem, the structure of radial basis networks is more complicated than that of BP neural networks. Keywords: Radial basis function; Neural network; Function approximation; Simulation; MATLAB
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Yingwei, Lu, N. Sundararajan, and P. Saratchandran. "A Sequential Learning Scheme for Function Approximation Using Minimal Radial Basis Function Neural Networks." Neural Computation 9, no. 2 (February 1, 1997): 461–78. http://dx.doi.org/10.1162/neco.1997.9.2.461.
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This article presents a sequential learning algorithm for function approximation and time-series prediction using a minimal radial basis function neural network (RBFNN). The algorithm combines the growth criterion of the resource-allocating network (RAN) of Platt (1991) with a pruning strategy based on the relative contribution of each hidden unit to the overall network output. The resulting network leads toward a minimal topology for the RBFNN. The performance of the algorithm is compared with RAN and the enhanced RAN algorithm of Kadirkamanathan and Niranjan (1993) for the following benchmark problems: (1) hearta from the benchmark problems database PROBEN1, (2) Hermite polynomial, and (3) Mackey-Glass chaotic time series. For these problems, the proposed algorithm is shown to realize RBFNNs with far fewer hidden neurons with better or same accuracy.
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Freeman, Jason A. S., and David Saad. "Online Learning in Radial Basis Function Networks." Neural Computation 9, no. 7 (October 1, 1997): 1601–22. http://dx.doi.org/10.1162/neco.1997.9.7.1601.
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An analytic investigation of the average case learning and generalization properties of radial basis function (RBFs) networks is presented, utilizing online gradient descent as the learning rule. The analytic method employed allows both the calculation of generalization error and the examination of the internal dynamics of the network. The generalization error and internal dynamics are then used to examine the role of the learning rate and the specialization of the hidden units, which gives insight into decreasing the time required for training. The realizable and some over realizable cases are studied in detail: the phase of learning in which the hidden units are unspecialized (symmetric phase) and the phase in which asymptotic convergence occurs are analyzed, and their typical properties found. Finally, simulations are performed that strongly confirm the analytic results.
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Babu, N. S. C., and V. C. Prasad. "Radial Basis Function Networks for Analog Circuit Fault Isolation." Journal of Circuits, Systems and Computers 07, no. 06 (December 1997): 643–55. http://dx.doi.org/10.1142/s0218126697000462.
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The application of a radial basis function neural network (RBFN) for analog circuit fault isolation is presented. In this method the RBFN replaces the fault dictionary of analog circuits. The proposed method for analog circuit fault isolation takes the advantage of extremely fast training of RBFN compared to earlier neural network methods. A method is suggested to select centers and widths of RBF units. This selection procedure accounts for the component tolerances. The effectiveness of the RBFN for the fault isolation problem is demonstrated with an illustrative example. RBFN performed well even when the input patterns are drawn directly from the test node voltages of the analog circuit under consideration. A method is suggested to modify the RBF network in the event of occurrence of a new fault. The suggested modifications do not affect the previous training.
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Almaita, Eyad K., and Jumana Al shawawreh. "Improving Stability and Convergence for Adaptive Radial Basis Function Neural Networks Algorithm. (On-Line Harmonics Estimation Application)." International Journal of Renewable Energy Development 6, no. 1 (March 22, 2017): 9–17. http://dx.doi.org/10.14710/ijred.6.1.9-17.
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In this paper, an adaptive Radial Basis Function Neural Networks (RBFNN) algorithm is used to estimate the fundamental and harmonic components of nonlinear load current. The performance of the adaptive RBFNN is evaluated based on the difference between the original signal and the constructed signal (the summation between fundamental and harmonic components). Also, an extensive investigation is carried out to propose a systematic and optimal selection of the Adaptive RBFNN parameters. These parameters will ensure fast and stable convergence and minimum estimation error. The results show an improving for fundamental and harmonics estimation comparing to the conventional RBFNN. Also, the results show how to control the computational steps and how they are related to the estimation error. The methodology used in this paper facilitates the development and design of signal processing and control systems.Article History: Received Dec 15, 2016; Received in revised form Feb 2nd 2017; Accepted 13rd 2017; Available onlineHow to Cite This Article: Almaita, E.K and Shawawreh J.Al (2017) Improving Stability and Convergence for Adaptive Radial Basis Function Neural Networks Algorithm (On-Line Harmonics Estimation Application). International Journal of Renewable Energy Develeopment, 6(1), 9-17.http://dx.doi.org/10.14710/ijred.6.1.9-17
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Rahmani, Reza, Saleh Mobayen, Afef Fekih, and Jong-Suk Ro. "Robust Passivity Cascade Technique-Based Control Using RBFN Approximators for the Stabilization of a Cart Inverted Pendulum." Mathematics 9, no. 11 (May 27, 2021): 1229. http://dx.doi.org/10.3390/math9111229.
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This paper proposes a novel passivity cascade technique (PCT)-based control for nonlinear inverted pendulum systems. Its main objective is to stabilize the pendulum’s upward states despite uncertainties and exogenous disturbances. The proposed framework combines the estimation properties of radial basis function neural networks (RBFNs) with the passivity attributes of the cascade control framework. The unknown terms of the nonlinear system are estimated using an RBFN approximator. The performance of the closed-loop system is further enhanced by using the integral of angular position as a virtual state variable. The lumped uncertainties (NN—Neural Network approximation, external disturbances and parametric uncertainty) are compensated for by adding a robustifying adaptive rule-based signal to the PCT-based control. The boundedness of the states is confirmed using the passivity theorem. The performance of the proposed approach was assessed using a nonlinear inverted pendulum system under both nominal and disturbed conditions.
