direct updating of damping and stiffness matrices this note has outlined an extension to the available direct methods of model updating to estimate both the damping and stiffness matrices of a structure the method minimizes the change in the damping and stiffness matrices with the constraint that the measured modal data is reproduced

partial eigenstructure assignment for the quadratic pencil abstract it is shown in this paper that by the appropriate choice of gain and input influence matrices certain eigenpairs of a vibrating system may be assigned while the other eigenpairs remain unchanged the system under consideration is modelled by a set of second order differential equations and the assignment is carried by multi input state feedback control the solution may be of particular interest in the stabilization and control of flexible structures using smart materials where only a small part of the eigenstructure is to be reassigned and the rest is required to remain unchanged the method presented is illustrated with a numerical example

new methods for finite element model updating problems we consider two finite element model updating problems which incorporate the measured modal data into the analytical finite element model producing an adjusted model on the mass damping and stiffness that closely matches the experimental modal data we develop two efficient numerical algorithms for solving these problems the new algorithms are direct methods that require o nk2 and o nk2 k6 flops respectively and employ sparse matrix techniques when the analytic model is sparse here n is the dimension of the coefficient matrices defining the analytical model and k is the number of measured eigenpairs

structured quadratic inverse eigenvalue problem i serially linked systems quadratic pencils arising from applications are often inherently structured factors contributing to the structure include the connectivity of elements within the underlying physical system and the mandatory nonnegativity of physical parameters for physical feasibility structural constraints must be respected consequently they impose additional challenges on the inverse eigenvalue problems which intend to construct a structured quadratic pencil from prescribed eigeninformation knowledge of whether a structured quadratic inverse eigenvalue problem is solvable is interesting in both theory and applications however the issue of solvability is problem dependent and has to be addressed structure by structure this paper considers one particular structure where the elements of the physical system if modeled as a mass spring system are serially linked the discussion recasts both undamped and damped problems in a framework of inequality systems that can be adapted for numerical computation some open questions are described

transfer matrix eigenvalues of the anisotropic multiparametric u model a multiparametric extension of the anisotropic u model is discussed which maintains integrability the r matrix solving the yang baxter equation is obtained through a twisting construction applied to the underlying u q sl 2 1 superalgebraic structure which introduces the additional free parameters that arise in the model three forms of bethe ansatz solution for the transfer matrix eigenvalues are given which we show to be equivalent

density estimation by wavelet thresholding density estimation is a commonly used test case for nonparametric estimation methods we explore the asymptotic properties of estimators based on thresholding of empirical wavelet coefficients minimax rates of convergence are studied over a large range of besov function classes b pq and for a range of global l p error measures 1 p p some form of nonlinearity is essential since the minimax linear estimators are suboptimal by polynomial powers of n a second approach using an approximation of a gaussian white noise model in a mallows metric is used to attain exactly optimal rates of convergence for quadratic error p 2

semidefinite inverse eigenvalue problems with prescribed entries and partial eigendata in this paper we study the semidefinite inverse eigenvalue problem of reconstructing a real n by n matrix c such that it is nearest to the original pre estimated real n by n matrix c o in the frobenius norm and satisfies the measured partial eigendata where the required matrix c should preserve the symmetry positive semidefiniteness and the prescribed entries of the pre estimated matrix c o we propose the alternating direction method of multipliers for solving the semidefinite inverse eigenvalue problem where three related iterative algorithms are presented we also extend our method to the case of lower bounds numerical experiments are reported to illustrate the efficiency of the proposed method for solving semidefinite inverse eigenvalue problems

multiscale autoregressive models and wavelets the multiscale autoregressive mar framework was introduced to support the development of optimal multiscale statistical signal processing its power resides in the fast and flexible algorithms to which it leads while the mar framework was originally motivated by wavelets the link between these two worlds has been previously established only in the simple case of the haar wavelet the first contribution of this paper is to provide a unification of the mar framework and all compactly supported wavelets as well as a new view of the multiscale stochastic realization problem the second contribution of this paper is to develop wavelet based approximate internal mar models for stochastic processes this will be done by incorporating a powerful synthesis algorithm for the detail coefficients which complements the usual wavelet reconstruction algorithm for the scaling coefficients taking advantage of the statistical machinery provided by the mar framework we will illustrate the application of our models to sample path generation and estimation from noisy irregular and sparse measurements

