Abstract: The adaptive network-based fuzzy inference systems (ANFIS) of Jang (1993) is extended to the generalized ANFIS (GANFIS) by proposing a generalized fuzzy model (GFM) and considering a generalized radial basis function (GRBF) network. The GFM encompasses both the Takagi-Sugeno (TS)-model and the compositional rule of inference (CRI) model. The conditions by which the proposed GFM converts to TS-model or the CRI-model are presented. The basis function in GRBF is a generalized Gaussian function of three parameters. The architecture of the GRBF network is devised to learn the parameters of GFM, where the GRBF network and GFM have been proved to be functionally equivalent. It Is shown that GRBF network can be reduced to either the standard RBF or the Hunt's RBF network. The issue of the normalized versus the non-normalized GRBF networks is investigated in the context of GANFIS. An interesting property of symmetry on the error surface of GRBF network is investigated. The proposed GANFIS is applied to the modeling of a multivariable system like stock market.

Abstract: A performance analysis is presented of the minimal resource allocating network (MRAN) algorithm for online identification of nonlinear dynamic systems. Using nonlinear time-invariant and time-varying identification benchmark problems, MRAN's performance is compared with the online structural adaptive hybrid learning (ONSAHL) algorithm. Results indicate that the MRAN algorithm realises networks using fewer hidden neurons than the ONSAHL algorithm, with better approximation accuracy. Methods for improving the run-time performance of MRAN for real-time identification of nonlinear systems are developed. An extension to MRAN is presented, which utilises a winner neuron strategy and is referred to as the extended minimum resource allocating network (EMRAN). This modification reduces the computation load for MRAN and leads to considerable reduction in the identification time, with only a small increase in the approximation error. Using the same benchmark problems, results show that EMRAN is well suited for fast online identification of nonlinear plants.

Abstract: A new high-resolution direction of arrival (DOA) estimation technique using a neural fuzzy network based on phase difference (PD) is proposed. The conventional DOA estimation method such as MUSIC and MLE, are computationally intensive and difficult to implement in real time. To attack these problems, neural networks have become popular for DOA estimation. However, the normal neural networks such as the multilayer perceptron (MLP) and radial basis function network (RBFN) usually produce the extra problems of low convergence speed and/or large network size (i.e., the number of network parameters is large). Also, the may to decide the network structure is heuristic. To overcome these defects and take use of neural learning ability, a powerful self-constructing neural fuzzy inference network (SONFIN) is used to develop a new DOA estimation algorithm. By feeding the PDs of the received radar-array signals, the trained SONFIN can give high-resolution DOA estimation. The proposed scheme is thus called PD-SONFIN. This new algorithm avoids the need of empirically determining the network size and parameters in normal neural networks due to the powerful on-line structure and parameter learning ability of SONFIN. The PD-SONFIN can always find itself an economical network size in the fast learning process. Our simulation results show that the performance of the new algorithm is superior to the RBFN in terms of convergence accuracy, estimation accuracy, sensitivity to noise, and network size.

Abstract: In intelligent control applications, neural models and controllers are usually designed by performing an off-line training, and then adapting it online when placed in the operating environment. It is therefore of crucial importance to obtain a good off-line model by means of a good off-line training algorithm. In the paper a method is presented that fully exploits the linear-nonlinear structure found in radial basis function networks, being additionally applicable to other feedforward supervised neural networks. The new algorithm is compared with two known hybrid methods.