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Haviluddin, Haviluddin, and Imam Tahyudin. "Time Series Prediction Using Radial Basis Function Neural Network." International Journal of Electrical and Computer Engineering (IJECE) 5, no. 4 (August 1, 2015): 765. http://dx.doi.org/10.11591/ijece.v5i4.pp765-771.
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This paper presents an approach for predicting daily network traffic using artificial neural networks (ANN), namely radial basis function neural network (RBFNN) method. The data is gained from 21-24 June 2013 (192 samples series data) in ICT Unit of Mulawarman University, East Kalimantan, Indonesia. The results of measurement are using statistical analysis, e.g. sum of square error (SSE), mean of square error (MSE), mean of absolute percentage error (MAPE), and mean of absolute deviation (MAD). The results show that values are the same, with different goals that have been set are 0.001, 0.002, and 0.003, and spread 200. The smallest MSE value indicates a good method for accuracy. Therefore, the RBFNN model illustrates the proposed best model to predict daily network traffic.
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Marrero, Isabel. "Radial basis function neural networks of Hankel translates as universal approximators." Analysis and Applications 17, no. 06 (September 23, 2019): 897–930. http://dx.doi.org/10.1142/s0219530519500064.
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Radial basis function neural networks (RBFNNs) of Hankel translates of order [Formula: see text] with a continuous activation function [Formula: see text] for which the limit [Formula: see text] exists are shown to possess the universal approximation property in spaces of continuous and of [Formula: see text]-integrable functions, [Formula: see text], on (compact subsets of) [Formula: see text] if, and only if, [Formula: see text] is not an even polynomial. This extends to the class of RBFNNs under consideration a result already known for RBFNNs of standard translates.
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Binaghi, E., V. Pedoia, A. Guidali, and M. Guglielmin. "Snow cover thickness estimation using radial basis function networks." Cryosphere 7, no. 3 (May 14, 2013): 841–54. http://dx.doi.org/10.5194/tc-7-841-2013.
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Abstract. This paper reports an experimental study designed for the in-depth investigation of how the radial basis function network (RBFN) estimates snow cover thickness as a function of climate and topographic parameters. The estimation problem is modeled in terms of both function regression and classification, obtaining continuous and discrete thickness values, respectively. The model is based on a minimal set of climatic and topographic data collected from a limited number of stations located in the Italian Central Alps. Several experiments have been conceived and conducted adopting different evaluation indexes. A comparison analysis was also developed for a quantitative evaluation of the advantages of the RBFN method over to conventional widely used spatial interpolation techniques when dealing with critical situations originated by lack of data and limited n-homogeneously distributed instrumented sites. The RBFN model proved competitive behavior and a valuable tool in critical situations in which conventional techniques suffer from a lack of representative data.
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PEDRYCZ, WITOLD, PARTAB RAI, and JOZEF ZURADA. "EXPERIENCE-CONSISTENT MODELING FOR RADIAL BASIS FUNCTION NEURAL NETWORKS." International Journal of Neural Systems 18, no. 04 (August 2008): 279–92. http://dx.doi.org/10.1142/s0129065708001592.
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We develop a new approach to the design of neural networks, which utilizes a collaborative framework of knowledge-driven experience. In contrast to the "standard" way of developing neural networks, which explicitly exploits experimental data, this approach incorporates a mechanism of knowledge-driven experience. The essence of the proposed scheme of learning is to take advantage of the parameters (connections) of neural networks built in the past for the same phenomenon (which might also exhibit some variability over time or space) for which are interested to construct the network on a basis of currently available data. We establish a conceptual and algorithmic framework to reconcile these two essential sources of information (data and knowledge) in the process of the development of the network. To make a presentation more focused and come up with a detailed quantification of the resulting architecture, we concentrate on the experience-based design of radial basis function neural networks (RBFNNs). We introduce several performance indexes to quantify an effect of utilization of the knowledge residing within the connections of the networks and establish an optimal level of their use. Experimental results are presented for low-dimensional synthetic data and selected datasets available at the Machine Learning Repository.
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Wang, Zhongbao, and Shaojun Fang. "ANN Synthesis Model of Single-Feed Corner-Truncated Circularly Polarized Microstrip Antenna with an Air Gap for Wideband Applications." International Journal of Antennas and Propagation 2014 (2014): 1–7. http://dx.doi.org/10.1155/2014/392843.
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A computer-aided design model based on the artificial neural network (ANN) is proposed to directly obtain patch physical dimensions of the single-feed corner-truncated circularly polarized microstrip antenna (CPMA) with an air gap for wideband applications. To take account of the effect of the air gap, an equivalent relative permittivity is introduced and adopted to calculate the resonant frequency andQ-factor of square microstrip antennas for obtaining the training data sets. ANN architectures using multilayered perceptrons (MLPs) and radial basis function networks (RBFNs) are compared. Also, six learning algorithms are used to train the MLPs for comparison. It is found that MLPs trained with the Levenberg-Marquardt (LM) algorithm are better than RBFNs for the synthesis of the CPMA. An accurate model is achieved by using an MLP with three hidden layers. The model is validated by the electromagnetic simulation and measurements. It is enormously useful to antenna engineers for facilitating the design of the single-feed CPMA with an air gap.
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Sharkawy, Abdel Badie. "Prediction of Surface Roughness in End Milling Process Using Intelligent Systems: A Comparative Study." Applied Computational Intelligence and Soft Computing 2011 (2011): 1–18. http://dx.doi.org/10.1155/2011/183764.
