computation and analysis of the asymptotic expansions of the compound means we derive algorithms for computing asymptotic expansion of the composite mean of two arbitrary means m and n then we analyse asymptotic behaviour of the compound mean mn examples and application to some classical means are also presented

a bootstrap method for structure detection of narmax models many systems may be described by narmax models using only a few terms however depending on the order of the system the number of candidate terms can become very large selection of a subset of these candidate terms is necessary for an efficient system description this is an unresolved issue in system identification for over parameterized models therefore in this paper we develop a bootstrap structure detection bsd algorithm as a means of determining the structure of highly over parameterized models the performance of this bsd technique was evaluated by using it to estimate the structure of a 1 simple narmax model 2 moderately over parameterized narmax model and 3 highly over parameterized narmax model the results demonstrate that the bsd algorithm is a robust method for detecting the structure of narmax models this method provides accurate estimates of parameter statistics without relying on assumptions made by traditional procedures and yields a parsimonious description of the system

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

two stage orthogonal least squares methods for neural network construction a number of neural networks can be formulated as the linear in the parameters models training such networks can be transformed to a model selection problem where a compact model is selected from all the candidates using subset selection algorithms forward selection methods are popular fast subset selection approaches however they may only produce suboptimal models and can be trapped into a local minimum more recently a two stage fast recursive algorithm tsfra combining forward selection and backward model refinement has been proposed to improve the compactness and generalization performance of the model this paper proposes unified two stage orthogonal least squares methods instead of the fast recursive based methods in contrast to the tsfra this paper derives a new simplified relationship between the forward and the backward stages to avoid repetitive computations using the inherent orthogonal properties of the least squares methods furthermore a new term exchanging scheme for backward model refinement is introduced to reduce computational demand finally given the error reduction ratio criterion effective and efficient forward and backward subset selection procedures are proposed extensive examples are presented to demonstrate the improved model compactness constructed by the proposed technique in comparison with some popular methods

non parametric nonlinear system identification a data driven orthogonal basis function approach in this paper a data driven orthogonal basis function approach is proposed for non parametric fir nonlinear system identification the basis functions are not fixed a priori and match the structure of the unknown system automatically this eliminates the problem of blindly choosing the basis functions without a priori structural information further based on the proposed basis functions approaches are proposed for model order determination and regressor selection along with their theoretical justifications

sparse kernel regression modeling using combined locally regularized orthogonal least squares and d optimality experimental design the note proposes an efficient nonlinear identification algorithm by combining a locally regularized orthogonal least squares lrols model selection with a d optimality experimental design the proposed algorithm aims to achieve maximized model robustness and sparsity via two effective and complementary approaches the lrols method alone is capable of producing a very parsimonious model with excellent generalization performance the d optimality design criterion further enhances the model efficiency and robustness an added advantage is that the user only needs to specify a weighting for the d optimality cost in the combined model selecting criterion and the entire model construction procedure becomes automatic the value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values

fuzzy adaptive control of a certain class of siso discrete time processes in this manuscript we address the problem of the stability of a certain class of siso discrete time processes controlled by an adaptive fuzzy controller by using lyapunov stability theory these results were recently obtained for adaptive neural controllers and are extended here to adaptive fuzzy controllers of sugeno s type in order to achieve tracking of a reference signal with this kind of fuzzy system we allow both the membership functions and the consequent part of the rules to be adjusted by a parameter adaptation law we first present the gradient based steepest descent adaptation law and we argue that this gradient based adaptation law can be simplified dramatically thereafter we show the asymptotic stability of the overall system the convergence of the tracking error to zero when using this simplified parameters adjustment law unfortunately this result can only be proved when the outputs of the fuzzy controller can be expanded to the first order around the optimal parameter values that allow perfect tracking that is when the parameters are initialized not too far from their optimal values local stability however when the set of tunable parameters is restricted to the set appearing in the linear consequent part of the rules i e the membership functions of the premises are not modified and when the reference signal is the delayed desired output the stability result is strictly valid the parameters do not have to be initialized around the perfectly tuned values in this case the algorithm can be simplified further by only considering the sign of the derivative of the output of the process in terms of its last influential input

