performance analysis of an adaptive notch filter with constrained poles and zeros a statistical analysis of the sine wave frequency estimate obtained by the adaptive notch filter anf recently proposed by a nehorai ibid vol assp 33 p 983 96 aug 1985 is presented asymptotically valid expressions for the bias and mean square error of the frequency estimate are provided the analysis verifies the performance exhibited by the anf and clarifies the role of some user variables such as the notch bandwidth and the number of data samples processed

a general method for recovering equilibrating element tractions abstract a new geometrical presentation of a general method for recovering equilibrating element tractions is developed for 2d finite element models of problems in structural mechanics the data for the method consists of the prescribed loading and the stress fields resulting from a conventional linear elastic finite element analysis the geometrical presentation utilises the physical concepts of nodal forces and maxwell force diagrams based on nodal equilibrium only small problems have to be solved for each node this presentation complements the original algebraic approach of ladeveze and extends the method to cover the use of hierarchical p elements in regular meshes and general higher order elements in 1 irregular meshes as encountered in h p mesh refinement the same presentation is considered for the recovery of residual tractions as required in the solution of the local residual problem comparison is made with related methods for obtaining residual tractions in particular those proposed by bank and weiser and ainsworth et al detailed examples are included to illustrate the presentation this paper considers only the fundamental aspects of recovering equilibrating tractions the knowledge gained may be used in various applications such as error analysis limit analysis and structural design

tracking properties of a gradient based second order adaptive iir notch filter with constrained poles and zeros gradient type adaptive iir notch filters have many attractive merits for various real life applications since they require a small number of computations and yet demonstrate practical performance however it is generally quite difficult to assess their performance analytically their tracking properties in particular have not yet been investigated in this paper the tracking performance of a plain gradient pg algorithm is analyzed in detail for a second order adaptive iir notch filter with constrained poles and zeros which takes a linear chirp signal as its input first two sets of difference equations for the frequency tracking error and mean square error mse are established in the sense of convergence in the mean and convergence in the mean square respectively closed form expressions for the asymptotic tracking error and mse are then derived from these difference equations an optimum step size parameter for the algorithm is also evaluated based on the minimization of the asymptotic tracking error or the tracking mse it is discovered that the asymptotic tracking error may be driven to zero for a positive chirp rate by selecting a proper step size which is an interesting property for a real valued adaptive filtering algorithm extensive simulations are performed to support the analytical findings

spectrum estimation notch filters and music a novel extension of the multiple signal classification music algorithm for the frequency estimation problem is proposed in this work it is shown that the music algorithm is a data dependent optimum notch filter design technique when the input data are passed through this optimum notch filter the signal to noise ratio snr of the output is minimized the zeros of the optimum notch filter are then used to estimate the frequencies in the classical music algorithm this optimization is carried out over the set of all finite impulse response fir filters having a fixed order the framework of this paper allows the use of rational notch filters the fact that the rational filters have sharper spectral characteristics is used to obtain improved estimates particularly at low snr some interesting properties of the proposed algorithm are derived and further perspectives on the implementation aspects are provided the analytical predictions are substantiated using numerical simulation results

patch recovery based on superconvergent derivatives and equilibrium in this paper a postprocessing technique is developed for determining first order derivatives fluxes stresses at nodal points based on derivatives in superconvergent points it is an extension of the superconvergent patch recovery technique presented by zienkiewicz and zhu in contrast to that technique all flux or stress components are interpolated at the same time coupled by equilibrium equations at the superconvergent points the equilibrium equations and use of one order higher degree of interpolation polynomials of stress give a dramatic decrease in error of recovered derivatives even at boundaries

a minimal parameter adaptive notch filter with constrained poles and zeros a new algorithm is presented for adaptive notch filtering and parametric spectral estimation of multiple narrow band or sine wave signals in an additive broad band process the algorithm is of recursive prediction error rpe form and uses a special constrained model of infinite impulse response iir with a minimal number of parameters the convergent filter is characterized by highly narrow bandwidth and uniform notches of desired shape for sufficiently large data sets the variances of the sine wave frequency estimates are of the same order of magnitude as the cramer rao bound results from simulations illustrate the performance of the algorithm under a wide range of conditions

a basis for bounding the errors of proper generalised decomposition solutions in solid mechanics summary this paper presents an approach that extends the classical error bounding techniques to parametric models it departs from appropriate pairs of complementary solutions of a linear elastic problem obtained using a proper generalised decomposition methodology to determine approximations of selected local outputs and strict bounds of the error of these approximations the paper starts by presenting the procedures used to obtain the complementary solutions the properties the convergence characteristics of the global error and the determination of an indicator of the error distribution are illustrated for a very simple example the demonstration of the procedure used for determining local outputs and their bounds also accompanied by illustrative examples completes the paper copyright 2013 john wiley sons ltd

fast estimation of discretization error for fe problems solved by domain decomposition this paper presents a strategy for a posteriori error estimation for substructured problems solved by non overlapping domain decomposition methods we focus on global estimates of the discretization error obtained through the error in constitutive relation for linear mechanical problems our method allows to compute error estimate in a fully parallel way for both primal bdd and dual feti approaches of non overlapping domain decomposition whatever the state converged or not of the associated iterative solver results obtained on an academic problem show that the strategy we propose is efficient in the sense that correct estimation is obtained with fully parallel computations they also indicate that the estimation of the discretization error reaches sufficient precision in very few iterations of the domain decomposition solver which enables to consider highly effective adaptive computational strategies

