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 symmetry measure for damage detection with mode shapes abstract this paper introduces a feature for detecting damage or changes in structures the continuous symmetry measure which can quantify the amount of a particular rotational mirror or translational symmetry in a mode shape of a structure many structures in the built environment have geometries that are either symmetric or almost symmetric however damage typically occurs in a local manner causing asymmetric changes in the structure s geometry or material properties and alters its mode shapes the continuous symmetry measure can quantify these changes in symmetry as a novel indicator of damage for data based structural health monitoring approaches this paper describes the concept as a basis for detecting changes in mode shapes and detecting structural damage application of the method is demonstrated in various structures with different symmetrical properties a pipe cross section with a finite element model and experimental study the nasa 8 bay truss model and the simulated iasc asce structural health monitoring benchmark structure the applicability and limitations of the feature in applying it to structures of varying geometries is discussed

the geometry of mixing in time periodic chaotic flows i asymptotic directionality in physically realizable flows and global invariant properties abstract this paper demonstrates that the geometry and topology of material lines in 2d time periodic chaotic flows is controlled by a global geometric property referred to as asymptotic directionality this property implies the existence of local asymptotic orientations at each point within the chaotic region determined by the unstable eigendirections of the jacobian matrix of the n th iterative of the poincare map associated with the flow asymptotic directionality also determines the geometry of the invariant unstable manifolds which are everywhere tangent to the field of asymptotic eigendirections this fact is used to derive simple non perturbative methods for reconstructing the global invariant manifolds to any desired level of detail the geometric approach associated with the existence of a field of invariant unstable subspaces permits us to introduce the concept of a geometric global unstable manifold as an intrinsic property of a poincare map of the flow defined as a class of equivalence of integral manifolds belonging to the invariant unstable foliation the connection between the geometric global unstable manifold and the global unstable manifold of hyperbolic periodic points is also addressed since material lines evolved by a chaotic flow are asymptotically attracted to the geometric global unstable manifold of the poincare map in a sense that will be made clear in the article the reconstruction of unstable integral manifolds can be used to obtain a quantitative characterization of the topological and statistical properties of partially mixed structures two physically realizable systems are analyzed closed cavity flow and flow between eccentric cylinders asymptotic directionality provides evidence of a global self organizing structure characterizing chaotic flow which is analogous to that of anosov diffeomorphisms which turns out to be the basic prototype of mixing systems in this framework we show how partially mixed structures can be quantitatively characterized by a nonuniform stationary measure different from the ergodic measure associated with the dynamical system generated by the field of asymptotic unstable eigenvectors

fractal basin boundaries abstract basin boundaries for dynamical systems can be either smooth or fractal this paper investigates fractal basin boundaries one practical consequence of such boundaries is that they can lead to great difficulty in predicting to which attractor a system eventually goes the structure of fractal basin boundaries can be classified as being either locally connected or locally disconnected examples and discussion of both types of structures are given and it appears that fractal basin boundaries should be common in typical dynamical systems lyapunov numbers and the dimension for the measure generated by inverse orbits are also discussed

multi dimensioned intertwined basin boundaries basin structure of the kicked double rotor abstract using numerical computations on a map which describes the time evolution of a particular mechanical system in a four dimensional phase space the kicked double rotor we have found that the boundaries separating basins of attraction can have different properties in different regions and that these different regions can be intertwined on arbitrarily fine scale in particular for the double rotor map if one chooses a restricted region of the phase space and examines the basin boundary in that region then either one observes that the boundary is a smooth three dimensional surface or one observes that the boundary is fractal with dimension d 3 9 and which of these two possibilities applies depends on the particular phase space region chosen for examination furthermore for any region no matter how small for which d 3 9 one can choose subregions within it for which d 3 hence d 3 9 region and d 3 region are intertwined on arbitrarily fine scale other examples will also be presented and analyzed to show how this situation can arise these include one dimensional map cases a map of the plane and the lorenz equations in one of our one dimensional map cases the boundary will be fractal everywhere but the dimension can take on either of two different values both of which lie between 0 and 1 these examples lead us to conjecture that basin boundaries typically can have at most a finite number of possible dimension values more specifically let these values be denoted d 1 d 2 d n choose a volume region of phase space whose interior contains some part of the basin boundary and evaluate the dimension of the boundary in that region then our conjecture is that for all typical volume choices the evaluated dimension within the chosen volume will be one of the values d 1 d 2 d n for example in our double rotor map it appears that n 2 and d 1 3 0 and d 2 3 9

