a modified orthogonal forward regression least squares algorithm for system modelling from noisy regressors in this paper a modified orthogonal forward regression ofr least squares algorithm is presented for system identification and modelling from noisy regressors under the assumption that the energy and signal to noise ratio snr of the signals are known or can be estimated it is shown that unbiased estimates of the error reduction ratios errs and the parameters can be obtained in each forward regression step examples are provided to illustrate the proposed approach

on the volume of the wiener sausage let w t varepsilon be the varepsilon wiener sausage i e the varepsilon neighborhood of the trace of the brownian motion up to time t it is shown that the results of donsker and varadhan on the behavior of e exp nu w t varepsilon nu 0 remain true if varepsilon depends on t and converges to 0 with a certain rate

a new extension of newton algorithm for nonlinear system modelling using rbf neural networks model performance and convergence rate are two key measures for assessing the methods used in nonlinear system identification using radial basis function neural networks a new extension of the newton algorithm is proposed to further improve these two aspects by extending the results of recently proposed continuous forward algorithm cfa and hybrid forward algorithm hfa computational complexity analysis confirms its efficiency and numerical examples show that it converges faster and potentially outperforms cfa and hfa

estimation of general linear model coefficients for real time application abstract an algorithm using an orthogonalization procedure to estimate the coefficients of general linear models glm for functional magnetic resonance imaging fmri calculations is described the idea is to convert the basis functions or explanatory variables of a glm into orthogonal functions using the usual gram schmidt orthogonalization procedure the coefficients associated with the orthogonal functions henceforth referred to as auxiliary coefficients are then easily estimated by applying the orthogonality condition the original glm coefficients are computed from these estimates with this formulation the estimates can be updated when new image data become available making the approach applicable for real time estimation since the contribution of each image data is immediately incorporated into the estimated values storing the data in memory during the estimation process becomes unnecessary minimizing the memory requirements of the estimation process by employing cholesky decomposition the algorithm is a factor of two faster than the standard recursive least squares approach results of the analysis of an fmri study using this approach showed the algorithm s potential for real time application

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

harmonic crystal on the wall a microscopic approach a three dimensional winterbottom type construction in the regime of partial wetting is derived in a scaling limit of a gas of microscopic gaussian sos droplets under the fixed volume constraint the proof is based on a coarse graining of the random microscopic region wetted by the crystal random walk representations of various quantities related to free massless fields and a stability analysis of the torsional rigidity problem

a prediction error and stepwise regression estimation algorithm for non linear systems the identification of non linear systems based on a narmax non linear autoregressive moving average model with exogenous inputs model representation is considered and a combined stepwise regression prediction error estimation algorithm is derived the stepwise regression routine determines the model structure by detecting significant terms in the model while the prediction error algorithm provides optimal estimates of the final model parameters implementation of the algorithms is discussed in detail and several simulated examples and industrial applications are included to illustrate that parsimonious models of non linear systems can be identified using the algorithm

state space reconstruction and spatio temporal prediction of lattice dynamical systems this paper addresses the problems of state space reconstruction and spatio temporal prediction for lattice dynamical systems it is shown that the state space of any finite lattice dynamical system can be embedded into a reconstruction space for almost every in the sense of prevalence smooth measurement mapping as long as the dimension of the reconstruction space is larger than twice the size of the lattice based on this result an input output spatio temporal dynamical relation for each site within the lattice is derived and used for spatio temporal prediction of the system in the case of infinite lattice dynamical systems an approach based on constructing local lattice dynamical systems is proposed it is shown that the finite dimensional results can be directly applied to the local modelling and spatio temporal prediction for infinite lattice dynamical systems two numerical examples are provided to demonstrate the proposed theory and approach

on the role of prefiltering in nonlinear system identification data prefiltering is often used in linear system identification to increase model accuracy in a specified frequency band as prefiltering is equivalent to a frequency weighting on the prediction error function however this interpretation applies only to a strictly linear setting of the identification problem in this note the role of data and error prefiltering in nonlinear system identification is analyzed and a frequency domain interpretation is provided based on the volterra series representation of nonlinear systems simulation results illustrate the conclusions of the analysis