performance analysis of the sign algorithm for a constrained adaptive iir notch filter adaptive infinite impulse response iir notch filters are very attractive in terms of their reasonable performances and low computational requirements generally it is very difficult to assess their performances analytically due to their iir nature this paper analyzes in detail the steady state performance of the sign algorithm sa for a well known adaptive iir notch filter with constrained poles and zeros slow adaptation and gaussianity of the notch filter output are assumed for the sake of analysis two difference equations are first established for the convergences in the mean and mean square in the vicinity of the steady state of the algorithm steady state estimation error or bias and mean square error mse of the sa are then derived in closed forms a coarse stability bound is also derived for the algorithm theory based comparison between the algorithm and the plain gradient pg algorithm is done in some detail extensive simulations are conducted to demonstrate the validity of the analytical results for both slow and relatively fast adaptations

statistical analysis of music and subspace rotation estimates of sinusoidal frequencies consideration is given to the analysis of the large sample second order properties of multiple signal classification music and subspace rotation sur methods such as esprit for sinusoidal frequency estimation explicit expressions for the covariance elements of the estimation errors associated with either method are derived these expressions of covariances are then used to analyze and compare the statistical performances of the music and sur estimation sure methods both music and sure are based on the eigendecomposition of a sample data covariance matrix the expressions for the estimation error variances derived are used to study the dependence of music and sure performances on the dimension of the data covariance matrix used

convergence analysis of recursive identification algorithms based on the nonlinear wiener model recursive identification algorithms based on the nonlinear wiener model are presented a recursive identification algorithm is first derived from a general parameterization of the wiener model using a stochastic approximation framework local and global convergence of this algorithm can be tied to the stability properties of an associated differential equation since inversion is not utilized noninvertible static nonlinearities can be handled which allows a treatment of for example saturating sensors and blind adaptation problems gauss newton and stochastic gradient algorithms for the situation where the static nonlinearity is known are then suggested in the single input single output case the proposed methods can outperform conventional linearizing inversion of the nonlinearity when measurement disturbances affect the output signal for fir finite impulse response models it is also proved that global convergence of the schemes is tied to sector conditions on the static nonlinearity in particular global convergence of the stochastic gradient method is obtained provided that the nonlinearity is strictly monotone the local analysis performed for iir infinite impulse response models illustrates the importance of the amplitude contents of the exciting signals

optimal instrumental variable estimation and approximate implementations the accuracy properties of instrumental variables iv methods are investigated extensions such as prefiltering of data and use of additional instruments are included in the analysis the parameter estimates are shown to be asymptotically gaussian distributed an explicit expression is given for the covariance matrix of their distribution the covariance matrix is then taken as a multivariable measure of accuracy it is shown how it can be optimized by an appropriate selection of instruments and prefilter the so obtained optimal instrumental variable estimates cannot be used directly since the true system and the statistical properties of the disturbance must be known in order to compute the optimal instruments and prefilters a multistep procedure consisting of three or four simple steps is then proposed as a way to overcome this difficulty this procedure includes modeling of the disturbance as an arma process using a statistically efficient method such as a prediction error method the statistical properties of the estimates obtained with the multistep procedure are also analyzed those estimates are shown to be asymptotically gaussian distributed as well the covariance matrix of the estimation errors is compared to that corresponding to a prediction error method for some model structures these two approaches give the same asymptotic accuracy the conclusion is that the multistep procedure which is quite easy to implement and also has nice uniqueness properties can be viewed as an interesting alternative to prediction error methods

analysis of a general recursive prediction error identification algorithm a general class of algorithms for recursive identification of stochastic dynamical systems is studied in this class the discrepancy between the measured output and the output predicted from previous data according to a candidate model the prediction error is minimized over the model set using a stochastic approximation approach it is proved that this class of methods has the same convergence properties as its off line counterparts under mild and general assumptions these assumptions do not for example include stationary conditions or conditions that the true system can be exactly represented within the model set the considered class of methods contains as special cases several well known algorithms other common recursive identification methods like the extended least squares method and the extended kalman filter can be interpreted as approximate prediction error methods with simplified gradient calculations therefore the approach taken here may also serve as a basis for unified description of many recursive identification methods

forced oscillation of nth order nonlinear differential equations the oscillation criteria result of agarwal and grace appl math lett 13 2000 53 is generalized to the following nonlinear equations of the formx n t email protected i 1 n 1a ix i t q t f x t e t email protected n where email protected c 1 r r and f is a strictly monotone increasing function email protected c r r a 1 a n 1 are real constants

recovery of equilibrium on star patches from conforming finite elements with a linear basis summary a previous technique for recovering equilibrated stresses from compatible finite element models of structural mechanics problems is extended to cover those cases where the partitioned loads applied to star patches are not initially balanced regarding rotational equilibrium the residual moments are removed by adding a suitable corrective stress field to the compatible one before deriving the fictitious body forces corrective stress fields are determined by solving another set of local problems based on subdomains that each contain elements forming a neighbourhood of a loaded kernel element the conditions for the existence of a solution of these problems are studied for simplicial elements the parameters that control the extended technique are assessed from numerical tests on a variety of two dimensional linear elastic problems based on constant strain elements for the compatible solutions these tests are presented in the context of computing bounds on quantities of interest such as total strain energy and local reactions and displacements copyright 2011 john wiley sons ltd

technical communique convergence analysis of recursive identification algorithms with forgetting factor a convergence analysis of a modified version of the least squares recursive identification algorithm with forgetting factor is given it is shown that the parametric distance converges to a zero mean random variable it is also shown that under persistent excitation condition on both system input and output the condition number of the adaptation gain matrix is bounded the variance of the parametric distance is bounded by the product of the noise variance times the upper bound of the condition number of the gain matrix this is done by normalizing the measurement vector entering in the identification algorithm and by using a forgetting factor verifying l t 0

arma spectral estimation for noisy signals observed through a linear system spectral estimation for autoregressive moving average arma processes observed through a known linear system is considered an algorithm based on a system identification parameter estimation technique known as the recursive prediction error method is used for spectral estimation the algorithm is formulated in the state space to incorporate the constraints imposed by the linear system the linear system may represent the distortion introduced by the sensor or the channel several simulation examples are presented to illustrate the performance of the estimator