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A study is presented to model surface roughness in end milling process. Three types of intelligent networks have been considered. They are (i) radial basis function neural networks (RBFNs), (ii) adaptive neurofuzzy inference systems (ANFISs), and (iii) genetically evolved fuzzy inference systems (G-FISs). The machining parameters, namely, the spindle speed, feed rate, and depth of cut have been used as inputs to model the workpiece surface roughness. The goal is to get the best prediction accuracy. The procedure is illustrated using experimental data of end milling 6061 aluminum alloy. The three networks have been trained using experimental training data. After training, they have been examined using another set of data, that is, validation data. Results are compared with previously published results. It is concluded that ANFIS networks may suffer the local minima problem, and genetic tuning of fuzzy networks cannot insureperfectoptimality unless suitable parameter setting (population size, number of generations etc.) and tuning range for the FIS, parameters are used which can be hardly satisfied. It is shown that the RBFN model has the best performance (prediction accuracy) in this particular case.
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Aziz, K. A. A., Abdul Kadir, Rostam Affendi Hamzah, and Amat Amir Basari. "Product Identification Using Image Processing and Radial Basis Function Neural Networks." Applied Mechanics and Materials 761 (May 2015): 120–24. http://dx.doi.org/10.4028/www.scientific.net/amm.761.120.
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This paper presents a product identification using image processing and radial basis function neural networks. The system identified a specific product based on the shape of the product. An image processing had been applied to the acquired image and the product was recognized using the Radial Basis Function Neural Network (RBFNN). The RBF Neural Networks offer several advantages compared to other neural network architecture such as they can be trained using a fast two-stage training algorithm and the network possesses the property of best approximation. The output of the network can be optimized by setting suitable values of the center and the spread of RBF. In this paper, fixed spread value was used for every cluster. The system can detect all the four products with 100% successful rate using ±0.2 tolerance.
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Guidali, A., E. Binaghi, V. Pedoia, and M. Guglielmin. "Snow cover thickness estimation by using radial basis function networks." Cryosphere Discussions 6, no. 4 (July 16, 2012): 2437–75. http://dx.doi.org/10.5194/tcd-6-2437-2012.
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Abstract. This work investigates learning and generalisation capabilities of radial basis function networks (RBFN) used to solve snow cover thickness estimation model as regression and classification. The model is based on a minimal set of climatic and topographic data collected from a limited number of stations located in the Italian Central Alps. Several experiments have been conceived and conducted adopting different evaluation indexes in both regression and classification tasks. The snow cover thickness estimation by RBFN has been proved a valuable tool able to deal with several critical aspects arising from the specific experimental context.
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Ghorbani, A., and M. R. Ghasemi. "Reliability analysis of frame structures using radial basis function neural networks." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 225, no. 1 (January 1, 2011): 163–70. http://dx.doi.org/10.1177/09544062jmes2047.
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In this study, a hybrid reliability methodology via Monte Carlo simulation techniques with radial basis function neural network (RBFNN) is presented. Monte Carlo simulation is a powerful tool, simple to implement, and capable of solving a broad range of reliability problems. However, its use for the evaluation of very low probabilities of failure implies a great number of analyses, and the computational time highly increases. In practice, the size of a design problem can be very large and the limit state functions (LSFs) are usually implicit in terms of the random variables. A hybrid method consisting of Monte Carlo simulation and RBFNN is proposed in the present study to approximate the LSF or failure function of the structure. Therefore, the computational burden of Monte Carlo simulation decreases significantly. A distinctive feature of this method is the introduction of an explicit approximate LSF. Using the parameters of the RBFNN, the explicit formulation of the LSF is derived. By introducing the derived approximate LSF, the failure probability can be easily estimated. In order to assess the effectiveness of the proposed methodology, some illustrative examples including frame structures are considered, and the numerical results are verified.
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Jankowski, Norbert. "Comparison of Prototype Selection Algorithms Used in Construction of Neural Networks Learned by SVD." International Journal of Applied Mathematics and Computer Science 28, no. 4 (December 1, 2018): 719–33. http://dx.doi.org/10.2478/amcs-2018-0055.
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Abstract Radial basis function networks (RBFNs) or extreme learning machines (ELMs) can be seen as linear combinations of kernel functions (hidden neurons). Kernels can be constructed in random processes like in ELMs, or the positions of kernels can be initialized by a random subset of training vectors, or kernels can be constructed in a (sub-)learning process (sometimes by k-means, for example). We found that kernels constructed using prototype selection algorithms provide very accurate and stable solutions. What is more, prototype selection algorithms automatically choose not only the placement of prototypes, but also their number. Thanks to this advantage, it is no longer necessary to estimate the number of kernels with time-consuming multiple train-test procedures. The best results of learning can be obtained by pseudo-inverse learning with a singular value decomposition (SVD) algorithm. The article presents a comparison of several prototype selection algorithms co-working with singular value decomposition-based learning. The presented comparison clearly shows that the combination of prototype selection and SVD learning of a neural network is significantly better than a random selection of kernels for the RBFN or the ELM, the support vector machine or the kNN. Moreover, the presented learning scheme requires no parameters except for the width of the Gaussian kernel.
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ZHAO, WEN-BO, DE-SHUANG HUANG, JI-YAN DU, and LI-MING WANG. "GENETIC OPTIMIZATION OF RADIAL BASIS PROBABILISTIC NEURAL NETWORKS." International Journal of Pattern Recognition and Artificial Intelligence 18, no. 08 (December 2004): 1473–99. http://dx.doi.org/10.1142/s0218001404003824.