a new discrete continuous algorithm for radial basis function networks construction the construction of a radial basis function rbf network involves the determination of the model size hidden nodes and output weights least squares based subset selection methods can determine a rbf model size and its parameters simultaneously although these methods are robust they may not achieve optimal results alternatively gradient methods are widely used to optimize all the parameters the drawback is that most algorithms may converge slowly as they treat hidden nodes and output weights separately and ignore their correlations in this paper a new discrete continuous algorithm is proposed for the construction of a rbf model first the orthogonal least squares ols based forward stepwise selection constructs an initial model by selecting model terms one by one from a candidate term pool then a new levenberg marquardt lm based parameter optimization is proposed to further optimize the hidden nodes and output weights in the continuous space to speed up the convergence the proposed parameter optimization method considers the correlation between the hidden nodes and output weights which is achieved by translating the output weights to dependent parameters using the ols method the correlation is also used by the previously proposed continuous forward algorithm cfa however unlike the cfa the new method optimizes all the parameters simultaneously in addition an equivalent recursive sum of squared error is derived to reduce the computation demanding for the first derivatives used in the lm method computational complexity is given to confirm the new method is much more computationally efficient than the cfa different numerical examples are presented to illustrate the effectiveness of the proposed method further friedman statistical tests on 13 classification problems are performed and the results demonstrate that rbf networks built by the new method are very competitive in comparison with some popular classifiers

an adaptive orthogonal search algorithm for model subset selection and non linear system identification a new adaptive orthogonal search aos algorithm is proposed for model subset selection and non linear system identification model structure detection is a key step in any system identification problem this consists of selecting significant model terms from a redundant dictionary of candidate model terms and determining the model complexity model length or model size the final objective is to produce a parsimonious model that can well capture the inherent dynamics of the underlying system in the new aos algorithm a modified generalized cross validation criterion called the adjustable prediction error sum of squares apress is introduced and incorporated into a forward orthogonal search procedure the main advantage of the new aos algorithm is that the mechanism is simple and the implementation is direct and easy and more importantly it can produce efficient model subsets for most non linear identification problems

variable selection via rival removing irrelevant variables amidst lasso iterations and its application to nuclear material detection in many situations the number of data points is fixed and the asymptotic convergence results of popular model selection tools may not be useful a new algorithm for model selection rival removing irrelevant variables amidst lasso iterations is presented and shown to be particularly effective for a large but fixed number of data points the algorithm is motivated by an application of nuclear material detection where all unknown parameters are to be non negative thus positive lasso and its variants are analyzed then rival is proposed and is shown to have some desirable properties namely the number of data points needed to have convergence is smaller than existing methods

the diffusive phase of a model of self interacting walks we consider simple random walk onzd perturbed by a factor exp t pjt wheret is the length of the walk and j t sum nolimits 0 leqslant i 0 ford 2 the diffusion constant is equal to 1 but ford 2 it is renormalized ford 1 andp 3 2 we prove diffusion for all real positive or negative ford 2 the scaling limit is brownian motion but ford 2 it is the edwards model with the wrong sign of the coupling when 0 which governs the limiting behaviour the latter arises since for p frac 4 d 2 t p j t is the discrete self intersection local time this establishes existence of a diffusive phase for this model existence of a collapsed phase for a very closely related model has been proven in work of bolthausen and schmock

extended model set global data and threshold model identification of severely non linear systems abstract new parameter estimation algorithms based on an extended model set a global data model and a threshold model formulation are derived for identifying severely non linear systems it is shown that in each case an integrated structure determination and parameter estimation algorithm based on an orthogonal decomposition of the regression matrix can be derived to provide procedures for identifying parsimonious models of unknown systems with complex structure simulation studies are included to illustrate the techniques discussed

geometry of the random walk range conditioned on survival among bernoulli obstacles we consider a discrete time simple symmetric random walk among bernoulli obstacles on mathbb z d d ge 2 where the walk is killed when it hits an obstacle it is known that conditioned on survival up to time n the random walk range is asymptotically contained in a ball of radius varrho n c n 1 d 2 for any d ge 2 for d 2 it is also known that the range asymptotically contains a ball of radius 1 epsilon varrho n for any epsilon 0 while the case d ge 3 remains open we complete the picture by showing that for any d ge 2 the random walk range asymptotically contains a ball of radius varrho n varrho n epsilon for some epsilon in 0 1 furthermore we show that its boundary is of size at most varrho n d 1 log varrho n a for some a 0

