on the order of approximation in approximative triadic decompositions of tensors abstract based on alder s 1984 result on the equivalence of algebraic and topological border rank of tensors over algebraically closed ground fields we give an upper bound for the order of approximation in approximative triadic decompositions we also treat the analogous question for real closed fields in particular we carry over alder s result to the case of real closed fields

estimation of reciprocal residual flexibility from experimental modal data a technique is presented for estimating the residual flexibility between nonexcited structural degrees of freedom from experimental structural vibration data using this method one can include the residual flexibility estimated from modal measurements in the computation of measured flexibility for experiments with incomplete reciprocity i e when the response and excitation measurement sensors are not fully collocated the method can also be used to estimate the unknown entries in the residual flexibility matrix for experimental component mode synthesis when excitations are not provided at all interface degrees of freedom a general solution is presented that contains an unknown positive semidefinite contribution the general solution satisfies modal orthogonality in the limit that all of the structural degrees of freedom are instrumented and when the positive semidefinite contribution lies in a nullspace defined by the stiffness matrix and the modal flexibility with a limited number of measurements modal orthogonality is shown to be satisfied to the extent that the measured modes are preserved by static condensation a rank deficient solution is presented that allows the residual to be used in the computation of the flexibility matrix without further modeling assumptions numerical and experimental results that demonstrate the application of the method to both flexibility matrix convergence and experimental component mode synthesis are presented

fast matrix multiplication without apa algorithms abstract the method of trilinear aggregating with implicit canceling for the design of fast matrix multiplication mm algorithms is revised and is formally presented with the use of generating tables and of linear transformations of the problem of mm it is shown how to derive the exponent of mm below 2 67 even without the use of approximation algorithms

a new parameterization for waveform inversion in acoustic orthorhombic media abstractorthorhombic anisotropic model inversion is extra challenging because of the multiple parameter nature of the inversion problem the high number of parameters required to describe the medium exerts considerable trade off and additional nonlinearity to a full waveform inversion fwi application choosing a suitable set of parameters to describe the model and designing an effective inversion strategy can help in mitigating this problem using the born approximation which is the central ingredient of the fwi update process we have derived radiation patterns for the different acoustic orthorhombic parameterizations analyzing the angular dependence of scattering radiation patterns of the parameters of different parameterizations starting with the often used thomsen tsvankin parameterization we have assessed the potential trade off between the parameters and the resolution in describing the data and inverting for the parameters the analysis led us to introduce new parameters ed d and d whic

detecting damage in beams through digital differentiator filters and continuous wavelet transforms several papers that have recently appeared in the literature have shown the potential offered by certain mathematical tools wavelets for detecting damage in systems such as transversally vibrating beams however although the applications shown by different authors suggest that the tools show promise the literature lacks a clear and concise collocation of the wavelets with respect to these previous methods that show similar if not identical in certain circumstances performances in this paper the continuous wavelet transforms cwts are discussed and compared from a theoretical and numerical point of view with those methods known as differentiator operators such differentiator operators adopted as filters are also able similarly to the cwts to reduce unwanted high frequency noise therefore literature concerning differentiator filters in the digital signal processing area is investigated and several digital filters known and modified are analyzed and compared with the cwts in the presence of gaussian noise the theoretical aspects are discussed in both the non transformed and fourier transformed domain this study results in an attempt to provide an elucidation on the effectiveness and the need to use the considered methods differentiator filters and or cwts for detecting damage in transversally vibrating beams

inversion of seismic reflection data in the acoustic approximation the nonlinear inverse problem for seismic reflection data is solved in the acoustic approximation the method is based on the generalized least squares criterion and it can handle errors in the data set and a priori information on the model multiply reflected energy is naturally taken into account as well as refracted energy or surface waves the inverse problem can be solved using an iterative algorithm which gives at each iteration updated values of bulk modulus density and time source function each step of the iterative algorithm essentially consists of a forward propagation of the actual sources in the current model and a forward propagation backward in time of the data residuals the correlation at each point of the space of the two fields thus obtained yields the corrections of the bulk modulus and density models this shows in particular that the general solution of the inverse problem can be attained by methods strongly related to the methods of migration of unstacked data and commerc

