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89
Nonlinear BlackBox Modeling in System Identification: a Unified Overview
 Automatica
, 1995
"... A nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area with structures based on neural networks, radial basis networks, wavelet networks, hinging hyperplanes, ..."
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Cited by 225 (16 self)
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A nonlinear black box structure for a dynamical system is a model structure that is prepared to describe virtually any nonlinear dynamics. There has been considerable recent interest in this area with structures based on neural networks, radial basis networks, wavelet networks, hinging hyperplanes, as well as wavelet transform based methods and models based on fuzzy sets and fuzzy rules. This paper describes all these approaches in a common framework, from a user's perspective. It focuses on what are the common features in the different approaches, the choices that have to be made and what considerations are relevant for a successful system identification application of these techniques. It is pointed out that the nonlinear structures can be seen as a concatenation of a mapping from observed data to a regression vector and a nonlinear mapping from the regressor space to the output space. These mappings are discussed separately. The latter mapping is usually formed as a basis function e...
Bayesian Wavelet Networks for Nonparametric Regression
, 1997
"... Radial wavelet networks have recently been proposed as a method for nonparametric regression. In this paper we analyse their performance within a Bayesian framework. We derive probability distributions over both the dimension of the networks and the network coefficients by placing a prior on the deg ..."
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Cited by 23 (6 self)
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Radial wavelet networks have recently been proposed as a method for nonparametric regression. In this paper we analyse their performance within a Bayesian framework. We derive probability distributions over both the dimension of the networks and the network coefficients by placing a prior on the degrees of freedom of the model. This process bypasses the need to test or select a finite number of networks during the modelling process. Predictions are formed by mixing over many models of varying dimension and parameterization. We show that the complexity of the models adapts to the complexity of the data and produces good results on a number of benchmark test series. Keywords: Wavelets, radial basis functions, model choice, Bayesian neural networks, reversible jump Markov chain Monte Carlo, nonparametric regression, splines. 1 Introduction Wavelet networks have previously been studied in relation to nonparametric regression by Zhang (1997), Kugarajah and Zhang (1995), Zhang and Benveni...
A new class of wavelet networks for nonlinear system identification
 IEEE Trans. Neural Netw
, 2005
"... Abstract—A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a highdimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet d ..."
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Cited by 23 (5 self)
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Abstract—A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a highdimensional system is chosen to be a superimposition of a number of functions with fewer variables. By expanding each function using truncated wavelet decompositions, the multivariate nonlinear networks can be converted into linearintheparameter regressions, which can be solved using leastsquares type methods. An efficient model term selection approach based upon a forward orthogonal least squares (OLS) algorithm and the error reduction ratio (ERR) is applied to solve the linearintheparameters problem in the present study. The main advantage of the new WN is that it exploits the attractive features of multiscale wavelet decompositions and the capability of traditional neural networks. By adopting the analysis of variance (ANOVA) expansion, WNs can now handle nonlinear identification problems in high dimensions. Index Terms—Nonlinear autoregressive with exogenous inputs (NARX) models, nonlinear system identification, orthogonal least squares (OLS), wavelet networks (WNs). I.
Initialization by selection for wavelet network training
 Neurocomputing
, 2000
"... We present an original initialization procedure for the parameters of feedforward wavelet networks, prior to training by gradientbased techniques. It takes advantage of wavelet frames stemming from the discrete wavelet transform, and uses a selection method to determine a set of best wavelets whose ..."
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Cited by 19 (2 self)
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We present an original initialization procedure for the parameters of feedforward wavelet networks, prior to training by gradientbased techniques. It takes advantage of wavelet frames stemming from the discrete wavelet transform, and uses a selection method to determine a set of best wavelets whose centers and dilation parameters are used as initial values for subsequent training. Results obtained for the modeling of two simulated processes are compared to those obtained with a heuristic initialization procedure, and demonstrate the effectiveness of the proposed method.
Neural Predictive Control for a Carlike Mobile Robot
 International Journal of Robotics and Autonomous Systems
, 2002
"... This paper presents a new pathtracking scheme for a carlike mobile robot based on neural predictive control. A multilayer backpropagation neural network is employed to model nonlinear kinematics of the robot instead of a linear regression estimator in order to adapt the robot to a large operati ..."
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Cited by 18 (0 self)
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This paper presents a new pathtracking scheme for a carlike mobile robot based on neural predictive control. A multilayer backpropagation neural network is employed to model nonlinear kinematics of the robot instead of a linear regression estimator in order to adapt the robot to a large operating range. The neural predictive control for path tracking is a modelbased predictive control based on neural network modelling, which can generate its output in term of the robot kinematics and a desired path. The desired path for the robot is produced by a polar polynomial with a simple closed form. The multilayer backpropagation neural network is constructed by a wavelet orthogonal decomposition to form a wavelet neural network that can overcome the problem caused by the local minima when training the neural network. The wavelet neural network has the advantage of using an explicit way to determine the number of the hidden nodes and initial value of weights. Simulation results for the modelling and control are provided to justify the proposed scheme.
Multiscale Approximation With Hierarchical Radial Basis Functions Networks
, 2004
"... An approximating neural model, called hierarchical radial basis function (HRBF) network, is presented here. This is a selforganizing (by growing) multiscale version of a radial basis function (RBF) network. It is constituted of hierarchical layers, each containing a Gaussian grid at a decreasing sc ..."