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

a new method for the design of energy transfer filters this paper is concerned with the development of a new method for the design of energy transfer filters etfs etfs are a new class of non linear filters recently proposed by the authors which employ non linear effects to transfer signal energy from one frequency band to a different frequency location the new method uses the powerful orthogonal least squares ols algorithm to solve the least squares problem associated with the design and compared with previous methods achieves much better filtering performance

polynomial search and global modeling two algorithms for modeling chaos global modeling aims to build mathematical models of concise description polynomial model search pomos and global modeling glomo are two complementary algorithms freely downloadable at the following address http www cesbio ups tlse fr us pomos et glomo html designed for the modeling of observed dynamical systems based on a small set of time series models considered in these algorithms are based on ordinary differential equations built on a polynomial formulation more specifically pomos aims at finding polynomial formulations from a given set of 1 to n time series whereas glomo is designed for single time series and aims to identify the parameters for a selected structure glomo also provides basic features to visualize integrated trajectories and to characterize their structure when it is simple enough one allows for drawing the first return map for a chosen poincare section in the reconstructed space another one computes the lyapunov exponent along the trajectory in the present paper global modeling from single time series is considered a description of the algorithms is given and three examples are provided the first example is based on the three variables of the rossler attractor the second one comes from an experimental analysis of the copper electrodissolution in phosphoric acid for which a less parsimonious global model was obtained in a previous study the third example is an exploratory case and concerns the cycle of rainfed wheat under semiarid climatic conditions as observed through a vegetation index derived from a spatial sensor

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

efficient least angle regression for identification of linear in the parameters models least angle regression as a promising model selection method differentiates itself from conventional stepwise and stagewise methods in that it is neither too greedy nor too slow it is closely related to l1 norm optimization which has the advantage of low prediction variance through sacrificing part of model bias property in order to enhance model generalization capability in this paper we propose an efficient least angle regression algorithm for model selection for a large class of linear in the parameters models with the purpose of accelerating the model selection process the entire algorithm works completely in a recursive manner where the correlations between model terms and residuals the evolving directions and other pertinent variables are derived explicitly and updated successively at every subset selection step the model coefficients are only computed when the algorithm finishes the direct involvement of matrix inversions is thereby relieved a detailed computational complexity analysis indicates that the proposed algorithm possesses significant computational efficiency compared with the original approach where the well known efficient cholesky decomposition is involved in solving least angle regression three artificial and real world examples are employed to demonstrate the effectiveness efficiency and numerical stability of the proposed algorithm

a new kernel based approach for nonlinearsystem identification we present a novel nonparametric approach for identification of nonlinear systems exploiting the framework of gaussian regression the unknown nonlinear system is seen as a realization from a gaussian random field its covariance encodes the idea of fading memory in the predictor and consists of a mixture of gaussian kernels parametrized by few hyperparameters describing the interactions among past inputs and outputs the kernel structure and the unknown hyperparameters are estimated maximizing their marginal likelihood so that the user is not required to define any part of the algorithmic architecture e g the regressors and the model order once the kernel is estimated the nonlinear model is obtained solving a tikhonov type variational problem the hilbert space the estimator belongs to is characterized benchmarks problems taken from the literature show the effectiveness of the new approach also comparing its performance with a recently proposed algorithm based on direct weight optimization and with parametric approaches with model order estimated by aic or bic

moderate deviations for the volume of the wiener sausage for a 0 let wa t be the a neighbourhood of standard brownian motion in rd starting at 0 and observed until time t it is well known that elwa t l ikat t oc for d 3 with kea the newtonian capacity of the ball with radius a we prove that lm t d 2 d log p wa t l oc this is markedly different from the optimal strategy for large deviations iwa t i 5 is nonanalytic at some critical point in 0 kia above which it follows a pure power law this crossover is associated with a collapse transition in the optimal strategy we also derive the analogous moderate deviation result for d 2 in this case eiwa t 2wrt logt t oc and we prove that

