inclusion principle for the rayleigh ritz based substructure synthesis according to this substructure synthesis the motion of every substructure is modeled in terms of quasicomparison functions which are linear combinations of admissible functions capable of satisfying all the boundary conditions

reduction of substructural interface degrees of freedom in flexibility based component mode synthesis a flexibility based component mode synthesis cms is proposed for reduced order modelling of dynamic behaviour of large structures the approach employs partitioning via the localized lagrange multiplier method the use of the localized lagrange multipliers leads to unlike the classical lagrange multipliers a linearly independent set of interface forces without any redundancies at multiply connected interface nodes the flexibility based cms method has shown significant advantages over the classical craig bampton method a key feature of the method is its substructural mode selection criterion that is independent of loading conditions unlike the majority of available cms approaches where one retains the full dimension of partition boundary degrees of freedom dofs the flexibility based method allows to reduce significantly the interface dofs the reduction of interface dofs represents the major contribution of the present communication the efficiency of the proposed approach is demonstrated on an analysis of a simple plate partitioned and of a more complex 3d structure both partitioned into several substructures copyright 2006 john wiley sons ltd

the complex cepstrum of higher order cumulants and nonminimum phase system identification a computationally efficient identification procedure is proposed for a nongaussian white noise driven linear time invariant nonminimum phase system the method is based on the idea of computing the complex cepstrum of higher order cumulants of the system output in particular the differential cepstrum parameters of the nonminimum phase impulse response are estimated directly from higher order cumulants by least squares solution or two dimensional fft operations the method reconstructs the minimum phase and maximum phase impulse response components separately it is flexible enough to be applied on autoregressive ar moving average ma or arma system without a priori knowledge of the type of the system benchmark simulation examples demonstrate the effectiveness of the method even with short length data records

rayleigh ritz based substructure synthesis for flexible multibody systems this paper is concerned with the modeling of flexible multibody systems by a rayleigh ritz based substructure synthesis method so that certain advantages can be accrued by using the variational approach to derive the eigenvalue problem as with the classical rayleigh ritz method if the admissible functions used to represent the motion of the substructures are not chosen properly convergence can suffer this paper presents a new substructure synthesis method with superior convergence characteristics achieved by representing the motion by means of a recently developed class of functions namely the class of quasi compari son functions this improved convergence is shown to be related to improved approximation of both the differential equations and the natural boundary conditions the theory is demonstrated by means of a numerical example i introduction t his investigation is concerned with the modeling of flexible multibody systems many structures such as fixedwing aircraft helicopters flexible spacecraft flexible robots etc can be modeled as assemblages of interacting flexible bodies a method proposed by hurty1 2 in the early 1960s and known as component mode synthesis consists of modeling the motion of the individual substructures referred to as components by means of component modes he uses three types of modes to represent the motion of a substructure rigid body modes constraint modes and normal modes to define constraint modes hurty divides the constraints into two classes statically determinate and redundant the constraint modes are equal in number to the number of redundant constraints and are defined by producing a unit displacement on each redundant constraint in turn with all other constraints fixed the normal modes represent the modes of vibration of the components with all constraints fixed an approach by craig and hampton3 differs from that of hurty 1 2 mainly in the selection of the component modes indeed craig and hampton suggest two types of component modes boundary modes providing for displacements and rotations at points along the substructure boundaries and related to the constraint modes of hurty and substructure modes corresponding to completely restrained boundaries the substructures modeled individually in refs 1 3 are made to act together as a single structure by eliminating the redundant generalized coordinates arising from the fact that displacements at points common to two adjacent substructures are included twice in the overall problem formulation once for each substructure the elimination process is based on the use of constraint equations resulting from the enforcement of compatibility conditions which amounts to saying that the displacement of a boundary point shared by two substructures is the same in another approach to the problem proposed by