eigenfilter design of higher order digital differentiators an effective approach is proposed for designing higher order differentiators by the eigenfilter method by minimizing a quadratic measure of the error in the frequency band an eigenvector of an appropriate matrix is computed to get the filter coefficients this method is not only simple and fast but also optimal in the least squares sense comparison to the mcclellan parks algorithm for minimax equiripple filters shows that both are optimal in the sense of different minimum norms of the error function but much better performance is obtained with the proposed approach in most of the frequency band except in the narrowband region near the cutoff edge

optimized damage detection of steel plates from noisy impact test summary model based non destructive evaluation proceeds measuring the response after an excitation on an accessible area of the structure the basis for processing this information has been established in recent years as an iterative scheme that minimizes the discrepancy between this experimental measurement and sequence of measurement trials predicted by a numerical model the unknown damage that minimizes this discrepancy by means of a cost functional is to be found the damage location and size is quantified and sought by means of a well conditioned parametrization the design of the magnitude to measure its filtering for reducing noise effects and calibration as well as the design of the cost functional and parametrization determines the robustness of the search to combat noise and other uncertainty factors these are key open issues to improve the sensitivity and identifiability during the information processing among them a filter for the cost functional is proposed in this study for maximal sensitivity to the damage detection of steel plate under the impact loading this filter is designed by means of a wavelet decomposition together with a selection of the measuring points and the optimization criterion is built on an estimate of the probability of detection using genetic algorithms numerical examples show that the use of the optimal filter allows to find damage of a magnitude several times smaller copyright 2006 john wiley sons ltd

on the asymptotic complexity of rectangular matrix multiplication abstract the numher of essential multiplications required to multiply matrices of size n x n and n x n is studied as a function f s 1 bounds to f x sharper than trivial ones are presented and the asymptotic behawour of f s 1 is studied an analogous investigation is performed for the problem of multiplying matrices of size n x n and n x n 1 introduction and preliminaries the complexity of square n x n matrix multiplication has been investigated by several authors l lo a lower bound to the number of operations is n and the best known upper bound is o n2 16h 8 some results on rectangular matrix multiplication have been obtained by brockett and dobkin a who have shown the upper bound n o n to the non scalar complexity of n x n by n x log n matrix multiplication recently coppersmith s found the upper bound o n log n for the n x n by n x n matrix multipli cation prnblem with n s 2 log 2 5 log 5 0 1722

matrix multiplication a little faster strassen s algorithm 1969 was the first sub cubic matrix multiplication algorithm winograd 1971 improved the leading coefficient of its complexity from 6 to 7 there have been many subsequent asymptotic improvements unfortunately most of these have the disadvantage of very large often gigantic hidden constants consequently strassen winograd s o nlog27 algorithm often outperforms other fast matrix multiplication algorithms for all feasible matrix dimensions the leading coefficient of strassen winograd s algorithm has been generally believed to be optimal for matrix multiplication algorithms with a 2 2 base case due to the lower bounds by probert 1976 and bshouty 1995 surprisingly we obtain a faster matrix multiplication algorithm with the same base case size and asymptotic complexity as strassen winograd s algorithm but with the leading coefficient reduced from 6 to 5 to this end we extend bodrato s 2010 method for matrix squaring and transform matrices to an alternative basis we also prove a generalization of probert s and bshouty s lower bounds that holds under change of basis showing that for matrix multiplication algorithms with a 2 2 base case the leading coefficient of our algorithm cannot be further reduced and is therefore optimal we apply our method to other fast matrix multiplication algorithms improving their arithmetic and communication costs by significant constant factors