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

tracking time varying causality and directionality of information flow using an error reduction ratio test with applications to electroencephalography data this paper introduces an error reduction ratio causality err causality test that can be used to detect and track causal relationships between two signals in comparison to the traditional granger method one significant advantage of the new err causality test is that it can effectively detect the time varying direction of linear or nonlinear causality between two signals without fitting a complete model another important advantage is that the err causality test can detect both the direction of interactions and estimate the relative time shift between the two signals numerical examples are provided to illustrate the effectiveness of the new method together with the determination of the causality between electroencephalograph signals from different cortical sites for patients during an epileptic seizure

on the diagonalization of quantum birkhoff gustavson normal form an application to quantum mechanics of one of classical perturbation theory methods the birkhoff gustavson normal form bgnf is described in the quantum case it results in the van vleck perturbation theory performed upon wick normal ordered operators algebraic aspects of this procedure and formal construction of invariants integrals of motion for a perturbed system are considered it turned out that a larger set of such operators existed in the quantum mechanics rather than in the classical one it is demonstrated that according to general results of the quantum mechanical perturbation theory the quantum bgnf may always be diagonalized and two formal processes for such diagonalization are constructed in the opposite case the classical bgnf is in general nondiagonalizable this reflects the fact that the classical perturbation theory cannot handle a system with two or more resonances possible reasons for such different behavior of two very close in spirit perturbation procedures are discussed results of the described procedure entirely performed upon the wick normal ordered operators are equivalent to those of rayleigh schrodinger perturbation expansion

practical identification of narmax models using radial basis functions a wide class of discrete time non linear systems can be represented by the nonlinear autoregressive moving average narmax model with exogenous inputs this paper develops a practical algorithm for identifying narmax models based on radial basis functions from noise corrupted data the algorithm consists of an iterative orthogonal forward regression routine coupled with model validity tests the orthogonal forward regression routine selects parsimonious radial basistunc tion models while the model validity tests measure the quality of fit the modelling of a liquid level system and an automotive diesel engine are included to demonstrate the effectiveness of the identification procedure

recovering map static nonlinearities from chaotic data using dynamical models abstract this paper is concerned with the estimation from chaotic data of maps with static nonlinearities a number of issues concerning model construction such as structure selection over parametrization and model validation are discussed in the light of the shape of the static non linearities reproduced by the estimated maps a new interpretation of term clusters and cluster coefficients of polynomial models is provided based on this approach the paper discusses model limitations and some useful principles to select the structure of nonlinear maps some of the ideas have been tested using several nonlinear systems including a boost voltage regulator map and a set of real data from a chaotic circuit

critical large deviations of one dimensional annealed brownian motion in a poissonian potential we derive a large deviation principle for the position at large times t of a one dimensional annealed brownian motion in a poissonian potential in the critical spatial scale t 1 3 here annealed means that averages are taken with respect to both the path and environment measures in contrast to the d dimensional case for d 2 in the critical scale t d d 2 as treated by sznitman the rate function which measures the large deviations exhibits three different regimes these regimes depend on the position of the path at time t our large deviation principle has a natural application to the study of a one dimensional annealed brownian motion with a constant drift in a poissonian potential

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

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

identification of iir nonlinear systems without prior structural information in this paper we propose a kernel method for identification of infinite impulse response iir nonlinear systems without prior structural information the main result of the paper is to establish the conditions for asymptotic convergence in terms of the input to output exponential stability the performance of the method is tested on real world applications and computer simulations the results obtained show the efficacy of the method

lattice dynamical wavelet neural networks implemented using particle swarm optimization for spatio temporal system identification in this brief by combining an efficient wavelet representation with a coupled map lattice model a new family of adaptive wavelet neural networks called lattice dynamical wavelet neural networks ldwnns is introduced for spatio temporal system identification a new orthogonal projection pursuit opp method coupled with a particle swarm optimization pso algorithm is proposed for augmenting the proposed network a novel two stage hybrid training scheme is developed for constructing a parsimonious network model in the first stage by applying the opp algorithm significant wavelet neurons are adaptively and successively recruited into the network where adjustable parameters of the associated wavelet neurons are optimized using a particle swarm optimizer the resultant network model obtained in the first stage however may be redundant in the second stage an orthogonal least squares algorithm is then applied to refine and improve the initially trained network by removing redundant wavelet neurons from the network an example for a real spatio temporal system identification problem is presented to demonstrate the performance of the proposed new modeling framework

biased random walk conditioned on survival among bernoulli obstacles subcritical phase we consider a discrete time biased random walk conditioned to avoid bernoulli obstacles on mathbb z d d ge 2 up to time n this model is known to undergo a phase transition for a large bias the walk is ballistic whereas for a small bias it is sub ballistic we prove that in the sub ballistic phase the random walk is contained in a ball of radius o n 1 d 2 which is the same scale as for the unbiased case as an intermediate step we also prove large deviation principles for the endpoint distribution for the unbiased random walk at scales between n 1 d 2 and o n d d 2 these results improve and complement earlier work by sznitman ann sci ecole norm sup 4 28 3 345 370 371 390 1995