Abstract: This paper considers the optimization of complex multi-parameter systems in which the objective function is not known explicitly, and can only be evaluated either through costly physical experiments or through computationally intensive numerical simulation. Furthermore, the objective function of interest may contain many local extrema. Given a data set consisting of the value of the objective function at a scattered set of parameter values, we are interested in developing a response surface model to reduce dramatically the required computation time for parameter optimization runs.To accomplish these tasks, a response surface model is developed using radial basis functions. Radial basis functions provide a way of creating a model whose objective function values match those of the original system at all sampled data points. Interpolation to any other point is easily accomplished and generates a model which represents the system over the entire parameter space. This paper presents the details of the use

Abstract: Volumetric scans of radar reflectivity Z and gage measurements of rainfall intensity R are used to explore the capabilities of three artificial neural networks to identify and reproduce the functional relationship between Z and R. The three networks are a multilayer perceptron, a Bayesian network, and a radial basis function network. For each of them, numerical experiments are conducted incorporating in the network inputs different descriptions of the space-time variability of Z. Space variability refers to the observations of Z along the vertical atmospheric profile, at 11 constant altitude plan position indicator levels, namely ZT = (Z1,…,Z11). Time variability refers to the observations of Z at the time intervals prior to that for which the estimate of R is provided. Space variability is evaluated by performing a principal component analysis over standardized values of Z, namely Z˜, and the first two principal components of Z˜ (which describe 91% of the original variance) are used to synthesize the elements of Z into fewer orthogonal inputs for the networks. Network predictions significantly improve when the models are trained with the two principal components of Z˜ with respect to the case in which only Z1 is used. Increasing the time horizon further improves the performances of the Bayesian network but is found to worsen the performances of the other two networks.

Abstract: One of the main obstacles to the widespread use of artificial neural networks is the difficulty of adequately defining values for their free parameters. The article discusses how radial basis function (RBF) networks can have their parameters defined by genetic algorithms. For such, it presents an overall view of the problems involved and the different approaches used to genetically optimize RBF networks. Finally, a model is proposed which includes representation, crossover operator and multiobjective optimization criteria. Experimental results using this model are presented.

Abstract: A model-based recurrent neural network (MBRNN) is introduced for modeling dynamic systems. This network has a fixed structure that is defined according to the linearized state-space model of the plant. Therefore, the MBRNN has the ability to incorporate the analytical knowledge of the plant in its formulation. With its original topology intact, the MBRNN can then be trained to represent the plant nonlinearities through modifying its nodes' activation functions, which consist of contours of Gaussian radial basis functions (RBFs). Training in MBRNN involves adjusting the weights of the RBF's so as to modify the contours representing the activation functions. The performance of the MBRNN is demonstrated via several examples. The results indicate that it requires much shorter training than needed by ordinary recurrent networks. This efficiency in training is attributed to the MBRNN's fixed topology which is independent of training.

Abstract: This paper proposes using a model predictive control (MPC) incorporating a radial basis function (RBF) network observer for the fuel injection problem. Two new contributions are presented. First, an RBF Network is used as an observer for the volumetric efficiency of the air system. This allows for gradual adaptation of the observer, ensuring the control scheme is capable of maintaining good performance under changing engine conditions brought about by engine wear, variations between individual engines and other similar factors. The other is the rise of model predictive control algorithms to compensate for the fuel pooling effect on the intake manifold walls. Two MPC algorithms are presented which enforce input, and input and state constraints. A comparison between the two constrained MPC algorithms is qualitatively presented, and some conclusions drawn about the necessity of constraints for the fuel injection problem. Simulation and actual engine results are presented that demonstrate the effectiveness of the control scheme.

Abstract: In this paper, we study approximation by radial basis functions including Gaussian, multiquadric, and thin plate spline functions, and derive order of approximation under certain conditions. Moreover, neural networks are also constructed by wavelet recovery formula and wavelet frames.

Abstract: A hybrid architecture that includes Radial Basis Functions (RBF) and projection based hidden units is introduced together with a simple gradient based training algorithm. Classification and regression results are demonstrated on various data sets and compared with several variants of RBF networks. In particular, best classification results are achieved on the vowel classification data [1].