equilibrated patch recovery error estimates simple and accurate upper bounds of the error this paper introduces a new recovery type error estimator ensuring local equilibrium and yielding a guaranteed upper bound of the error the upper bound property requires the recovered solution to be both statically equilibrated and continuous the equilibrium is obtained locally patch by patch and the continuity is enforced by a postprocessing based on the partition of the unity concept this postprocess is expected to preserve the features of the locally equilibrated stress field nevertheless the postprocess phase modifies the equilibrium which is no longer exactly fulfilled a new methodology is introduced that yields upper bound estimates by taking into account this lack of equilibrium this requires computing the 2 norm of the error or relating it with the energy norm the guaranteed upper bounds are obtained by using a pessimistic bound of the error 2 norm derived from an eigenvalue problem nevertheless these bounds are not sharp an additional strategy based on a more accurate assessment of the error 2 norm is introduced providing sharp estimates which are practical upper bounds as it is demonstrated in the numerical tests copyright 2006 john wiley sons ltd

recovery of strong equilibrium from displacement based finite element models of reissner mindlin plates recovery of strong equilibrium from displacement based finite element models of reissner mindlin plates

a unified approach to strict upper and lower bounds of quantities in linear elasticity based on constitutive relation error estimation abstract this paper presents a unified approach to acquiring strict upper and lower bounds of various quantities in linear elasticity the key ingredient lies in a unified representation of linear quantities including displacement integrals stress integrals and even pointwise quantities with the unified representation dual error analysis can be performed easily which results in a unified approximation and thereby a unified error representation via the primal dual equivalence theorem then the constitutive relation error cre estimation featured with the ability to provide strict upper bound of global energy norm error is utilized and strict upper and lower bounds of the quantities are obtainable thereafter moreover two extant bounding approaches to goal oriented error estimation are analyzed and optimized and as a result optimal approximation and bounds are obtained numerical examples are studied to validate the proposed unified approach

a note on nasr s and wong s papers abstract in the case of oscillatory potentials we give sufficient conditions for the oscillation of the forced nonlinear second order differential equations with delayed argument in the form x t q t x t sgn x t f t in the linear 1 and the superlinear 1 cases

stochastic approximation method with gradient averaging for unconstrained problems a stochastic approximation algorithm is studied in which random gradient estimates are averaged by an auxiliary filter convergence of the algorithm is proved under a rather general noise condition a practical version of the method is described and numerical results are given

a recursive maximum likelihood algorithm for arma line enhancement optimal filtering of narrow band signals corrupted by noise requires an infinite impulse response iir filter a recursive maximum likelihood algorithm is proposed for adaptively adjusting the coefficients of an iir line enhancer the performance of this adaptive iir filter is analyzed and compared to that of a finite impulse response filter preliminary simulation results are presented to illustrate the behavior of the proposed algorithm under various signal to noise conditions

factorized all pass based iir adaptive notch filters this paper introduces a new family of infinite impulse response adaptive notch filters that forms multiple notches using a second order factorization of an all pass transfer function the new orthogonal realization is amenable for adaptive filtering to obtain the unknown frequencies of interest two new adaptive filtering algorithms are presented that can achieve fast convergence at low computational cost local convergence analysis for the new algorithms is performed and a detailed discussion of their properties is provided the new all pass based notch realization introduces a different compromise between bias and signal to noise ratio snr when compared with realizations previously reported in the literature specifically it achieves lower bias than other approaches at low snr this property is particularly attractive for the estimation and tracking of multiple sinusoids furthermore the bias can be made arbitrarily small or can be accurately estimated and compensated for extensive computer simulations are provided to illustrate the performance of the proposed adaptive notch filters in terms of bias speed of convergence and tracking capability

new bounding techniques for goal oriented error estimation applied to linear problems the paper deals with the accuracy of guaranteed error bounds on outputs of interest computed from approximate methods such as the finite element method a considerable improvement is introduced for linear problems thanks to new bounding techniques based on saint venant s principle the main breakthrough of these optimized bounding techniques is the use of properties of homothetic domains which enables to cleverly derive guaranteed and accurate boundings of contributions to the global error estimate over a local region of the domain performances of these techniques are illustrated through several numerical experiments

note on forced oscillation of nth order sublinear differential equations in the case of oscillatory potentials we establish an oscillation theorem for the forced sublinear differential equation x n q t x sgnx e t t t0 no restriction is imposed on the forcing term e t to be the nth derivative of an oscillatory function in particular we show that all solutions of the equation x t sint x sgnx mt cost t 0 0 2 1 this provides an analogue of a result of nasr proc amer math soc 126 1998 123 for the forced superlinear equation and answers a question raised in an earlier paper j s w wong siam j math anal 19 1988 673

analysis and performance evaluation of an adaptive notch filter an adaptive notch filter is derived by using a general prediction error framework the proposed infinite impulse response filler has a special structure that guarantees the desired transfer characteristics the filter coefficients are updated by a version of the recursive maximum likelihood algorithm the convergence properties of the algorithm and its asymptotic behavior are discussed and its performance is evaluated by simulation results

gradient based adaptive iir notch filtering for frequency estimation the use of gradient based algorithms with infinite impulse response iir notch filtering for estimating sinusoids imbedded in noise is investigated two notch filter model structures are presented the first is for applications where two signal sources with correlated noise components can be assessed the second can be used in situations where only one composite signal source is available error surface analysis indicates that second order modules are unimodal and result in guaranteed convergence higher order modules are multimodal and require judicious choice of initial parameter estimates simulation results are included to demonstrate the performance characteristics of both filter structures