new symmetry preserving method for optimal correction of damping and stiffness matrices using measured modes measured and analytical data are unlikely to be equal due to measured noise model inadequacies structural damage etc it is necessary to update the physical parameters of analytical models for proper simulation and design studies starting from simulated measured modal data such as natural frequencies and their corresponding mode shapes a new computationally efficient and symmetry preserving method and associated theories are presented in this paper to update the physical parameters of damping and stiffness matrices simultaneously for analytical modeling a conjecture which is proposed in y x yuan h dai a generalized inverse eigenvalue problem in structural dynamic model updating j comput appl math 226 2009 42 49 is solved two numerical examples are presented to show the efficiency and reliability of the proposed method it is more important that some numerical stability analysis on the model updating problem is given combining with numerical experiments

a karhunen loeve like expansion for 1 f processes via wavelets while so called 1 f or scaling processes emerge regularly in modeling a wide range of natural phenomena as yet no entirely satisfactory framework has been described for the analysis of such processes orthonormal wavelet bases are used to provide a new construction for nearly 1 f processes from a set of uncorrelated random variables

multiscale recursive estimation data fusion and regularization we describe a framework for modeling stochastic phenomena at multiple scales and for their efficient estimation or reconstruction given partial and or noisy measurements which may also be at several scales in particular multiscale signal representations lead naturally to pyramidal or tree like data structures in which each level in the tree corresponds to a particular scale of representation a class of multiscale dynamic models evolving on dyadic trees is introduced the main focus of this paper is on the description analysis and application of an extremely efficient optimal estimation algorithm for this class of models this algorithm consists of a fine to coarse filtering sweep followed by a coarse to fine smoothing step corresponding to the dyadic tree generalization of kalman filtering and rauch tung striebel smoothing the kalman filtering sweep consists of the recursive application of three steps a measurement update step a fine to coarse prediction step and a fusion step we illustrate the use of our methodology for the fusion of multiresolution data and for the efficient solution of fractal regularizations of ill posed signal and image processing problems encountered

estimation of fractal signals from noisy measurements using wavelets the role of the wavelet transformation as a whitening filter for 1 f processes is exploited to address problems of parameter and signal estimations for 1 f processes embedded in white background noise robust computationally efficient and consistent iterative parameter estimation algorithms are derived based on the method of maximum likelihood and cramer rao bounds are obtained included among these algorithms are optimal fractal dimension estimators for noisy data algorithms for obtaining bayesian minimum mean square signal estimates are also derived together with an explicit formula for the resulting error these smoothing algorithms find application in signal enhancement and restoration the parameter estimation algorithms find application in signal enhancement and restoration the parameter estimation algorithms in addition to solving the spectrum estimation problem and to providing parameters for the smoothing process are useful in problems of signal detection and classification results from simulations are presented to demonstrated the viability of the algorithms

inverse vibration problem for un damped 3 dimensional multi story shear building models various researchers have contributed to the identification of the mass and stiffness matrices of two dimensional 2 d shear building structural models for a given set of vibratory frequencies the suggested methods are based on the specific characteristics of the jacobi matrices i e symmetric tri diagonal and semi positive definite matrices however in case of three dimensional 3 d structural models those methods are no longer applicable since their stiffness matrices are not tri diagonal in this paper the inverse problem for a special class of vibratory structural systems i e 3 d shear building models is investigated a practical algorithm is proposed for solving the inverse eigenvalue problem for un damped 3 d shear buildings the problem is addressed in two steps first using the target frequencies a so called normalized eigenvector matrix which is a banded matrix containing the information related to the frequencies and mode shapes of the target structural system is determined in this regard similar to the solution of inverse problem for 2 d shear building structural models in which an auxiliary structure is constructed by adding constraints or springs to the original system three auxiliary structures are proposed to solve the problem for 3 d cases in the second step the normalized eigenvector matrix is utilized to obtain the normalized stiffness matrix in turn this matrix is decomposed into the stiffness and mass matrices of the system finally a numerical example is presented to demonstrate the efficiency of the proposed algorithm in determining the mass and stiffness matrices of a 3 d structural model for a given set of target vibrational frequencies