Abstract: This chapter deals with a special class of artificial neural networks (ANNs) called radial-basis function (RBF) networks. These networks derive their structure and interpretation from the theory of interpolation in multidimensional spaces, and have a mathematical foundation imbedded in regularization theory for solving ill-conditioned problems. Such networks, almost invariably, consist of three layers — a transparent input layer, a hidden layer with sufficiently large number of nodes, and an output layer. As their name implies, radially symmetric basis functions are used as activation functions of hidden nodes. The networks are organized so that transformations at the hidden units are equivalent to a set of functions that form a basis allowing input patterns to be mapped into output patterns. The number of units in the hidden layer, therefore, needs to be sufficiently large so as to span the space in which the interpolation is being performed. A careful design is required to prevent the hidden layer of an RBF network from becoming too large as that can lead to over-fitting.

Abstract: We propose a framework for constructing and training a radial basis function (RBF) neural network. The structure of the gaussian functions is modified using a pseudo-gaussian function (PG) in which two scaling parameters σ are introduced, which eliminates the symmetry restriction and provides the neurons in the hidden layer with greater flexibility with respect to function approximation. We propose a modified PG-BF (pseudo-gaussian basis function) network in which the regression weights are used to replace the constant weights in the output layer. For this purpose, a sequential learning algorithm is presented to adapt the structure of the network, in which it is possible to create a new hidden unit and also to detect and remove inactive units. A salient feature of the network systems is that the method used for calculating the overall output is the weighted average of the output associated with each receptive field. The superior performance of the proposed PG-BF system over the standard RBF are illustrated using the problem of short-term prediction of chaotic time series.

Abstract: A novel approach to adaptive direct neurocontrol is discussed in this paper. The objective is to construct an adaptive control scheme for unknown time-dependent nonlinear plants without using a model of the plant. The proposed approach is neural-network based and combines the self-tuning principle with reinforcement learning. The control scheme consists of a controller, a utility estimator, an exploration module, a learning module and a rewarding module. The controller and the utility estimator are implemented together in a single radial basis function network. The learning method involves structural adaptation (growing neural network) and parameter adaptation. No prior knowledge of the plant is assumed, and the controller has to begin with exploration of the state space. The exploration–exploitation dilemma is solved through smooth transitions between the two modes. This enables rapid exploration response to novel plant dynamics and stable operation in the absence of changes in plant dynamics. The controller is capable of asymptotically approaching the desired reference trajectory, which is demonstrated in a simulation study.

Abstract: An online control scheme that utilizes a dynamically structured radial basis function network (RBFN) is developed for aircraft control. By using Lyapunov synthesis approach, the tuning rule for updating all the parameters of the dynamic RBFN which guarantees the stability of the overall system is derived. The robustness of the proposed tuning rule is also analyzed. Simulation studies using the F8 aircraft longitudinal model demonstrates the efficiency of the method and also show that with a dynamically structured RBFN, a more compact network structure can be implemented.

Abstract: It is often assumed that interference or noise signals are Gaussian stochastic processes. Gaussian noise models are appealing as they usually result in noise suppression algorithms that are simple: i.e. linear and closed form. However, such linear techniques may be sub-optimal when the noise process is either a non-Gaussian stochastic process or a chaotic deterministic process. In the event of encountering such noise processes, improvements in noise suppression, relative to the performance of linear methods, may be achievable using nonlinear signal processing techniques. The application of interest for this thesis is maritime surveillance radar, where the main source of interference, termed sea clutter, is widely accepted to be a non-Gaussian stochastic process at high resolutions and/or at low grazing angles. However, evidence has been presented during the last decade which suggests that sea clutter may be better modelled as a chaotic deterministic process. While the debate over which model is more suitable continues, this thesis investigates whether nonlinear processing techniques can be used to improve the performance of maritime surveillance radar, relative to the performance achievable using linear techniques. Linear and nonlinear prediction of chaotic signals, sea clutter data sets, and stochastic surrogate clutter data sets is carried out. Volterra series filter networks and radial basis function networks are used to implement nonlinear predictors. A novel structure for a forward-backward nonlinear predictor, using a radial basis function network, is presented. Prediction results provide evidence to support the view that sea clutter is better modelled as a stochastic process, rather than as a chaotic process. The clutter data sets are shown to have linear predictor functions. Linear and nonlinear predictors are used as the basis of target detection algorithms. The performance of these predictor-detectors, against backgrounds of sea clutter data and against a background of chaotic noise data is evaluated. The detection results show that linear predictor-detectors perform as well as, or better than, nonlinear predictor-detectors against the non-Gaussian clutter backgrounds considered in this thesis, whilst the reverse is true for a background of chaotic noise. An existing, nonlinear inverse, noise cancellation technique, referred to as Broomhead’s filtering technique in this thesis, is re-investigated using a sine wave corrupted by broadband chaotic noise. It is demonstrated that significant improvements can be obtained using this nonlinear inverse technique, relative to results obtained using linear alternatives, despite recent work which suggested otherwise. A novel bandstop filtering approach is applied to Broomhead’s filtering method, which allows the technique to be applied to the cancellation of signals with a band of interest greater than that of a sine wave. This modified Broomhead filtering technique is shown to cancel broadband chaotic noise from a narrowband Gaussian signal better than alternative linear methods. The modified Broomhead filtering technique is shown to only perform as well as, or more poorly than, a linear technique on narrowband Gaussian signals corrupted by clutter data.