a general procedure for improving substructures representation in dynamic synthesis in the general substructure synthesis method for the dynamic analysis of complex flexible structures developed earlier by the authors the motion of each substructure is represented by a given number of substructure admissible functions and the otherwise disjoint substructures are connected together to form a whole structure by imposing approximate geometric compatibility conditions by means of weighted residuals in this paper a general procedure for improving the admissible functions representing each substructure in the synthesis is developed the procedure is an iterative one and it leads to an improved eigensolution for the intermediate structure i e a fictitious structure defined by the approximate compatibility conditions where the improved eigensolution is obtained while always using the same number of degrees of freedom to represent a given substructure in any iteration the computations associated with each substructure are independent of those for all other substructures and they can be performed in parallel by increasing the number of iterations the eigensolution for the intermediate structure is approached the procedure is applicable to assembled structures that are either positive definite or positive semidefinite moreover the procedure represents an extension of the concept of subspace iteration to structures composed of substructures

signal reconstruction from the phase of the bispectrum the authors present a simple procedure the bispectrum signal reconstruction bsr algorithm to recover the fourier phase of a signal from the phase of its bispectrum by simple analogy a procedure that recovers the fourier magnitude of a signal from the magnitude of its bispectrum is also presented in addition the authors propose an iterative scheme the bicepstrum iterative reconstruction algorithm bira for the reconstruction of a finite impulse response fir sequence from only the phase of its bispectrum and they demonstrate how some a priori information on the energy of the cepstra coefficients can improve significantly the convergence rate of the algorithm both schemes are based on the key observation that the differences of the bispectrum coefficients contain all the information concerning the fourier phase of the signal whereas their sums contain the fourier magnitude information

on a new iterative approach of component mode synthesis a wholly new concept of intermediate structure is developed in this paper based on this a new component mode iteration cmi or subdomain subspace iteration method is proposed in the new cmi method the ordinarily required step of ensuring interface compatibility is eliminated an outstanding achievement of this method is that it retains the merit of the standard subspace iteration ssi technique concerning the number of vectors required in computation in the present method iteraton is carried out at subdomain levels on machines capable of parallel processing this work can be performed simultaneously numerical examples clearly demonstrate the excellence of this new method

a general dynamic synthesis for structures with discrete substructures abstract this paper presents a substructure synthesis method for the dynamic simulation of complex structures where the structures consist of an assemblage of discrete substructures an analogy between distributed and discrete structures is extensively invoked to stimulate the motion of discrete substructures the concept of admissible vectors is introduced where admissible vectors represent the discrete counterpart of admissible functions for distributed substructures the individual substructures are forced to act as a whole structure by imposing certain geometric compatibility on internal boundaries shared by any two substructures a numerical example illustrating the method is presented

linear non linear dynamic substructures the dynamic substructure method is extended to linear and non linear coupling systems only those master co ordinates with non linear nature non linear co ordinates are retained other slave co ordinates relating to the linear part linear co ordinates are eliminated by the dynamic substructure method the dynamic flexibility matrix associated with the linear co ordinates is first expanded in terms of the fixed interface natural modes the condensed dynamic stiffness matrix associated with the non linear co ordinates is formed subsequently the convergence of the condensed dynamic stiffness matrix with respect to the natural modes can be improved by means of matrix manipulations and taylor series expansion to find the steady state solutions the non linear responses are expanded into a fourier series responses of the linear co ordinates are related to the non linear co ordinates analytically to solve for the unknown fourier coefficients the harmonic balance method gives a set of non linear algebraic equations relating the vibrating frequency and the nodal displacement coefficients a newtonian algorithm is adopted to solve for the unknown fourier coefficients iteratively the computational cost of a non linear analysis depends heavily on the number of degrees of freedom encountered in the method the number of degrees of freedom is kept to a minimum and the computational cost is greatly reduced

accurate computing of higher vibration modes of thin flexible structures motivated by the need for high fidelity modeling and accurate control of future hypersonic vehicles subjected to complex aerothermomechanical loads and many other such applications a novel scheme is proposed to accurately compute higher modes of vibration for one dimensional structures by coupling the classic ritz method as a predictor and the linear two point boundary value problem solver supore as a corrector the ritz method is used to compute a preliminary estimate of the natural frequencies for the desired modes these estimates are then used as initial guesses by supore which employs superposition and reorthonormalization to accurately solve the governing boundary value problem compared to a high fidelity ritz approximation or a highly refined finite element modeling procedure this is a simple computationally less expensive and yet highly accurate method to compute mode shapes for applications that require higher modes this scheme is used to compute mode shapes within an absolute and relative