tracking characteristics of the constrained iir adaptive notch filter the tracking behavior of a constrained iir notch filter the coefficients of which are estimated using a constant step size gauss newton algorithm is studied using weak convergence theory and the concept of prescaling it is shown that the mean behavior of the adaptive filter coefficients can be studied by using an ordinary differential equation ode approximate and simple closed form results are derived for the tracking behavior of a second order notch filter computer simulations are presented to substantiate the analysis

adaptive methods for hybrid equilibrium finite element models this paper presents initial results of work directed at the development of practical adaptive methods for equilibrium finite element models of elastostatic problems in solid mechanics the formulation of hybrid elements is reviewed with particular emphasis on recent developments for equilibrium elements compatibility defaults for 3d and 2d models are proposed together with an explicit expression for an error indicator based on such defaults two further error indicators are defined which are based on the availability of dual conforming displacement solutions these solutions are derived from two forms of dual analysis the one may be considered as being in parallel the other as being sequential with conforming displacements recovered locally from an equilibrium solution the two latter error indicators provide upper bounds to the global error a self adaptive strategy is proposed to exploit any of these error indicators and estimators and numerical results are presented and compared for a simple plane stress problem

a globally convergent frequency estimator online estimation of the frequency of a sinusoidal signal is a classical problem in systems theory that has many practical applications in this paper the authors provide a solution to the problem of ensuring a globally convergent estimation more specifically they propose a new adaptive notch filter whose dynamic equations exhibit the following remarkable features 1 all signals are globally bounded and the estimated frequency is asymptotically correct for all initial conditions and all frequency values 2 the authors obtain a simple tuning procedure for the estimator design parameters which trades off the adaptation tracking capabilities with noise sensitivity ensuring exponential stability of the desired orbit and 3 transient performance is considerably enhanced even for small or large frequencies as witnessed by extensive simulations to reveal some of the stability instability mechanisms of the existing algorithms and motivate our modifications the authors make appeal to a novel nonlinear state dependent time scaling the main advantage of working in the new time scale is that they remove the coupling between the parameter update law and the filter itself decomposing the system into a feedback form where the required modifications to ensure stability become apparent even though they limit their attention here to the simplest case of a single constant frequency without noise the algorithm is able to track time varying frequencies preserve local stability in the presence of multiple sinusoids and is robust with respect to noise

error estimate procedure in the finite element method and applications statically and kinematically admissible fields are explicitly derived from the finite element solution of the primal form of linear models the error on constitutive law for these fields yields an expression of the finite element error moreover the contribution of each element to this error allows to implement an automatic mesh refinement procedure leading to a uniform distribution of a given accuracy

forced oscillation of nth order functional differential equations abstract in this paper we investigate the oscillation of forced functional differential equations x n t a t f x q t e t when the forcing term e t is not required to be the nth derivative of an oscillatory function some new oscillatory criteria are given we also apply our technique to the forced neutral differential equation of the form x t cx t n a t x t b t x t e t c t f 1 x t d t f 2 x t where xf1 x 0 and xf2 x 0 for x 0 n 1 are nonnegative constants a t 0 b t 0 c t 0 d t 0 which includes the special case f1 x x sgn x f2 x x sgn x 1 and 1

adaptive stochastic filters with no strict positive real condition a new adaptive stochastic filter structure is introduced which avoids the strict passivity test used as a sufficient condition for convergence required by existing adaptive schemes the proposed algorithm consists of three stages in the first stage an autoregressive model is fitted and the residue obtained is used as an estimate of the noise in the second stage an autoregressive recursive moving average model is fitted using the residual of the first stage a modified residual is then filtered using a parameter and the model obtained from the second stage to generate an improved estimate of the noise in the third stage this improved estimate of the noise is used to obtain a better autoregressive moving average model it is shown that the proposed algorithm will also reduce the bias in the estimated parameters the simulation results given show that the proposed filter compares favorably to the algorithm introduced by mayne and clark and also landau this filter is then applied to the adaptive line enhancement sinusoidal detection and adaptive spectral estimation problems to illustrate its usefulness

an adaptive notch filter with improved tracking properties an analysis of the properties of an adaptive notch filter anf applied to time varying frequency tracking is presented starting from the derivation of an expression for anf output power asymptotically optimal values for the pole contraction and forgetting factors are derived for recursive prediction error rpe type anf algorithms based on the obtained results a new anf algorithm that includes adaptation of both pole contraction and forgetting factors is proposed the given experimental results confirm the theoretical conclusions and show that the proposed algorithm is highly efficient in practice

on the techniques for constructing admissible stress fields in model verification performances on engineering examples robust global goal oriented error estimation is used nowadays to control the approximate finite element solutions obtained from simulation in the context of computational mechanics the construction of admissible stress fields ie stress tensors which verify the equilibrium equations is required to set up strict and guaranteed error bounds using residual based error estimators and plays an important role in the quality of the error estimates this work focuses on the different procedures used in the calculation of admissible stress fields which is a crucial and technically complicated point the three main techniques that currently exist called the element equilibration technique eet the star patch equilibration technique spet and the element equilibration star patch technique eespt are investigated and compared with respect to three different criteria namely the quality of associated error estimators computational cost and easiness of practical implementation into commercial finite element codes the numerical results which are presented focus on industrial problems they highlight the main advantages and drawbacks of the different methods and show that the behavior of the three estimators which have the same convergence rate as the exact global error is consistent two and three dimensional experiments have been carried out in order to compare the performance and the computational cost of the three different approaches the analysis of the results reveals that the spet is more accurate than eet and eespt methods but the corresponding computational cost is higher overall the numerical tests prove the interest of the hybrid method eespt and show that it is a correct compromise between quality of the error estimate practical implementation and computational cost furthermore the influence of the cost function involved in the eet and the eespt is studied in order to optimize the estimators