algebraic bethe ansatz for 19 vertex models with reflection conditions in this work we solve the 19 vertex models with the use of algebraic bethe ansatz for diagonal reflection matrices sklyanin k matrices the eigenvectors eigenvalues and bethe equations are given in a general form quantum spin chains of spin one derived from the 19 vertex models were also discussed

quantum spin chain with soliton non preserving boundary conditions we consider the case of an integrable quantum spin chain with soliton non preserving boundary conditions this is the first time that such boundary conditions have been considered in the spin chain framework we construct the transfer matrix of the model we study its symmetry and we find explicit expressions for its eigenvalues moreover we derive a new set of bethe ansatz equations by means of the analytical bethe ansatz method

long range deformations for integrable spin chains we present a recursion relation for the explicit construction of integrable spin chain hamiltonians with long range interactions based on arbitrary shortrange e g nearest neighbor integrable spin chains it allows us to construct an infinite set of conserved long range charges we explain the moduli space of deformation parameters by different classes of generating operators the rapidity map and dressing phase in the long range bethe equations are a result of these deformations the closed chain asymptotic bethe equations for long range spin chains transforming under a generic symmetry algebra are derived notably our construction applies to generalizations of standard nearest neighbor chains such as alternating spin chains we also discuss relevant properties for its application to planar d 4 n 4 and d 3 n 6 supersymmetric gauge theories finally we present a map between long range and inhomogeneous spin chains delivering more insight into the structures of these models as well as their limitations at wrapping order

multiscale representations of markov random fields recently a framework for multiscale stochastic modeling was introduced based on coarse to fine scale recursive dynamics defined on trees this model class has some attractive characteristics which lead to extremely efficient statistically optimal signal and image processing algorithms the authors show that this model class is also quite rich in particular they describe how 1 d markov processes and 2 d markov random fields mrfs can be represented within this framework the recursive structure of 1 d markov processes makes them simple to analyze and generally leads to computationally efficient algorithms for statistical inference on the other hand 2 d mrfs are well known to be very difficult to analyze due to their noncausal structure and thus their use typically leads to computationally intensive algorithms for smoothing and parameter identification in contrast their multiscale representations are based on scale recursive models and thus lead naturally to scale recursive algorithms which can be substantially more efficient computationally than those associated with mrf models in 1 d the multiscale representation is a generalization of the midpoint deflection construction of brownian motion the representation of 2 d mrfs is based on a further generalization to a midline deflection construction the exact representations of 2 d mrfs are used to motivate a class of multiscale approximate mrf models based on one dimensional wavelet transforms they demonstrate the use of these latter models in the context of texture representation and in particular they show how they can be used as approximations for or alternatives to well known mrf texture models

spectral decomposition of real symmetric quadratic λ matrices and its applications spectral decomposition provides a canonical representation of an operator over a vector space in terms of its eigenvalues and eigenfunctions the canonical form often facilitates discussions which otherwise would be complicated and involved spectral decomposition is of fundamental importance in many applications the well known glr theory generalizes the classical result of eigendecomposition to matrix polynomials of higher degrees but its development is based on complex numbers this paper modifies the glr theory for the special application to real symmetric quadratic matrix polynomials q a mx2 cx k m nonsingular subject to the specific restriction that all matrices in the representation be realvalued it is shown that the existence of the real spectral decomposition can be characterized through the notion of real standard pair which in turn can be constructed from the spectral data applications to a variety of challenging inverse problems are discussed

