Gaussian Radial Basis Function Networks Research Articles

Wind Speed Estimation Based Sensorless Output Maximization Control for a Wind Turbine Driving a DFIG

This paper proposes a wind speed estimation based sensorless maximum wind power tracking control for variable-speed wind turbine generators (WTGs). A specific design of the proposed control algorithm for a wind turbine equipped with a doubly fed induction generator (DFIG) is presented. The aerodynamic characteristics of the wind turbine are approximated by a Gaussian radial basis function network based nonlinear input-output mapping. Based on this nonlinear mapping, the wind speed is estimated from the measured generator electrical output power while taking into account the power losses in the WTG and the dynamics of the WTG shaft system. The estimated wind speed is then used to determine the optimal DFIG rotor speed command for maximum wind power extraction. The DFIG speed controller is suitably designed to effectively damp the low-frequency torsional oscillations. The resulting WTG system delivers maximum electrical power to the grid with high efficiency and high reliability without mechanical anemometers. The validity of the proposed control algorithm is verified by simulation studies on a 3.6MW WTG system. In addition, the effectiveness of the proposed wind speed estimation algorithm is demonstrated by experimental studies on a small emulational WTG system.

Prediction of leakage current of non-ceramic insulators in early aging period

The paper presents a neural network based prediction technique for the leakage current (LC) of non-ceramic insulators during salt-fog test. Nearly 50 distribution class silicone rubber (SIR) insulators with three different voltage classes have been tested in a salt-fog chamber, where the LC has been continuously recorded for at least 100 h. A boundary for early aging period is defined by the rate of change of the LC instead of a fixed threshold value. Consequently, the Gaussian radial basis network has been adopted to predict the level of LC at the early stage of aging of the SIR insulators and is compared with a classical network. The initial values of LC and its rate of change at 10 min intervals for the first 5 h are selected as the input to the network, and the final value of LC of the early aging period is considered as the output of the network. It is found that Gaussian radial basis function network with a random optimizing training method is an appropriate network to predict the LC with a 3.5–5.3% accuracy, if the training data and the testing data are selected from the same type of SIR insulators.

An Adaptive Approximator-Based Backstepping Control Approach for Piezoactuator-Driven Stages

This paper investigates precise trajectory tracking of a piezoactuator-driven stage with hysteresis behavior by using an approximator-based adaptive tracking control approach. Differential equations consisting of the dynamics of a linear motion system and a hysteresis function are first studied for describing the dynamics of motion of the piezoactuator-driven stage with hysteresis behavior. Then, a numerical optimization method is taken to identify the values of the parameters adopted in the differential equations. From the differential equations, an equivalent state-space model with an augmented integral input and with a defined hysteresis variable is established. Moreover, to approximate the unavailable hysteresis variable, an adaptive approximator that comprises a Gaussian radial-basis function network is adopted. Furthermore, from the state-space model, an adaptive approximator-based backstepping trajectory-tracking control is developed. Using the proposed control approach to trajectory tracking of the piezoactuator-driven stage, an improvement in transient performance and tracking errors, and robustness to the disturbance load, can be provided. Last, to show the validity of the proposed control approach, an implementation of the control algorithm on the computer-controlled single-axis piezoactuator-driven stage was developed. From the experimental results, the feasibility of the proposed control for practical applications can be confirmed.

Kernel Classifier Construction Using Orthogonal Forward Selection and Boosting With Fisher Ratio Class Separability Measure

A greedy technique is proposed to construct parsimonious kernel classifiers using the orthogonal forward selection method and boosting based on Fisher ratio for class separability measure. Unlike most kernel classification methods, which restrict kernel means to the training input data and use a fixed common variance for all the kernel terms, the proposed technique can tune both the mean vector and diagonal covariance matrix of individual kernel by incrementally maximizing Fisher ratio for class separability measure. An efficient weighted optimization method is developed based on boosting to append kernels one by one in an orthogonal forward selection procedure. Experimental results obtained using this construction technique demonstrate that it offers a viable alternative to the existing state-of-the-art kernel modeling methods for constructing sparse Gaussian radial basis function network classifiers that generalize well.

Model combination in neural-based forecasting

This paper discusses different ways of combining neural predictive models or neural-based forecasts. The proposed approaches consider Gaussian radial basis function networks, which can be efficiently identified and estimated through recursive/adaptive methods. The usual framework for linearly combining estimates from different models is extended, to cope with the case where the forecasting errors from those models are correlated. A prefiltering methodology is proposed, addressing the problems raised by heavily nonstationary time series. Moreover, the paper discusses two approaches for decision-making from forecasting models: either inferring decisions from combined predictive estimates, or combining prescriptive solutions derived from different forecasting models.