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This paper discusses using genetic algorithms (GA) to optimize the structure of radial basis probabilistic neural networks (RBPNN), including how to select hidden centers of the first hidden layer and to determine the controlling parameter of Gaussian kernel functions. In the process of constructing the genetic algorithm, a novel encoding method is proposed for optimizing the RBPNN structure. This encoding method can not only make the selected hidden centers sufficiently reflect the key distribution characteristic in the space of training samples set and reduce the hidden centers number as few as possible, but also simultaneously determine the optimum controlling parameters of Gaussian kernel functions matching the selected hidden centers. Additionally, we also constructively propose a new fitness function so as to make the designed RBPNN as simple as possible in the network structure in the case of not losing the network performance. Finally, we take the two benchmark problems of discriminating two-spiral problem and classifying the iris data, for example, to test and evaluate this designed GA. The experimental results illustrate that our designed GA can significantly reduce the required hidden centers number, compared with the recursive orthogonal least square algorithm (ROLSA) and the modified K-means algorithm (MKA). In particular, by means of statistical experiments it was proved that the optimized RBPNN by our designed GA, have still a better generalization performance with respect to the ones by the ROLSA and the MKA, in spite of the network scale having been greatly reduced. Additionally, our experimental results also demonstrate that our designed GA is also suitable for optimizing the radial basis function neural networks (RBFNN).
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El-Dahshan, El-Sayed A. "Modeling of heavy ion collisions using radial basis function and generalized regression neural networks." Canadian Journal of Physics 89, no. 10 (October 2011): 1051–60. http://dx.doi.org/10.1139/p11-094.
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Artificial neural networks (ANNs) have been applied to heavy ion collisions. In the present work, the possibility of using ANN methods for modeling the multiplicity distributions, P(ns), of shower particles produced from p, d, 4He, 6Li, 7Li, 12C, 16O, and 24Mg interactions with light (CNO) as well as heavy (AgBr) emulsions at 4.5 A GeV/c was investigated. Two different ANN approaches, namely radial basis function neural network (RBFNN) and generalized regression neural network (GRNN), were employed to obtain a mathematical formula describing these collisions. The results from RBFNN and GRNN models showed good agreement with the experimental data. GRNN models have a better performance than the RBFNN models. This study showed that the RBFNN and GRNN models are capable of accurately predicting the P(ns) of shower particles in the training and testing phases.
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Aik, Lim Eng, Tan Wei Hong, and Ahmad Kadri Junoh. "An Improved Radial Basis Function Networks Based on Quantum Evolutionary Algorithm for Training Nonlinear Datasets." IAES International Journal of Artificial Intelligence (IJ-AI) 8, no. 2 (June 1, 2019): 120. http://dx.doi.org/10.11591/ijai.v8.i2.pp120-131.
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In neural networks, the accuracies of its networks are mainly relying on two important factors which are the centers and spread value. Radial basis function network (RBFN) is a type of feedforward network that capable of perform nonlinear approximation on unknown dataset. It has been widely used in classification, pattern recognition, nonlinear control and image processing. Thus, with the increases in RBFN application, some problems and weakness of RBFN network is identified. Through the combination of quantum computing and RBFN provides a new research idea in design and performance improvement of RBFN system. This paper describes the theory and application of quantum computing and cloning operators, and discusses the superiority of these theories and the feasibility of their optimization algorithms. This proposed improved RBFN (I-RBFN) that combined with cloning operator and quantum computing algorithm demonstrated its ability in global search and local optimization to effectively speed up learning and provides better accuracy in prediction results. Both the algorithms that combined with RBFN optimize the centers and spread value of RBFN. The proposed I-RBFN was tested against the standard RBFN in predictions. The experimental models were tested on four literatures nonlinear function and four real-world application problems, particularly in Air pollutant problem, Biochemical Oxygen Demand (BOD) problem, Phytoplankton problem, and forex pair EURUSD. The results are compared to I-RBFN for root mean square error (RMSE) values with standard RBFN. The proposed I-RBFN yielded better results with an average improvement percentage more than 90 percent in RMSE.
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Aik, Lim Eng, Tan Wei Hong, and Ahmad Kadri Junoh. "An Improved Radial Basis Function Networks in Networks Weights Adjustment for Training Real-World Nonlinear Datasets." IAES International Journal of Artificial Intelligence (IJ-AI) 8, no. 1 (March 1, 2019): 63. http://dx.doi.org/10.11591/ijai.v8.i1.pp63-76.
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In neural networks, the accuracies of its networks are mainly relying on two important factors which are the centers and the networks weight. The gradient descent algorithm is a widely used weight adjustment algorithm in most of neural networks training algorithm. However, the method is known for its weakness for easily trap in local minima. It suffers from a random weight generated for the networks during initial stage of training at input layer to hidden layer networks. The performance of radial basis function networks (RBFN) has been improved from different perspectives, including centroid initialization problem to weight correction stage over the years. Unfortunately, the solution does not provide a good trade-off between quality and efficiency of the weight produces by the algorithm. To solve this problem, an improved gradient descent algorithm for finding initial weight and improve the overall networks weight is proposed. This improved version algorithm is incorporated into RBFN training algorithm for updating weight. Hence, this paper presented an improved RBFN in term of algorithm for improving the weight adjustment in RBFN during training process. The proposed training algorithm, which uses improved gradient descent algorithm for weight adjustment for training RBFN, obtained significant improvement in predictions compared to the standard RBFN. The proposed training algorithm was implemented in MATLAB environment. The proposed improved network called IRBFN was tested against the standard RBFN in predictions. The experimental models were tested on four literatures nonlinear function and four real-world application problems, particularly in Air pollutant problem, Biochemical Oxygen Demand (BOD) problem, Phytoplankton problem, and forex pair EURUSD. The results are compared to IRBFN for root mean square error (RMSE) values with standard RBFN. The IRBFN yielded a promising result with an average improvement percentage more than 40 percent in RMSE.
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Haviluddin, Haviluddin, and Imam Tahyudin. "Prediction of Daily Network Traffic based on Radial Basis Function Neural Network." IAES International Journal of Artificial Intelligence (IJ-AI) 3, no. 4 (August 20, 2016): 145. http://dx.doi.org/10.11591/ijai.v3.i4.pp145-149.