dual adaptive finite element refinement for multiple local quantities in linear elastostatics in this paper we summarize how dual analysis techniques can be used to determine upper bounds of the discretization error both in terms of global and local outputs we present formulas for the bounds of the error in local outputs based on the approach proposed by greenberg in 1948 and we show that the resulting intervals are the same as those previously presented based on the approach proposed by washizu in 1953 we then explain how the elemental contributions to these bounds can be used to define an adaptive strategy that considers multiple quantities and we present its application to a simple plane stress problem copyright 2010 john wiley sons ltd

a recursive maximum likelihood algorithm for arma spectral estimation a spectral estimation technique is presented for autoregressive moving average arma processes the technique is based on a parameter estimation technique known as the rec ursive maximum likelihood rml method the recursive spectral estimation algorithm is presented and its asymptotic properties are discussed simulation results are presented to illustrate the performance of the estimator for various types of data

on nonparametric identification of wiener systems in this paper a new method for the identification of the wiener nonlinear system is proposed the system being a cascade connection of a linear dynamic subsystem and a nonlinear memoryless element is identified by a two step semiparametric approach the impulse response function of the linear part is identified via the nonlinear least squares approach with the system nonlinearity estimated by a pilot nonparametric kernel regression estimate the obtained estimate of the linear part is then used to form a nonparametric kernel estimate of the nonlinear element of the wiener system the proposed method permits recovery of a wide class of nonlinearities which need not be invertible as a result the proposed algorithm is computationally very efficient since it does not require a numerical procedure to calculate the inverse of the estimate furthermore our approach allows non gaussian input signals and the presence of additive measurement noise however only linear systems with a finite memory are admissible the conditions for the convergence of the proposed estimates are given computer simulations are included to verify the basic theory

a new non intrusive technique for the construction of admissible stress fields in model verification in this paper we investigate a new procedure for constructing admissible stress tensors that are needed in some methods for robust global goal oriented error estimation this procedure is based on properties of the approximate finite element solution which are applied through prolongation conditions it involves the calculation of equilibrated tractions along element boundaries leading to the determination of admissible stress tensors at the element level the main idea of the proposed approach is to use the partition of unity method for the calculation of the equilibrated tractions thus defining local problems on patches of elements which can be solved in an automatic and non intrusive manner therefore this hybrid procedure leads to reasonable computational costs and can be easily implemented into existing finite element codes two dimensional experiments illustrate the capabilities of the method as compared to alternative approaches

a recovery explicit error estimator in energy norm for linear elasticity significant research effort has been devoted to produce one sided error estimates for finite element analyses in particular to provide upper bounds of the actual error typically this has been achieved using residual type estimates one of the most popular and simpler in terms of implementation techniques used in commercial codes is the recovery based error estimator this technique produces accurate estimations of the exact error but is not designed to naturally produce upper bounds of the error in energy norm some attempts to remedy this situation provide bounds depending on unknown constants here a new step towards obtaining error bounds from the recovery based estimates is proposed the idea is 1 to use a locally equilibrated recovery technique to obtain an accurate estimation of the exact error 2 to add an explicit type error bound of the lack of equilibrium of the recovered stresses in order to guarantee a bound of the actual error and 3 to efficiently and accurately evaluate the constants appearing in the bounding expressions thus providing asymptotic bounds the numerical tests with h adaptive refinement process show that the bounding property holds even for coarse meshes providing upper bounds in practical applications

iterative filtering for multiple frequency estimation it is well known that prony s least squares estimator gives inconsistent estimates for multiple frequency estimation in a recent attempt to diminish this problem dragosevic and stankovic 1989 couple the least squares method of autoregressive ar estimation with an iterative filtering scheme discussed by kay 1988 using an all pole filter but the inconsistency still persists this paper attacks the chronic inconsistency with a general approach of parametric filtering that unifies and extends the previous work it is shown that the inconsistency can be eliminated with an appropriately parametrized filter the clue for the correct parametrization comes from a formula for the bias of the least squares ar estimator the fact of the matter is that as long as a filter satisfies the parametrization requirement consistent estimates can be obtained from the least squares ar estimator on the basis of the filtered data in particular the all pole filter considered by dragosevic and stankovic can be easily reparametrized so that it too satisfies the parametrization requirement and thus leads to a consistent estimator experimental results show that the modified method has a higher resolution than the discrete fourier transform and that its overall performance is quite remarkable

a stable and efficient adaptive notch filter for direct frequency estimation we investigate the problem of direct frequency estimation a new adaptive algorithm is developed for constrained pole zero notch filters the basic characteristic of this algorithm is that the notch filter is cascaded and hence purely parametrized by the notching frequencies this makes the algorithm much simpler and hence more efficient and more robust such that the poles and zeros are automatically located on the respective constrained circle no matter if the algorithm is implemented with infinite or finite precision the algorithm is analyzed and compared with some existing algorithms several numerical examples are given as well as the corresponding simulations

a structural view of stability in adaptive iir filters this correspondence deals with the stability issue in adaptive iir filters from a structural view a new condition under which the bounded input bounded output bibo stability of the filters can be ensured is derived based on this result a normal state space realization for second order iir filters is proposed it is shown that the adaptive iir filter realized with such a structure is bibo stable no matter it is implemented with infinite or finite precision this property is very important for real time applications though both the proposed and the normalized lattice based structures are bibo stable the former is simpler and has minimal pole sensitivities two adaptive iir filter structures are developed based on a cascade form of second order filters the first structure is fit for the filters whose poles are all complex and the second one is for the constrained notch filters simulations are given to demonstrate the performance of the proposed structures