Neural model adaptation and predictive control of a chemical process rig

An adaptation algorithm for Gaussian radial basis function (RBF) network models is proposed. The model structure is adapted to cope with operating region change, while the weight parameters are updated to model time varying dynamics or uncertainties. The special feature is that the modeling accuracy is maintained during adaptation and, therefore, the control performance will not be degraded when the model structure changes. A localized forgetting method is proposed to deal with nonlinearities in different operating regions, and is implemented with the recursive orthogonal least squares (ROLS) training algorithm. The developed adaptive model is evaluated by real data modeling of a three-input three-output chemical process rig. Online model predictive control (MPC) of the rig is also conducted. Improved tracking performance with the adaptive model is demonstrated in comparison with nonadaptive model-based control and decentralized propotional-integral-differential (PID) control.

An online learning algorithm with dimension selection using minimal hyper basis function networks

In this study, the authors propose an HMRAN (Hyper MRAN) for which dimension selection is possible, by extending a minimal resource allocating network (MRAN) for online learning with minimized resources, with the application of a growth strategy and pruning strategy for hidden units in a Gaussian radial basis function (GRBF) network. When the input is a multidimensional pattern, it is often the case that dimensions with an explicit relationship to the output are limited to a single section and it is difficult to develop a correspondence with a MRAN having an isotropic Gaussian function as the basis function. Dimension selection can be flexibly performed in basis function units with the use of a hyper basis function (Hyper BF) instead of a Gaussian function. Furthermore, computational complexity is reduced by using a localized extended Kalman filter (LEKF) and the introduction of a merging strategy for the basis function and improvements to the pruning strategy resulted in a reduction of the resources needed. A number of benchmark tests were performed and it was confirmed that the proposed technique can be implemented with good accuracy and minimal resources compared to the conventional technique. © 2006 Wiley Periodicals, Inc. Syst Comp Jpn, 37(11): 11–21, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/scj.20507

ON THE STRUCTURE AND INITIAL PARAMETER IDENTIFICATION OF GAUSSIAN RBF NETWORKS

We consider the efficient initialization of structure and parameters of generalized Gaussian radial basis function (RBF) networks using fuzzy decision trees generated by fuzzy ID3 like induction algorithms. The initialization scheme is based on the proposed functional equivalence property of fuzzy decision trees and generalized Gaussian RBF networks. The resulting RBF network is compact, easy to induce, comprehensible, and has acceptable classification accuracy with stochastic gradient descent learning algorithm.

A Localized Forgetting Method for Gaussian RBFN Model Adaptation

In this paper a localized forgetting method is proposed for on-line adaptation of Gaussian radial basis function network models. It is realised that the commonly used exponential forgetting applies to the past data from the entire operating space uniformly and therefore, is not correct for nonlinear systems where dynamics are different in different operating regions. The new method proposed in this paper sets different forgetting factors in different regions according to the response of the local centre to the current measurement data. The method is applied in conjunction with the recursive orthogonal Least Squares algorithm and the computing is consequently very efficient. The developed method is applied to modelling of dissolved oxygen in a chemical reactor rig. It shows a smaller mean squared error for one-step-ahead prediction than using the uniform forgetting.

A View-Invariant Face Detection Method Based on Local PCA Cells

This paper presents a view-invariant face detection method based on local PCA cells. In order to extract the general features of faces at each view and position, Gabor filters and local PCA (Principal Component Analysis) are used. Local PCA cells specialized for each view and position are made by applying the Gaussian to the outputs of local PCA of Gabor features. By applying the Gaussian, only local PCA cells having a view similar to an input give large values. This decreases an adverse influence of the local PCA cells of other views. As a result, only one classifier can treat multi-view faces well by integrating the outputs of local PCA cells. The effectiveness of the proposed method is confirmed by comparison with Support Vector Machine using Gaussian kernel and Radial Basis Function network. It is also confirmed that generalization ability is improved by selecting local PCA cells using the reconstruction error of local PCA.

Adaptive forecasting of irregular demand processes

The paper presents some comparative results from different approaches for solving the problem of forecasting irregularly spaced time series, including those representing irregular demand processes in inventory management or production planning problems. The best-known methods for that purpose are based on simple exponential smoothing of the time and magnitude of occurrence of demand. It is shown how supervised neural networks can be used as suitable filtering and forecasting models for many of those processes. In particular, we discuss the identification and estimation issues, as well as the limitations associated to the application of Gaussian radial or elliptical basis function networks.

Selecting input factors for clusters of gaussian radial basis function networks to improve market clearing price prediction

In a deregulated power market, bidding decisions rely on good market clearing price prediction. One of the common forecasting methods is Gaussian radial basis function (GRBF) networks that approximate input-output relationships by building localized Gaussian functions (clusters). Currently, a cluster uses all the input factors. Certain input factors, however, may not be significant and should be deleted because they mislead local learning and result in poor predictions. Existing pruning methods for neural networks examine the significance of connections between neurons, and are not applicable to deleting center and standard deviation parameters in a GRBF network since those parameters bear no sense of significance of connection. In this paper, the inverses of standard deviations are found to capture a sense of connection, and based on this finding, a new training method to identify and eliminate unimportant input factors is developed. Numerical testing results from two classroom problems and from New England Market Clearing Price prediction show that the new training method leads to significantly improved prediction performance with a smaller number of network parameters.