damped dynamic substructures the dynamic substructure method is extended to lightly or heavily damped systems both internal and external dampings are considered the damped dynamic flexibility associated with the slave co ordinates is first expanded in terms of the damped fixed interface natural modes and the condensed dynamic stiffness associated with the master co ordinates is formed subsequently the convergence of the condensed dynamic stiffness with respect to the damped natural modes can be improved by means of the static matrices since the dynamic stiffness method is equivalent to the modal synthesis method the component mode method and kron s method the theory presented here is readily applicable to these methods are restricted to symmetric damping matrices

derived categories of quadric fibrations and intersections of quadrics abstract we construct a semiorthogonal decomposition of the derived category of coherent sheaves on a quadric fibration consisting of several copies of the derived category of the base of the fibration and the derived category of coherent sheaves of modules over the sheaf of even parts of the clifford algebras on the base corresponding to this quadric fibration generalizing the kapranov s description of the derived category of a single quadric as an application we verify that the noncommutative algebraic variety p s 2 w b 0 where b 0 is the universal sheaf of even parts of clifford algebras is homologically projectively dual to the projective space p w in the double veronese embedding p w p s 2 w using the properties of the homological projective duality we obtain a description of the derived category of coherent sheaves on a complete intersection of any number of quadrics

fourier series based nonminimum phase model for statistical signal processing in this paper a parametric fourier series based model fsbm for or as an approximation to an arbitrary nonminimum phase linear time invariant lti system is proposed for statistical signal processing applications where a model for lti systems is needed based on the fsbm a minimum phase linear prediction error lpe filter for amplitude estimation of the unknown lti system together with the cramer rao cr bounds is presented then an iterative algorithm for obtaining the optimum lpe filter with finite data is presented that is also an approximate maximum likelihood algorithm when data are gaussian then three iterative algorithms using higher order statistics hos with finite non gaussian data are presented to estimate parameters of the fsbm followed by some simulation results as well as some experimental results with real speech data to support the efficacy of the proposed algorithms using the fsbm finally we draw some conclusions

the complex cepstrum and bicepstrum analytic performance evaluation in the presence of gaussian noise an analytic performance evaluation of the complex cepstrum power cepstrum bicepstrum and power bicepstrum is presented by providing approximate expressions of the bias and variance of the cepstrum parameters due to the presence of gaussian noise the approximations are based on the asymptotic properties of bispectrum estimates and they are valid for moderate signal to noise ratios snrs the assumed model consists of a deterministic signal e g multiple echoes in additive white gaussian noise and finite length data the validity of the analytic expressions is verified with monte carlo simulations performance comparisons between bicepstrum and cepstrum methods suggest that the improved performance of the bicepstrum is a function of snr a omega m and n

equivalences between git quotients of landau ginzburg b models we define the category of b branes in a not necessarily affine landau ginzburg b model incorporating the notion of r charge our definition is a direct generalization of the category of perfect complexes we then consider pairs of landau ginzburg b models that arise as different git quotients of a vector space by a one dimensional torus and show that for each such pair the two categories of b branes are quasi equivalent in fact we produce a whole set of quasi equivalences indexed by the integers and show that the resulting auto equivalences are all spherical twists

a new exact substructure method using mixed modes in this paper the use of free or fixed interface modes in exact substructure displacement expansions is briefly summarized then the substructural displacements are expressed exactly in terms of mixed modes i e the displacements consist of linear combinations of fixed and free interface modes this yields a new exact mixed mode substructure method it is demonstrated that the exact substructure methods with fixed or free interfaces are two limiting cases of this new mixed mode exact method thus the exact substructure method variants with free interface fixed interface or mixed modes form a systematic theory of substructure methods which is unified by the new mixed mode variant this new exact variant not only has this important theoretical significance but also has great practical significance because it can lead to new approximate methods and to a deeper understanding of existing ones e g quasi comparison function methods dynamic condensation methods or substructure modal synthesis methods