tracer dynamics in open hydrodynamical flows as chaotic scattering abstract methods coming from the theory of chaotic scattering are applied to the advection of passive particles in an open hydrodynamical flow in a region of parameters where a von karman vortex street is present with a time periodic velocity field behind a cylinder in a channel particles can temporarily be trapped in the wake they exhibit chaotic motion there due to the presence of a nonattracting chaotic set the experimentally well known concept of streaklines is interpreted as a structure visualising asymptotically the unstable manifold of the full chaotic set the evaluation of streaklines can also provide characteristic numbers of this invariant set e g topological entropy lyapunov exponent escape rate the time delay distributions are also evaluated we demonstrate these ideas with the aid of both computer simulations of the navier stokes equations and analytical model computations properties that could be measured in a laboratory experiment are discussed

crises sudden changes in chaotic attractors and transient chaos abstract the occurrence of sudden qualitative changes of chaotic dynamics as a parameter is varied is discussed and illustrated it is shown that such changes may result from the collision of an unstable periodic orbit and a coexisting chaotic attractor we call such collisions crises phenomena associated with crises include sudden changes in the size of chaotic attractors sudden appearances of chaotic attractors a possible route to chaos and sudden destructions of chaotic attractors and their basins this paper presents examples illustrating that crisis events are prevalent in many circumstances and systems and that just past a crisis certain characteristic statistical behavior whose type depends on the type of crisis occurs in particular the phenomenon of chaotic transients is investigated the examples discussed illustrate crises in progressively higher dimension and include the one dimensional quadratic map the two dimensional henon map systems of ordinary differential equations in three dimensions and a three dimensional map in the case of our study of the three dimensional map a new route to chaos is proposed which is possible only in invertible maps or flows of dimension at least three or four respectively based on the examples presented the following conjecture is proposed almost all sudden changes in the size of chaotic attractors and almost all sudden destruction or creations of chaotic attractors and their basins are due to crises

structural damage localization from modal strain energy change a method based on modal strain energy is presented for locating damage in a structure this method makes use of the change of modal strain energy in each structural element before and after the occurrence of damage some properties of this modal strain energy change are given to illustrate its sensitivity in locating the structural damage information required in the identification are the measured mode shapes and elemental stiffness matrix only without knowledge of the complete stiffness and mass matrices of the structure several damage cases in a simulated structure are studied in which the effect of random error in terms of measurement noise in the mode shapes and systematic error in terms of errors from incomplete measurements are considered this method is then applied to detect damage in a single bay two storey portal steel frame structure results illustrate that the msec is sensitive to damage and the proposed method is simple and robust in locating single or multiple damages in a structure

fundamental mode shape and its derivatives in structural damage localization abstract various techniques for structural damage detection involving modal parameters have widely been used over the past few decades this is because the modal parameters of a structure can easily be obtained from forced free or ambient vibration measurements in many of these techniques mode shape curvature has been used for localization of damage in this paper a mathematical basis is provided to show the correlation between a structural damage and a change in the fundamental mode shape and its derivatives this has been achieved by deriving the expression of a damaged mode shape utilizing a perturbation approach for a cantilever shear beam discretized into a large number of elements this approach demonstrates that the change in the fundamental mode shape due to any damage is an excellent indicator of damage localization as it is found to be discontinuous at the location of damage further the change in higher derivatives i e slope and curvature of the fundamental mode shape is shown to be sensitive enough in damage localization a numerical study involving a shear building and a steel moment resisting frame is conducted to show the effectiveness of the proposed approach in damage localization it has been found from this study that spline fitting of mode shapes in case of a limited number of degrees of freedom which is generally adopted for plotting mode shapes and their derivatives may lead to false detection of damage

wada dye boundaries in open hydrodynamical flows abstract dyes of different colors advected by two dimensional flows which are asymptotically simple can form a fractal boundary that coincides with a chaotic saddle s unstable manifold we show that such dye boundaries can have the wada property every boundary point of a given color on this fractal set is on the boundary of at least two other colors the condition for this is the nonempty intersection of the saddle s stable manifold with at least three differently colored domains in the asymptotic inflow region

certainty equivalents and information measures duality and extremal principles given a convex function ir ir the csiszar divergence csiszar 1978 is a function i ir n ir n ir

devil staircase behavior of dynamical invariants in chaotic scattering a crisis in chaotic scattering is characterized by the merging of two or more nonattracting chaotic saddles the fractal dimension of the resulting chaotic saddle increases through the crisis we present a rigorous analysis for the behavior of dynamical invariants associated with chaotic scattering by utilizing a representative model system that captures the essential dynamical features of crisis our analysis indicates that the fractal dimension and other dynamical invariants are a devil staircase type of function of the system parameter our results can also provide insight for similar devil staircase behaviors observed in the parametric evolution of chaotic saddles of general dissipative dynamical systems and in communicating with chaos 2000 elsevier science b v all rights reserved

