an identification algorithm for polynomial narx models based on simulation error minimization classical prediction error approaches for the identification of non linear polynomial narx narmax models often yield unsatisfactory results for long range prediction or simulation purposes mainly due to incorrect or redundant model structure selection the paper discusses some limitations of the standard approach and suggests two modifications namely a new index based on the simulation error is employed as the regressor selection criterion and a pruning mechanism is introduced in the model selection algorithm the resulting algorithm is shown to be effective in the identification of compact and robust models generally yielding model structures closer to the correct ones computational issues are also discussed finally the identification algorithm is tested on a long range prediction benchmark application

building dynamical models from data and prior knowledge the case of the first period doubling bifurcation this paper reviews some aspects of nonlinear model building from data with gray box and without black box prior knowledge the model class is very important because it determines two aspects of the final model namely i the type of nonlinearity that can be accurately approximated and ii the type of prior knowledge that can be taken into account such features are usually in conflict when it comes to choosing the model class the problem of model structure selection is also reviewed it is argued that such a problem is philosophically different depending on the model class and it is suggested that the choice of model class should be performed based on the type of a priori available a procedure is proposed to build polynomial models from data on a poincare section and prior knowledge about the first period doubling bifurcation for which the normal form is also polynomial the final models approximate dynamical data in a least squares sense and by design present the first period doubling bifurcation at a specified value of parameters the procedure is illustrated by means of simulated examples

multiobjective parameter estimation for non linear systems affine information and least squares formulation this paper defines a class of system information affine information that includes both the dynamic residuals and some types of auxiliary information that can be used in system parameter estimation as special cases the types of information that can be cast under the affine information format give rise to quadratic functions that measure the extent to which a model fits such information and that can be aggregated in a single weighted quadratic cost functional this allows the definition of a multiobjective methodology for parameter estimation in non linear system identification which allows taking into account any type of affine information the results are presented in terms of a set of efficient solutions of the multiobjective estimation problem such a solution set is more meaningful than a single model since any affine information leads to a convex quadratic functional the whole set of efficient solutions is exactly accessible via the minimization of the quadratic functional with different weighti

algorithms for minimal model structure detection in nonlinear dynamic system identification the minimal model structure detection mmsd problem in nonlinear dynamic system identification is formulated as a search for the optimal orthogonalization path while an exhaustive search for a model with 20 candidate terms would involve 2 43 1018 possible paths it is shown that this can typically be reduced to 2 103 by augmenting the orthogonal estimation algorithm with genetic search procedures the mmsd algorithm provides the first practical solution for optimal structure detection in narmax modelling training neural networks and fuzzy systems modelling based on the mmsd algorithm a refined forward regression orthogonal rfro algorithm is developed the rfro algorithm initially detects a parsimonious model structure using the forward regression orthogonal algorithm and then refines the model structure by applying the mmsd algorithm to the reduced model term set the rfro algorithm cannot guarantee to find the minimal model structure but it is computationally more efficient than the mmsd algori

integral equations for a fluid near a random substrate the fluid distribution functions near the surface of a random porous solid are investigated by the methods of liquid state theory the presence of the surface is taken into account by modifying the two body interaction potential between fluid and matrix particles cluster expansions and ornstein zernike equations for the correlation functions are derived as well as exact equations for the fluid density profile

improved structure selection for nonlinear models based on term clustering in this paper the concepts of term clusters and cluster coefficients are defined and used in the context of system identification it is argued that if a certain type of term in a nonlinear model is spurious the respective cluster coefficient is small compared with the coefficients of the other clusters represented in the model once the spurious clusters have been detected the corresponding terms can be deleted from the set of candidate terms the consequences of doing this are i a drastic reduction in the size of the set of candidate terms and consequently a substantial gain in computation time is achieved ii the final estimated model is more likely to reproduce the dynamics of the original system and iii the final model is more robust to overparametrization numerical examples are included to illustrate the new procedure

brief paper structure detection and parameter estimation for narx models in a unified em framework in this paper we consider structure detection and parameter estimation of the nonlinear auto regressive with exogenous inputs narx model using the em expectation maximisation algorithm the parameter estimation step uses particle smoothing to obtain the necessary expectations in the e step and the parameters are then estimated in closed form in the m step the model structure detection is performed using an f test which makes use of the parameter information matrix inverse of the covariance matrix obtained from an augmentation of the em algorithm the steps for obtaining the information matrix are robust guaranteeing a positive semi definite information matrix to use in the structure detection step for the case of unknown model orders a method is proposed using the stochastic complexity sc information criterion for selecting between candidate models the sc is composed of the information matrix representing model complexity and a likelihood estimate representing model accuracy which are both generated as byproducts of the augmented em algorithm numerical results demonstrate that the em approach performs well in comparison to a standard alternative based on orthogonal least squares and also avoids the need to estimate a noise model for the case of measurement noise corrupted output signals