parameter reconstruction of vibration systems from partial eigeninformation quadratic matrix polynomials are fundamental to vibration analysis because of the predetermined interconnectivity among the constituent elements and the mandatory nonnegativity of the physical parameters most given vibration systems will impose some inherent structure on the coefficients of the corresponding quadratic matrix polynomials in the inverse problem of reconstructing a vibration system from its observed or desirable dynamical behavior respecting the intrinsic structure becomes important and challenging both theoretically and practically the issue of whether a structured inverse eigenvalue problem is solvable is problem dependent and has to be addressed structure by structure in an earlier work physical systems that can be modeled under the paradigm of a serially linked mass spring system have been considered via specifically formulated inequality systems in this paper the framework is generalized to arbitrary generally linked systems in particular given any configuration of interconnectivity in a mass spring system this paper presents a mechanism that systematically and automatically generates a corresponding inequality system a numerical approach is proposed to determine whether the inverse problem is solvable and if it is so computes the coefficient matrices while providing an estimate of the residual error the most important feature of this approach is that it is problem independent that is the approach is general and robust for any kind of physical configuration the ideas discussed in this paper have been implemented into a software package by which some numerical experiments are reported

integrable spin chains associated with slq n and slp q n the hopf structure of the central extension of the uq sl n algebra is considered the intertwine matrix induces new integrable chain models we show the relation of these models and the biparametric spin chain slp q n models the cases n 2 are n 3 are discussed and for n 2 we obtain the model of dasgupta and chowdhury 1993 the case n 3 is solved by the nested bethe ansatz method and the dependence of the bethe equations on the second parameter introduced is demonstrated

new fast smoothers for multiscale systems we consider the smoothing problem for multiscale stochastic systems based on the wavelet transform these models involve processes indexed by the nodes of a dyadic tree each level of the dyadic tree represents one scale or resolution of the process therefore moving upward on the tree divides the resolution by 2 whereas moving downward multiplies it by 2 the processes are built according to a recursion in scale from coarse to fine to which random details are added to operate the change in scale one must perform an interpolation this is achieved using the qmf pair of operators attached to a wavelet transform these models have proved to be of great value to capture textures or fractal like processes as well as to perform multiresolution sensor fusion an example of which is given here up to now however only subclasses of multiscale systems were amenable to fast algorithms and through different formalisms those relying on haar s wavelet and those involving only one of the two wavelet interpolators we provide here a unifying framework that handles any system based on orthogonal wavelets a smoothing theory is presented to define the field of fast algorithms for markov random fields and give intuition on how to design them this theory reveals the difficulties arising with general multiscale systems we then prove that orthogonality properties of wavelets are the gate to fastness

inverse problems for damped vibrating systems abstract linear damped vibrating systems are defined by three real definite matrices m 0 d 0 and k 0 the mass damping and stiffness matrices respectively it is assumed that all eigenvalues of the system are simple and nonreal so that the eigenvectors columns of a matrix x c c n n are also complex it is shown that when properly defined the eigenvectors have a special structure consistent with x c x r i i where x r r n n x r is nonsingular and is orthogonal by taking advantage of this structure solutions of the inverse problem are obtained i e given complete information on the eigenvalues and eigenvectors it is shown how m d and k can be found three points of view are developed and compared namely using spectral theory structure preserving similarities and factorisation theory

multiply rooted multiscale models for large scale estimation divide and conquer or multiscale techniques have become popular for solving large statistical estimation problems the methods rely on defining a state which conditionally decorrelates the large problem into multiple subproblems each more straightforward than the original however this step cannot be carried out for asymptotically large problems since the dimension of the state grows without bound leading to problems of computational complexity and numerical stability in this paper we propose a new approach to hierarchical estimation in which the conditional decorrelation of arbitrarily large regions is avoided and the problem is instead addressed piece by piece the approach possesses promising attributes it is not a local method the estimate at every point is based on all measurements it is numerically stable for problems of arbitrary size and the approach retains the benefits of the multiscale framework on which it is based a broad class of statistical models a stochastic realization theory an algorithm to calculate statistical likelihoods and the ability to fuse local and nonlocal measurements

