structural modal reanalysis for topological modifications with extended kirsch method in this paper a new effective method for modal reanalysis of structures subjected to topological modifications is presented the effect of inertia coupling between the old degrees of freedom and the new added degrees of freedom is introduced with iterative perturbation furthermore the extended kirsch method is utilized to improve the accuracy of the starting solutions the numerical examples are given for frame and truss structures results are compared to the exact solution and prove that the proposed method is effective

random matrix eigenvalue problems in structural dynamics natural frequencies and mode shapes play a fundamental role in the dynamic characteristics of linear structural systems considering that the system parameters are known only probabilistically we obtain the moments and the probability density functions of the eigenvalues of discrete linear stochastic dynamic systems current methods to deal with such problems are dominated by mean centred perturbation based methods here two new approaches are proposed the first approach is based on a perturbation expansion of the eigenvalues about an optimal point which is best in some sense the second approach is based on an asymptotic approximation of multidimensional integrals a closed form expression is derived for a general rth order moment of the eigenvalues two approaches are presented to obtain the probability density functions of the eigenvalues the first is based on the maximum entropy method and the second is based on a chi square distribution both approaches result in simple closed form expressions which can be easily calculated the proposed methods are applied to two problems and the analytical results are compared with monte carlo simulations it is expected that the small randomness assumption usually employed in mean centred perturbation based methods can be relaxed considerably using these methods

reduced order multiple tuned mass damper optimization a bounded real lemma for descriptor systems approach abstract this paper presents a novel technique for multiple tuned mass damper optimization based on the dissipativity inequalities for a class of descriptor systems under the assumptions of regularity asymptotic stability and index one property of the descriptor system representing the structure with tuned mass dampers optimization criterion is defined in terms of h norm of the system in doing so special structure of the system matrices is utilized to eliminate some of the optimization variables to overcome its high computational cost and make it applicable for optimization of large scale structures a novel reduced order optimization algorithm is proposed unlike the existing approaches the presented optimization framework does not impose restrictions regarding regularity and constantness of the mass matrix and consequently allows simultaneous optimization of mass damping and stiffness matrices numerical examples which clearly illustrate the applicability and effectiveness of the proposed optimization procedure as well as the comparison with other methods are presented

eigenderivative analysis of asymmetric non conservative systems in general the damping matrix of a dynamic system or structure is such that it can not be simultaneously diagonalized with the mass and stiffness matrices by any linear transformation for this reason the eigenvalues and eigenvectors and consequently their derivatives become complex expressions for the first and second order derivatives of the eigenvalues and eigenvectors of these linear non conservative systems are given traditional restrictions of symmetry and positive definiteness have not been imposed on the mass damping and stiffness matrices the results are derived in terms of the eigenvalues and left and right eigenvectors of the second order system so that the undesirable use of the first order representation of the equations of motion can be avoided the usefulness of the derived expressions is demonstrated by considering a non proportionally damped two degree of freedom symmetric system and a damped rigid rotor on flexible supports copyright 2001 john wiley sons ltd

numerical presentation of eigenvalue curve veering and mode localization in coupled pendulums to be 0 01 0 01 0 01 0 0 and 0 01 0 the e rst variations and the eigenvalues obtained by the classic method and the improved calculation are given in table 1 the relative errors of the variations are shown in fig 2 the result of the improved calculation is in the very good agreementwith the exact one apartfromthe third mode the e rst variations given by the improved calculation are even better than those with the second variations by the classic method a large modie cation of the truss is considered by multiplying a and b with a factor from 1 through 10 the relative errors of the e rst variations are shown in fig 3 the errors in the e rst mode increase from 0 0827 to 0 8410 whereas those of the classic method change from 0 4159 to 4 1834 the fourth mode shows the biggest difference as the largest error of the improved calculation is 0 0023 but 9 9982 for the classic method conclusions an improved calculation of eigenvalue variations has been presented the eigenvalue approximation from the e rst variation is a rayleigh quotient the variations are different from those in the classic method when there is a variation of b which is the inertiarelated matrix in a structural dynamics although there are more terms in the variations of eigenvalues no extra matrix operation is required thegivenexamplecone rmsthattheaccuracyoftheeigenvalue variations is much better than that obtained with the classic method

adaptive estimation for a class of nonlinearly parameterized dynamical systems the technical note presents a new technique for the adaptive parameter estimation in nonlinear parameterized dynamical systems the technique proposes an uncertainty set update approach that guarantees forward invariance of the true value of the parameters in addition it is shown that in the presence of sufficiently exciting state trajectories the parameter estimates converge to the true values and the uncertainty set vanishes around the true value of the parameters the set based approach is also shown to identify when the parameter estimates are biased two simulation examples are presented that demonstrate the effectiveness of the technique