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

parameterized convergence bounds for volterra series expansion of narx models evaluation of the convergence bound in the frequency domain for volterra series expansion of nonlinear systems described by narx models is studied this provides new convergence criteria under which the nonlinear system of interest has a convergent volterra series expansion and the new criteria are expressed explicitly in terms of the input magnitude model parameters and frequency variable the new convergence criteria are firstly developed for harmonic inputs and then extended to multi tone and general input cases based on the theoretical analysis a general procedure for calculating the convergence bound is provided the results provide a fundamental basis for nonlinear signal processing using the volterra series theory

fast and stable contour integration for high order divided differences via elliptic functions in this paper we will present a new method for evaluating high order divided differences for certain classes of analytic possibly operator values functions this is a classical problem in numerical mathematics but also arises in new applications such as e g the use of generalized convolution quadrature to solve retarded potential integral equations the functions which we will consider are allowed to grow exponentially to the left complex half plane and the interpolation points are scattered in a large real interval our approach is based on the representation of divided differences as contour integral and we will employ a subtle parameterization of the contour in combination with a quadrature approximation by the trapezoidal rule

rapid solution of the wave equation in unbounded domains in this paper we propose and analyze a new fast method for the numerical solution of time domain boundary integral formulations of the wave equation we employ lubich s convolution quadrature method for the time discretization and a galerkin boundary element method for the spatial discretization the coefficient matrix of the arising system of linear equations is a triangular block toeplitz matrix possible choices for solving the linear system arising from the above discretization include the use of fast fourier transform fft techniques and the use of data sparse approximations by using fft techniques the computational complexity can be reduced substantially while the storage cost remains unchanged and is typically high using data sparse approximations the gain is reversed i e the computational cost is approximately unchanged while the storage cost is substantially reduced the method proposed in this paper combines the advantages of these two approaches first the discrete convolution related to the block toeplitz system is transformed into the discrete fourier image thereby arriving at a decoupled system of discretized helmholtz equations with complex wave numbers a fast data sparse e g fast multipole or panel clustering method can then be applied to the transformed system additionally significant savings can be achieved if the boundary data are smooth and time limited in this case the right hand sides of many of the helmholtz problems are almost zero and hence can be disregarded finally the proposed method is inherently parallel we analyze the stability and convergence of these methods thereby deriving the choice of parameters that preserves the convergence rates of the unperturbed convolution quadrature we also present numerical results which illustrate the predicted convergence behavior

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

structurally dynamic wavelet networks for adaptive control of robotic systems the practical applicability of recently developed adaptive neurocontrol algorithms for poorly modelled robotic systems depends crucially upon the accuracy and efficiency of the neural network used

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 fast identification algorithm for box cox transformation based radial basis function neural network in this letter a box cox transformation based radial basis function rbf neural network is introduced using the rbf neural network to represent the transformed system output initially a fixed and moderate sized rbf model base is derived based on a rank revealing orthogonal matrix triangularization qr decomposition then a new fast identification algorithm is introduced using gauss newton algorithm to derive the required box cox transformation based on a maximum likelihood estimator the main contribution of this letter is to explore the special structure of the proposed rbf neural network for computational efficiency by utilizing the inverse of matrix block decomposition lemma finally the box cox transformation based rbf neural network with good generalization and sparsity is identified based on the derived optimal box cox transformation and a d optimality based orthogonal forward regression algorithm the proposed algorithm and its efficacy are demonstrated with an illustrative example in comparison with support vector machine regression

designing fuzzy inference systems from data an interpretability oriented review fuzzy inference systems fis are widely used for process simulation or control they can be designed either from expert knowledge or from data for complex systems fis based on expert knowledge only may suffer from a loss of accuracy this is the main incentive for using fuzzy rules inferred from data designing a fis from data can be decomposed into two main phases automatic rule generation and system optimization rule generation leads to a basic system with a given space partitioning and the corresponding set of rules system optimization can be done at various levels variable selection can be an overall selection or it can be managed rule by rule rule base optimization aims to select the most useful rules and to optimize rule conclusions space partitioning can be improved by adding or removing fuzzy sets and by tuning membership function parameters structure optimization is of a major importance selecting variables reducing the rule base and optimizing the number of fuzzy sets over the years many methods have become available for designing fis from data their efficiency is usually characterized by a numerical performance index however for human computer cooperation another criterion is needed the rule interpretability an implicit assumption states that fuzzy rules are by nature easy to be interpreted this could be wrong when dealing with complex multivariable systems or when the generated partitioning is meaningless for experts the paper analyzes the main methods for automatic rule generation and structure optimization they are grouped into several families and compared according to the rule interpretability criterion for this purpose three conditions for a set of rules to be interpretable are defined

modelling and identification of non linear deterministic systems in the delta domain this paper provides a formulation for using the delta operator in the modelling of non linear systems it is shown that a unique representation of a deterministic non linear auto regressive with exogenous input narx model can be obtained for polynomial basis functions using the delta operator and expressions are derived to convert between the shift and delta domain a delta narx model is applied to the identification of a test problem a van der pol oscillator a comparison is made with the standard shift operator non linear model and it is demonstrated that the delta domain approach improves the numerical properties of structure detection leads to a parsimonious description and provides a model that is closely linked to the continuous time non linear system in terms of both parameters and structure

