identification of systems containing linear dynamic and static nonlinear elements identification of nonlinear systems which can be represented by combinations of linear dynamic and static nonlinear elements are considered previous results by the authors based on correlation analysis are combined to provide a unified treatment for this class of systems it is shown that systems composed of cascade feedforward feedback and multiplicative connections of linear dynamic and zero memory nonlinear elements can be identified in terms of the individual component subsystems from measurements of the system input and output only

testing for the cointegrating rank of a var process with a time trend standard tests for the cointegrating rank of a vector autoregressive var process have nonstandard limiting distributions which depend on the characteristics of intercept terms and time trends in the system in practice these characteristics are often unknown therefore modified tests are considered which allow for deterministic linear trends in the data generation process dgp the tests are based on the lagrange multiplier lm principle and in contrast to likelihood ratio lr tests proposed for this situation our tests take into account the cointegrating rank specified under the null hypothesis in estimating the trend parameters the tests are shown to have nonstandard limiting distributions which do not depend on deterministic terms and have better local power and small sample properties than the competing lr tests in many situations

on numerical cubatures of singular surface integrals in boundary element methods we present and analyze methods for the accurate and efficient evaluation of weakly cauchy and hypersingular integrals over piecewise analytic curved surfaces in 3 the class of admissible integrands includes all kernels arising in the numerical solution of elliptic boundary value problems in three dimensional domains by the boundary integral equation method the possibly not absolutely integrable kernels of boundary integral operators in local coordinates are pseudohomogeneous with analytic characteristics depending on the local geometry of the surface at the source point this rules out weighted quadrature approaches with a fixed singular weight for weakly singular integrals it is shown that duffy s triangular coordinates leadalways to a removal of the kernel singularity also asymptotic estimates of the integration error are provided as the size of the boundary element patch tends to zero these are based on the rabinowitz richter estimates in connection with an asymptotic estimate of domains of analyticity in 2 it is further shown that the modified extrapolation approach due to lyness is in the weakly singular case always applicable corresponding error and asymptotic work estimates are presented for the weakly singular as well as for cauchy and hypersingular integrals which e g arise in the study of crack problems we analyze a family of product integration rules in local polar coordinates these rules are hierarchically constructed from finite part integration formulas in radial and gaussian formulas in angular direction again we show how the rabinowitz richter estimates can be applied providing asymptotic error estimates in terms of orders of the boundary element size

a sinh transformation for evaluating two dimensional nearly singular boundary element integrals a new transformation technique is introduced for evaluating the two dimensional nearly singular integrals which arise in the solution of laplace s equation in three dimensions using the boundary element method when the source point is very close to the element of integration the integrals are evaluated using in a product fashion a transformation which has recently been used to evaluate one dimensional near singular integrals this sinh transformation method automatically takes into account the position of the projection of the source point onto the element and also the distance b between the source point and the element the method is straightforward to implement and when it is compared with a number of existing techniques for evaluating two dimensional near singular integrals it is found that the sinh method is superior to the existing methods considered both for potential integrals across the full range of b values considered 0 0 01 for smaller values of b the use of the lmethod is recommended for flux integrals copyright 2006 john wiley sons ltd

evaluation of hypersingular and nearly singular integrals in the isogeometric boundary element method for acoustics abstract special integration routines for hypersingular and nearly singular integrals that arise in an isogeometric boundary element method igabem are presented the igabem is applied to an acoustic problem in the frequency domain that corresponds to the helmholtz equation in three dimensions a major topic of such an acoustical bem is the non uniqueness of the conventional boundary integral equation which can be corrected by the burton miller formulation at the cost of a hypersingular integral that requires the presented routines the combination of the bem with an isogeometric analysis iga is advantageous since the exact cad description is directly incorporated to the numerical simulation as the geometry is represented exactly the integration routines become even more relevant and cannot be masked by the geometrical approximation for the conventional approximation with plane lagrange elements a variety of different integration routines exist but are not investigated in the scope of an iga therefore the hypersingular integration scheme of guiggiani is adapted to be applicable to this new methodology a direct evaluation of the hypersingular integral is possible instead of an integration over the complete surface as in the often used regularized boundary integral equation additionally the sinh transformation for nearly singular integrals is introduced to achieve more accurate results with the same number of integration points as the conventional gaussian integration the new formulation is analyzed under the special case of the oscillatory kernels in acoustics