survival asymptotics for brownian motion in a poisson field of decaying traps let w t be the wiener sausage in mathbb r d that is the a neighborhood for some a 0 of the path of brownian motion up to time t it is shown that integrals of the type int t 0 nu s d w s with t rightarrow nu t nonincreasing and nu t sim nu t gamma t rightarrow infty have a large deviation behavior similar to that of w t established by donsker and varadhan such a result gives information about the survival asymptotics for brownian motion in a poisson field of spherical traps of radius a when the traps decay independently with lifetime distribution nu t nu 0 there are two critical phenomena i in d geq 3 the exponent of the tail of the survival probability has a crossover at gamma 2 d ii in d geq 1 the survival strategy changes at time s lbrack gamma 1 gamma rbrack t provided gamma 1 2 d 1 respectively gamma 2 d d geq 2

data driven non markovian closure models abstract this paper has two interrelated foci i obtaining stable and efficient data driven closure models by using a multivariate time series of partial observations from a large dimensional system and ii comparing these closure models with the optimal closures predicted by the mori zwanzig mz formalism of statistical physics multilayer stochastic models msms are introduced as both a generalization and a time continuous limit of existing multilevel regression based approaches to closure in a data driven setting these approaches include empirical model reduction emr as well as more recent multi layer modeling it is shown that the multilayer structure of msms can provide a natural markov approximation to the generalized langevin equation gle of the mz formalism a simple correlation based stopping criterion for an emr msm model is derived to assess how well it approximates the gle solution sufficient conditions are derived on the structure of the nonlinear cross interactions between the constitutive layers of a given msm to guarantee the existence of a global random attractor this existence ensures that no blow up can occur for a broad class of msm applications a class that includes non polynomial predictors and nonlinearities that do not necessarily preserve quadratic energy invariants the emr msm methodology is first applied to a conceptual nonlinear stochastic climate model of coupled slow and fast variables in which only slow variables are observed it is shown that the resulting closure model with energy conserving nonlinearities efficiently captures the main statistical features of the slow variables even when there is no formal scale separation and the fast variables are quite energetic second an msm is shown to successfully reproduce the statistics of a partially observed generalized lotka volterra model of population dynamics in its chaotic regime the challenges here include the rarity of strange attractors in the model s parameter space and the existence of multiple attractor basins with fractal boundaries the positivity constraint on the solutions components replaces here the quadratic energy preserving constraint of fluid flow problems and it successfully prevents blow up

birkhoff gustavson normal form in classical and quantum mechanics a quantum analogue of the classical transformations to the birkhoff gustavson normal form is derived with unitary transformations taking over the role of canonical transformations the author finds a striking similarity to lie transformations in the classical case the author suggests that the quantum normal form is identical to the rayleigh schrodinger perturbation series and thus usually only asymptotic to the eigenvalues the convergence question of both classical and quantum normal forms is discussed in some detail

brownian survival and lifshitz tail in perturbed lattice disorder abstract we consider the annealed asymptotics for the survival probability of brownian motion among randomly distributed traps the configuration of the traps is given by independent displacements of the lattice points we determine the long time asymptotics of the logarithm of the survival probability up to a multiplicative constant as applications we show the lifshitz tail effect of the density of states of the associated random schrodinger operator and derive a quantitative estimate for the strength of intermittency in the parabolic anderson problem

free energy and some sample path properties of a random walk with random potential we study the asymptotic behavior of the free energy for a model defined by sinai of one dimensional random walk with random potential in particular we obtain a central limit theorem and a strong law of large numbers for this free energy we use some results on the free energy to study some sample path properties of this random walk which are related respectively to its recurrence and localization some exponents describing the recurrence and localization are found

term and variable selection for non linear system identification the purpose of variable selection is to pre select a subset consisting of the significant variables or to eliminate the redundant variables from all the candidate variables of a system under study prior to model term detection it is required that the selected significant variables alone should sufficiently represent the system generally not all the model terms which are produced by combining different variables make an equal contribution to the system output and terms which make little contribution can be omitted a parsimonious representation which contains only the significant terms can often be obtained without the loss of representational accuracy by eliminating the redundant terms based on these observations a new variable and term selection algorithm is proposed in this paper the term detection algorithm can be applied to the general class of non linear modelling problems which can be expressed as a linear in the parameters form the variable selection procedure is based on locally linea