approximate eigensolutions for arbitrarily damped nearly proportional systems two efficient methods for determining the approximate eigenvalues and eigenvectors for arbitrarily damped nearly proportional systems are developed both approaches are formulated by means of a first order perturbation technique whereby the real modes of vibration of the undamped system are used to derive approximate expressions for the complex eigenvalues and eigenvectors of a nearly proportionally damped system using either approach the unperturbed configuration corresponds to a damped one whose damping matrix can be diagonalized by the same transformation that uncouples the undamped system and the perturbation consists of the deviation of this diagonalizable damping matrix from the actual damping matrix the proposed approaches are easy to code implement and solve and do not require forming state equations numerical examples are presented to validate the effectiveness of the current methods

adaptation and parameter estimation in systems with unstable target dynamics and nonlinear parametrization in this paper we propose a solution to the problem of adaptive control and parameter estimation in systems with unstable target dynamics models of uncertainties are allowed to be nonlinearly parameterized and required to be smooth and monotonic functions of linear functionals of the parameters the mere assumption of existence of nonlinear operator gains for the target dynamics is sufficient to guarantee that system solutions are bounded reach a neighborhood of the target set and the mismatches between the modeled uncertainties and their compensator converge to zero with respect to parameter convergence a standard persistent excitation condition suffices to ensure that it is exponential when a weaker nonlinear version of persistent excitation is satisfied asymptotic convergence is guaranteed the spectrum of possible applications ranges from tyre road slip control to asynchronous message transmission in spiking neural oscillators

computational procedure for a fast calculation of eigenvectors and eigenvalues of structures with random properties abstract the inherent uncertainties in geometry material properties etc of engineering structures can be represented by stochastic models where the parameters are described by probabilistic laws results from any analysis based on stochastic models inherit probabilistic information as well which can be used e g for reliability analysis particularly in linear dynamics of structures the calculation and analysis of random eigenvalues and eigenvectors is crucial a very flexible however computationally intensive way to analyze such systems is direct monte carlo simulation mcs in this paper procedures are shown which allow a significant reduction of computational efforts of the simulation using a subspace iteration scheme with optimally selected start vectors the procedures are not restricted to any kind of sampling technique

random vibration of the functionally graded laminates in thermal environments this work deals with the random free vibration of functionally graded laminates with general boundary conditions and subjected to a temperature change taking into account the randomness in a number of independent input variables such as young s modulus poisson s ratio and thermal expansion coefficient of each constituent material based on third order shear deformation theory the mixed type formulation and a semi analytical approach are employed to derive the standard eigenvalue problem in terms of deflection mid plane rotations and stress function a mean centered first order perturbation technique is adopted to obtain the second order statistics of vibration frequencies a detailed parametric study is conducted and extensive numerical results are presented in both tabular and graphical forms for laminated plates that contain functionally graded material which is made of aluminum and zirconia showing the effects of scattering in thermo elastic material constants temperature change edge support condition side to thickness ratio and plate aspect ratio on the stochastic characteristics of natural frequencies

an approximate numerical method for the complex eigenproblem in systems characterised by a structural damping matrix this paper presents an efficient numerical method that approximates the complex eigenvalues and eigenvectors in structural systems with viscoelastic damping materials characterised by the complex structural damping matrix this new method begins from the solution of the undamped system and approximates the complex eigenpair by finite increments using the eigenvector derivatives and the rayleigh quotient it is implemented in three different approaches single step incremental and iterative schemes the single step technique is presented for systems with low and medium damping from numerical examples it can be verified that the errors committed by the approximate single step technique with respect to the exact solutions obtained by the iram method are less than 0 2 when the loss factor of the material damping is lower than 1 this is a considerable improvement on other approximate methods for higher damped systems an improvement to the previous approach is proposed by an incremental technique that keeps the accuracy without significantly increasing the computational time the complex eigenproblem for materials whose mechanical properties are dependent on frequency is solved by a fast iterative approach whose validity is proved using a four parameter fractional derivative model

approximate vibration reanalysis of structures thecombinedapproximationsmethodisdevelopedforvibrationreanalysisofstructures inthesolution process the terms of local series approximations are used as basis vectors in global reduced basis approximations the solution steps are straightforward and the method can be readily used with a general e nite element system the computational effort needed by the method is usually much smaller than the effort needed for complete vibration analysis the efe ciency of the calculations and the accuracy of the results can be controlled by the amount of information considered efe cient solutions are obtained by low order approximations and accurate results can be achievedbyconsideringhigher orderterms numericalexamplesshowthataccurateresultsareachievedefe ciently for very large changes in the design nomenclature b matrix dee ned by eq 21 c matrix dee ned by eq 16 e modulus of elasticity i moment of inertia i identity matrix k stiffness matrix kr reduced stiffness matrix l length m mass matrix mr reduced mass matrix r right hand side vector r displacement vector rb matrix of basis vectors s number of basis vectors u upper triangular matrix y vector of coefe cients coefe cient dee ned by eq 35 angle between vectors 1k change in the stiffness matrix 1m change in the mass matrix kronecker delta eigenvalue circular frequency