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

on determining the structure of a non linear system abstract a method is presented for constructing a model of a non linear system from the input output data the structure of the system is assembled from a library of nonlinear terms that are possible suspects for inclusion in the model while each possible model structure is represented by a node in a tree it is shown that searching the tree for the optimal n term model structure can be done in n stages using an algorithm based on conjugate direction ideas the essential feature of the technique is that it generates a sequence of projection matrices such that the original vector valued functions become conjugate directions this leaves the original non linear terms intact and allows the structure for the optimal n term model to be assembled in n selections from the library examples are presented from regression analysis and non linear dynamic systems

focused local learning with wavelet neural networks a novel objective function is presented that incorporates both local and global errors as well as model parsimony in the construction of wavelet neural networks two methods are presented to assist in the minimization of this objective function especially the local error term first during network initialization a locally adaptive grid is utilized to include candidate wavelet basis functions whose local support addresses the local error of the local feature set this set can be either user defined or determined using information derived from the wavelet transform modulus maxima representation next during the network construction a new selection procedure based on a subspace projection operator is presented to help focus the selection of wavelet basis functions to reduce the local error simulation results demonstrate the effectiveness of these methodologies in minimizing local and global error while maintaining model parsimony and incurring a minimal increase on computational complexity

random and pseudorandom inputs for volterra filter identification this paper studies input signals for the identification of nonlinear discrete time systems modeled via a truncated volterra series representation a kronecker product representation of the truncated volterra series is used to study the persistence of excitation pe conditions for this model it is shown that i i d sequences and deterministic pseudorandom multilevel sequences prms s are pe for a truncated volterra series with nonlinearities of polynomial degree n if and only if the sequences take on n 1 or more distinct levels it is well known that polynomial regression models such as the volterra series suffer from severe ill conditioning if the degree of the polynomial is large the condition number of the data matrix corresponding to the truncated volterra series for both prms and i i d inputs is characterized in terms of the system memory length and order of nonlinearity hence the trade off between model complexity and ill conditioning is described mathematically a computationally efficient least squares identification algorithm based on prms or i i d inputs is developed that avoids directly computing the inverse of the correlation matrix in many applications short data records are used in which case it is demonstrated that volterra filter identification is much more accurate using prms inputs rather than gaussian white noise inputs

on the multistep time discretization of linear initial boundary value problems and their boundary integral equations convergence estimates in terms of the data are shown for multistep methods applied to non homogeneous linear initial boundary value problems similar error bounds are derived for a new class of time discrete and fully discrete approximation schemes for boundary integral equations of such problems e g for the single layer potential equation of the wave equation in both cases the results are obtained from convergence and stability estimates for operational quadrature approximations of convolutions these estimates which are also proved here depend on bounds of the laplace transform of the distributional convolution kernel outside the stability region scaled by the time stepsize and on the smoothness of the data

sparse total least squares analysis and greedy algorithms linear systems where both the matrix and the right hand side are affected by noise or uncertainties are typically solved via a total least squares tls approach we study the sparse tls problem with solutions having s nonzero elements we present a set of conditions under which the sparse least squares ls and tls problems have the same support the conditions are expressed in terms of the restricted isometry constants and the minimum nonzero principal angle between subspaces made of s columns of the matrix we also study several greedy algorithms for solving the sparse tls problem inspired by our theoretical results we infer that an effective approach is to compute the support of the ls solution then solve the standard tls problem restrained to that support indeed doing so with orthogonal matching pursuit omp gives consistently good results another greedy strategy is to extend the support with the column that minimizes the smallest angle with the subspace sas corresponding to the already chosen support which is a combined ls tls heuristic we show via simulations that sas gives the best results for small problem sizes and high and medium signal to noise ratio snr while omp is best or nearly best in almost all cases