damage detection using a modified laplacian operator on mode shape data abstract localized damage to a structure affects its dynamic properties and much work has been undertaken investigating the variation of natural frequencies with damage however use of mode shape data has seen much less effort this paper develops and presents a technique for identifying the location of structural damage in a beam the procedure operates solely on the mode shape from the damaged structure and does not requirea prioriknowledge of the undamaged structure the procedure is developed using a one dimensional finite element model of a beam and demonstrated by experiment when damage is severe a localized thickness reduction of more than 10 applying a finite difference approximation of laplace s differential operator to the mode shape successfully identifies the location of the damage however when damage is less severe further processing of the laplacian output is required before the location can be determined this post processing enables the location of thickness reductions of less than 0 5 to be identified the procedure is best suited to the mode shape obtained from the fundamental natural frequency the mode shapes from higher natural frequencies can be used to verify the location of damage but they are not as sensitive as the lower modes

analytic closed form matrix for designing higher order digital differentiators using eigen approach the eigenfilter method has been proposed for designing higher order differentiators very effectively the design method is based on the computation of an eigenvector of an appropriate real symmetric and positive definite matrix the elements of this matrix are usually evaluated by very time consuming numerical integration we present simple analytic closed form formulas to compute these matrix elements very efficiently hence the eigenfilter approach for differentiators becomes much easier and more accurate than before and design time is reduced greatly for designing long filters

an acoustic wave equation for anisotropic media a wave equation derived using the acoustic medium assumption for p waves in transversely isotropic ti media with a vertical symmetry axis vti media yields a good kinematic approximation to the familiar elastic wave equation for vti media the wavefield solutions obtained using this vti acoustic wave equation are free of shear waves which significantly reduces the computation time compared to the elastic wavefield solutions for exploding reflector type applications from this vti acoustic wave equation the eikonal and transport equations that describe the ray theoretical aspects of wave propagation in a ti medium are derived these equations based on the acoustic assumption shear wave velocity 0 are much simpler than their elastic counterparts yet they yield an accurate description of traveltimes and geometrical amplitudes numerical examples prove the usefulness of this acoustic equation in simulating the kinematic aspects of wave propagation in complex ti models

improved bound for complexity of matrix multiplication in 1968 strassen 16 described a method of multiplying two 2 2 matrices using only seven multiplications by applying it recursively it was shown that two n n matrices could be multiplied using o n operations in all where log2 7 2 81 this discovery led to a period of activity devoted to the improvement of this bound one can define an exponent of complexity which is in effect the smallest number such that two n n matrices can be multiplied using o n operations using an method of the type described by strassen a precise definition is given in 2 then strassen s result says that log2 7 so it is natural to wish to determine the true value of in the decade or so after 1978 several successive reductions in the upper bound for were achieved 2 3 6 8 10 12 14 17 leading to the bound 2 375477 obtained by coppersmith and winograd 7 it is an open question whether 2 we present a small improvement of the coppersmith winograd bound namely 2 3736897 which was first obtained in stothers 15 the proof uses an extension of the ideas of 7 and relies heavily on a combinatorial construction from 7 which depends on probabilistic arguments and a theorem of salem and spencer on sets of integers containing no three terms in arithmetical progression we have tried to organize the proof so that it is reasonably concise but also self contained to make it more accessible in the belief that at least parts of the argument may be of wider interest outside the algebraic complexity community to this end we derive the results we need from algebraic complexity theory in 2 which also contains general background material in 3 we present the essence of the combinatorial construction as a lemma which we subsequently apply several times we first apply it in 4 to recover the coppersmith winograd bound although our presentation is rather different the proof is essentially the same as that of 7 except for the proof of lemma 4 1 for which we give a somewhat simpler argument using 4 as preparation and motivation we obtain our new bound in 5 the argument is similar but more complicated and technical

graph expansion and communication costs of fast matrix multiplication the communication cost of algorithms also known as i o complexity is shown to be closely related to the expansion properties of the corresponding computation graphs we demonstrate this on strassen s and other fast matrix multiplication algorithms and obtain the first lower bounds on their communication costs in the sequential case where the processor has a fast memory of size m too small to store three n by n matrices the lower bound on the number of words moved between fast and slow memory is for a large class of matrix multiplication algorithms n m 0 m where 0 is the exponent in the arithmetic count e g 0 lg 7 for strassen and 0 3 for conventional matrix multiplication with p parallel processors each with fast memory of size m the lower bound is asymptotically lower by a factor of p these bounds are attainable both for sequential and for parallel algorithms and hence optimal