efficient modal analysis of systems with local stiffness uncertainties the characterization of the uncertainty in modal quantities of an uncertain linear structural system is essential to the rapid determination of its response to arbitrary loadings although the size of many computational structural models used is extremely large i e thousands of equations the uncertainty to be analyzed is oftentimes localized to very small regions of the model this paper addresses the development of an efficient computational methodology for the modal analysis of linear structural systems with local stiffness uncertainties the newly developed methodology utilizes an enriched basis that consists of the sub spectrum of a nominal structural system augmented with additional basis vectors generated from a knowledge of the structure of the stiffness uncertainty in addition methods for determining bounds on the approximate modal frequencies and mode shapes are discussed numerical results demonstrate that the algorithm produces highly accurate results with greatly reduced computational effort copyright 2009 john wiley sons ltd

improved first order approximation of eigenvalues and eigenvectors a method based on reduced basis approximation concepts is presented for improved first order approximation of eigenvalues and eigenvectors of modified structural dynamic systems the terms of a local approximation based on taylor or matrix power series are used as basis vectors for approximating the perturbed eigenparameters for each eigenmode a reduced eigensystem is generated by using the baseline eigenvector and the first order approximation term as ritz vectors the solution of the reduced eigensystem leads to two possible estimates of each perturbed eigenvalue and eigenvector criteria for selection of the best approximation are presented the zero and first order rayleigh quotient approximation can be directly recovered as special cases of the present method results are presented for approximate dynamic reanalysis of a 25 bar planar truss structure it is shown that high quality approximation of the perturbed eigenparameters can be obtained for moderate perturbations in the stiffness and mass matrices for very large local perturbations of the structure including deletion of some structural members it is shown that the present method yields reasonable quality approximations

efficient characterization of the random eigenvalue problem in a polynomial chaos decomposition a new procedure for characterizing the solution of the eigenvalue problem in the presence of uncertainty is presented the eigenvalues and eigenvectors are described through their projections on the polynomial chaos basis an efficient method for estimating the coefficients with respect to this basis is proposed the method uses a galerkin based approach by orthogonalizing the residual in the eigenvalue eigenvector equation to the subspace spanned by the basis functions used for approximation in this way the stochastic problem is framed as a system of deterministic non linear algebraic equations this system of equations is solved using a newton raphson algorithm although the proposed approach is not based on statistical sampling the efficiency of the proposed method can be significantly enhanced by initializing the non linear iterative process with a small statistical sample synthesized through a monte carlo sampling scheme the proposed method offers a number of advantages over existing methods based on statistical sampling first it provides an approximation to the complete probabilistic description of the eigensolution second it reduces the computational overhead associated with solving the statistical eigenvalue problem finally it circumvents the dependence of the statistical solution on the quality of the underlying random number generator copyright 2007 john wiley sons ltd

adaptive observers and parameter estimation for a class of systems nonlinear in the parameters we consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations a solution to this problem is proposed for a class of systems of which the unknowns are allowed to be nonlinearly parameterized functions of state and time reconstruction of state and parameter values is based on the concepts of weakly attracting sets and non uniform convergence and is subjected to persistency of excitation conditions in the absence of nonlinear parametrization the resulting observers reduce to standard estimation schemes in this respect the proposed method constitutes a generalization of the conventional canonical adaptive observer design

eigensolutions of non proportionally damped systems based on continuous damping sensitivity abstract the viscous damping model has been widely used to represent dissipative forces in structures under mechanical vibrations in multiple degree of freedom systems such behavior is mathematically modeled by a damping matrix which in general presents non proportionality that is it does not become diagonal in the modal space of the undamped problem eigensolutions of non proportional systems are usually estimated assuming that the modal damping matrix is diagonally dominant neglecting the off diagonal terms or in the general case using the state space approach in this paper a new closed form expression for the complex eigenvalues of non proportionally damped system is proposed the approach is derived assuming small damping and involves not only the diagonal terms of the modal damping matrix but also the off diagonal terms which appear under higher order the validity of the proposed approach is illustrated through a numerical example

a singular perturbation analysis of eigenvalue veering and modal sensitivity in perturbed linear periodic systems abstract an investigation into the eigenvalue loci veering and modal sensitivity is presented for mistuned structural systems examples from both the weakly coupled uniaxial component systems and the cyclic symmetric systems are considered the analysis is based on singular perturbation techniques it is shown that uniform asymptotic expansions for the eigenvalues and eigenvectors can be constructed in terms of the mistuning parameters and that these solutions are in excellent agreement with the exact solutions the modal sensitivity function and the eigenvector rotations are then used to show the singular behavior of the eigenvectors in the neighborhood of a singular point rapid changes in the sensitivity function may signify large relative differences in the amplitudes of forced vibratory response between the tuned and the mistuned states