Abstract: We apply complexity regularization to learn normalized radial basis function networks in nonparametric classification. We study convergence and the rates of convergence of the empirically trained networks and verify the results in computer experiments.

Abstract: This is basic research for assigning color values to voxels of multichannel MRI volume data. The MRI volume data sets obtained under different scanning conditions are transformed into their components by independent component analysis (ICA), which enhances the physical characteristics of the tissue. The transfer functions for generating color values from independent components are obtained using a radial basis function network, a kind of neural net, by training the network with sample data chosen from the Visible Female data set. The resultant color volume data sets correspond well with the full-color cross-sections of the Visible Human data sets.

Abstract: A GRBF network is designed for VLSI implementation. Building blocks of the network consist mainly of analog circuits: op amp, multiplier, multiplying DAC (digital to analog converter), floating resistor, summer and exponentiator. Parameters of the network (center, width of the Gaussian function and output layer weights) are represented digitally for convenient interfacing. It is shown that individual GRBF units allow independent tuning of center, width and amplitude. Several network structures are simulated as function approximation examples, and the performance is verified to be satisfactory.

Abstract: In order to reduce the complexity of a radial basis function (RBF) network as a multiuser demodulator and an equalizer, we propose a simplified hybrid neural network architecture. The proposed neural network, which is called RN, has the structure of combining a radial basis function network with multilayer perceptrons (MLPs). The RBF network yields the linear combining output of the hidden layer while the proposed hybrid neural network produces the output using nonlinear combining techniques. From computer simulation results, the RN with the reduced structure from about 50% to about 70% over the RBF network shows better than or almost equal performance to the RBF network as a multiuser demodulator and an equalizer.

Abstract: We explore the use of various learning algorithms to predict the user's measure of similarity between a given query image and images in a database. Our aim is to obtain a similarity coefficient, for use in image retrieval, that more accurately reflects that of the user. The performance of a variety of learning machines was evaluated using statistical resampling to estimate the prediction error and retrieval effectiveness. The proposed approach was demonstrated using synthetic shape and texture examples. The results of the study are very promising, especially those obtained by the general regression neural network and the support vector machine/radial basis function method.

Abstract: A general framework for similarity-based (SB) classification methods is presented. Neural networks, such as the Radial Basis Function (RBF) and the Multilayer Perceptrons (MLPs) models, are special cases of SB methods. Many new versions of minimal distance methods are derived from this framework.

Abstract: Builds upon an axiomatic approach proposed for constructing reformulated radial basis function (RBF) neural networks suitable for gradient descent learning. This approach reduces the construction of RBF models to the selection of admissible generator functions. The selection of generator functions relies on criteria resulting from the analysis of the sensitivity of reformulated RBF models to gradient descent learning. The results of the study outlined in the paper are verified by a series of experiments on speech data.