waveform inversion including well constraints anisotropy and attenuation the goal of full waveform inversion wfi is to derive high fidelity earth models for seismic imaging from the full waveforms of the acquired seismic data the attractiveness of wfi lies mainly in its limited number of approximations at least in a theoretical sense in contrast to other model determination techniques such as semblance or ray based tomography despite this various methodologies must be utilized to make the technique viable with today s computing technology and restrictions of seismic acquisition these are collectively referred to as waveform inversion strategies and in this article we discuss mainly regularization and preconditioning strategies as the wavefields need to be accurately modeled to represent the kinematics of all the waves during wfi iterations the inclusion of anisotropy often helps to improve the wfi results in the first section of this article we introduce forward modeling and its adjoint based on acoustic wave equations in vertical transversely isotropic vti med

damage detection using the lipschitz exponent estimated by the wavelet transform applications to vibration modes of a beam damage detection by the wavelet transform of the fundamental vibration mode receives much attention recently many investigations report successful applications of the wavelet transform in damage detection but most of them appear to lack theoretical justifications the objective of this contribution is to show the effectiveness of the wavelet transform by means of its capability to estimate the lipschitz exponent it is also addressed that the magnitude of the lipschitz exponent can be used as a useful indicator of the damage extent as a specific example damaged beams are investigated both numerically and experimentally the continuous wavelet transform cwt by a mexican hat wavelet having two vanishing moments is utilized for the estimation of the lipschitz exponent the analysis by the cwt also gives a guideline to choose appropriate discrete wavelet transforms

a new parameter set for anisotropic multiparameter full waveform inversion and application to a north sea data set abstractparameterization lies at the center of anisotropic full waveform inversion fwi with multiparameter updates this is because fwi aims to update the long and short wavelengths of the perturbations thus it is important that the parameterization accommodates this recently there has been an intensive effort to determine the optimal parameterization centering the fundamental discussion mainly on the analysis of radiation patterns for each one of these parameterizations and aiming to determine which is best suited for multiparameter inversion we have developed a new parameterization in the scope of fwi based on the concept of kinematically equivalent media as originally proposed in other areas of seismic data analysis our analysis is also based on radiation patterns as well as the relation between the perturbation of this set of parameters and perturbation in traveltime the radiation pattern reveals that this parameterization combines some of the characteristics of parameterizations with on

a numerical study of the eigenparameters of a damaged cantilever abstract when a structure is subjected to damage its dynamic response changes characterized by shifts in the eigenvalues and modifications of the eigenvectors considerable effort has been put into investigating the relationship between the damage location the damage size and the corresponding changes in the eigenparameters in most cases emphasis has been on using the shift in eigenvalues as a means of determining the damage location and the information derived from the change in eigenvectors has largely remained obscure in this paper a systematic study is presented of the relationship between damage location damage size and the changes in the eigenvalues and eigenvectors of a cantilever when subjected to damage a finite element model of a uniform cross sectioned cantilever was chosen to provide data for analysis the changes in the eigenvalues and eigenvectors are shown to follow a definite trend in relation to the location and extent of damage

the techniques of trilinear aggregating and the recent progress in the asymptotic acceleration of matrix operations abstract the recent progress in the asymptotic acceleration of matrix multiplication and of related matrix operations is surveyed the techniques of trilinear aggregating and their applications to the above problems and to the disproval of the direct sum conjecture over some rings of constants are presented in some detail