Indexed families of functionals and gaussian radial basis functions.

We report on results concerning the capabilities of gaussian radial basis function networks in the setting of inner product spaces that need not be finite dimensional. Specifically, we show that important indexed families of functionals can be uniformly approximated, with the approximation uniform also with respect to the index. Applications are described concerning the classification of signals and the synthesis of reconfigurable classifiers.

Evolving mixture of experts for nonlinear time series modelling and prediction

The evolutionary structure optimisation (ESO) method for Gaussian radial basis function (RBF) networks has already been presented by the authors. Here, they improve the ESO method in its mutation operator and apply it to a mixture of experts (ME) for modelling and predicting nonlinear time series. The ME implementation provides much better generalisation performance with fewer network parameters, compared to the Gaussian RBF networks.

Evolving Basis Function Networks for System Identification

This paper is concerned with learning and optimization of different basis function networks in the aspect of structure adaptation and parameter tuning. Basis function networks include the Volterra polynomial, Gaussian radial, B-spline, fuzzy, recurrent fuzzy, and local Gaussian basis function networks. Based on creation and evolution of the type constrained sparse tree, a unified framework is constructed, in which structure adaptation and parameter adjustment of different basis function networks are addressed using a hybrid learning algorithm combining a modified probabilistic incremental program evolution (MPIPE) and random search algorithm. Simulation results for the identification of nonlinear systems show the feasibility and effectiveness of the proposed method.

Controlling a MIMO process with actuator and component faults

A fault tolerant control strategy for dynamical non-linear processes without mathematical model is proposed in this paper. The approach is based on an adaptive neural network model and a stable control law is used to guarantee convergence of the tracking error between the set-point and the model output. Model adaptation using on-line input/output data is realised by applying the recursive orthogonal least squares algorithm. Since the parameters (centre and weight) of a Gaussian radial basis function network is online adapted, the plant change due to component and actuator faults can be modelled and compensated using the adaptive model based control. A two-input two-output non-linear process simulation is used to demonstrate the performance and effectiveness of the method.

Nonlinear time series modelling and prediction using Gaussian RBF network with evolutionary structure optimisation

An evolutionary structure optimisation method for the Gaussian radial basis function network is presented for modelling and predicting nonlinear time series. The generalisation performance is significantly improved with a much smaller network, compared with that of the previous clustering and least square learning method.

Fuzzy neural network with general parameter adaptation for modeling of nonlinear time-series

By taking advantage of fuzzy systems and neural networks, a fuzzy-neural network with a general parameter (GP) learning algorithm and heuristic model structure determination is proposed in this paper. Our network model is based on the Gaussian radial basis function network (RBFN). We use the flexible GP approach both for initializing the off-line training algorithm and fine-tuning the nonlinear model efficiently in online operation. A modification of the robust unbiasedness criterion using distorter (UCD) is utilized for selecting the structural parameters of this adaptive model. The UCD approach provides the desired modeling accuracy and avoids the risk of over-fitting. In order to illustrate the operation of the proposed modeling scheme, it is experimentally applied to a fault detection application.

Nonlinear System Identification Using Lyapunov Based Fully Tuned Dynamic RBF Networks

This paper presents a stable, on-line identification scheme for multivariable nonlinear dynamic system. Growing Gaussian Radial Basis Function (GRBF) network with all its parameters being adaptable is used to approximate an unknown nonlinear system. Based on a continuous-time framework, the parameter adjustment law is derived using Lyapunov synthesis approach, which guarantees the stability of the overall system. In addition, to ensure the convergence of the approximation error, a growing strategy for the network is selected and a dead zone is incorporated in the tuning law. Simulation studies on identifying a time-varying nonlinear missile dynamics illustrate the superior performance of the proposed scheme. The studies also indicate that stability and reduction in approximation error can be extended to a network with pruning strategy, thereby resulting in a Growing and Pruning (GAP) RBF network, which can implement a more compact network structure.

Time series analysis and prediction on complex dynamical behavior observed in a blast furnace

This paper describes a strategy for building a predictive model for actual complex time series. Time series data of temperature fluctuations observed in a blast furnace for iron-making are taken as an example. Chaotic features of the data are investigated with diagnostic algorithm for instability and parallelism of neighboring trajectories in phase space reconstructed from the time series data. Stationarity of the data is examined with diagnostic algorithm based on the KM 2O–Langevin equations developed by Okabe. A short time series for which no control actions were taken to the plant during measurement is diagnosed as possibly low-dimensional chaos, while for a long time series including many control actions during measurement, determinism is less visible and its predicted behavior exhibits a scaling property similar to self-affine random noise. Characteristic exponents are estimated from the scaling properties of the prediction error as a function of the prediction-time interval. Such information is exploited as prior knowledge for designing a generalized Gaussian radial basis function network as a predictor. The performance of the network is improved when linear algebraic polynomials are added to the network. The characteristic exponents estimated are used as reliability indices of forecasting future trends of the data.