hammerstein system identification by non parametric instrumental variables a mixed parametric non parametric routine for hammerstein system identification is presented parameters of a non linear characteristic and of arma linear dynamical part of hammerstein system are estimated by least squares and instrumental variables assuming poor a priori knowledge about the random input and random noise both subsystems are identified separately thanks to the fact that the unmeasurable interaction inputs and suitable instrumental variables are estimated in a preliminary step by the use of a non parametric regression function estimation method a wide class of non linear characteristics including functions which are not linear in the parameters is admitted it is shown that the resulting estimates of system parameters are consistent for both white and coloured noise the problem of generating optimal instruments is discussed and proper non parametric method of computing the best instrumental variables is proposed the analytical findings are validated using numerical simulation results

testing for the cointegrating rank of a var process with level shift at unknown time a systems cointegration rank test is proposed that is applicable for vector autoregressive var processes with a structural shift at unknown time the structural shift is modeled as a simple shift in the level of the process it is proposed to estimate the break date first on the basis of a full unrestricted var model two alternative estimators are considered and their asymptotic properties are derived in the next step the deterministic part of the process including the shift size is estimated and the series are adjusted by subtracting the estimated deterministic part a johansen type test for the cointegrating rank is applied to the adjusted series the test statistic is shown to have a well known asymptotic null distribution that does not depend on the break date the performance of the procedure in small samples is investigated by simulations

a modified multilevel algorithm for large scale scientific and engineering computing abstract a modified multilevel algorithm for solving the excessive storage requirements and ill conditioning encountered in the boundary type discretization method is proposed the modified multilevel algorithm is an extension of the modified dual level algorithm from dual levels to multiple levels the method is a kernel independent method the core idea is the layer by layer calculation and then layer by layer correction making use of a multilevel structure the original sparse matrix of the modified dual level algorithm breaks down into a series of smaller sparse matrices corresponding to different fine meshes the final matrix to be solved is hereby transformed to a series of smaller sparse matrices instead of a fully populated matrix the preconditioning effect originating from the recursive computations among the coarse mesh and fine meshes constitutes its core competitive attribute the method evaluates far field contributions only by the coarse mesh and uses a gradual approach to evaluate the near field contributions the storage requirements and computing complexity are hereby further reduced significantly

nonlinearity estimation in hammerstein systems based on ordered observations the nonlinear subsystem of a hammerstein system is identified i e its characteristic is recovered from input output ohservations of the whole system the input and disturbance are white stochastic processes the identified characteristic satisfies a piecewise lipschitz condition only algorithms presented in the paper are calculated from ordered input output observations i e from pairs of observations arranged in a sequence in which input measurements increase in value the mean integrated square error converges to zero as the number of observations tends to infinity convergence rates are insensitive to the shape of the probability density of the input signal results of numerical simulation are also shown

identification of discrete hammerstein systems using kernel regression estimates in this note a discrete time hammerstein system is identified the weighting function of the dynamical subsystem is recovered by the correlation method the main results concern estimation of the nonlinear memoryless subsystem no conditions concerning functional form of the transform characteristic of the subsystem are made and an algorithm for estimation of the characteristic is presented the algorithm is a nonparametric kernel estimate of regression functions calculated from dependent data it is shown that the algorithm converges to the characteristic as the number of observations tend to infinity for sufficiently smooth characteristics the rate of convergence is o n 2 5 in probability