waveform inversion using a logarithmic wavefield although waveform inversion has been studied extensively since its beginning 20 years ago applications to seismic field data have been limited and most of those applications have been for global seismology or engineering seismology scale problems not for exploration scale data as an alternative to classical waveform inversion we propose the use of a new objective function constructed by taking the logarithm of wavefields allowing consideration of three types of objective function namely amplitude only phase only or both in our waveform inversion we estimate the source signature as well as the velocity structure by including functions of amplitudes and phases of the source signature in the objective function we compute the steepest descent directions by using a matrix formalism derived from a frequency domain finite element finite difference modeling technique our numerical algorithms are similar to those of reverse time migration and waveform inversion based on the adjoint state of the wave equation in order to demonstrate the practical applicability of our algorithm we use a synthetic data set from the marmousi model and seismic data collected from the korean continental shelf for noisefree synthetic data the velocity structure produced by our inversion algorithm is closer to the true velocity structure than that obtained with conventional waveform inversion when random noise is added the inverted velocity model is also close to the true marmousi model but when frequencies below 5 hz are removed from the data the velocity structure is not as good as those for the noise free and noisy data for field data we compare the time domain synthetic seismograms generated for the velocity model inverted by our algorithm with real seismograms and find that the results show that our inversion algorithm reveals short period features of the subsurface although we use wrapped phases in our examples we still obtain reasonable results we expect that if we were to use correctly unwrapped phases in the inversion algorithm we would obtain better results

modeling of a constant q methodology and algorithm for an efficient and optimally inexpensive viscoelastic technique linear anelastic phenomena in wave propagation problems can be well modeled through a viscoelastic mechanical model consisting of standard linear solids in this paper we present a method for modeling of constant q as a function of frequency based on an explicit closed formula for calculation of the parameter fields several standard linear solids connected in parallel can be tuned through a single parameter to yield an excellent constant q approximation the proposed method enables substantial savings in computations and memory requirements experiments show that the new method also yields higher accuracy in the modeling of q than e g the pade approximant method

some properties of disjoint sums of tensors related to matrix multiplication let t be a disjoint sum of tensors associated to matrix multiplication the rank of the tensorial powers of t is bounded by an expression involving the elements of t and an exponent for matrix multiplication this relation leads to a trascendental equation defining a new exponent for matrix multiplication

how can we speed up matrix multiplication due to the new algebraic methods of algorithm design recently it became possible to perform multiplication and inversion of n times n matrices using o n 2 496 rather than o n 3 arithmetical operations consequently algorithms for several other computational problems of linear algebra and combinatorics have been accelerated the major ideas and techniques that have led to that progress are surveyed

a new method to extract modal parameters using output only responses this work proposes a new output only modal analysis method to extract mode shapes and natural frequencies of a structure the proposed method is based on an approach with a single degree of freedom in the time domain for a set of given mode isolated signals the un damped mode shapes are extracted utilizing the singular value decomposition of the output energy correlation matrix with respect to sensor locations the natural frequencies are extracted from a noise free signal that is projected on the estimated modal basis the proposed method is particularly efficient when a high resolution of mode shape is essential the accuracy of the method is numerically verified using a set of time histories that are simulated using a finite element method the feasibility and practicality of the method are verified using experimental data collected at the newly constructed king storm water bridge in california united states

damage estimation on beam like structures using the multi resolution analysis abstract this work proposes a vibration based damage evaluation method that can detect locate and size damage utilizing only a few of the lower mode shapes the proposed method is particularly advantageous for beam like structures with uncertain applied axial load mass density and foundation stiffness based on a small damage assumption a linear relationship between damaged and undamaged curvatures is revealed in the context of elasticity it turns out that the resulting damage index equation inherently suffers from singularities near inflection nodes the transformation of the problem into the multi resolution wavelet domain provides a set of coupled linear equations with the aid of the singular value decomposition technique the solution to the damage index equation is achieved in the wavelet space next the desired physical solution to the damage index equation is reconstructed from the one in the wavelet space the performance of the proposed method is compared with two existing damage detection methods using a set of numerical simulations the proposed method attempts to resolve the mode selection problem the singularity problem the axial force problem and the absolute severity estimation problem all of which remained unsolved by earlier attempts