eigenvalue error analysis of viscously damped structures using a ritz reduction method the efficient solution of the eigenvalue problem that results from inserting passive dampers with variable stiffness and damping coefficients into a structure is addressed eigenanalysis of reduced models obtained by retaining a number of normal modes augmented with ritz vectors corresponding to the static solutions resulting from the load patterns introduced by the dampers has been empirically shown to yield excellent approximations to the full eigenvalue problem an analysis of this technique in the case of a single damper is presented a priori and a posteriori error estimates are generated and tested on numerical examples comparison theorems with modally truncated models and a markov parameter matching reduced order model are derived these theorems corroborate the heuristic that residual flexibility methods improve low frequency approximation of the system the analysis leads to other techniques for eigenvalue approximation approximate closed form solutions are derived that include a refinement to eigenvalue derivative methods for approximation an efficient newton scheme is also developed a numerical example is presented demonstrating the effectiveness of each of these methods

eigenvalue reanalysis by improved perturbation a new efficient method of eigenvalue reanalysis has been developed based on the perturbation method such that first the differential equations which describe the change of the eigenvalues and eigenvectors of a system being modified are derived from the perturbation method and then the solutions of these equations are obtained by following them up with the solutions of more simple equations the special features of this method are that it can give a clear correspondence between the eigenpairs before and after system modification and that the computer run time spent by this method is far shorter than that of revised analysis by fem when only a few selected modes are used in the form of an approximate computation in addition this approximate computation can give more accurate results than the perturbation method the efficiency of the proposed method has been verified by applying it to a simple spring mass model as well as a 600 degrees of freedom model which receive structural modification

brief adaptive estimation of discrete time systems with nonlinear parameterization this paper concerns adaptive estimation of dynamic systems which are nonlinearly parameterized a majority of adaptive algorithms employ a gradient approach to determine the direction of adjustment which ensures stable estimation when parameters occur linearly these algorithms however do not suffice for estimation in systems with nonlinear parameterization we introduce in this paper a new algorithm for such systems and show that it leads to globally stable estimation by employing a different regression vector and selecting a suitable step size both concave convex parameterizations as well as general nonlinear parameterizations are considered stable estimation in the presence of both nonlinear parameters and linear parameters which may appear multiplicatively is established for the case of concave convex parameterizations parameter convergence is shown to result under certain conditions of persistent excitation

two mode adaptive fuzzy control with approximation error estimator in this paper we propose a two mode adaptive fuzzy controller with approximation error estimator in the learning mode the controller employs some modified adaptive laws to tune the fuzzy system parameters and an approximation error estimator to compensate for the inherent approximation error in the operating mode the fuzzy system parameters are fixed only the estimator is updated online mathematically we show that the closed loop system is stable in the sense that all the variables are bounded in both modes we also establish mathematical bounds on the tracking error state vector control signal and the rms error using these bounds we show that controller s design parameters can be chosen to achieve desired control performance after that an algorithm to automatically switch the controller between two modes is presented finally simulation studies of an inverted pendulum system and a chua s chaotic circuit demonstrate the usefulness of the proposed controller

parameter estimation and compensation in systems with nonlinearly parameterized perturbations we consider a class of systems influenced by perturbations that are nonlinearly parameterized by unknown constant parameters and develop a method for estimating the unknown parameters the method applies to systems where the states are available for measurement and perturbations with the property that an exponentially stable estimate of the unknown parameters can be obtained if the whole perturbation is known the main contribution is to introduce a conceptually simple modular design that gives freedom to the designer in accomplishing the main task which is to construct an update law to asymptotically invert a nonlinear equation compensation for the perturbations in the system equations is considered for a class of systems with uniformly globally bounded solutions for which the origin is uniformly globally asymptotically stable when no perturbations are present we also consider the case when the parameters can only be estimated when the controlled state is bounded away from the origin and show that we may still be able to achieve convergence of the controlled state we illustrate the method through examples and apply it to the problem of downhole pressure estimation during oil well drilling

random eigenvalues algebraic methods and structural dynamic models a review of the literature of the study of structural vibration problems with random parameters is provided there have been several approaches to this problem these have been encapsulated in this paper for the benefit of those who need to assess such possibilities in particular the algebraic theory of random variables is delineated here with the application in mind being the determination or estimation of the statistics of the eigenvalues of linear dynamical systems various transformation techniques are summarized and discussed with simple examples

a hierarchical discretized parameter polynomial adaptive estimator for non linearly parameterized systems in this paper we propose a hierarchical discretized parameter polynomial adaptive estimator hdpae to estimate parameters that occur non linearly in dynamic systems that are non linear and lipschitz continuous a non linear persistent excitation nlpe condition is introduced under which it is shown that the hdpae is able to estimate the unknown parameters this nlpe condition is shown to be entirely equivalent to and is no more restrictive than the linear persistent excitation lpe condition for linearly parameterized systems