a hybrid constructive algorithm for single layer feedforward networks learning single layer feedforward networks slfns have been proven to be a universal approximator when all the parameters are allowed to be adjustable it is widely used in classification and regression problems the slfn learning involves two tasks determining network size and training the parameters most current algorithms could not be satisfactory to both sides some algorithms focused on construction and only tuned part of the parameters which may not be able to achieve a compact network other gradient based optimization algorithms focused on parameters tuning while the network size has to be preset by the user therefore trial and error approach has to be used to search the optimal network size because results of each trial cannot be reused in another trial it costs much computation in this paper a hybrid constructive hc algorithm is proposed for slfn learning which can train all the parameters and determine the network size simultaneously at first by combining levenberg marquardt algorithm and least square method a hybrid algorithm is presented for training slfn with fixed network size then with the hybrid algorithm an incremental constructive scheme is proposed a new randomly initialized neuron is added each time when the training entrapped into local minima because the training continued on previous results after adding new neurons the proposed hc algorithm works efficiently several practical problems were given for comparison with other popular algorithms the experimental results demonstrated that the hc algorithm worked more efficiently than those optimization methods with trial and error and could achieve much more compact slfn than those construction algorithms

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

runge kutta convolution quadrature for operators arising in wave propagation an error analysis of runge kutta convolution quadrature is presented for a class of non sectorial operators whose laplace transform satisfies besides the standard assumptions of analyticity in a half plane re s 0 and a polynomial bound operatorname o s mu 1 there the stronger polynomial bound operatorname o s mu 2 in convex sectors of the form operatorname arg s leq pi 2 theta for 0 the order of convergence of the runge kutta convolution quadrature is determined by 2 and the underlying runge kutta method but is independent of 1 time domain boundary integral operators for wave propagation problems have laplace transforms that satisfy bounds of the above type numerical examples from acoustic scattering show that the theory describes accurately the convergence behaviour of runge kutta convolution quadrature for this class of applications our results show in particular that the full classical order of the runge kutta method is attained away from the scattering boundary

bernoulli polynomials and asymptotic expansions of the quotient of gamma functions the main subject of this paper is the analysis of asymptotic expansions of wallis quotient function c x t c x s and wallis power function c x t c x s 1 t s when x tends to infinity coefficients of these expansions are polynomials derived from bernoulli polynomials the key to our approach is the introduction of two intrinsic variables a 12 t s 1 and b 14 1 t s 1 t s which are naturally connected with bernoulli polynomials and wallis functions asymptotic expansion of wallis functions in terms of variables t and s and also a and b is given application of the new method leads to the improvement of many known approximation formulas of the stirling s type

on the efficiency of the orthogonal least squares training method for radial basis function networks the efficiency of the orthogonal least squares ols method for training approximation networks is examined using the criterion of energy compaction we show that the selection of basis vectors produced by the procedure is not the most compact when the approximation is performed using a nonorthogonal basis hence the algorithm does not produce the smallest possible networks for a given approximation error specific examples are given using the gaussian radial basis functions type of approximation networks

blind identification of second order volterra systems with complex random inputs using higher order cumulants in this correspondence closed form expressions for the blind identification of linear quadratic volterra systems are established the system is excited by a complex valued random sequence and the output cumulants of order up to 4 are employed it is assumed that the memory of the linear part is greater than or equal to the memory of the quadratic part cumulant based formulas are developed demonstrating that the system is uniquely identifiable an svd based variant with improved performance is also derived simulations and comparisons with existing techniques are presented

symmetric rbf classifier for nonlinear detection in multiple antenna aided systems in this paper we propose a powerful symmetric radial basis function rbf classifier for nonlinear detection in the so called overloaded multiple antenna aided communication systems by exploiting the inherent symmetry property of the optimal bayesian detector the proposed symmetric rbf classifier is capable of approaching the optimal classification performance using noisy training data the classifier construction process is robust to the choice of the rbf width and is computationally efficient the proposed solution is capable of providing a signal to noise ratio snr gain in excess of 8 db against the powerful linear minimum bit error rate ber benchmark when supporting four users with the aid of two receive antennas or seven users with four receive antenna elements

asymptotic analysis of the iterative power means abstract we investigate the asymptotic expansion of the compound mean obtained by the iterative process of two power means we present the stationary and convergence properties of the coefficients in the expansions

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

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

regularized orthogonal least squares algorithm for constructing radial basis function networks the paper presents a regularized orthogonal least squares learning algorithm for radial basis function networks the proposed algorithm combines the advantages of both the orthogonal forward regression and regularization methods to provide an efficient and powerful procedure for constructing parsimonious network models that generalize well examples of nonlinear modelling and prediction are used to demonstrate better generalization performance of this regularized orthogonal least squares algorithm over the unregularized one