portal frame inertia and stiffness matrices by substructure synthesis generic expressions of mass and stiffness matrices of the portal frame are presented these are derived by means of the substructure synthesis method this method is exceptionally characterised by low order eigenvalue problems and highly accurate eigensolutions

partitioned component mode synthesis via a flexibility approach a new flexibility based component mode synthesis method is presented which is derived by approximating the partitioned equations of motion that employ a localized method of lagrange multipliers the use of the localized lagrange multipliers leads to unlike the classical lagrange multipliers a linearly independent set of interface forces without any redundancies at multiply connected interface nodes hence the resulting interface flexibility matrices are uniquely determined and well suited for the present method development an attractive feature of the present method is its substructural mode selection criterion that is independent of loading conditions numerical experiments show that the present modal selection criterion is reliable and that the proposed flexibility based component mode synthesis method performs well relative to the classical craig bampton method in terms of accuracy and of its ability to include dominant substructural modes for simple plates and a relatively complex solid ring

substructure synthesis and its iterative improvement for large nonconservative vibratory systems a general synthesis method is developed for the dynamic analysis of nonconservati ve vibratory systems composed of substructures the idea of the synthesis is to represent each substructure by a reduced order model and to couple the substructure models together to act as the whole system for general nonconservative systems a state space formulation is adopted for each substructure reduced order substructure models are obtained by approximating each state vector as a linear combination of a small number of real trial vectors the accuracy with which the synthesized model represents the whole system depends on the choices of trial vectors and the number of vectors used a procedure is developed for increasing the accuracy by iteratively generating improved substructure trial state vectors

hori mological projective duality kuznetsov has conjectured that pfaffian varieties should admit noncommutative crepant resolutions which satisfy his homological projective duality we prove half the cases of this conjecture by interpreting and proving a duality of nonabelian gauged linear sigma models proposed by hori

exceptional collections for grassmannians of isotropic lines we construct a full exceptional collection of vector bundles in the derived categories of coherent sheaves on the grassmannian of isotropic two dimensional subspaces in a symplectic vector space of dimension 2n and in an orthogonal vector space of dimension 2n 1 for all n

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

a least squares approach to blind channel identification conventional blind channel identification algorithms are based on channel outputs and knowledge of the probabilistic model of channel input in some practical applications however the input statistical model may not be known or there may not be sufficient data to obtain accurate enough estimates of certain statistics in this paper we consider the system input to be an unknown deterministic signal and study the problem of blind identification of multichannel fir systems without requiring the knowledge of the input statistical model a new blind identification algorithm based solely on the system outputs is proposed necessary and sufficient identifiability conditions in terms of the multichannel systems and the deterministic input signal are also presented

a procedure for improving discrete substructure representation in dynamic synthesis n important problem in the dynamic analysis for flexible structures is that of determining the natural frequencies and associated natural modes of vibration particularly the lower ones complex structures are often represented by mathematical models such as finite element models possessing a very large number of degrees of freedom where the number can reach into the tens of thousands because of the large number of degrees of freedom a direct iterative method for obtaining a partial eigensolution know as subspace iteration was developed the subspace iteration method has a long history an extensive bibliography is given in ref 1 and the current status of the method is discussed in refs 2 4 in the context of structural dynamics even the subspace iteration method however can be overwhelmed by the large number of degrees of freedom in the mathematical model so that a method for prior reduction of the number of degrees of freedom is desirable complex structures are often modeled by breaking the structure into a number of simpler components or substructures the substructure models are then coupled together to form the whole structure model the technique is known as substructure synthesis and its origin can be found in refs 5 and 6 the idea of refs 5 and 6 is to represent the motion of each substructure by a set of substructure normal modes obtained by solving an eigenvalue problem for each substructure then each substructure is represented in the synthesis process by a reduced number of lower substructure modes the synthesis leads to an eigenvalue problem for the assembled structure of a substantially smaller order than that of the original formulation the price paid in reducing the order of the eigenvalue problem is that its solution is only an approximation of the actual eigensolution of the original structure