a two stage algorithm for identification of nonlinear dynamic systems this paper investigates the two stage stepwise identification for a class of nonlinear dynamic systems that can be described by linear in the parameters models and the model has to be built from a very large pool of basis functions or model terms the main objective is to improve the compactness of the model that is obtained by the forward stepwise methods while retaining the computational efficiency the proposed algorithm first generates an initial model using a forward stepwise procedure the significance of each selected term is then reviewed at the second stage and all insignificant ones are replaced resulting in an optimised compact model with significantly improved performance the main contribution of this paper is that these two stages are performed within a well defined regression context leading to significantly reduced computational complexity the efficiency of the algorithm is confirmed by the computational complexity analysis and its effectiveness is demonstrated by the simulation results

dynamical effects of overparametrization in nonlinear models abstract this paper is concemed with dynamical reconstruction for nonlinear systems the effects of the driving function and of the complexity of a given representation on the bifurcation patter are investigated it is shown that the use of different driving functions to excite the system may yield models with different bifurcation patterns the complexity of the reconstructions considered is quantified by the embedding dimension and the number of estimated parameters in this respect it appears that models which reproduce the original bifurcation behaviour are of limited complexity and that excessively complex models tend to induce ghost bifurcations and spurious dynamical regimes moreover some results suggest that the effects of overparametrization on the global dynamical behaviour of a nonlinear model may be more deleterious than the presence of moderate noise levels in order to precisely quantify the complexity of the reconstructions global polynomials are used although the results are believed to apply to a much wider class of representations including neural networks

model selection and validation methods for non linear systems the theory of hypothesis testing is used to select a model with the correct structure and the relation of such a method to the aic and fpe criteria is investigated parametric validation and correlation validation methods are developed for non non linear difference equation models several shortcomings of traditional methods especially when applied to non linear systems are described

recursive algorithm for computing the frequency response of a class of non linear difference equation models abstract a recursive algorithm is developed which is both computationally compact and enables the nth order frequency response functions of a large class of non linear difference equation models to be found without restriction on the order n

fluids with highly directional attractive forces ii thermodynamic perturbation theory and integral equations the formalism of statistical thermodynamics developed in the preceding paper is used as a basis for deriving tractable approximations the system treated is one where repulsion and highly directional attraction due to a single molecular site combine to allow the formation of dimers but no highers mers we derive thermodynamic perturbation theory using the system interacting with only the repulsive potential as a reference system two distinct integral equations for the pair correlation are derived the first one treats both parts of the interaction approximately the other one employs the repulsive reference system used in perturbation theory we show that each of these integral equations permits the calculation of an important thermodynamic function directly from the solution at a single state of density and temperature in the first case this applies to a pressure consistent with the compressibility relation in the second to the excess helmholtz free energy over the reference system

input output parametric models for non linear systems part ii stochastic non linear systems recursive input output models for non linear multivariate discrete time systems are derived and sufficient conditions for their existence are defined the paper is divided into two parts the first part introduces and defines concepts such as nerode realization multistructural forms and results from differential geometry which are then used to derive a recursive input output model for multivariable deterministic non linear systems the second part introduces several examples compares the derived model with other representations and extends the results to create prediction error or innovation input output models for non linear stochastic systems these latter models are the generalization of the multivariable arm ax models for linear systems and are referred to as narmax or non linear autoregressive moving average models with exogenous inputs

eigenstructure techniques for 2 d angle estimation with uniform circular arrays the problem of 2d angle estimation azimuth and elevation of multiple plane waves incident on a uniform circular array uca of antennas is considered two eigenstructure based estimation algorithms that operate in beamspace and employ phase mode excitation based beamformers have been developed the first uca rb music is a beamspace version of music that offers numerous advantages over element space operation including reduced computation as subspace estimates are obtained via real valued eigendecompositions enhanced performance in correlated source scenarios due to the attendant forward backward averaging effect and the applicability of root music the second uca esprit represents a significant advance in the area of 2d angle estimation it is a novel closed form algorithm that provides automatically paired source azimuth and elevation estimates with uca esprit the eigenvalues of a matrix have the form spl mu sub i sin spl theta sub i e sup j spl phi i where spl theta sub i and spl phi sub i are the elevation and azimuth angles respectively expensive search procedures being thus avoided uca esprit is superior to existing 2d angle estimation algorithms with respect to computational complexity finally asymptotic expressions for the variances of the element space music and uca rb music estimators for the 2d scenario have been derived results of simulations that compare uca rb music and uca esprit and also validate the theoretical performance expressions are presented

application of a general multi model approach for identification of highly nonlinear processes a case study an identification method for highly nonlinear processes is proposed based on a multi model approach and kolmogorov gabor polynomials owing to the large number of possible terms in this general model structure the significant terms are selected by several statistical test procedures leading automatically to a minimal order model realization the performance of this method is evaluated in an in depth case study using a simulated ph neutralization process the effects of important variables such as range of operating conditions signal noise ratio and data length are discussed