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

runge kutta methods for parabolic equations and convolution quadrature we study the approximation properties of runge kutta time discretizations of linear and semilinear parabolic equations including incompressible navier stokes equations we derive asymptotically sharp error bounds and relate the temporal order of convergence which is generally noninteger to spatial regularity and the type of boundary conditions the analysis relies on an interpretation of runge kutta methods as convolution quadratures in a different context these can be used as efficient computational methods for the approximation of convolution integrals and integral equations they use the laplace transform of the confolution kernal via a discrete operational calculus 23 refs 2 tabs

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

predictive uncertainty of chaotic daily streamflow using ensemble wavelet networks approach 1 perfect or even mediocre weather predictions over a long period are almost impossible because of the ultimate growth of a small initial error into a significant one even though the sensitivity of initial conditions limits the predictability in chaotic systems an ensemble of prediction from different possible initial conditions and also a prediction algorithm capable of resolving the fine structure of the chaotic attractor can reduce the prediction uncertainty to some extent all of the traditional chaotic prediction methods in hydrology are based on single optimum initial condition local models which can model the sudden divergence of the trajectories with different local functions conceptually global models are ineffective in modeling the highly unstable structure of the chaotic attractor this paper focuses on an ensemble prediction approach by reconstructing the phase space using different combinations of chaotic parameters i e embedding dimension and delay time to quantify the uncertainty in initial conditions the ensemble approach is implemented through a local learning wavelet network model with a global feed forward neural network structure for the phase space prediction of chaotic streamflow series quantification of uncertainties in future predictions are done by creating an ensemble of predictions with wavelet network using a range of plausible embedding dimensions and delay times the ensemble approach is proved to be 50 more efficient than the single prediction for both local approximation and wavelet network approaches the wavelet network approach has proved to be 30 50 more superior to the local approximation approach compared to the traditional local approximation approach with single initial condition the total predictive uncertainty in the streamflow is reduced when modeled with ensemble wavelet networks for different lead times localization property of wavelets utilizing different dilation and translation parameters helps in capturing most of the statistical properties of the observed data the need for taking into account all plausible initial conditions and also bringing together the characteristics of both local and global approaches to model the unstable yet ordered chaotic attractor of a hydrologic series is clearly demonstrated

convolution quadrature and discretized operational calculus ii operational quadrature rules are applied to problems in numerical integration and the numerical solution of integral equations singular integrals power and logarithmic singularities finite part integrals multiple timescale convolution volterra integral equations wiener hopf integral equations frequency domain conditions which determine the stability of such equations can be carried over to the discretization

combined genetic algorithm optimization and regularized orthogonal least squares learning for radial basis function networks presents a two level learning method for radial basis function rbf networks a regularized orthogonal least squares rols algorithm is employed at the lower level to construct rbf networks while the two key learning parameters the regularization parameter and the rbf width are optimized using a genetic algorithm ga at the upper level nonlinear time series modeling and prediction is used as an example to demonstrate the effectiveness of this hierarchical learning approach

improved structure optimization for fuzzy neural networks fuzzy neural network based inference systems are well known universal approximators which can produce linguistically interpretable results unfortunately their dimensionality can be extremely high due to an excessive number of inputs and rules which raises the need for overall structure optimization in the literature various input selection methods are available but they are applied separately from rule selection often without considering the fuzzy structure this paper proposes an integrated framework to optimize the number of inputs and the number of rules simultaneously first a method is developed to select the most significant rules along with a refinement stage to remove unnecessary correlations an improved information criterion is then proposed to find an appropriate number of inputs and rules to include in the model leading to a balanced tradeoff between interpretability and accuracy simulation results confirm the efficacy of the proposed method

generalized convolution quadrature based on runge kutta methods in this paper we develop the runge kutta generalized convolution quadrature with variable time stepping for the numerical solution of convolution equations for time and space time problems and present the corresponding stability and convergence analysis for this purpose some new theoretical tools such as tensorial divided differences summation by parts with runge kutta differences and a calculus for runge kutta discretizations of generalized convolution operators such as an associativity property will be developed in this paper numerical examples will illustrate the stable and efficient behavior of the resulting discretization