on the substructure synthesis method substructure synthesis is a model reduction method whereby a complex structure is regarded as an assemblage of substructures the motion of each of the substructures is represented by a series of admissible functions vectors and the substructures are made to act as a single structure by imposing certain geometric compatibility conditions at the boundary between any two adjacent substructures because the series of admissible functions vectors represents the motion of the substructures only approximately and because the geometric compatibility conditions are only approximations of the true conditions the computed eigensolution is only an approximation of the actual one convergence of computed eigenvalues to actual eigenvalues requires two limiting processes one in which the number of admissible functions vectors is increased and the other in which the number of geometric compatibility conditions is increased

an efficient general approach to modal analysis of frame resonators with applications to support loss in microelectromechanical systems abstract the design of high q resonators such as xylophone bar resonators xbrs capable of being fabricated using micro electro mechanical systems mems processes is of considerable interest in light of the widespread and rapidly growing use of systems dependent on their availability and performance this paper is concerned with vibration analysis and q optimisation of an xbr with the method extending directly to other planar frames and straightforwardly to more complex structures the rayleigh ritz method is discussed in some detail first treating the discrete case followed by developing and applying a kinematical procedure to an l frame structure attention is given to geometric interpretation of the rayleigh ritz procedure and to developing an intuitive understanding the method before turning to the xbr case having developed an approximation for system dynamics the results are used in conjunction with an analytical model of elastic wave propagation in the substrate to obtain an estimate for the support q factor natural frequencies mode shapes and support q values are presented and compared to finite element models of the same problem with excellent agreement observed at substantially lower computational cost for the first time in the literature the geometric impedance tuning principle underlying the xbr design is validated and quantified including sensitivity to manufacturing error

reference motion in deformable bodies under rigid body motion and vibration part i theory abstract this paper examines the motions of reference systems linked to deformable bodies under simultaneously vibration and large translations and rotations these motions depend on the particular type of linkage between the moving reference system and the deformable body which is defined by the so called reference conditions when using the rayleigh ritz method the reference conditions also dictate the boundary conditions to be fulfilled by the shape functions used to describe the body s elasticity this paper analyses three different types of reference conditions namely free linkage rigid linkage and two point linkage it is shown that moving reference frames only evolve at a constant velocity in the absence of external forces when the free linkage is used the reference velocities for systems with a free linkage are designated rigid body equivalent velocities for the deformable body here such velocities can also be calculated under other types of reference conditions and are usually functions of the elastic and reference co ordinates and also of their derivatives rigid body equivalent velocities are useful for purposes such as estimating the trajectory of deformable bodies moving freely in space without the need to examine the deformations they undergo also their calculation is required with a view to determining the kinematic restitution coefficient for deformable body collisions which is dealt within part ii of this series

a novel blind deconvolution scheme for image restoration using recursive filtering we present a novel blind deconvolution technique for the restoration of linearly degraded images without explicit knowledge of either the original image or the point spread function the technique applies to situations in which the scene consists of a finite support object against a uniformly black grey or white background this occurs in certain types of astronomical imaging medical imaging and one dimensional 1 d gamma ray spectra processing among others the only information required are the nonnegativity of the true image and the support size of the original object the restoration procedure involves recursive filtering of the blurred image to minimize a convex cost function we prove convexity of the cost function establish sufficient conditions to guarantee a unique solution and examine the performance of the technique in the presence of noise the new approach is experimentally shown to be more reliable and to have faster convergence than existing nonparametric finite support blind deconvolution methods for situations in which the exact object support is unknown we propose a novel support finding algorithm

a reduction method for nonlinear structural dynamic analysis abstract a computational algorithm for predicting the nonlinear dynamic response of a structure is presented the nonlinear system of ordinary differential equations resulting from the finite element discretization is highly reduced by means of a rayleigh ritz analysis the basis vectors are chosen to be the current tangent eigenmodes together with some modal derivatives that indicate the way in which the spectrum is changing only a few basis updatings are required during the whole time integration the truncation error introduced at every change of basis is pointed out as the cause for a divergence type behaviour and some means for eliminating it are discussed results for examples involving large displacements are shown and compared to the results obtained by integrating the complete system of equations