solution of eigenvalue problems for non classically damped systems with multiple frequencies abstract an efficient solution method is presented to solve the eigenvalue problem arising in the dynamic analysis of non classically damped structural systems with multiple eigenvalues the proposed method is obtained by applying the modified newton raphson technique and the orthonormal condition of the eigenvectors to the linear eigenproblem through matrix augmentation of the quadratic eigenvalue problem in the iteration methods such as the inverse iteration method and the subspace iteration method singularity may occur during the factorizing process when the shift value is close to an eigenvalue of the system however even though the shift value is an eigenvalue of the system the proposed method provides non singularity and that is analytically proved since the modified newton raphson technique is adapted to the proposed method initial values are needed because the lanczos method effectively produces better initial values than other methods the results of the lanczos method are taken as the initial values of the proposed method two numerical examples are presented to demonstrate the effectiveness of the proposed method and the results are compared with those of the well known subspace iteration method and the lanczos method

adaptive control of continuous time systems with convex concave parametrization this paper deals with adaptive control of a class of nonlinear dynamic systems with nonlinear parametrization in this class the state variables are assumed to be accessible and the nonlinearity in the parameters is assumed to be either convex or concave by introducing a tuning function and an adaptive law based on a min max strategy it is shown that such a class of dynamic systems can be adaptively controlled in a stable manner global boundedness of the overall adaptive system and tracking to within a desired precision are established with the new adaptive controller the proposed controller is applied to a precise positioning problem in the presence of nonlinearly parametrized friction dynamics it is shown that the controller leads to position errors and friction compensation that are orders of magnitude better than those based on estimation of linear parametrizations the fact that the new parameter estimation strategy used is distinct from the traditionally used gradient schemes permits the expansion of the scope of adaptive control which has been restricted hitherto in most cases to systems with linear parametrization

kernel based object tracking a new approach toward target representation and localization the central component in visual tracking of nonrigid objects is proposed the feature histogram based target representations are regularized by spatial masking with an isotropic kernel the masking induces spatially smooth similarity functions suitable for gradient based optimization hence the target localization problem can be formulated using the basin of attraction of the local maxima we employ a metric derived from the bhattacharyya coefficient as similarity measure and use the mean shift procedure to perform the optimization in the presented tracking examples the new method successfully coped with camera motion partial occlusions clutter and target scale variations integration with motion filters and data association techniques is also discussed we describe only a few of the potential applications exploitation of background information kalman tracking using motion models and face tracking

higher order eigenpair perturbations a matrix method is presented for the exact calculation of large eigenpair perturbations arising from design variable changes this method of forward analysis is presented that takes into account all order of the perturbation expansion

on eigenproblem solution of damped vibrations associated with gyroscopic moments a new efficient approach is presented for solving the quadratic eigenvalue problem of weakly nonproportionally damped vibration systems in the analysis of these systems gyroscopic moments and external damping are both considered traditional restriction of symmetry of inertia damping and stiffness matrices is slightly relaxed a second order perturbation theory is developed such that the perturbed solution is based on the eigensolution of an unperturbed subproblem this subproblem considers the unperturbed system in two different forms i a conservative gyroscopic part of an original problem or ii a nonconservative gyroscopic part of an original problem that is proportionally damped to cope with asymmetry of the system matrices a duncan s like state formulation is used to bring these matrices into a suitable form for perturbations two numerical examples are introduced for explaining the detailed implementation of the presented approach additionally a practical problem of rotor supported by two tilting pad bearings is investigated the eigensolutions obtained by the current approach match to a great extent other solutions obtained by time consuming exact methods the investigation procedure given here gives a framework to handle vibration problems of weakly nonproportional damping and or weakly asymmetric inertia damping and stiffness matrices

localization of vibrations by structural irregularity an investigation of the localization phenomenon is presented for disrodered structural systems consisting of weakly coupled component systems emphasis is placed on the development of a perturbation method that allows one to obtain the localized modes of vibration of the disordered system from the modes of the individual subsystems the principal feature of this perturbation method is that it not only considers the variations of the parameters as perturbations but it also treats the small coupling between subsystems as a perturbation such a perturbation analysis is cost effective as compared to a global eigenvalue analysis of the entire system and proves to be very accurate moreover it provides physical insight into the localization phenomenon and allows one to formulate a criterion that predicts the occurrence of strongly localized modes results are obtained for a chain of single degree of freedom coupled oscillators but these can be readilt generalized to deal with chains of multi degree of freedom component systems

a method for modal reanalysis of topological modifications of structures a method for structural modal reanalysis for three cases of topological modifications the number of degrees of freedom dofs is unchanged decreased and increased is presented in this method the newly added dofs are linked to the original dofs of the modified structure by means of the dynamic reduction so as to obtain the condensed equation the methods for forming the stiffness and mass increments k and m resulting from the three cases of topological modifications of structures are discussed the extended kirsch method is used to improve the accuracy of the starting solutions of the initial structure and then the eigenvectors of newly added dofs resulting from topological modification can be recovered at last the rayleigh ritz analysis is used to evaluate the eigenvalues and eigenvectors for the modified structure three numerical examples are given to illustrate the applications of the present approach the results show that the proposed method is effective for structural modal reanalysis of three cases of the topological modifications and it is easy to implement on a computer by comparing with previous method it can be seen that the present method can give good approximate eigenvalues and eigenvectors even if the topological modifications are very large copyright 2005 john wiley sons ltd