crack identification in plates using wavelet analysis in this paper a method for crack identification in plates based on wavelet analysis is presented the case of an all over part through crack parallel to one edge of the plate is considered the vibration modes of the plate are analyzed using the continuous wavelet transform and both the location and depth of the crack are estimated the position of the crack is determined by the sudden change in the spatial variation of the transformed displacement response to estimate the depth of the crack an intensity factor is defined which relates the depth of the crack to the coefficients of the wavelet transform an intensity factor law is established which allows accurate prediction of crack depth the viability of the proposed approach is demonstrated using simulation examples in view of the obtained results the advantages and limitations of the proposed approach as well as suggestions for future work are presented and discussed

trilinear aggregating with implicit canceling for a new acceleration of matrix multiplication abstract a new improvement of author s techniques of trilinear aggregating uniting and canceling is presented and applied to accelerate multiplication of matrices of moderate sizes this results in the exact computing algorithms for n n matrix multiplication in only n 2 1 75 n 2 n 2 4 n 3 3 essential multiplication steps for arbitrary even n also the new techniques allow us to simplify the design of the fastest known apa algorithms for matrix multiplication

the bit operation complexity of matrix multiplication and of all pair shortest path problem abstract an n n matrix product can be evaluated with precision e 0 in o n s log m e log log m e log log log m e bit operations 0 arbitrary m the maximum absolute value of the entries of given matrices o n s the arithmetic complexity of n n matrix multiplication s h can be solved in o n s h bit operations

refinements of damage detection methods based on wavelet analysis of dynamical shapes this manuscript aims at illustrating significant refinements concerning the use of wavelets when these latter are used in the guise of continuous wavelet transforms cwt for identifying damage on transversally vibrating structural components e g beams plates and shells the refinements regard the presentation of wavelet algorithms which are aimed at significantly reducing those border distortions normally arising during a wavelet damage detection procedure the main advantage of the algorithms is that they are self contained namely i the wavelet transforms do not undergo any own variation and their application follows the convolution laws established in the past ii it is not necessary to design a specific boundary wavelet iii no significant analytical treatment neither of the wavelets nor of the signal is required and finally iv the algorithms can be adapted to different boundary conditions and different physical situations besides all the specified advantages the wavelet damage detection procedure is still carried out by excluding historical data the effectiveness of the algorithms is shown through numerical and experimental examples these latter are illustrated along with reduced outliers of experimental estimation through a related consistent statistical procedure

damage identification for beams in noisy conditions based on teager energy operator wavelet transform modal curvature abstract modal curvatures have been widely used in the detection of structural damage attractive features of modal curvature include great sensitivity to damage and instant determination of damage location however an intrinsic deficiency in a modal curvature is its susceptibility to the measurement noise present in the displacement mode shape that produces the modal curvature likely obscuring the features of damage to address this deficiency the teager energy operator together with wavelet transform is tactically utilized to treat modal curvature producing a new modal curvature termed the teager energy operator wavelet transform modal curvature this new modal curvature features distinct capabilities of suppressing noise canceling global trends and intensifying the singular feature caused by damage for a measured mode shape involving noise these features maximize the sensitivity to damage and accuracy of damage localization the proposed modal curvature is demonstrated in several analytical cases of cracked pinned pinned clamped free and clamped clamped beams with emphasis on characterizing damage in noisy conditions and it is further validated by an experimental program using a scanning laser vibrometer to acquire mode shapes of a cracked aluminum beam the teager energy operator wavelet transform modal curvature essentially overcomes the deficiency of conventional modal curvature providing a new dynamic feature well suited for damage characterization in noisy environments the matlab code for implementing teager energy operator wavelet transform modal curvature can be provided by the corresponding author on request

least squares design of higher order nonrecursive differentiators a method is described that can be used to design non recursive linear phase higher order differentiators that can perform differentiation over any frequency range the method is based on formulating the absolute mean square error between the amplitude responses of the practical and ideal differentiator as a quadratic function the coefficients of the differentiators are obtained by solving a set of linear equations this method leads to a lower mean square error and is computationally more efficient than both the eigenfilter method and the method based on the remez exchange algorithm design of differentiators based on minimization of the relative mean square error is also carried out finally the method is extended to the design of frequency selective higher order differentiators