fractal boundaries in open hydrodynamical flows signatures of chaotic saddles we introduce the concept of fractal boundaries in open hydrodynamical flows based on two gedanken experiments carried out with passive tracer particles colored differently it is shown that the signature for the presence of a chaotic saddle in the advection dynamics is a fractal boundary between regions of different colors the fractal parts of the boundaries found in the two experiments contain either the stable or the unstable manifold of this chaotic set we point out that these boundaries coincide with streak lines passing through appropriately chosen points as an illustrative numerical experiment we consider a model of the von k arm an vortex street a time periodic two dimensional flow of a viscous fluid around a cylinder

damage localization in plate structures from uniform load surface curvature although a large number of methods exist for detecting damage in a structure using measured modal parameters many of them require a correlated finite element model or at least modal data of the structure for the intact state as baseline for one dimensional beam like structures curvature techniques e g mode shape curvature and flexibility curvature have been applied to localize damage in this paper a damage localization method based on changes in uniform load surface uls curvature is developed for two dimensional plate structures a new approach to compute the uls curvature is proposed based on the chebyshev polynomial approximation instead of the central difference method the proposed method requires only the frequencies and mode shapes of the first few modes of the plate before and after damage or only the eigenpairs for the damaged state if a gapped smoothing technique is applied numerical simulations considering different supported conditions measurement noise mode truncation and sensor sparsity are studied to evaluate the effectiveness of the proposed method it is found that the uls curvature is sensitive to the presence of local damages even with truncated incomplete and noisy measurements

single beam analysis of damaged beams verified using a strain energy based damage measure analytical expression of a new damage measure which relates the strain energy to the damage location and magnitude is presented in this paper the strain energy expression is calculated using modes and natural frequencies of damaged beams that are derived based on single beam analysis considering both decrease in mass and stiffness decrease in mass and stiffness are a fallout of geometric discontinuity and no assumptions regarding the physical behavior of damage are made the method is applicable to beams with notch like non propagating cracks with arbitrary boundary conditions the analytical expressions derived for mode shapes curvature shapes natural frequencies and an improved strain energy based damage measure are verified using experiments the improvement in the damage measure is that it is not assumed that the bending stiffness of the damaged beam is constant and equal to that of undamaged beam when calculating the strain energy of the entire beam it is also not assumed that the bending stiffness of the element in which the damage is located is constant

convex solutions of a functional equation arising in information theory abstract given a convex function f defined for positive real variables the so called csiszar f divergence is a function i f defined for two n dimensional probability vectors p p 1 p n and q q 1 q n as i f p q i 1 n q i f p i q i for this generalized measure of entropy to have distance like properties especially symmetry it is necessary for f to satisfy the following functional equation f x x f 1 x for all x 0 in the present paper we determine all the convex solutions of this functional equation by proposing a way of generating all of them in doing so existing usual f divergences are recovered and new ones are proposed

farkas type results for inequality systems with composed convex functions via conjugate duality we present some farkas type results for inequality systems involving finitely many functions therefore we use a conjugate duality approach applied to an optimization problem with a composed convex objective function and convex inequality constraints some recently obtained results are rediscovered as special cases of our main result

a procedure for finding numerical trajectories on chaotic saddles abstract examples are common in dynamical systems in which there are regions containing chaotic sets that are not attractors if almost every trajectory eventually leaves some region but the region contains a chaotic set then typical trajectories will behave chaotically for a while and then will leave the region and so we will observe chaotic transients the main objective that will be addressed is the dynamic restraint problem given a region that contains a chaotic set but does not contain an attractor find a chaotic trajectory numerically that remains in the regionfor an arbituarily long period of time systems with horseshoes have such regions as do systems with fractal basin boundaries as does the henon map for suitably chosen parameters we present a numerical technique for finding trajectories which will stay in such chaotic sets for arbitrarily long periods of time and it leads to a saddle straddle trajectory the method is called the pim triple procedure since it is based on so called pim triples a pim proper interior maximum triple is three points a c b in a straight line segment such that the interior point c i e c is between a and b has the maximum escape time that is its escape time from the region is greater than the escape time of both a and b proper means the segment from a to b is smaller than a previously obtained segment we show rigorously that the pim triple procedure works in ideal situations we find it works well even in less than ideal cases this procedure can also be used for the computation of lyapunov exponents furthermore the accessible pim triple procedure a refined pim triple procedure for finding accessible trajectories on the chaotic saddle will also be discussed