modeling and estimation of multiresolution stochastic processes an overview is provided of the several components of a research effort aimed at the development of a theory of multiresolution stochastic modeling and associated techniques for optimal multiscale statistical signal and image processing a natural framework for developing such a theory is the study of stochastic processes indexed by nodes on lattices or trees in which different depths in the tree or lattice correspond to different spatial scales in representing a signal or image in particular it is shown how the wavelet transform directly suggests such a modeling paradigm this perspective then leads directly to the investigation of several classes of dynamic models and related notions of multiscale stationarity in which scale plays the role of a time like variable the investigation of models on homogeneous trees is emphasized the framework examined here allows for consideration in a very natural way of the fusion of data from sensors with differing resolutions also thanks to the fact that wavelet transforms do an excellent job of compressing large classes of covariance kernels it is seen that these modeling paradigms appear to have promise in a far broader context than one might expect

an inverse eigenvalue problem for the symmetric tridiagonal quadratic pencil with application to damped oscillatory systems a method is presented which constructs an n by n tridiagonal symmetric quadratic pencil which has its 2n eigenvalues and the 2n 2 of its n 1 dimensional leading principal subpencil prescribed it is shown that if the given eigenvalues are distinct there are at most 2 n 2n 3 n 2 different solutions in the degenerate case where some of the given eigenvalues are common there are an infinite number of solutions apart from finding the roots of certain polynomials the problem is solved in a finite number of steps where the problem has only a finite number of solutions they can all be found in a systematic manner the method is demonstrated with a simple example and its use is illustrated with a practical engineering application in vibrations

integrability of a t j model with impurities a t j model for correlated electrons with impurities is proposed the impurities are introduced in such a way that integrability of the model in one dimension is not violated the algebraic bethe ansatz solution of the model is also given and it is shown that the bethe states are highest weight states with respect to the supersymmetry algebra

an augmented lagrangian dual optimization approach to the h weighted model updating problem abstract model updating for the quadratic eigenvalue problem aims to update the model q 2 m c k by given eigendata in this paper we consider the h weighted model updating problem which can not only preserve the symmetry and definiteness of the original model but also express our confidence in the original model through assigning different confidence weights we propose an augmented lagrangian dual method for the h weighted model updating problem under some mild assumptions our method is shown to converge at least linearly numerical results illustrate the effectiveness of our method in addition we compare our method with the semi definite programming sdp method numerical results illustrate that when the scale of the model becomes large our method still works but the sdp method failed to converge

a dual optimization approach to inverse quadratic eigenvalue problems with partial eigenstructure the inverse quadratic eigenvalue problem iqep arises in the field of structural dynamics it aims to find three symmetric matrices known as the mass the damping and the stiffness matrices such that they are closest to the given analytical matrices and satisfy the measured data the difficulty of this problem lies in the fact that in applications the mass matrix should be positive definite and the stiffness matrix positive semidefinite based on an equivalent dual optimization version of the iqep we present a quadratically convergent newton type method our numerical experiments confirm the high efficiency of the proposed method

diagonalisation of gl n invariant transfer matrices and quantum n wave system lee model the algebraic bethe ansatz is constructed for the gl n invariant transfer matrices with arbitrary gl n spin for this purpose the notion of vacuum subspace is introduced it is shown that the gl n magnet can be interpreted as an integrable discrete approximation of vector or matrix nonlinear schrodinger models or of the quantum n wave system

multiscale systems kalman filters and riccati equations an algorithm analogous to the rauch tung striebel algorithm spl minus consisting of a fine to coarse kalman filter like sweep followed by a coarse to fine smoothing step spl minus was developed previously by the authors ibid vol 39 no 3 p 464 78 1994 in this paper they present a detailed system theoretic analysis of this filter and of the new scale recursive riccati equation associated with it while this analysis is similar in spirit to that for standard kalman filters the structure of the dyadic tree leads to several significant differences in particular the structure of the kalman filter error dynamics leads to the formulation of an ml version of the filtering equation and to a corresponding smoothing algorithm based on triangularizing the hamiltonian for the smoothing problem in addition the notion of stability for dynamics requires some care as do the concepts of reachability and observability using these system theoretic constructs the stability and steady state behavior of the fine to coarse kalman filter and its riccati equation are analysed