a general formulation of equilibrium macro elements with control of spurious kinematic modes the exorcism of an old curse this paper illustrates a method whereby a family of robust equilibrium elements can be formulated in a general manner the effects of spurious kinematic modes present to some extent in all primitive equilibrium elements are eliminated by judicious assembly into macro equilibrium elements these macroelements are formulated with sufficient generality so as to retain the polynomial degree of the stress field as a variable such a family of macro elements is a new development and results for polynomials of degree greater than two have not been seen before the quality of results for macro equilibrium elements with varying degrees of polynomial is demonstrated by numerical examples

local error estimators for finite element linear analysis local error estimators on stresses displacements etc are derived from constitutive relation error estimators examples show that they can be considered as an upper bound

maximum likelihood estimation of the parameters of multiple sinusoids from noisy measurements the problem of estimating the frequencies phases and amplitudes of sinusoidal signals is considered a simplified maximum likelihood gauss newton algorithm which provides asymptotically efficient estimates of these parameters is proposed initial estimates for this algorithm are obtained by a variation of the overdetermined yule walker method and periodogram based procedure use of the maximum likelihood gauss newton algorithm is not however limited to this particular initialization method some other possibilities to get suitable initial estimates are briefly discussed an analytical and numerical study of the shape of the likelihood function associated with the sinusoids in noise process reveals its multimodal structure and clearly sets the importance of the initialization procedure some numerical examples are presented to illustrate the performance of the proposed estimation procedure comparison to the performance corresponding to the cramer rao lower bound is also presented using a simple expression for the asymptotic cramer rao bound covariance matrix derived in the paper

stationary points of the recursive generalized least squares algorithm for adaptive notch filtering possible convergence points of the generalized least squares adaptive notch filtering algorithm are analytically derived for the multiple sinusoid case showing explicitly the dependence of the asymptotic bias on the pole contraction factor signal to noise ratio and the true model parameters the results for symmetric and nonsymmetric parameterization are compared

strict and effective bounds in goal oriented error estimation applied to fracture mechanics problems solved with xfem in this work we analyze a method that leads to strict and high quality local error bounds in the context of fracture mechanics we investigate in particular the capability of this method to evaluate the discretization error for quantities of interest computed using the extended finite element method xfem the goal oriented error estimation method we are focusing on uses the concept of constitutive relation error along with classical extraction techniques the main innovation in this paper resides in the methodology employed to construct admissible fields in the xfem framework which involves enrichments with singular and level set basis functions we show that this construction can be performed through a generalization of the classical procedure used for the standard finite element method thus the resulting goal oriented error estimation method leads to relevant and very accurate information on quantities of interest that are specific to fracture mechanics such as mixed mode stress intensity factors the technical aspects and the effectiveness of the method are illustrated through two dimensional numerical examples

unbiased estimation of a sinusoid in colored noise via adapted notch filters standard notch models for the estimation of a sinusoid in noise are characterized by two poles on the unit circle and two zeros aligned with the poles these models provide biased estimates of the unknown frequency the bias increasing with the zero pole distance on the other hand keeping the zeros far from the poles has the beneficial effect of making the identification algorithm less sensitive to the adopted initialization in this paper we remove the pole zero alignment constraint the extra degree of freedom thus obtained is used to alleviate the traditional trade off between unbiasedness of the estimates and robustness against poor initializations the proposed technique applies to the case of both white and colored additive noise

exponential convergence of adaptive identification and control algorithms output and equation error adaptive identification algorithms are shown to be exponentially convergent under a deterministic or stochastic persistently exciting or spanning condition on the system inputs together with several other standard conditions an adaptive control algorithm is shown to be exponentially convergent under a deterministic or stochastic persistently exciting condition on the reference trajectory together with some standard conditions

funnel filters a new class of filters for frequency estimation of harmonic signals second order notch filters are commonly used for frequency estimation purposes they are characterized by a single design parameter the value of which is selected so as to achieve a suitable compromise between tracking performance and bias variance errors in this paper a new class of filters of fourth order is presented the funnel shaped filters or funnel filters for short these filters enables one to estimate harmonic signals with enhanced tracking capability without any deterioration of the steady state performance

adaptive notch filtering for the retrieval of sinusoids in noise in this paper an adaptive notch filter is developed employing a frequency domain and time domain analysis for the enhancement and tracking of sinusoids in additive noise colored or white the notch filter is implemented as a constrained infinite impulse response filter with the constraint enforced by a single parameter termed the debiasing parameter the resulting notch filter requires few parameters facilitates the formation of the desired band rejection filter response and also leads to various useful implementations cascade parallel for the adaptation of the filter coefficients the stochastic gauss newton algorithm is used the convergence of this updating procedure is established by studying the associated differential equation also it is shown that the structure present in the problem enables truncation of the gradient thereby reducing the complexity of adapting the filter coefficients simulation results are presented to substantiate the analysis and to demonstrate the potential of the notch filtering technique

oscillation of higher order forced nonlinear differential equations abstract some new criteria are established for the oscillation of higher order forced nonlinear differential equations by introducing a class of new auxiliary functions no restriction is imposed on the forcing term as is generally assumed with the help of the new auxiliary functions the main results in this paper are different from those in the paper y g sun s h saker forced oscillation of higher order nonlinear differential equations appl math comput 173 2006 1219 1226 and are more effective than many existing results