estimation of spatial derivatives and identification of continuous spatio temporal dynamical systems a new approach for the estimation of spatial derivatives and the identification of a class of continuous spatio temporal dynamical systems from experimental data is presented in this study the proposed identification approach is a combination of implicit adams integration and an orthogonal forward regression algorithm ofr in which the operators are expanded using polynomials as basis functions the noisy experimental data are de noised by using biorthogonal spline wavelet filters and the spatial derivatives are estimated using a multiresolution analysis method finally a bootstrap method is applied to refine the identified parameters from the ofr algorithm the resulting identified models of the spatio temporal evolution form a system of partial differential equations examples are provided to demonstrate the efficiency of the proposed method

on operators commutative with all invariants for a harmonic oscillator with commensurable frequencies for the d dimensional quantum mechanical harmonic oscillator with r commensurability relation between frequencies d independent operators commutative with the oscillator hamiltonian and all other commutative with hamiltonian operators are constructed these operators form a basis in the centre of the algebra of invariants integrals of motion for the quantum mechanical oscillator with commensurable frequencies not all of these d operators have classical analogues a classical harmonic oscillator only has d r commutative with all other invariants these classical integrals first appeared in the gustavson work on the birkhoff normalization operators with such properties are of interest for the perturbation theory since any of them may be at least formally continued to become the invariant of the perturbed hamiltonian

orthogonal least squares methods and their application to non linear system identification abstract identification algorithms based on the well known linear least squares methods of gaussian elimination cholesky decomposition classical gram schmidt modified gram schmidt householder transformation givens method and singular value decomposition are reviewed the classical gram schmidt modified gram schmidt and householder transformation algorithms are then extended to combine structure determination or which terms to include in the model and parameter estimation in a very simple and efficient manner for a class of multivariate discrete time non linear stochastic systems which are linear in the parameters

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

localization for random walks among random obstacles in a single euclidean ball place an obstacle with probability 1 p independently at each vertex of mathbb z d and run a simple random walk before hitting one of the obstacles for d ge 2 and p strictly above the critical threshold for site percolation we condition on the environment where the origin is contained in an infinite connected component free of obstacles and we show that for environments with probability tending to one as n rightarrow infty there exists a unique discrete euclidean ball of volume d log 1 p n asymptotically such that the following holds conditioned on survival up to time n we have that at any time t in epsilon n n n for some epsilon n rightarrow n rightarrow infty 0 with probability tending to one the simple random walk is in this ball this work relies on and substantially improves a previous result of the authors on localization in a region of volume poly logarithmic in n for the same problem

identification of smooth nonlinear dynamical systems with non smooth steady state features abstract this work discusses the identification of single block smooth nonlinear discrete time polynomial models with non smooth steady state features based on bifurcation theory conditions are developed and used to determine some general aspects of the model structure and also to determine some constraints on the parameters required to guarantee the aforementioned features the procedure uses only smooth functions of the regressors a single possibly smooth input and some prior knowledge about the steady state behavior the non smooth static function is here obtained by interchanging the stability of two sets of equilibria at the break point which corresponds to guaranteeing a transcritical bifurcation this work discusses how to determine the domain over which the results are valid the procedure is illustrated with simulated and experimental data

identification of partial differential equation models for a class of multiscale spatio temporal dynamical systems in this article the identification of a class of multiscale spatio temporal dynamical systems which incorporate multiple spatial scales from observations is studied the proposed approach is a combination of adams integration and an orthogonal least squares algorithm in which the multiscale operators are expanded using polynomials as basis functions and the spatial derivatives are estimated by finite difference methods the coefficients of the polynomials can vary with respect to the space domain to represent the feature of multiple scales involved in the system dynamics and are approximated using a b spline wavelet multi resolution analysis the resulting identified models of the spatio temporal evolution form a system of partial differential equations with different spatial scales examples are provided to demonstrate the efficiency of the proposed method