an improved computational technique for perturbations of the generalized symmetric linear algebraic eigenvalue problem a technique is developed and presented which improves the accuracy of the predictions for the eigenvalues of the usual first order perturbation scheme for the generalized symmetric linear algebraic eigenvalue problem the improved method very simply replaces the usual b norms appearing in the denominator of the expressions for the first order changes in the eigenvalues by bp norms where bp is the perturbed b matrix with increasing sizes for the perturbations the improved technique produces results whose accuracy approaches those of the usual second order predictions numerical studies are presented to support the analysis

perturbation method for the eigenvalue problem of lightly damped systems abstract an efficient method for the determination of the eigenvalues and eigenvectors of lightly damped systems is developed by means of a perturbation technique the second order matrix differential equation containing mass stiffness and damping matrices is normally transformed into a first order state equation to deal with the general damping matrix however the method described in this paper enables us to predict the complex eigenvalues and eigenvectors with relative ease without forming the state equation the light damping implies that the eigensolution of the damped system differs slightly from the eigensolution of the undamped system which also implies that we can express the eigensolution of the lightly damped system in terms of a power series expanded from the eigensolution of the undamped system once the eigenvalue problem of the undamped system is solved the higher order terms which reflect the effect of damping can be obtained from the matrix equations which reduce to simple algebraic equations a numerical example illustrates the effectiveness of the new method

dynamic analysis using a reduced basis of exact modes and ritz vectors the problem of obtaining an approximate solution for the response of a structure under dynamic forces is addressed the structure is modeled using mass and stiffness matrices and has n degrees of freedom an dimensional approximation is sought in a subspace defined by an arbitrary m orthogonal array a residual vector which is smaller in magnitude the more accurate the approximation is derived the residual contains two terms one is the error involved representing the force vector in the subspace the other is smaller the better the array leads to m approximate solutions of the exact eigenproblem numerical experiments are performed using arrays that are combinations of exact eigenvectors and of ritz vectors in one case when 11 different 10 dimensional bases are used to approximate the solution of a 60 degree of freedom problem it is found that a root mean square measure of relative error is smallest for the basis formed using the 6 lowest exact eigenvectors plus 4 ritz vectors generated from the spatial distribution of the loading

extended kirsch combined method for eigenvalue reanalysis based on the kirsch combined method and the rayleigh quotient a new eigenvalue reanalysis method for modified structures is developed using this method the accuracy of the eigenvalues reanalysis of large modifications of structural parameters is improved as an application of the method a numerical example is given to illustrate the accuracy by comparing the second order perturbation method with the proposed method if the large modifications of structural parameters are made the calculated results show that the proposed method is effective

reduced basis approximations of structural displacements for optimaldesign a new solution procedure for improved approximate reanalyses of structures using results of a single precise analysis is presented the proposed procedure is based on combining the computed terms of a series expansion used as high quality basis vectors with coefficients of a reduced basis expression the latter coefficients can readily be determined for each trial design by various criteria the results are measured by the errors in satisfying the analysis equations and are compared in terms of the quality of the approximations the proposed approach is suitable for various types of design variables and can be used with a general finite element model a general reanalysis procedure is introduced and the physical significance of first order approximations is demonstrated several numerical examples illustrate the effectiveness of the solution process it is shown that high quality approximations of displacements can be obtained with a small computational effort for very large changes in the design variables

reanalysis of linear and nonlinear structures using iterated shanks transformation reanalysis of structures is a common task in two important fields of structural engineering namely optimization and reliability it implies the solution of the kinematic equations for each new set of data in order to simplify this task several approximate methods have been developed in this paper a simple method for reanalysis applicable to either linear or nonlinear structures is proposed it is based on the improvement of the neumann resolvent series which diverges beyond a certain radius by means of the iterated shanks transformation the method is compared with two relevant proposals intended to improve the convergence of the neumann series namely the pade series and the scaled approximation methods the accuracy and simplicity of the proposed method is demonstrated through some examples concerning linear and nonlinear structures

distortion aware correlation tracking recently correlation filter cf based tracking methods have attracted considerable attention because of their high speed performance however distortion which refers to the phenomenon that the correlation outputs of cf based trackers are distorted remains a major obstacle for these methods in this paper we propose a distortion aware correlation filter framework which can detect distortions and recover from tracking failures our framework employs a simple yet effective feature termed normed correlation response to detect distortions meanwhile we introduce a competition mechanism to handle distortions in which we build a specialized graph to formulate and handle tracking under distortion as a maximum multi clique problem furthermore a global local context model is exploited to alleviate underlying distortions during the tracking process extensive experiments on the online tracking benchmark show that our tracker can find the optimal target trajectory during the distortion period and retrieve the possibly missing target consequently outperforms the state of the art methods and improves the performance of cf based trackers favorably