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This paper presents an approach for predicting daily network traffic using artificial neural networks (ANN), namely radial basis function neural network (RBFNN) method. The data is gained from 21 – 24 June 2013 (192 samples series data) in ICT Unit Universitas Mulawarman, East Kalimantan, Indonesia. The results of measurement are using statistical analysis, e.g. sum of square error (SSE), mean of square error (MSE), mean of percentage error (MPE), mean of absolute percentage error (MAPE), and mean of absolute deviation (MAD). The results show that values are the same, with different goals that have been set are 0.001, 0.002, and 0.003, and spread 200. The smallest MSE value indicates a good method for accuracy. Therefore, the RBFNN model illustrates the proposed best model to predict daily network traffic.
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El Shafie, Amr H., A. El-Shafie, A. Almukhtar, Mohd R. Taha, Hasan G. El Mazoghi, and A. Shehata. "Radial basis function neural networks for reliably forecasting rainfall." Journal of Water and Climate Change 3, no. 2 (June 1, 2012): 125–38. http://dx.doi.org/10.2166/wcc.2012.017.
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Rainfall forecasting is an interesting task especially in a modern city facing the problem of global warming; in addition rainfall is a necessary input for the analysis and design of hydrologic systems. Most rainfall real-time forecasting models are based on conceptual models simulating the complex hydrological process under climate variability. As there are a lot of variables and parameters with uncertainties and non-linear relationships, the calibration of conceptual or physically based models is often a difficult and time-consuming procedure. Simpler artificial neural network (ANN) forecasts may therefore seem attractive as an alternative model. The present research demonstrates the application of the radial basis function neural network (RBFNN) to rainfall forecasting for Alexandria City, Egypt. A significant feature of the input construction of the RBF network is based on the use of the average 10 year rainfall in each decade to forecast the next year. The results show the capability of the RBF network in forecasting the yearly rainfall and two highest rainfall monsoon months, January and December, compared with other statistical models. Based on these results, the use of the RBF model can be recommended as a viable alternative for forecasting the rainfall based on historical rainfall recorded data.
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Aik, Lim Eng, Tan Wei Hong, and Ahmad Kadri Junoh. "Distance Weighted K-Means Algorithm for Center Selection in Training Radial Basis Function Networks." IAES International Journal of Artificial Intelligence (IJ-AI) 8, no. 1 (March 1, 2019): 54. http://dx.doi.org/10.11591/ijai.v8.i1.pp54-62.
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The accuracies rates of the neural networks mainly depend on the selection of the correct data centers. The K-means algorithm is a widely used clustering algorithm in various disciplines for centers selection. However, the method is known for its sensitivity to initial centers selection. It suffers not only from a high dependency on the algorithm's initial centers selection but, also from data points. The performance of K-means has been enhanced from different perspectives, including centroid initialization problem over the years. Unfortunately, the solution does not provide a good trade-off between quality and efficiency of the centers produces by the algorithm. To solve this problem, a new method to find the initial centers and improve the sensitivity to the initial centers of K-means algorithm is proposed. This paper presented a training algorithm for the radial basis function network (RBFN) using improved K-means (KM) algorithm, which is the modified version of KM algorithm based on distance-weighted adjustment for each centers, known as distance-weighted K-means (DWKM) algorithm. The proposed training algorithm, which uses DWKM algorithm select centers for training RBFN obtained better accuracy in predictions and reduced network architecture compared to the standard RBFN. The proposed training algorithm was implemented in MATLAB environment; hence, the new network was undergoing a hybrid learning process. The network called DWKM-RBFN was tested against the standard RBFN in predictions. The experimental models were tested on four literatures nonlinear function and four real-world application problems, particularly in Air pollutant problem, Biochemical Oxygen Demand (BOD) problem, Phytoplankton problem, and forex pair EURUSD. The results are compared to proposed method for root mean square error (RMSE) in radial basis function network (RBFN). The proposed method yielded a promising result with an average improvement percentage more than 50 percent in RMSE.
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Kumar, Shiva, P. Srinivasa Pai, and B. R. Shrinivasa Rao. "Radial-Basis-Function-Network-Based Prediction of Performance and Emission Characteristics in a Bio Diesel Engine Run on WCO Ester." Advances in Artificial Intelligence 2012 (November 4, 2012): 1–7. http://dx.doi.org/10.1155/2012/610487.
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Radial basis function neural networks (RBFNNs), which is a relatively new class of neural networks, have been investigated for their applicability for prediction of performance and emission characteristics of a diesel engine fuelled with waste cooking oil (WCO). The RBF networks were trained using the experimental data, where in load percentage, compression ratio, blend percentage, injection timing, and injection pressure were taken as the input parameters, and brake thermal efficiency (BTE), brake specific energy consumption (BSEC), exhaust gas temperature (), and engine emissions were used as the output parameters. The number of RBF centers was selected randomly. The network was initially trained using variable width values for the RBF units using a heuristic and then was trained by using fixed width values. Studies showed that RBFNN predicted results matched well with the experimental results over a wide range of operating conditions. Prediction accuracy for all the output parameters was above 90% in case of performance parameters and above 70% in case of emission parameters.
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Sofian, Ian Mochamad, Azhar Kholiq Affandi, Iskhaq Iskandar, and Yosi Apriani. "Monthly rainfall prediction based on artificial neural networks with backpropagation and radial basis function." International Journal of Advances in Intelligent Informatics 4, no. 2 (July 31, 2018): 154. http://dx.doi.org/10.26555/ijain.v4i2.208.