viscoelastic finite difference modeling real earth media disperse and attenuate propagating mechanical waves this anelastic behavior can be described well by a viscoelastic model we have developed a finite difference simulator to model wave propagation in viscoelastic media the finite difference method was chosen in favor of other methods for several reasons finite difference codes are more portable than for example pseudospectral codes moreover finite difference schemes provide a convenient environment in which to define complicated boundaries a staggered scheme of second order accuracy in time and fourth order accuracy in space appears to be optimally efficient because of intrinsic dispersion no fixed grid points per wavelength rule can be given instead we present tables which enable a choice of grid parameters for a given level of accuracy since the scheme models energy absorption natural and efficient absorbing boundaries may be implemented merely by changing the parameters near the grid boundary the viscoelastic scheme is

3d finite difference frequency domain modeling of visco acoustic wave propagation using a massively parallel direct solver a feasibility study we present a finite difference frequency domain method for 3d visco acoustic wave propagation modeling in the frequency domain the underlying numerical problem is the resolution of a large sparse system of linear equations whose right hand side term is the source this system is solved with a massively parallel direct solver we first present an optimal 3d finite difference stencil for frequency domain modeling the method is based on a parsimonious staggered grid method differential operators are discretized with second order accurate staggered grid stencils on different rotated coordinate systems to mitigate numerical anisotropy an antilumped mass strategy is implemented to minimize numerical dispersion the stencil incorporates 27 grid points and spans two grid intervals dispersion analysis shows that four grid points per wavelength provide accurate simulations in the 3d domain to assess the feasibility of the method for frequency domain full waveform inversion we computed simulations in the 3d seg eage overthrust model for frequencies 5 7 and 10 hz results confirm the huge memory requirement of the factorization several hundred figabytes but also the cpu efficiency of the resolution phase few seconds per shot heuristic scalability analysis suggests that the memory complexity of the factorization is o 35n 4 for a n 3 grid our method may provide a suitable tool to perform frequency domain full waveform inversion using a large distributed memory platform further investigation is still necessary to assess more quantitatively the respective merits and drawbacks of time and frequency domain modeling of wave propagation to perform 3d full waveform inversion

damage detection from changes in curvature mode shapes abstract a damage in a structure alters its dynamic characteristics the change is characterized by changes in the eigenparameters i e natural frequency damping values and the mode shapes associated with each natural frequency considerable effort has been spent in obtaining a relationship between the changes in eigenparameters the damage location and the damage size most of the emphasis has been on using the changes in the natural frequencies and the damping values to determine the location and the size of the damage in this paper a new parameter called curvature mode shape is investigated as a possible candidate for identifying and locating damage in a structure by using a cantilever and a simply supported analytical beam model it is shown here that the absolute changes in the curvature mode shapes are localized in the region of damage and hence can be used to detect damage in a structure the changes in the curvature mode shapes increase with increasing size of damage this information can be used to obtain the amount of damage in the structure finite element analysis was used to obtain the displacement mode shapes of the two models by using a central difference approximation curvature mode shapes were then calculated from the displacement mode shapes

a new damage detection approach for beam type structures based on the combination of continuous and discrete wavelet transforms in this work a new wavelet based damage detection approach has been proposed the method is based on the assumption that a damaged mode shape of a beam is approximately composed of an undamaged mode and other contributors such as measurement and local damage induced variations then a proper approximation function af to be used as undamaged mode can be extracted from the damaged one by the discrete wavelet transform dwt provided a suitable wavelet and a decomposition level dl are determined by this way a reliable damage index can be defined taking the difference of the continuous wavelet transform cwt coefficients of the damaged mode and those of the af it is demonstrated that the af which is well correlated with the numerical undamaged mode of beam can be obtained at the dl after which the approximation energy ratio ea drops significantly if a suitable wavelet having sufficient number of vanishing moments nvm is selected in order to test the method the first two numerically obtained modes of a damaged beam as well as the first two experimental modes of another damaged beam are employed although the physical properties and damage features of these two beams are quite different it is concluded that the afs which are derived from these modes by the proposed method can be conveniently used as baseline data for damage detection purpose