a perturbation method for reduction of eigenvalue analysis of structures with large stiffnesses and small masses a perturbation method to reduce the computing time for the eigenvalue analysis of structural dynamics is introduced in this paper a simplified structural model in which the degrees of freedom associated with the large stiffnesses are eliminated from the eigenvalue equation and the small masses are not considered is set up and analysed the eigenvalues and eigenvectors are served as the zeroth order solution and a perturbation procedure is performed to restore the eigensolution for the model of full degrees of freedom the method is successfully applied to the plane frame the numerical results show that the computing time can be greatly reduced while the high accuracy for the eigensolution is achieved the good perturbed result of both eigenvalues and eigenvectors is obtained even from the first order perturbation and the accurate normality of eigenvectors is achieved in the higher order perturbation for the perturbation with small masses a step perturbation is suggested to obtain a better result 1997 by john wiley sons ltd

analysis of eigenvalues and modal interaction of stochastic systems an eigenvalue spectral analysis of stochastic engineering systems is presented a comparative numerical study between approximations based on monte carlo sampling a taylor series based perturbation approach and the polynomial chaos representation is conducted it is observed that the polynomial chaos representation gives more accurate estimates of the statistical moments than the perturbation method especially for the higher modes the differences of accuracy in the two methods are more pronounced as the system variability increases moreover the chaos expansion gives a more detailed probabilistic description of the eigenvalues and the eigenvectors in addition a method for representing the statistical modal overlapping is presented that characterizes the statistical interaction between the various modes

adaptive control of a class of nonlinearly parameterized plants a stable adaptive control method is developed for a class of first order nonlinearly parameterized plants the method is based on modified adaptive algorithms that yield a stable system in which the output errors are guaranteed to converge to zero the stability analysis is carried out using suitably constructed lyapunov functions

asymptotic numerical methods and pade approximants for non linear elastic structures in this paper we apply asymptotic numerical methods for computing non linear equilibrium paths of elastic beam plate and shell structures the non linear branches are sought in the form of asymptotic expansions and they are determined by solving numerically fem several linear problems with a single stiffness matrix a large number of terms of the series can be easily computed by using recurrence formulas in comparison with a more classical step by step procedure the method is rapid and automatic we show with some examples that the choice of the expansion s parameter and the use of pade approximants play an important role in the determination of the size of the domain of convergence

composite model reference adaptive control with parameter convergence under finite excitation a new parameter estimation method is proposed in the framework of composite model reference adaptive control for improved parameter convergence without persistent excitation the regressor filtering scheme is adopted to perform the parameter estimation with signals that can be obtained easily a new framework for residual signal construction is proposed the incoming data are first accumulated to build the information matrix and then its quality is evaluated with respect to a chosen measure to select and store the best one the information matrix is built to have full rank after sufficient but not persistent excitation in this way the exponential convergence of both tracking error and parameter estimation error can be guaranteed without persistent oscillation in the external command which drives the system numerical simulations are performed to verify the theoretical findings and to demonstrate the advantages of the proposed adaptation law over the standard direct adaptation law

parameter convergence in nonlinearly parameterized systems a large class of problems in parameter estimation concerns nonlinearly parametrized systems over the past few years a stability framework for estimation and control of such systems has been established we address the issue of parameter convergence in such systems in this paper systems with both convex concave and general parameterizations are considered in the former case sufficient conditions are derived under which parameter estimates converge to their true values using a min max algorithm in the latter case to achieve parameter convergence a hierarchical min max algorithm is proposed where the lower level consists of a min max algorithm and the higher level component updates the bounds on the parameter region within which the unknown parameter is known to lie using this hierarchical algorithm a necessary and sufficient condition is established for global parameter convergence in systems with a general nonlinear parameterization in both cases the conditions needed are shown to be stronger than linear persistent excitation conditions that guarantee parameter convergence in linearly parametrized systems explanations and examples of these conditions and simulation results are included to illustrate the nature of these conditions a general definition of nonlinear persistent excitation that leads to parameter convergence is proposed at the end of this paper

eigensolution reanalysis of modified structures using epsilon algorithm based on the neumann series expansion and epsilon algorithm a new eigensolution reanalysis method is developed in the solution process the basis vectors can be obtained using the matrix perturbation or the neumann series expansion to construct the vector sequence and then using the epsilon algorithm table to obtain the approximate eigenvectors the approximate eigenvalues are computed from the rayleigh quotients the solution steps are straightforward and it is easy to implement with the general finite element analysis system two numerical examples a 40 storey frame and a chassis structure are given to demonstrate the application of the present method by comparing with the exact solutions and the kirsch method solutions it is shown that the excellent results are obtained for very large changes in the design and that the accuracy of the epsilon algorithm is higher than that of the kirsch method and the computation time is less than that of the kirsch method