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Two models of Artificial Neural Network (ANN) algorithm have been developed for monthly rainfall prediction, namely the Backpropagation Neural Network (BPNN) and Radial Basis Function Neural Network (RBFNN). A total data of 238 months (1994-2013) was used as the input data, in which 190 data were used as training data and 48 data used as testing data. Rainfall data has been tested using architecture BPNN with various learning rates. In addition, the rainfall data has been tested using the RBFNN architecture with maximum number of neurons K = 200, and various error goals. Statistical analysis has been conducted to calculate R, MSE, MBE, and MAE to verify the result. The study showed that RBFNN architecture with error goal of 0.001 gives the best result with a value of MSE = 0.00072 and R = 0.98 for the learning process, and MSE = 0.00092 and R = 0.86 for the testing process. Thus, the RBFNN can be set as the best model for monthly rainfall prediction.
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Safavi, A., M. H. Esteki, S. M. Mirvakili, and M. Khaki. "Comparison of back propagation network and radial basis function network in Departure from Nucleate Boiling Ratio (DNBR) calculation." Kerntechnik 85, no. 1 (December 1, 2020): 15–25. http://dx.doi.org/10.1515/kern-2020-850105.
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Abstract Since estimating the minimum departure from nucleate boiling ratio (MDNBR) requires complex calculations, an alternative method has always been considered. One of these methods is neural network. In this study, the Back Propagation Neural network (BPN) and Radial Basis Function Neural network (RBFN) are introduced and compared in order to estimate MDNBR of the VVER-1000 light water reactor. In these networks, the MDNBR were predicted with the inputs including core mass flux, core inlet temperature, pressure, reactor power level and position of the control rods. To obtain the data required to design these neural networks, an externally coupledcode was developed and its ability to estimate the thermo-hydraulic parameters of the VVER-1000 reactor was compared with other numerical solutions of this benchmark and the Final Safety Analysis Report (FSAR). After ensuring the accuracy of this coupled-code, MDNBR was calculated for 272 different conditions of reactor operating, and it was used to design BPN and RBFN. Comparison of these two neural networks revealed that when the output SMEs of the two systems were approximately the same, the training process in RBFN was much faster than in BPN and the maximum network error in RBFN was less than in BPN.
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Juliani, Cyril, and Steinar Ellefmo. "Prospectivity Mapping of Mineral Deposits in Northern Norway Using Radial Basis Function Neural Networks." Minerals 9, no. 2 (February 24, 2019): 131. http://dx.doi.org/10.3390/min9020131.
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In this paper, the radial basis function neural network (RBFNN) is used to generate a prospectivity map for undiscovered copper-rich (Cu) deposits in the Finnmark region, northern Norway. To generate the input data for RBFNN, geological and geophysical data, including up to 86 known mineral occurrences hosted in mafic host-rocks, were combined at different resolutions. Mineral occurrences were integrated into “deposit” and “non-deposit” training sets. Running RBFNN on different input vectors, with a k-fold cross-validation method, showed that increasing the number of iterations and radial basis functions resulted in: (1) a reduction of training mean squared error (MSE) down to 0.1, depending on the grid resolution, and (2) reaching correct classification rates of 0.9 and 0.6 for training and validation, respectively. The latter depends on: (1) the selection of “non-deposit” training data throughout the study area, (2) the scale at which data was acquired, and (3) the dissimilarity of input vectors. The “deposit” input data were correctly identified by the trained model (up to 83%) after proceeding to classification of non-training data. Up to 885 km2 of the Finnmark region studied is favorable for Cu mineralization based on the resulting mineral prospectivity map. The prospectivity map can be used as a reconnaissance guide for future detailed ground surveys.
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Huang, Wei, and Jinsong Wang. "Design of Polynomial Fuzzy Radial Basis Function Neural Networks Based on Nonsymmetric Fuzzy Clustering and Parallel Optimization." Mathematical Problems in Engineering 2013 (2013): 1–10. http://dx.doi.org/10.1155/2013/745314.
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We first propose a Parallel Space Search Algorithm (PSSA) and then introduce a design of Polynomial Fuzzy Radial Basis Function Neural Networks (PFRBFNN) based on Nonsymmetric Fuzzy Clustering Method (NSFCM) and PSSA. The PSSA is a parallel optimization algorithm realized by using Hierarchical Fair Competition strategy. NSFCM is essentially an improved fuzzy clustering method, and the good performance in the design of “conventional” Radial Basis Function Neural Networks (RBFNN) has been proven. In the design of PFRBFNN, NSFCM is used to design the premise part of PFRBFNN, while the consequence part is realized by means of weighted least square (WLS) method. Furthermore, HFC-PSSA is exploited here to optimize the proposed neural network. Experimental results demonstrate that the proposed neural network leads to better performance in comparison to some existing neurofuzzy models encountered in the literature.
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Chen, Xu Sheng, Chen Peng Xu, and Hong Qi Wang. "Equipment Manufacturing Industry Knowledge Chain Efficiency Prediction Algorithm Based on Improved RBFNN." Applied Mechanics and Materials 441 (December 2013): 776–79. http://dx.doi.org/10.4028/www.scientific.net/amm.441.776.
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A new knowledge chain efficiency prediction arithmetic in equipment manufacturing industry in China was proposed, Radial basis function neural network (RBFNN) was designed, and initial temperature numerical calculation arithmetic was adopted to adjust the network weights. MATLAB program was compiled; experiments on related data have been done employing the program. All experiments have shown that the arithmetic can efficiently approach the precision with 10-4 error, also the learning speed is quick and predictions are ideal. Trainings have been done with other networks in comparison. Back-propagation learning algorithm network does not converge until 2400 iterative procedure, and Efficiency design Radial basis function neural network is time-consuming and has big error. The arithmetic in paper can approach nonlinear function by arbitrary precision, and also keep the network from getting into partial minimum.
