15,202 research outputs found
A new class of wavelet networks for nonlinear system identification
A new class of wavelet networks (WNs) is proposed for nonlinear system identification. In the new networks, the model structure for a high-dimensional 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 linear-in-the-parameter regressions, which can be solved using least-squares 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 linear-in-the-parameters 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
A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure
A new unified modelling framework based on the superposition of additive submodels, functional components, and
wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented
using a multivariate non-linear function, is initially decomposed into a number of functional components via the wellknown
analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear
autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional
component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and
multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-theparameters
problem, which can be solved using least-squares type methods. An efficient model structure determination
approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization
of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is
employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to
as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to
represent high-order and high dimensional non-linear systems
Modeling of complex-valued Wiener systems using B-spline neural network
In this brief, a new complex-valued B-spline neural network is introduced in order to model the complex-valued Wiener system using observational input/output data. The complex-valued nonlinear static function in the Wiener system is represented using the tensor product from two univariate Bspline neural networks, using the real and imaginary parts of the system input. Following the use of a simple least squares parameter initialization scheme, the Gauss–Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first-order derivatives recursion. Numerical examples, including a nonlinear high-power amplifier model in communication systems, are used to demonstrate the efficacy of the proposed approaches
Adaptive Predictive Control Using Neural Network for a Class of Pure-feedback Systems in Discrete-time
10.1109/TNN.2008.2000446IEEE Transactions on Neural Networks1991599-1614ITNN
A hybrid neuro--wavelet predictor for QoS control and stability
For distributed systems to properly react to peaks of requests, their
adaptation activities would benefit from the estimation of the amount of
requests. This paper proposes a solution to produce a short-term forecast based
on data characterising user behaviour of online services. We use \emph{wavelet
analysis}, providing compression and denoising on the observed time series of
the amount of past user requests; and a \emph{recurrent neural network} trained
with observed data and designed so as to provide well-timed estimations of
future requests. The said ensemble has the ability to predict the amount of
future user requests with a root mean squared error below 0.06\%. Thanks to
prediction, advance resource provision can be performed for the duration of a
request peak and for just the right amount of resources, hence avoiding
over-provisioning and associated costs. Moreover, reliable provision lets users
enjoy a level of availability of services unaffected by load variations
Neural Modeling and Control of Diesel Engine with Pollution Constraints
The paper describes a neural approach for modelling and control of a
turbocharged Diesel engine. A neural model, whose structure is mainly based on
some physical equations describing the engine behaviour, is built for the
rotation speed and the exhaust gas opacity. The model is composed of three
interconnected neural submodels, each of them constituting a nonlinear
multi-input single-output error model. The structural identification and the
parameter estimation from data gathered on a real engine are described. The
neural direct model is then used to determine a neural controller of the
engine, in a specialized training scheme minimising a multivariable criterion.
Simulations show the effect of the pollution constraint weighting on a
trajectory tracking of the engine speed. Neural networks, which are flexible
and parsimonious nonlinear black-box models, with universal approximation
capabilities, can accurately describe or control complex nonlinear systems,
with little a priori theoretical knowledge. The presented work extends optimal
neuro-control to the multivariable case and shows the flexibility of neural
optimisers. Considering the preliminary results, it appears that neural
networks can be used as embedded models for engine control, to satisfy the more
and more restricting pollutant emission legislation. Particularly, they are
able to model nonlinear dynamics and outperform during transients the control
schemes based on static mappings.Comment: 15 page
The wavelet-NARMAX representation : a hybrid model structure combining polynomial models with multiresolution wavelet decompositions
A new hybrid model structure combing polynomial models with multiresolution wavelet decompositions is introduced for nonlinear system identification. Polynomial models play an important role in approximation theory, and have been extensively used in linear and nonlinear system identification. Wavelet decompositions, in which the basis functions have the property of localization in both time and frequency, outperform many other approximation schemes and offer a flexible solution for approximating arbitrary functions. Although wavelet representations can approximate even severe nonlinearities in a given signal very well, the advantage of these representations can be lost when wavelets are used to capture linear or low-order nonlinear behaviour in a signal. In order to sufficiently utilise the global property of polynomials and the local property of wavelet representations simultaneously, in this study polynomial models and wavelet decompositions are combined together in a parallel structure to represent nonlinear input-output systems. As a special form of the NARMAX model, this hybrid model structure will be referred to as the WAvelet-NARMAX model, or simply WANARMAX. Generally, such a WANARMAX representation for an input-output system might involve a large number of basis functions and therefore a great number of model terms. Experience reveals that only a small number of these model terms are significant to the system output. A new fast orthogonal least squares algorithm, called the matching pursuit orthogonal least squares (MPOLS) algorithm, is also introduced in this study to determine which terms should be included in the final model
B-spline neural networks based PID controller for Hammerstein systems
A new PID tuning and controller approach is introduced for Hammerstein systems based on input/output data. A B-spline neural network is used to model the nonlinear static function in the Hammerstein system. The control signal is composed of a PID controller together with a correction term. In order to update the control signal, the multi-step ahead predictions of the Hammerstein system based on the B-spline neural networks and the associated Jacobians matrix are calculated using the De Boor algorithms including both the functional and derivative recursions. A numerical example is utilized to demonstrate the efficacy of the proposed approaches
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