fusion and propagation with multiple observations in belief networks abstract the polytree algorithm of kim and pearl 16 19 is a fundamental method for evidential reasoning in belief networks not only does it provide exact solutions to singly connected networks using efficient local computations but variations of it can be applied to more general networks as well when a belief network is singly connected the polytree algorithm can compute a posterior marginal distribution for each variable by visiting each node at most once for each piece of evidence by contrast the related algorithms based on undirected graphs 1 14 16 28 only need to visit each node at most twice no matter how much evidence is observed in this paper a revised polytree algorithm is developed with the same complexity as the undirected methods but within the directed framework of the polytree algorithm when this new algorithm is applied via cutset conditioning to general networks it obtains not just the corresponding significant improvement in speed but also a much simpler form for combination furthermore the revised algorithm requires only minor modifications to existing implementations of the polytree algorithm

quadratic inverse eigenvalue problem for damped gyroscopic systems in this paper we discuss the quadratic inverse eigenvalue problem for damped gyroscopic systems that is we are to construct a damped gyroscopic second order system having given 2n eigenvalues and associated eigenvectors as its full eigenstructure under some mild assumptions the coefficient matrices are constructed in a recursive process we also discuss how to obtain a damped gyroscopic system with the leading coefficient matrix m being positive definite

improvement of a large analytical model using test data a method has been developed which uses measured normal modes and natural frequencies to improve an analytical mass and stiffness matrix model of a structure the method directly identifies without iteration a set of minimum changes in the analytical matrices which force the eigensolutions to agree with the test measurements an application is presented in which the analytical model had 508 degrees of freedom and 19 modes were measured at 101 locations on the structure the resulting changes in the model are judged to be small compared to expectations of error in the analysis thus the improved model is accepted as a reasonable model of the structure with improved dynamic response characteristics in addition it is shown that the procedure may be a useful tool in identifying apparent measured modes which are not true normal modes of the structure nomenclature analytical matrix matrix of changes identity matrix full improved stiffness and mass matrices n x n full analytical k m matrices n x n partitions of ka ma corresponding to test coordinates partitions of ka ma corresponding to coupling elements partitions of ka ma corresponding to unmea sured coordinates number of measured modes number of degrees of freedom in the model measures of changes eqs 15 17 matrix norm sum of the squares of all the elements rectangular modal matrix normalized n x m th mode th column of measured and unmeasured partitions of diagonal matrix of measured natural frequencies m xm natural frequency of th mode 12 17 sum of the squares of all elements of matrix

wavelet analysis and synthesis of fractional brownian motion fractional brownian motion fbm offers a convenient modeling for nonstationary stochastic processes with long term dependencies and 1 f type spectral behavior over wide ranges of frequencies statistical self similarity is an essential feature of fbm and makes natural the use of wavelets for both its analysis and its synthesis a detailed second order analysis is carried out for wavelet coefficients of fbm it reveals a stationary structure at each scale and a power law behavior of the coefficients variance from which the fractal dimension of fbm can be estimated conditions for using orthonormal wavelet decompositions as approximate whitening filters are discussed consequences of discretization are considered and some connections between the wavelet point of view and previous approaches based on length measurements analysis or dyadic interpolation synthesis are briefly pointed out

integrable su 3 spin chain combining different representations the general expression for the local matrix of a quantum chain with the site space in any representation of su 3 is obtained this is made by generalizing from the fundamental representation and imposing the fulfilment of the yang baxter equation then a non homogeneous spin chain combining different representations of su 3 is solved by developing a method inspired in the nested bethe ansatz the solution for the eigenvalues of the trace of the monodromy matrix is given as two coupled bethe equations a conjecture about the solution of a chain with the site states in different representations of su n is presented the thermodynamic limit of the ground state is calculated

new integrable quantum chains combining different kinds of spins a general procedure to generate new integrable hamiltonians combining to any kind of spins distributed arbitrarily on the line is given as a concrete application anisotropic chains formed by spin 1 2 and spin 1 operators at alternating sites are presented and solved exactly by the bethe ansatz ba the authors compute the ground state and excitation energies and momentum the higher order ba equations are derived depending on the choice these new hamiltonians exhibit or not conformal invariance in their low energy spectrum