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Saxena, Akash, and Ankit Kumar Sharma. "Assessment of Global Voltage Stability Margin through Radial Basis Function Neural Network." Advances in Electrical Engineering 2016 (September 29, 2016): 1–11. http://dx.doi.org/10.1155/2016/4858431.
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Dynamic operating conditions along with contingencies often present formidable challenges to the power engineers. Decisions pertaining to the control strategies taken by the system operators at energy management centre are based on the information about the system’s behavior. The application of ANN as a tool for voltage stability assessment is empirical because of its ability to do parallel data processing with high accuracy, fast response, and capability to model dynamic, nonlinear, and noisy data. This paper presents an effective methodology based on Radial Basis Function Neural Network (RBFN) to predict Global Voltage Stability Margin (GVSM), for any unseen loading condition of the system. GVSM is used to assess the overall voltage stability status of the power system. A comparative analysis of different topologies of ANN, namely, Feedforward Backprop (FFBP), Cascade Forward Backprop (CFB), Generalized Regression (GR), Layer Recurrent (LR), Nonlinear Autoregressive Exogenous (NARX), ELMAN Backprop, and Feedforward Distributed Time Delay Network (FFDTDN), is carried out on the basis of capability of the prediction of GVSM. The efficacy of RBFN is better than other networks, which is validated by taking the predictions of GVSM at different levels of Additive White Gaussian Noise (AWGN) in input features. The results obtained from ANNs are validated through the offline Newton Raphson (N-R) method. The proposed methodology is tested over IEEE 14-bus, IEEE 30-bus, and IEEE 118-bus test systems.
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Gil Vera, Víctor Daniel, Catalina Quintero López, Isabel Cristina Puerta Lópera, and Gabriel Jaime Correa Henao. "Classification of Adolescent Offenders of the Law with Radial Neural Network Bases Function." Modern Applied Science 13, no. 10 (September 17, 2019): 39. http://dx.doi.org/10.5539/mas.v13n10p39.
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Radial Basis Function Neural Networks (RBFNN) are a type of artificial neuronal network (ANN) that estimate the output of the function taking as a reference the distance to a point called center. This paper presents a RBFNN for the classification of adolescents’ offenders of the law according to their dangerousness level, that have been admitted to the Specialized Attention Center (SAC), “El Redentor” in Bogotá, Colombia in the year 2017. This classification may be utilized by psychosocial teams of the SAC in order to customize and make more effective the therapeutic pedagogical treatment. The ANN developed is particularly good for identifying adolescents with a high, low and null dangerousness level.
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ANAND, P., B. V. N. SIVA PRASAD, and CH VENKATESWARLU. "MODELING AND OPTIMIZATION OF A PHARMACEUTICAL FORMULATION SYSTEM USING RADIAL BASIS FUNCTION NETWORK." International Journal of Neural Systems 19, no. 02 (April 2009): 127–36. http://dx.doi.org/10.1142/s0129065709001896.
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A Pharmaceutical formulation is composed of several formulation factors and process variables. Quantitative model based pharmaceutical formulation involves establishing mathematical relations between the formulation variables and the resulting responses, and optimizing the formulation conditions. In a formulation system involving several objectives, the desirable formulation conditions for one property may not always be desirable for other characteristics, thus leading to the problem of conflicting objectives. Therefore, efficient modeling and optimization techniques are needed to devise an optimal formulation system. In this work, a novel method based on radial basis function network (RBFN) is proposed for modeling and optimization of pharmaceutical formulations involving several objectives. This method has the advantage that it automatically configures the RBFN using a hierarchically self organizing learning algorithm while establishing the network parameters. This method is evaluated by using a trapidil formulation system as a test bed and compared with that of a response surface method (RSM) based on multiple regression. The simulation results demonstrate the better performance of the proposed RBFN method for modeling and optimization of pharmaceutical formulations over the regression based RSM technique.
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Hidayat, M. I. P., and Wajan Berata. "Neural Networks with Radial Basis Function and NARX Structure for Material Lifetime Assessment Application." Advanced Materials Research 277 (July 2011): 143–50. http://dx.doi.org/10.4028/www.scientific.net/amr.277.143.
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In the present paper, neural networks (NN) with radial basis function and non-linear auto-regressive exogenous inputs (NARX) structure is introduced and first applied for predicting fatigue lives of composite materials. Fatigue life assessment of multivariable amplitude loading linked to the concept of constant life diagrams (CLD), the well known concept in fatigue of material analysis and design, was investigated. With this respect, fatigue life assessment using the RBFNN-NARX model was realized as one-step ahead prediction with respect to each stress level-S corresponding to stress ratio values-R arranged in such a way that transition took place from a fatigue region to another one in the CLD. As a result, composite materials lifetime assessment can be fashioned for a wide spectrum of loading in an efficient manner. In addition, the produced mean squared error (MSE) values of fatigue life prediction results of the RBFNN-NARX model competed favorably, even better, with those of the MLP-NARX model previously obtained. The simulation results for different multidirectional laminates of polymeric-based composites and loading situations were presented and discussed.
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Wang, Feilu, and Yang Song. "Three-Dimensional Force Prediction of a Flexible Tactile Sensor Based on Radial Basis Function Neural Networks." Journal of Sensors 2021 (March 16, 2021): 1–12. http://dx.doi.org/10.1155/2021/8825019.