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Cited by 14 (3 self)
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An approximating neural model, called hierarchical radial basis function (HRBF) network, is presented here. This is a selforganizing (by growing) multiscale version of a radial basis function (RBF) network. It is constituted of hierarchical layers, each containing a Gaussian grid at a decreasing scale. The grids are not completely filled, but units are inserted only where the local error is over threshold. This guarantees a uniform residual error and the allocation of more units with smaller scales where the data contain higher frequencies. Only local operations, which do not require any iteration on the data, are required; this allows to construct the network in quasireal time. Through harmonic analysis, it is demonstrated that, although a HRBF cannot be reduced to a traditional waveletbased multiresolution analysis (MRA), it does employ Riesz bases and enjoys asymptotic approximation properties for a very large class of functions. HRBF networks have been extensively applied to the reconstruction of threedimensional (3D) models from noisy range data. The results illustrate their power in denoising the original data, obtaining an effective multiscale reconstruction of better quality than that obtained by MRA.
Wavelet adaptive backstepping control for a class of nonlinear systems
 IEEE Trans. Neural Netw
, 2006
"... Abstract—This paper proposes a wavelet adaptive backstepping control (WABC) system for a class of secondorder nonlinear systems. The WABC comprises a neural backstepping controller and a robust controller. The neural backstepping controller containing a wavelet neural network (WNN) identifier is t ..."
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Cited by 11 (4 self)
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Abstract—This paper proposes a wavelet adaptive backstepping control (WABC) system for a class of secondorder nonlinear systems. The WABC comprises a neural backstepping controller and a robust controller. The neural backstepping controller containing a wavelet neural network (WNN) identifier is the principal controller, and the robust controller is designed to achieveL 2 tracking performance with desired attenuation level. Since the WNN uses wavelet functions, its learning capability is superior to the conventional neural network for system identification. Moreover, the adaptation laws of the control system are derived in the sense of Lyapunov function and Barbalat’s lemma, thus the system can be guaranteed to be asymptotically stable. The proposed WABC is applied to two nonlinear systems, a chaotic system and a wingrock motion system to illustrate its effectiveness. Simulation results verify that the proposed WABC can achieve favorable tracking performance by incorporating of WNN identification, adaptive backstepping control, and L 2 robust control techniques. Index Terms—Adaptive control, backstepping control, chaotic system, robust control, wavelet neural network (WNN), wingrock system. I.
Function Approximation Using Artificial Neural Networks
 WSEAS Transcations on Mathematics
"... Abstract: Function approximation, which finds the underlying relationship from a given finite inputoutput data is the fundamental problem in a vast majority of real world applications, such as prediction, pattern recognition, data mining and classification. Various methods have been developed to a ..."
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Cited by 8 (1 self)
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Abstract: Function approximation, which finds the underlying relationship from a given finite inputoutput data is the fundamental problem in a vast majority of real world applications, such as prediction, pattern recognition, data mining and classification. Various methods have been developed to address this problem, where one of them is by using artificial neural networks. In this paper, the radial basis function network and the wavelet neural network are applied in estimating periodic, exponential and piecewise continuous functions. Different types of basis functions are used as the activation function in the hidden nodes of the radial basis function network and the wavelet neural network. The performance is compared by using the normalized square root mean square error function as the indicator of the accuracy of these neural network models. KeyWords: function approximation, artificial neural network, radial basis function network, wavelet neural network 1
Neural network structures and training algorithms for microwave applications
 Int. J. RF Microwave CAE
, 1999
"... ABSTRACT: Neural networks recently gained attention as fast and flexible vehicles to microwave modeling, simulation, and optimization. After learning and abstracting from microwave data, through a process called training, neural network models are used during microwave design to provide instant answ ..."
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Cited by 4 (2 self)
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ABSTRACT: Neural networks recently gained attention as fast and flexible vehicles to microwave modeling, simulation, and optimization. After learning and abstracting from microwave data, through a process called training, neural network models are used during microwave design to provide instant answers to the task learned. Appropriate neural network structure and suitable training algorithm are two of the major issues in developing neural network models for microwave applications. Together, they decide amount of training data required, accuracy that could possibly be achieved, and more importantly developmental cost of neural models. A review of the current status of this emerging technology is presented, with emphasis on neural network structures and training algorithms suitable for microwave applications. Present challenges and future directions of the area are discussed.
Capturing people in surveillance video
 In IEEE International Workshop on Visual Surveillance
, 2007
"... This paper presents reliable techniques for detecting, tracking, and storing keyframes of people in surveillance video. The first component of our system is a novel face detector algorithm, which is based on first learning local adaptive features for each training image, and then using Adaboost lear ..."
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Cited by 4 (3 self)
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This paper presents reliable techniques for detecting, tracking, and storing keyframes of people in surveillance video. The first component of our system is a novel face detector algorithm, which is based on first learning local adaptive features for each training image, and then using Adaboost learning to select the most general features for detection. This method provides a powerful mechanism for combining multiple features, allowing faster training time and better detection rates. The second component is a face tracking algorithm that interleaves multiple viewbased classifiers along the temporal domain in a video sequence. This interleaving technique, combined with a correlationbased tracker, enables fast and robust face tracking over time. Finally, the third component of our system is a keyframe selection method that combines a person classifier with a face classifier. The basic idea is to generate a person keyframe in case the face is not visible, in order to reduce the number of false negatives. We performed quantitatively evaluation of our techniques on standard datasets and on surveillance videos captured by a camera over several days. 1.