the computation of bounds for linear functional outputs of weak solutions to the two dimensional elasticity equations we present a method for the computation of upper and lower bounds for linear functional outputs of the exact solutions to the two dimensional elasticity equations the method can be regarded as a generalization of the well known complementary energy principle the desired output is cast as the supremum of a quadratic linear convex functional over an infinite dimensional domain using duality the computation of an upper bound for the output of interest is reduced to a feasibility problem for the complementary or dual problem in order to make the problem tractable from a computational perspective two additional relaxations that preserve the bounding properties are introduced first the domain is triangulated and a domain decomposition strategy is used to generate a sequence of independent problems to be solved over each triangle the lagrange multipliers enforcing continuity are approximated using piecewise linear functions over the edges of the triangulation second the solution of the adjoint problem is approximated over the triangulation using a standard galerkin finite element approach a lower bound for the output of interest is computed by repeating the process for the negative of the output reversing the sign of the computed upper bound for the negative of the output yields a lower bound for the actual output the method can be easily generalized to three dimensions however a constructive proof for the existence of feasible solutions for the outputs of interest is only given in two dimensions the computed bound gaps are found to converge optimally that is at the same rate as the finite element approximation an attractive feature of the proposed approach is that it allows for a data set to be generated that can be used to certify and document the computed bounds using this data set and a simple algorithm the correctness of the computed bounds can be established without recourse to the original code used to compute them in the present paper only computational domains whose boundary is made up of straight sided segments and polynomially varying loads are considered two examples are given to illustrate the proposed methodology

on forced oscillation of higher order functional differential equations abstract in this paper we establish some new oscillation criteria for the following forced functional differential equation x n t q t x t 1 x t e t t t 0 no restriction is imposed on the forcing term e t to be the n th derivative of an oscillatory function two cases have been taken into consideration i q t 0 1 and t t t ii q t changes its sign 0 t t t the main results generalize some existing results and can be applied to the oscillation problem that are not covered in the literature

forced oscillation of higher order nonlinear differential equations some new criteria have been established for the oscillation of higher order forced nonlinear differential equation of the form l nx t q t f x t e t according to the smart choice of a class of new auxiliary functions no restriction is imposed on the forcing term e t as those assumed in a g kartsatos maintenance of oscillations under the effect of a periodic forcing term proc amer math soc 33 1972 377 383 a g kartsatos recent results on oscillation of solutions of forced and perturbed nonlinear differential equations of even order in stability of dynamical systems theory and applications marcel dekker new york 1977 pp 17 72 the main results of this paper are different from most known ones in the sense that they are given in the form lim inf t 0

least squares yule walker and overdetermined yule walker estimation of ar parameters a monte carlo analysis of finite sample properties a monte carlo analysis of the accuracy properties of least squares ls yule walker yw and overdetermined yule walker oyw methods for estimating the parameters of autoregressive ar processes is presented comparisons of the estimated finite sample accuracy to the theoretical asymptotic accuracy are included it is shown that considerable differences may occur in some cases choice of the number of equations in the yw system of equations is discussed some remarks concerning the feasiblity and usefulness of an analytical study of the finite sample accuracy properties are also included

the extended kalman filter as a pulmonary blood flow estimator pulmonary blood flow is represented as a time varying parameter in a simple model of the bodily uptake of gases that are soluble in blood the pulmonary blood flow is estimated on line using ljung s modification of the extended kalman filter the experimental technique for estimation of pulmonary blood flow is based on zwart s soluble gas method modified to permit time varying ventilation and pulmonary perfusion and also to permit binary dynamic forcing of the inhaled soluble gas computer simulations were performed to determine the convergence time and to choose values of algorithmic parameters experiments done in humans gave agreement to within the accuracy of that measured invasively by a thermal dilution technique the method shows promise for use in many biomedical applications including patient monitoring physiological experimentation and clinical heart function tests

the stability of stars of triangular equilibrium plate elements equilibrium models for finite element analyses are becoming increasingly important in complementary roles to those from conventional conforming models but when formulating equilibrium models questions of stability or admissibility of loads are of major concern this paper addresses these questions in the context of flat plates modelled with triangular hybrid elements involving membrane and or flexural actions patches of elements that share a common vertex are considered and such patches are termed stars stars may be used in global analyses as assemblies of elements forming macro elements or in local analyses the conditions for stability or the existence and number of spurious kinematic modes are determined in a general algebraic procedure for any degree of the interpolation polynomials and for any geometric configuration the procedure involves the determination of the rank of a compatibility matrix by its transformation to row echelon form examples are presented to illustrate some of the characteristics of spurious kinematic modes when they exist in stars with open or closed links copyright 2008 john wiley sons ltd

a set of hybrid equilibrium finite element models for the analysis of three dimensional solids in this paper an approach to the formulation of equilibrium elements for the analysis of three dimensional elasticity problems is presented this formulation is an extension of the approach previously proposed for the analysis of two dimensional elasticity problems the general aspects of the formulation remain unchanged when applied to the new problem but new points are considered namely the way to perform volume integrations for general elements and the techniques used to obtain the self equilibrated three dimensional stress approximation functions the numerical behaviour of such elements is presented and discussed

recursive identification algorithms for right matrix fraction description models multivariable identification algorithms are usually designed only for left matrix fraction description lmfd models in this paper we consider recursive identification algorithms for right matrix fraction description rmfd models with diagonal denominator matrices the algorithms are of prediction error pe and model reference mr type results from simulations illustrate the performance of the algorithms

local problems on stars a posteriori error estimators convergence and performance a new computable a posteriori error estimator is introduced which relies on the solution of small discrete problems on stars it exhibits built in flux equilibration and is equivalent to the energy error up to data oscillation without any saturation assumption a simple adaptive strategy is designed which simultaneously reduces error and data oscillation and is shown to converge without mesh pre adaptation nor explicit knowledge of constants numerical experiments reveal a competitive performance show extremely good effectivity indices and yield quasi optimal meshes

adaptive algorithms for joint time delay estimation and iir filtering a new class of gradient based algorithms for joint adaptive time delay estimation and iir filtering for the recursive identification of systems with long pure delays is introduced the algorithms update an adaptive delay estimate and the coefficients of an iir filter using familiar gradient descent methods in addition interpolation of the input sequence is used to obtain delays that are not constrained to integer numbers of samples three algorithms using a direct form filter parametrization and one using a normalized lattice filter are derived and computer simulations are used to demonstrate their convergence and tracking properties