dynamic system identification with order statistics systems consisting of linear dynamic and memory less nonlinear subsystems are identified the paper deals with systems in which the nonlinear element is followed by a linear element as well as systems in which the subsystems are connected in parallel the goal of the identification is to recover the nonlinearity from noisy input output observations of the whole system signals interconnecting the elements are not measured observed values of the input signal are rearranged in increasing order and coefficients for the expansion of the nonlinearity in trigonometric series are estimated from the new sequence of observations obtained in this way two algorithms are presented and their mean integrated square error is examined conditions for pointwise convergence are also established for the nonlinearity satisfying the lipschitz condition the error converges to zero the rate of convergence derived for differentiable nonlinear characteristics is insensitive to the roughness of the probability density of the input signal results of numerical simulation are also presented

wavelet amendment of polynomial models in hammerstein systems identification a new wavelet algorithm for on line improvement of an existing polynomial model of nonlinearity in a hammerstein system is proposed and its properties are examined the algorithm employs wavelet bases on interval convergence of the resulting assembly comprising the parametric polynomial model and a nonparametric wavelet add on to the system nonlinearity is shown rates of convergence for uniformly smooth and piecewise smooth nonlinearities with discontinuities are both established

combined parametric nonparametric identification of hammerstein systems a novel parametric nonparametric methodology for hammerstein system identification is proposed assuming random input and correlated output noise the parameters of a nonlinear static characteristic and finite impulse response system dynamics are estimated separately each in two stages first the inner signal is recovered by a nonparametric regression function estimation method stage 1 and then system parameters are solved independently by the least squares stage 2 convergence properties of the scheme are established and rates of convergence are given

identification of quasi periodically varying systems using the combined nonparametric parametric approach the problem of identification of quasi periodically varying finite impulse response systems is considered neither the number of system frequency modes nor the initial frequency values are assumed to be known a priori the proposed solution is a blend of the parametric model based and nonparametric discrete fourier transform based approach to system identification it is shown that the results of nonparametric analysis can be used to identify the number of frequency modes and to determine initial conditions needed to smoothly start or restart the model based tracking algorithm such a combined nonparametric parametric approach allows one to preserve advantages of both frameworks leading to an estimation procedure which guarantees global frequency search high frequency resolution fast initial convergence and good steady state tracking capabilities

hp fast multipole boundary element method for 3d acoustics summary a fast multipole boundary element method fmbem extended by an adaptive mesh refinement algorithm for solving acoustic problems in three dimensional space is presented in this paper the collocation method is used and the burton miller formulation is employed to overcome the fictitious eigenfrequencies arising for exterior domain problems due to the application of the combined integral equation chbie the developed fmbem is feasible for all positive wave numbers even up to high frequencies in order to evaluate the hypersingular integral resulting from the burton miller formulation of the bie an integration technique for arbitrary element order is applied the fast multipole method combined with an arbitrary order h p mesh refinement strategy enables accurate computation of large scale systems numerical examples substantiate the high accuracy attainable by the developed fmbem while requiring only moderate computational effort at the same time this article is protected by copyright all rights reserved

a new form of the hypersingular boundary integral equation for 3 d acoustics and its implementation with c0 boundary elements abstract an improved weakly singular form of the hypersingular boundary integral equation hbie for 3 d acoustic wave problems is presented in this paper compared with the weakly singular form of the hbie published earlier y j liu and f j rizzo a weakly singular form of the hypersingular boundary integral equation applied to 3 d acoustic wave problems comput methods appl mech engrg 96 1992 271 287 this new form involves only tangential derivatives of the density function and thus its discretization using the boundary element method bem is easier to perform instead of using nonconforming and c1 continuous boundary elements advocated earlier c0 continuous conforming quadratic elements are employed in the discretization of this weakly singular form of the hbie some justifications on using c0 elements for hbies are provided to reflect the current views on this crucial issue for hbies it is postulated that the original c1 continuity requirement for the density function in the analytical hbie formulation can be relaxed to piecewise c1 continuity in the numerical implementation of the weakly singular forms of the hbie numerical examples of both scattering and radiation problems clearly demonstrate the accuracy and versatility of the new weakly singular form of the hbie for 3 d acoustics