another look at admissible functions abstract problems associated with using global admissible functions in boundary value problems are discussed it is shown that if care is not taken it is possible to construct sets of trial functions that yield inaccurate results which take too long to converge the concept of complementary boundary conditions is introduced and their existence is established complementary boundary conditions indicate that the solution to the boundary value problem cannot take certain values at the boundaries it is shown that trial functions that yield incorrect or very slowly converging results are those that violate the complementary boundary conditions a revision for the definition of admissible and comparison functions is proposed that takes the complementary boundary conditions into consideration

on the inclusion principle for the hierarchical finite element method the inclusion principle provides a qualitative characterization of the eigenvalues of a matrix the principle has been shown to apply to systems described by a single hermitian matrix the most important of which being the real symmetric matrix self adjoint distributed systems when discretized by either the classical rayleigh ritz method or by the finite element method lead to algebraic eigenvalue problems described in terms of two real symmetric matrices the algebraic eigenvalues problem derived by the classical rayleigh ritz method possesses the embedding feature required by the inclusion principle but that derived by the finite element method in general does not this paper demonstrates that the inclusion principle can be extended to discretized systems derived by the hierarchical finite element method

matrix factorizations for nonaffine lg models we propose a natural definition of a category of matrix factorizations for nonaffine landau ginzburg models for any lg model we construct a fully faithful functor from the category of matrix factorizations defined in this way to the triangulated category of singularities of the corresponding fiber we also show that this functor is an equivalence if the total space of the lg model is smooth

convergence of the classical rayleigh ritz method and the finite element method it is demonstrated in this paper that convergence of the classical rayleigh ritz method can be vastly improved by introducing a new class of admissible functions called quasi comparison functions

substructure synthesis method for frequency response of viscoelastic structures the method of substructure synthesis previously applicable to undamped and viscously damped systems has been extended to systems with viscoelastic damping in hereditary integral form differential operator form and steady state corm based on a variational principle for symmetric systems the corresponding substructure synthesis method is formulated in the frequency domain each substructure is represented by a set of admissible trial vectors in the rayleigh ritz method eigenvectors of the corresponding undamped substructure and ritz vectors obtained by spatial discretization of admissible functions are recommended as trial vectors the traditional state space formulation is avoided by the proposed substructure synthesis method so that the approach is independent of the form of viscoelastic models the effectiveness of the proposed method in terms of reducing the size of final equations is illustrated through numerical examples

noncausal nonminimum phase arma modeling of non gaussian processes a method is presented for the estimation of the parameters of a noncausal nonminimum phase arma model for non gaussian random processes using certain higher order cepstra slices the fourier phases of two intermediate sequences h sub min n and h sub max n can be computed where h sub min n is composed of the minimum phase parts of the ar and ma models and h sub max n of the corresponding maximum phase parts under the condition that there are no zero pole cancellations in the arma model these two sequences can be estimated from their phases only and lead to the reconstruction of the ar and ma parameters within a scalar and a time shift the ar and ma orders do not have to be estimated separately but they are by product of the parameter estimation procedure through simulations it is shown that unlike existing methods the estimation procedure is fairly robust if a small order mismatch occurs since the robustness of the method in the presence of additive noise depends on the accuracy of the estimated phases of h sub min n and h sub max n the phase errors due to finite length data are studied and their statistics are derived

blind convolution using signal reconstruction from partial higher order cepstral information a blind deconvolution scheme for the reconstruction of a signal that propagates in the presence of reverberation and additive noise is presented the reconstruction employs data collected by two receivers placed well apart from each other each received sequence consists of the convolution of the transmitted signal with a channel applying the bicepstrum iterative reconstruction algorithm on the differences of the cepstra coefficients of the two received sequences the cepstra coefficients of the transmission channels can be computed and used for the reconstruction of the transmitted signal the deconvolution can be performed even if the data sequences are corrupted by additive noise the computation of the cepstra coefficients is based on the cross bispectrum if the noise processes present in the observation sequences are zero mean and uncorrelated while the bicepstrum of each observation is used if the noise processes are zero mean correlated with a symmetric probability density function