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

from local similarities to global coding a framework for coding applications feature coding has received great attention in recent years as a building block of many image processing algorithms in particular the importance of the locality assumption in coding approaches has been studied in many previous works we review this assumption and claim that using the similarity of data points to a more global set of anchor points does not necessarily weaken the coding method as long as the underlying structure of the anchor points is considered we propose to capture the underlying structure by assuming a random walker over the anchor points we also show that our method is a fast approximation to the diffusion map kernel experiments on various data sets show that with a knowledge of the underlying structure of anchor points different state of the art coding algorithms may boost their performance in different learning tasks by utilizing the proposed method

sparse density estimation on the multinomial manifold a new sparse kernel density estimator is introduced based on the minimum integrated square error criterion for the finite mixture model since the constraint on the mixing coefficients of the finite mixture model is on the multinomial manifold we use the well known riemannian trust region rtr algorithm for solving this problem the first and second order riemannian geometry of the multinomial manifold are derived and utilized in the rtr algorithm numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with an accuracy competitive with those of existing kernel density estimators

a novel chaotic neural network with the ability to characterize local features and its application to provide an ability to characterize local features for the chaotic neural network cnn gauss wavelet is used for the self feedback of the cnn with the dilation parameter acting as the bifurcation parameter the exponentially decaying dilation parameter and the chaotically varying translation parameter not only govern the wavelet self feedback transform but also enable the cnn to generate complex dynamics behavior preventing the network from being trapped in the local minima analysis of the energy function of the cnn indicates that the local characterization ability of the proposed cnn is effectively provided by the wavelet self feedback in the manner of inverse wavelet transform and that the proposed cnn can achieve asymptotical stability the experimental results on traveling salesman problem tsp suggest that the proposed cnn has a higher average success rate for obtaining globally optimal or near optimal solutions

asymptotic expansions of integral means and applications to the ratio of gamma functions integral means are important class of bivariate means in this paper we prove the very general algorithm for calculation of coefficients in asymptotic expansion of integral mean it is based on explicit solving the equation of the form b a x c x where asymptotic expansions of b and c are known the results are illustrated by calculation of some important integral means connected with gamma function

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

distributed dictionary learning for sparse representation in sensor networks this paper develops a distributed dictionary learning algorithm for sparse representation of the data distributed across nodes of sensor networks where the sensitive or private data are stored or there is no fusion center or there exists a big data application the main contributions of this paper are 1 we decouple the combined dictionary atom update and nonzero coefficient revision procedure into two stage operations to facilitate distributed computations first updating the dictionary atom in terms of the eigenvalue decomposition of the sum of the residual correlation matrices across the nodes then implementing a local projection operation to obtain the related representation coefficients for each node 2 we cast the aforementioned atom update problem as a set of decentralized optimization subproblems with consensus constraints then we simplify the multiplier update for the symmetry undirected graphs in sensor networks and minimize the separable subproblems to attain the consistent estimates iteratively and 3 dictionary atoms are typically constrained to be of unit norm in order to avoid the scaling ambiguity we efficiently solve the resultant hidden convex subproblems by determining the optimal lagrange multiplier some experiments are given to show that the proposed algorithm is an alternative distributed dictionary learning approach and is suitable for the sensor network environment

sparse multinomial kernel discriminant analysis smkda dimensionality reduction via canonical variate analysis cva is important for pattern recognition and has been extended variously to permit more flexibility e g by kernelizing the formulation this can lead to over fitting usually ameliorated by regularization here a method for sparse multinomial kernel discriminant analysis smkda is proposed using a sparse basis to control complexity it is based on the connection between cva and least squares and uses forward selection via orthogonal least squares to approximate a basis generalizing a similar approach for binomial problems classification can be performed directly via minimum mahalanobis distance in the canonical variates smkda achieves state of the art performance in terms of accuracy and sparseness on 11 benchmark datasets

prediction error estimation algorithm for non linear output affine systems a prediction error estimation algorithm is developed for non linear discrete time systems which can be represented by the output affine difference equation model the theory of hypothesis testing is employed to select a model with the correct structure problems relating to the use of output affine models in the identification of non linear systems are discussed and a comparison with the narmax nonlinear armax model is given

variable selection algorithm for the construction of mimo operating point dependent neurofuzzy networks an input variable selection procedure is introduced for the identification and construction of multi input multi output mimo neurofuzzy operating point dependent models the algorithm is an extension of a forward modified gram schmidt orthogonal least squares procedure for a linear model structure which is modified to accommodate nonlinear system modeling by incorporating piecewise locally linear model fitting the proposed input nodes selection procedure effectively tackles the problem of the curse of dimensionality associated with lattice based modeling algorithms such as radial basis function neurofuzzy networks enabling the resulting neurofuzzy operating point dependent model to be widely applied in control and estimation some numerical examples are given to demonstrate the effectiveness of the proposed construction algorithm