upper bounds of the error in local quantities using equilibrated and compatible finite element solutions for linear elastic problems abstract when local quantities are computed using the principle of virtual work dual analysis which provides an upper bound of the global error may also be applied to the virtual problem greenberg and washizu proposed alternative approaches to combine the global error bounds of the real and virtual problems providing upper bounds of the local error it is shown in this paper that optimising greenberg s approach corresponds to using washizu s approach which in turn may be further improved these approaches are used to provide finite element error indicators for adaptive refinement

subdomain based flux free a posteriori error estimators a new residual type flux free error estimator is presented it estimates upper and lower bounds of the error in energy norm the proposed approach precludes the main drawbacks of standard residual type estimators circumvents the need of flux equilibration and results in a simple implementation that uses standard resources available in finite element codes this is specially interesting for 3d applications where the implementation of this technique is as simple as in 2d recall that on the contrary the complexity of the flux equilibration techniques increases drastically in the 3d case the bounds for the energy norm of the error are used to produce upper and lower bounds of linear functional outputs representing quantities of engineering interest the presented estimators demonstrate their efficiency in numerical tests producing sharp estimates both for the energy and the quantities of interest

stability bounds and steady state coefficient variance for a second order adaptive iir notch filter in this correspondence we present a stochastic convergence analysis of a second order adaptive iir notch filter the approach is based on a linearization of the gradient in the vicinity of the optimal solution expressions for stability bounds on the algorithm step size and the steady state coefficient variance are derived these closed form analytical results are verified by computer simulations for different signal and noise conditions

multiple fully adaptive notch filter design based on allpass sections we develop a canonical adaptive cascade structure iir notch filter to detect and track multiple time varying frequencies in additive white gaussian noise the algorithm uses allpass frequency transformation filters and a truncated gradient simulations indicate that our algorithm is computationally simple converges rapidly and has good frequency resolution

an improved lattice based adaptive iir notch filter a novel lattice based adaptive infinite impulse response iir notch filter is developed which features independent tuning of the notch frequency and attenuation bandwidth the internal structure is based on planar rotators ensuring reliable numerical behaviour and high processing rates in cordic environments a simple update law allows a simpler implementation than previously proposed designs rather than minimizing an output error cost function the algorithm is designed to achieve a stable associated differential equation resulting in a globally convergent unbiased frequency estimator in the single sinusoid case independent of the notch filter bandwidth using a second order structure in the multiple sinusoid case unbiased estimation of one of the input frequencies is achieved by thinning the notch bandwidth the tracking behavior is superior to conventional output error designs and the estimation of extremal frequencies is less prone to overflow instability than previously reported structures

recursive parameter estimation for noisy autoregressive signals corresp the problem of recursively estimating the unknown parameters of a scalar autoregressive ar signal observed in additive white noise including signal power and noise variance is considered a state space model in a canonical but noninnovations form is used to represent the noisy ar signal an algorithm based on a system identification parameter estimation technique known as the recursive prediction error method is presented for recursive parameter estimation two simulation examples illustrate the effectiveness of the proposed algorithm

a posteriori error estimation and adaptive strategy for pgd model reduction applied to parametrized linear parabolic problems abstract we define an a posteriori verification procedure that enables to control and certify pgd based model reduction techniques applied to parametrized linear elliptic or parabolic problems using the concept of constitutive relation error it provides guaranteed and fully computable global goal oriented error estimates taking both discretization and pgd truncation errors into account splitting the error sources it also leads to a natural greedy adaptive strategy which can be driven in order to optimize the accuracy of pgd approximations the focus of the paper is on two technical points i construction of equilibrated fields required to compute guaranteed error bounds ii error splitting and adaptive process when performing pgd based model reduction performances of the proposed verification and adaptation tools are shown on several multi parameter mechanical problems

recovery of equilibrium on star patches using a partition of unity technique a technique for recovering equilibrated element stresses is developed for finite element models of structural mechanics problems the data for the method consist of the prescribed loading and the stress and displacement fields resulting from a conventional compatible finite element model local problems are defined for each star of elements via the introduction of fictitious body forces and strains these problems can be solved independently for equilibrium in a process that can be easily parallelized the quality of the solutions is assessed for two dimensional linear elastic problems by using them to compute bounds of the error of the finite element solutions in terms of both global and local quantities of interest copyright 2009 john wiley sons ltd

reproducing kernel hierarchical partition of unity part i formulation and theory this work is concerned with developing the hierarchical basis for meshless methods a reproducing kernel hierarchical partition of unity is proposed in the framework of continuous representation as well as its discretized counterpart to form such hierarchical partition a class of basic wavelet functions are introduced based upon the built in consistency conditions the differential consistency conditions for the hierarchical kernel functions are derived it serves as an indispensable instrument in establishing the interpolation error estimate which is theoretically proven and numerically validated for a special interpolant with different combinations of the hierarchical kernels a synchronized convergence effect may be observed being different from the conventional legendre function based p type hierarchical basis the new hierarchical basis is an intrinsic pseudo spectral basis which can remain as a partition of unity in a local region because the discrete wavelet kernels form a partition of nullity these newly developed kernels can be used as the multi scale basis to solve partial differential equations in numerical computation as a p type refinement copyright 1999 john wiley sons ltd

tracking analysis of an adaptive notch filter with constrained poles and zeros this paper analyzes the asymptotic tracking properties of an adaptive notch filter anf with pole zero constraints for the cancellation or retrieval of multiple time varying sine waves in additive noise the asymptotic mean square error mse is analyzed using the methods of ljung and gunnarsson 1990 when the variations in the underlying frequencies are assumed to be sufficiently small closed form expressions for the mse are derived as functions of the tuning variables of the algorithm the results give insight into the operational properties of the algorithm and are used in order to minimize the mse with respect to the tuning variables computer simulations confirm the validity of the derived results