a self adaptive co ordinate transformation for efficient numerical evaluation of general boundary element integrals almost all general purpose boundary element computer packages include a curved geometry modelling capability thus numerical quadrature schemes play an important role in the efficiency of programming the technique the present work discusses this problem in detail and introduces efficient means of computing singular or nearly singular integrals currently found in two dimensional axisymmetric and three dimensional applications emphasis is given to a new third degree polynomial transformation which was found greatly to improve the accuracy of gaussian quadrature scheme s within the near singularity range the procedure can easily be implemented into existing be codes and presents the important feature of being self adaptive i e it produces a variable lumping of the gauss stations toward the singularity depending on the minimum distance from the source point to the element the self adaptiveness of the scheme also makes it inactive when not useful large source distances which makes it very safe for general usage

optimal additive schwarz preconditioning for adaptive 2d iga boundary element methods abstract we define and analyze local multilevel diagonal preconditioners for isogeometric boundary elements on locally refined meshes in two dimensions hypersingular and weakly singular integral equations are considered we prove that the condition number of the preconditioned systems of linear equations is independent of the mesh size and the refinement level therefore the computational complexity when using appropriate iterative solvers is optimal our analysis is carried out for closed and open boundaries and numerical examples confirm our theoretical results

quadrature over a pyramid or cube of integrands with a singularity at a vertex a simple transformation is introduced which facilitates the evaluation of integrals over certain square based pyramids or cubes in cases where the integrand has a singularity at a vertex

a nystrom method for weakly singular integral operators on surfaces we describe a modified nystrom method for the discretization of the weakly singular boundary integral operators which arise from the formulation of linear elliptic boundary value problems as integral equations standard nystrom and collocation schemes proceed by representing functions via their values at a collection of quadrature nodes our method uses appropriately scaled function values in lieu of such representations this results in a scheme which is mathematically equivalent to galerkin discretization in that the resulting matrices are related to those obtained by galerkin methods via conjugation with well conditioned matrices but which avoids the evaluation of double integrals moreover we incorporate a new mechanism for approximating the singular integrals which arise from the discretization of weakly singular integral operators which is considerably more efficient than standard methods we illustrate the performance of our method with numerical experiments

wiener system modelling by exponentially weighted aggregation abstractin the paper the aggregation algorithm for wiener system modelling is proposed the method uses exponential weights to combine aggregate models from a given collection of d linear dynamic and dm nonlinear static models of the genuine system blocks that can be a priori hypotheses other system identification outcomes etc the resulting model has a noteworthy property it is almost as accurate as the best hypothetical wiener model built from a given collection this is caused by the fact that the error introduced by the aggregation routine decreases in the mean squared sense with growing number of measurements n as fast as cqn 1ln dmd where c and q are known constants simulations confirm theoretical findings and demonstrate applicability of the algorithm in engineering problems for small and moderate measurement data sets