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

consistent identification of narx models via regularization networks generalization networks are nonparametric estimators obtained from the application of tychonov regularization or bayes estimation to the hypersurface reconstruction problem under symmetry assumptions they are a particular type of radial basis function neural network in this correspondence it is shown that such networks guarantee consistent identification of a very general infinite dimensional class of narx models the proofs are based on the theory of reproducing kernel hilbert spaces and the notion of frequency of time probability by means of which it is not necessary to assume that the input is sampled from a stochastic process

using data driven discrete time models and the unscented kalman filter to estimate unobserved variables of nonlinear systems this paper addresses the problem of state estimation for nonlinear systems by means of the unscented kalman filter ukf compared to the traditional extended kalman filter the ukf does not require the local linearization of the system equations used in the propagation stage important results using the ukf have been reported recently but in every case the system equations used by the filter were considered known not only that such models are usually considered to be differential equations which requires that numerical integration be performed during the propagation phase of the filter in this paper the dynamical equations of the system are taken to be difference equations thus avoiding numerical integration and are built from data without prior knowledge the identified models are subsequently implemented in the filter in order to accomplish state estimation the paper discusses the impact of not knowing the exact equations and using data driven models in the context of state and joint state and parameter estimation the procedure is illustrated by means of examples that use simulated and measured data

feature subset selection and ranking for data dimensionality reduction a new unsupervised forward orthogonal search fos algorithm is introduced for feature selection and ranking in the new algorithm features are selected in a stepwise way one at a time by estimating the capability of each specified candidate feature subset to represent the overall features in the measurement space a squared correlation function is employed as the criterion to measure the dependency between features and this makes the new algorithm easy to implement the forward orthogonalization strategy which combines good effectiveness with high efficiency enables the new algorithm to produce efficient feature subsets with a clear physical interpretation

displacement in the parameter space versus spurious solution of discretization with large time step in order to investigate a possible correspondence between differential and difference equations it is important to possess discretization of ordinary differential equations it is well known that when differential equations are discretized the solution thus obtained depends on the time step used in the majority of cases such a solution is considered spurious when it does not resemble the expected solution of the differential equation this often happens when the time step taken into consideration is too large in this work we show that even for quite large time steps some solutions which do not correspond to the expected ones are still topologically equivalent to solutions of the original continuous system if a displacement in the parameter space is considered to reduce such a displacement a judicious choice of the discretization scheme should be made to this end a recent discretization scheme based on the lie expansion of the original differential equations proposed by monaco and normand cyrot will be analysed such a scheme will be shown to be sufficient for providing an adequate discretization for quite large time steps compared to the pseudo period of the underlying dynamics

on self attracting d dimensional random walks let x t t geq 0 be a symmetric nearest neighbor random walk on mathbb z d with exponential holding times of expectation 1 d starting at the origin for a potential v mathbb z d to 0 infty with finite and nonempty support define transformed path measures by d hat mathbb p t equiv exp t 1 int 0 t int 0 t v x s x t ds dt d mathbb p z t for t 0 where z t is the normalizing constant if d 1 or if the self attraction is sufficiently strong then x t infty has an exponential moment under mathbb p t which is uniformly bounded for t 0 and t in 0 t we also prove that x t t geq 0 under suitable subsequences of hat mathbb p t t 0 behaves for large t asymptotically like a mixture of space inhomogeneous ergodic random walks for special cases like a sufficiently strong dirac type interaction we even prove convergence of the transformed path measures and the law of x t as well as of the law of the empirical measure l t under hat mathbb p t t 0

sparse model identification using a forward orthogonal regression algorithm aided by mutual information a sparse representation with satisfactory approximation accuracy is usually desirable in any nonlinear system identification and signal processing problem a new forward orthogonal regression algorithm with mutual information interference is proposed for sparse model selection and parameter estimation the new algorithm can be used to construct parsimonious linear in the parameters models

confinement of brownian motion among poissonian obstacles in ℝ d d 3 consider brownian motion among random obstacles obtained by translating a fixed compact nonpolar subset of d d 1 at the points of a poisson cloud of constant intensity v 0 assume that brownian motion is absorbed instantaneously upon entering the obstacle set in szn conf sznitman has shown that in d 2 conditionally on the event that the process does not enter the obstacle set up to time t the probability that brownian motion remains within distance t1 4 from its starting point is going to 1 as t goes to infinity we show that the same result holds true for d 3 with t1 4 replaced by t1 d 2 the proof is based on sznitmans refined method of enlargement of obstacles 10 as well as on a quantitative isoperimetric inequality due to hall 4