high speed tracking with kernelized correlation filters the core component of most modern trackers is a discriminative classifier tasked with distinguishing between the target and the surrounding environment to cope with natural image changes this classifier is typically trained with translated and scaled sample patches such sets of samples are riddled with redundancies any overlapping pixels are constrained to be the same based on this simple observation we propose an analytic model for datasets of thousands of translated patches by showing that the resulting data matrix is circulant we can diagonalize it with the discrete fourier transform reducing both storage and computation by several orders of magnitude interestingly for linear regression our formulation is equivalent to a correlation filter used by some of the fastest competitive trackers for kernel regression however we derive a new kernelized correlation filter kcf that unlike other kernel algorithms has the exact same complexity as its linear counterpart building on it we also propose a fast multi channel extension of linear correlation filters via a linear kernel which we call dual correlation filter dcf both kcf and dcf outperform top ranking trackers such as struck or tld on a 50 videos benchmark despite running at hundreds of frames per second and being implemented in a few lines of code algorithm 1 to encourage further developments our tracking framework was made open source

adaptive control of a class of non linearly parametrized systems using convexification in this paper we deal with the problem of adaptive control of a class of non linearly parametrized plants the main contribution is to show that through a well chosen reparametrization it is possible to transform the non convex nonlinear parametrization into a convex one a property that is used to design a globally stable adaptive controller

a multiple model mrac scheme for multivariable systems with matching uncertainties this paper develops a multivariable multiple model adaptive control scheme for adaptive state feedback state tracking control of systems whose plant model matching conditions are uncertain and parameters are unknown to deal with the uncertainty of plant model matching conditions needed for adaptive control multiple reference model systems are employed to generate multiple parameter estimation and feedback control signals from which a most suitable control input is selected by a control switching mechanism designed using multiple estimation errors such a new multiple model control design is based on an expanded control system parametrization which has the capacity to cover system structural uncertainties stability analysis and simulation results ensure and verify the desired adaptive control system stability and tracking performance

structural reanalysis for general layout modifications a procedure for reanalysis of structures subjected to various layout modifications is presented the procedure is based on exact analysis of the initial design it is suitable for all types of layout changes including the general case in which some members and joints are added other members and joints are deleted and some joint coordinates are modified in the particular and challenging case of addition of joints where the number of degrees of freedom is increased a simple reanalysis of a modified initial design is first carried out further changes are then applied to the latter design it is shown that for changes in a limited number of members of a truss structure an exact solution is readily achieved for changes in numerous members of a general structure an approximate solution can be efficiently obtained high quality approximations are demonstrated for various types of layout modifications

derivatives of eigenvalues and eigenvectors of a general complex matrix a survey of methods for sensitivity analysis of the algebraic eigenvalue problem for non hermitian matrices is presented in addition a modification of one method based on a better normalizing condition is proposed methods are classified as direct or adjoint and are evaluated for efficiency operation counts are presented in terms of matrix size number of design variables and number of eigenvalues and eigenvectors of interest the effect of the sparsity of the matrix and its derivatives is also considered and typical solution times are given general guidelines are established for the selection of the most efficient method

adaptive classification of temporal signals in fixed weight recurrent neural networks an existence proof recurrent neural networks with fixed weights have been shown in practice to successfully classify adaptively signals that vary as a function of time in the presence of additive noise and parametric perturbations we address the question can this ability be explained theoretically we provide a mathematical proof that these networks have this ability even when parametric perturbations enter the signals nonlinearly the restrictions that we impose on the signals to be classified are that they satisfy an assumption of nondegeneracy and that noise amplitude is sufficiently small further we demonstrate that the recurrent neural networks may not only classify uncertain signals adaptively but also can recover the values of uncertain parameters of the signals up to their equivalence classes

rapid reanalysis of the generalized eigenvalue problem of locally modified linear dynamical systems abstract a computationally efficient method for the reanalysis of the damped generalized eigenvalue problems associated with linear dynamical systems with local damping and stiffness modifications is developed no restrictions are imposed on the damping of the system and the modifications in the damping and the stiffness can be independent of each other the application of the developed method to the undamped generalized eigenvalue problem with mass and stiffness modifications is also discussed the proposed method achieves up to three orders of magnitude gains in computational efficiency compared to the conventional solution procedures

on the modal analysis of non conservative linear systems this paper applies the results of classical eigenvalue theory to the analysis of a non conservative vibratory system general results are obtained for the response of a multiple degree of freedom system which is represented by a set of linear second order differential equations with constant coefficients for the case when the eigenvalues of the system are distinct these results confirm those obtained by 1 fawzy and bishop by a different method the latter results are restricted to distinct eigenvalues but the more general analysis presented here allows the case of multiple eigenvalues to be included the physical interpretation of complex normal co ordinate vectors is discussed and some simple numerical examples illustrate the results the approach described here lends itself to numerical computation using computer library programs for eigenvalue determination