an interpolation based fast multipole method for higher order boundary elements on parametric surfaces in this article a black box higher order fast multipole method for solving boundary integral equations on parametric surfaces in three spatial dimensions is proposed such piecewise smooth surfaces are the topic of recent studies in isogeometric analysis due to the exact surface representation the rate of convergence of higher order methods is not limited by approximation errors of the surface an element wise clustering strategy yields a balanced cluster tree and an efficient numerical integration scheme for the underlying galerkin method by performing the interpolation for the fast multipole method directly on the reference domain the cost complexity in the polynomial degree is reduced by one order this gain is independent of the application of either mathcal h or mathcal h 2 matrices in fact several simplifications in the construction of mathcal h 2 matrices are pointed out which are a by product of the surface representation extensive numerical examples are provided in order to quantify and qualify the proposed method in this article a black box higher order fast multipole method for solving boundary integral equations on parametric surfaces in three spatial dimensions is proposed such piecewise smooth surfaces are the topic of recent studies in isogeometric analysis due to the exact surface representation the rate of convergence of higher order methods is not limited by approximation errors of the surface an element wise clustering strategy yields a balanced cluster tree and an efficient numerical integration scheme for the underlying galerkin method by performing the interpolation for the fast multipole method directly on the reference domain the cost complexity in the polynomial degree is reducedby one order this gain is independent of the application of either h or h 2 matrices in fact several simplificationsin the construction of h 2 matrices are pointed out which are a by product of the surface representation extensive numerical examples are provided in order to quantify and qualify the proposed method

fast isogeometric boundary element method based on independent field approximation abstract an isogeometric boundary element method for problems in elasticity is presented which is based on an independent approximation for the geometry traction and displacement field this enables a flexible choice of refinement strategies permits an efficient evaluation of geometry related information a mixed collocation scheme which deals with discontinuous tractions along non smooth boundaries and a significant reduction of the right hand side of the system of equations for common boundary conditions all these benefits are achieved without any loss of accuracy compared to conventional isogeometric formulations the system matrices are approximated by means of hierarchical matrices to reduce the computational complexity for large scale analysis for the required geometrical bisection of the domain a strategy for the evaluation of bounding boxes containing the supports of nurbs basis functions is presented the versatility and accuracy of the proposed methodology are demonstrated by convergence studies showing optimal rates and real world examples in two and three dimensions

tests of cointegrating rank with a trend break abstract the conventional testing procedure may mislead one into accepting the null of no cointegration or the null of a cointegrating rank smaller than the true rank when there is a trend break under the alternative hypothesis this paper proposes tests for cointegrating rank that have power against the trend break alternative the proposed tests are applied to the us money demand function the results support the campbell perron conjecture money income and interest rates are cointegrated around a broken trend

acoustic isogeometric boundary element analysis an isogeometric boundary element method based on t splines is used to simulate acoustic phenomena we restrict our developments to low frequency problems to establish the fundamental properties of the proposed approach using t splines the computer aided design cad and boundary element analysis are integrated without recourse to geometry clean up or mesh generation a regularized burton miller formulation is used resulting in integrals which are at most weakly singular we employ a collocation based approach to generate the linear system of equations the method is verified against closed form solutions and direct comparisons are made with conventional lagrangian discretizations it is demonstrated that the superior accuracy of the isogeometric approach emanates from the exact geometric description encapsulated in the t spline the method is then applied to a real world application to illustrate the potential for integrated engineering design and analysis

computational algorithms for multiscale identification of nonlinearities in hammerstein systems with random inputs simple and efficient computational algorithms for nonparametric wavelet based identification of nonlinearities in hammerstein systems driven by random signals are proposed they exploit binary grid interpolations of compactly supported wavelet functions the main contribution consists in showing how to use the wavelet values from the binary grid together with the fast wavelet algorithms to obtain the practical counterparts of the wavelet based estimates for irregularly and randomly spaced data without any loss of the asymptotic accuracy the convergence and the rates of convergence are examined for the new algorithms and in particular conditions for the optimal convergence speed are presented efficiency of the algorithms for a finite number of data is also illustrated by means of the computer simulations

comparison of tests for the cointegrating rank of a var process with a structural shift two different types of tests for the cointegrating rank of vector autoregressive processes with a deterministic shift in the level have been proposed in the literature the first proposal is based on the likelihood ratio principle using a specific gaussian model set up in the second proposal the time series are adjusted for deterministic terms first and then lr type tests are applied to the adjusted series the local power of the two types of tests is derived and compared moreover the small sample size and power properties of the tests are explored it is found that the tests based on adjusted series generally have superior local power and size properties