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A flexible tactile sensor array with 6 × 6 N-type sensitive elements made of conductive rubber is presented in this paper. The property and principle of the tactile sensor are analyzed in detail. Based on the piezoresistivity of conductive rubber, this paper takes full advantage of the nonlinear approximation ability of the radial basis function neural network (RBFNN) method to approach the high-dimensional mapping relation between the resistance values of the N-type sensitive element and the three-dimensional (3D) force and to accomplish the accurate prediction of the magnitude of 3D force loaded on the sensor. In the prediction process, the k -means algorithm and recursive least square (RLS) method are used to optimize the RBFNN, and the k -fold cross-validation method is conducted to build the training set and testing set to improve the prediction precision of the 3D force. The optimized RBFNN with different spreads is used to verify its influence on the performance of 3D force prediction, and the results indicate that the spread value plays a very important role in the prediction process. Then, sliding window technology is introduced to build the RBFNN model. Experimental results show that setting the size of the sliding window appropriately can effectively reduce the prediction error of the 3D force exerted on the sensor and improve the performance of the RBFNN predictor, which means that the sliding window technology is very feasible and valid in 3D force prediction for the flexible tactile sensor. All of the results indicate that the optimized RBFNN with high robustness can be well applied to the 3D force prediction research of the flexible tactile sensor.
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Sarboland, Maryam, and Azim Aminataei. "On the Numerical Solution of One-Dimensional Nonlinear Nonhomogeneous Burgers’ Equation." Journal of Applied Mathematics 2014 (2014): 1–15. http://dx.doi.org/10.1155/2014/598432.
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The nonlinear Burgers’ equation is a simple form of Navier-Stocks equation. The nonlinear nature of Burgers’ equation has been exploited as a useful prototype differential equation for modeling many phenomena. This paper proposes two meshfree methods for solving the one-dimensional nonlinear nonhomogeneous Burgers’ equation. These methods are based on the multiquadric (MQ) quasi-interpolation operatorℒ𝒲2and direct and indirect radial basis function networks (RBFNs) schemes. In the present schemes, the Taylors series expansion is used to discretize the temporal derivative and the quasi-interpolation is used to approximate the solution function and its spatial derivatives. In order to show the efficiency of the present methods, several experiments are considered. Our numerical solutions are compared with the analytical solutions as well as the results of other numerical schemes. Furthermore, the stability analysis of the methods is surveyed. It can be easily seen that the proposed methods are efficient, robust, and reliable for solving Burgers’ equation.
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Lee, Dongwoo, Sybil Derrible, and Francisco Camara Pereira. "Comparison of Four Types of Artificial Neural Network and a Multinomial Logit Model for Travel Mode Choice Modeling." Transportation Research Record: Journal of the Transportation Research Board 2672, no. 49 (September 20, 2018): 101–12. http://dx.doi.org/10.1177/0361198118796971.
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Discrete choice modeling is a fundamental part of travel demand forecasting. To date, this field has been dominated by parametric approaches (e.g., logit models), but non-parametric approaches such as artificial neural networks (ANNs) possess much potential since choice problems can be assimilated to pattern recognition problems. In particular, ANN models are easily applicable with their higher capability to identify nonlinear relationships between inputs and designated outputs to predict choice behaviors. This article investigates the capability of four types of ANN model and compares their prediction performance with a conventional multinomial logit model (MNL) for mode choice problems. The four ANNs are: backpropagation neural networks (BPNNs), radial basis function networks (RBFNs), probabilistic neural networks (PNNs), and clustered probabilistic neural networks (CPNNs). To compare the modeling techniques, we present the algorithmic differences of each ANN technique, and we assess their prediction accuracy with a 10-fold cross-validation method. Furthermore, we assess the contribution of explanatory variables by conducting sensitivity analyses on significant variables. The results show that ANN models outperform MNL, with prediction accuracies around 80% compared with 70% for MNL. Moreover, PNN performs best out of all ANNs, especially to predict underrepresented modes.
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Ma, Y., A. Engeda, M. Cave, and J.-L. Di Liberti. "Improved centrifugal compressor impeller optimization with a radial basis function network and principle component analysis." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 224, no. 4 (April 1, 2010): 935–45. http://dx.doi.org/10.1243/09544062jmes1635.
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The development of a fast and reliable computer-aided design and optimization procedure for centrifugal compressors has attracted a great deal of attention both in the industry and in academia. Artificial neural networks (ANNs) have been widely used to create an approximate performance map to substitute the direct application of flow solvers in the optimization procedure. Although ANNs greatly decrease the computational time for the optimization, their accuracies still limit their applications. Furthermore, ANNs also bring errors to the final results. In this study, principal component analysis (PCA) or independent component analysis (ICA) is applied to transform the training database and make a radial basis function network (RBFN), a type of ANN, trained in a new coordinate system. The present study compares the accuracies of three different trained ANNs: RBFN, RBFN with PCA, and RBFN with ICA. Furthermore, the total performances of the centrifugal compressor impeller optimization procedures using these three different trained ANNs are compared. Genetic algorithm (GA) is used as an optimization method in the optimization procedure and influences of GA parameters on the optimization procedure performances are also studied. All results demonstrate that the application of PCA significantly increases the accuracy of trained ANN as well as the total performance of the centrifugal compressor impeller optimization procedure.
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Ali, Syed Saad Azhar, Muhammad Moinuddin, Kamran Raza, and Syed Hasan Adil. "An Adaptive Learning Rate for RBFNN Using Time-Domain Feedback Analysis." Scientific World Journal 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/850189.
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Radial basis function neural networks are used in a variety of applications such as pattern recognition, nonlinear identification, control and time series prediction. In this paper, the learning algorithm of radial basis function neural networks is analyzed in a feedback structure. The robustness of the learning algorithm is discussed in the presence of uncertainties that might be due to noisy perturbations at the input or to modeling mismatch. An intelligent adaptation rule is developed for the learning rate of RBFNN which gives faster convergence via an estimate of error energy while giving guarantee to thel2stability governed by the upper bounding via small gain theorem. Simulation results are presented to support our theoretical development.