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

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 well known 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 the parameters 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 o

an extended orthogonal forward regression algorithm for system identification using entropy in this paper a fast identification algorithm for non linear dynamic stochastic system identification is presented the algorithm extends the classical orthogonal forward regression ofr algorithm so that instead of using the error reduction ratio err for term selection a new optimality criterion shannon s entropy power reduction ratio eprr is introduced to deal with both gaussian and non gaussian signals it is shown that the new algorithm is both fast and reliable and examples are provided to illustrate the effectiveness of the new approach

asymptotics for the wiener sausage among poissonian obstacles we consider the wiener sausage among poissonian obstacles the obstacle is called hard if brownian motion entering the obstacle is immediately killed and is called soft if it is killed at certain rate it is known that brownian motion conditioned to survive among obstacles is confined in a ball near its starting point we show the weak law of large numbers large deviation principle in special cases and the moment asymptotics for the volume of the corresponding wiener sausage one of the consequence of our results is that the trajectory of brownian motion almost fills the confinement ball

lifschitz tail and wiener sausage ii the present paper is a continuation of 23 we present here two examples of situations where the method developed in 23 applies the first example is that of a periodic diffusion z in r n 1 with generator l isia dj where a is a c2 z periodic elliptic matrix we consider the wiener sausage w u0 c u i z c where c is a nonpolar compact subset of r for instance a closed ball or disc in r if a denotes the constant matrix of homogenized coefficients of the periodic diffusion see 1 i we show that

method for the control of a special class of non linear systems abstract a method for the numerical synthesis of compensators for non linear control systems is proposed the non linear systems investigated are the type in which the system can be represented by two separate parts a linear element and a non linear element as shown in fig 1 the approach adopted is called the method of inequalities in which the problem is formulated as a set of inequalities which represent the specified closed loop performance of the system as well as constraints of an engineering and financial kind the non linear part of the system is linearized using an exponential input describing function an inequality is then formulated concerning the non linear element to ensure that every point in the admissible space represents a closed loop system which does not exhibit autonomous limit cycle oscillation this inequality is defined by using an enhanced sinusoidal describing function which takes account of the effects of higher harmonic signal components as well as of a fundamental sinusoi

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

recursive direct weight optimization in nonlinear system identification a minimal probability approach in this paper a direct weight optimization method is proposed for nonlinear system identification based on a minimal probability idea the approach has several quite attractive features and is very different from existing ones it is optimal for any given number of finite data points and at the same time possesses asymptotic convergence the estimator admits a closed form and no numerical optimization is needed theoretical analysis and numerical simulations show that the approach is a very competitive alternative to existing nonlinear identification methods

frequency domain truncation of volterra series for weakly non linear systems subject to harmonic excitation new results for model order reduction for weakly non linear systems in the frequency domain are derived based on a parametric modelling approach

identification of finite dimensional models of infinite dimensional dynamical systems the identification of finite dimensional discrete time models of deterministic linear and nonlinear infinite dimensional systems from pointwise observations is investigated the input and output observations are used to construct finite dimensional approximations of the solution and the forcing function which are expanded in terms of a finite element basis an algorithm to determine a minimal basis to approximate the data is introduced subsequently the resulting coordinate vectors are used to identify a finite dimensional discrete time model theoretical results concerning the existence stability and convergence of the finite dimensional representation are established numerical results involving identification of finite dimensional models for both linear and nonlinear infinite dimensional systems are presented

improved parameter estimates for non linear dynamical models using a bootstrap method it is known that the least squares ls class of algorithms produce unbiased estimates providing certain assumptions are met there are many practical problems however where the required assumptions are violated typical examples include non linear dynamical system identification problems where the input and output observations are affected by measurement uncertainty and possibly correlated noise this will result in biased ls estimates and the identified model will exhibit poor generalisation properties model estimation for this type of error in variables problem is investigated in this study and a new identification scheme based on a bootstrap algorithm is proposed to improve the model estimates for non linear dynamical system identification

structure selection techniques applied to continous time nonlinear models this paper addresses the problem of choosing the multinomials that should compose a polynomial mathematical model starting from data the mathematical representation used is a nonlinear differential equation of the polynomial type some approaches that have been used in the context of discrete time models are adapted and applied to continuous time models two examples are included to illustrate the main ideas models obtained with and without structure selection are compared using topological analysis the main differences between structure selected models and complete structure models are i the former are more parsimonious than the latter ii a predefined fixed point configuration can be guaranteed for the former and iii the former set of models produce attractors that are topologically closer to the original attractor than those produced by the complete structure models 2001 elsevier science b v all rights reserved