fluids with highly directional attractive forces i statistical thermodynamics a new formulation of statistical thermodynamics is derived for classical fluids of molecules that tend to associate into dimers and possibly highers mers due to highly directional attraction a breakup of the pair potential into repulsive and highly directionally attractive parts is introduced into the expansion of the logarithm of the grand partition function in fugacity graphs the bonding by the directional attraction is used to classify the graphs and to introduce a topological reduction which results in the replacement of the fugacity by two variables singlet density and monomer density 0 results for the thermodynamic functions as functionals of and 0 are given in the form of graph sums pair correlations are analyzed in terms of a new matrix analog of the direct correlation function it is shown that the low density limit is treated exactly while major difficulties arise when the mayer expansion which employs onlyp is used the intricate resummations required for the mayer expansion are illustrated for the case where dimers are the only association products

distribution functions for fluids in random media a random medium is considered composed of identifiable interactive sites or obstacles equilibrated at a high temperature and then quenched rapidly to form a rigid structure statistically homogeneous on all but molecular length scales the equilibrium statistical mechanics of a fluid contained inside this quenched medium is discussed various particle particle and particle obstacle correlation functions which differ from the corresponding functions for a fully equilibrated binary mixture are defined through an averaging process over the static ensemble of obstacle configurations and application of topological reduction techniques the ornstein zernike equations also differ from their equilibrium counterparts

adsorption of dimerizing fluids in disordered porous networks abstract we consider the application of the integral equation theory to the study of associative fluids in disordered porous networks the theory also takes into account associative fluid network interactions the calculations reported here illustrate the effect of associative forces on the fluid fluid and fluid network correlation functions we find that an associative interaction gives rise to a strong intracore peak in the correlation functions but dampens the peaks outside the core

identification of mimo non linear systems using a forward regression orthogonal estimator abstract an orthogonal least squares estimator which was originally derived for single input single output systems is extended to multi input multi output non linear systems the estimator can provide information about the structure or which terms to include in the model and final parameter estimates in a very simple and efficient manner multivariable non linear model validity tests are also discussed and the results of applying the orthogonal estimator to both simulated and real data are included

regressor and structure selection in narx models using a structured anova approach regressor selection can be viewed as the first step in the system identification process the benefits of finding good regressors before estimating complex models are especially clear for nonlinear systems where the class of possible models is huge in this article a structured way of using the tool analysis of variance anova is presented and used for narx model nonlinear autoregressive model with exogenous input identification with many candidate regressors

orthogonal parameter estimation algorithm for non linear stochastic systems an orthogonal parameter estimation algorithm is derived which allows each parameter in a linear in the parameters non linear difference equation model to be estimated sequentially and quite independently of the other parameters in the model the algorithm can be applied for any persistently exciting input and provides both unbiased estimates in the presence of correlated noise and an indication of which terms to include in the model several simulated examples are included to demonstrate the effectiveness of the algorithm

a gradient free adaptation method for nonlinear active noise control abstract active noise control anc problems are often affected by nonlinear effects such as saturation and distortion of microphones and loudspeakers nonlinear models and specific adaptation algorithms must be employed to properly account for these effects the nonlinear structure of the problem complicates the application of gradient based least mean squares lms algorithms due to the fact that exact gradient calculation requires executing nonlinear recursive filtering operations which pose computational and stability issues one favored solution to this problem consists in neglecting recursive terms in the gradient calculation an approximation which is not always without consequences on the convergence performance besides an efficient application of nonlinear models cannot avoid some form of model structure selection to avoid the well known effects of overparametrization and to reduce the computational load on line unfortunately the standard anc setting configures an indirect identification problem due to the presence of the secondary path in the control loop in the nonlinear case this destroys the linear regression structure of the problem even if the control filter is linear in the parameters thereby making it impossible to apply the many existing model selection methods for linear regression problems a simple and computationally wise low demanding approach is here proposed for parameter estimation and model structure selection that provides an answer to the mentioned issues the proposed method avoids altogether the use of the error gradient and relies on direct cost function evaluations a virtualization scheme is used to assess the accuracy improvements when the model is subject to parametric or structural modifications without directly affecting the control performance several simulation examples are discussed to show the effectiveness of the proposed algorithms

nonlinear black box modeling in system identification a unified overview 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 and 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 form 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 expansion the basis functions are typically formed from one simple scalar function which is modified in terms of scale and location the expansion from the scalar argument to the regressor space is achieved by a radial or a ridge type approach basic techniques for estimating the parameters in the structures are criterion minimization as well as two step procedures where first the relevant basis functions are determined using data and then a linear least squares step to determine the coordinates of the function approximation a particular problem is to deal with the large number of potentially necessary parameters this is handled by making the number of used parameters considerably less than the number of offered parameters by regularization shrinking pruning or regressor selection