closed form solutions of a multi cracked circular arch under static loads abstract generalised functions have been widely adopted in structural mechanics to treat singularities of beam like structures however due to the curved geometry that couples axial and transversal displacements their use has never been explored for curved beams in this paper the capability of distributions of leading to closed form exact solutions for multi cracked circular arch is shown the exact closed form solution of a circular euler arch in presence of any number of discontinuities due to concentrated damage and subjected to an arbitrary distribution of static loads is obtained damage under the form of concentrated cracks has been modeled through the widely adopted and validated equivalent elastic hinge concept and has been introduced in the governing differential equations by making use of dirac s delta functions the resulting nontrivial generalised six order differential equations have been derived and solved in closed form independently of the number of along arch concentrated cracks the solution is expressed as a function of six integration constants only in which the damage positions and intensities are given data appearing explicitly in the solution expression this latter aspect constitutes a fundamental aid towards the resolution of the static damage inverse identification problem the results have been validated through some comparisons with finite element numerical simulations examples referred to multi cracked euler arches with different boundary conditions damage and load scenarios are presented

identification of the stiffness distribution in statically indeterminate beams an identification procedure is presented for the stiffness distribution in statically indeterminate structures the proposed procedure analogous to direct calculation of the dynamic stiffness the inverse problem algorithm used in it is based on a finite element fe model of the damaged structure with unknown stiffness distribution and on a subset of measured vibration frequencies and vibration modes the bending stiffness is updated for each element in the fe model by an iterative procedure in order to improve its practicability the effect of random measurement noise is taken into consideration a numerical study of statically indeterminate beams shows that it is able to locate both localized and multiple damage and determine its severity with a high level of reliability

curvature rate approach to the evaluation of the stiffness distribution in plate like structures abstract a procedure for identifying the bending stiffness distribution in plate like structures is presented the algorithm is based on the correlation between a parameter called curvature increased factor cif and the bending stiffness of the plate d accurate correlation can be achieved only by considering the effect of the redistribution of internal forces and moments due to the damage on the curvature distribution in order to achieve this goal the study offers an iterative procedure which eliminates the effect of the moment redistribution from the cif and eventually correlates accurately between cif and d the curvature rate is evaluated from the displacement mode shape using a 2d smoothing technique the procedure takes into account the presence of random errors and the limited number of measured nodes the procedure s effectiveness reliability and range of applicability are demonstrated using numerical examples

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 chain rule for ɛ subdifferentials with applications to approximate solutions in convex pareto problems abstract in this work we obtain a chain rule for the approximate subdifferential considering a vector valued proper convex function and its post composition with a proper convex function of several variables nondecreasing in the sense of the pareto order we derive an interesting formula for the conjugate of a composition in the same framework and we prove the chain rule using this formula to get the results we require qualification conditions since in the composition the initial function is extended vector valued this chain rule extends analogous well known calculus rules obtained when the functions involved are finite and it gives a complementary simple expression for other chain rules proved without assuming any qualification condition as application we deduce the well known calculus rule for the addition and we extend the formula for the maximum of functions finally we use them and a scalarization process to obtain kuhn tucker type necessary and sufficient conditions for approximate solutions in convex pareto problems these conditions extend other obtained in scalar optimization problems

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

structural damage detection based on proper orthogonal decomposition experimental verification the present paper describes a new structural damage detection method based on the monitoring of vibrational properties of the structure sensors record the accelerations of several points of the structure the recorded data are then used to compute the proper orthogonal modes the comparison between the proper orthogonal modes of the undamaged structure and those of the damaged structure provides information on damage location experimental results are presented

vibration analysis of edge cracked beam on elastic foundation with axial loading using the differential quadrature method abstract the eigenvalue problems of clamped free and hinged hinged bernoulli euler beams on elastic foundation with a single edge crack axial loading and excitation force were numerically formulated using the differential quadrature method dqm appropriate boundary conditions accompanied the dqm to transform the partial differential equation of a bernoulli euler beam with a single edge crack into a discrete eigenvalue problem the dqm results for the natural frequencies of cracked beams agree well with other literature values the sampling point number effect the location of the crack effect and the depth of the crack effect on the accuracy variation of calculated natural frequencies are presented by using two elements in this work the effects of axial loading foundation stiffness opening crack and closing crack are also studied

analysis of chaotic saddles in low dimensional dynamical systems the derivative nonlinear schrodinger equation abstract in this paper we present a computational study of nonattracting chaotic sets known as chaotic saddles in a low dimensional dynamical system describing stationary solutions of the derivative nonlinear schrodinger equation a driven dissipative model for alfven waves these chaotic saddles have gaps which are filled at chaotic transitions such as a saddle node bifurcation and an interior crisis we give a detailed explanation of how to numerically determine the chaotic saddles and describe how a chaotic attractor after an interior crisis point can be decomposed into two chaotic saddles dynamically connected by a set of coupling unstable periodic orbits created by a gap filling explosion after the crisis this coupling between two chaotic saddles is responsible for the intermittent dynamics displayed by the chaotic system after the interior crisis

structural damage identification a probabilistic approach a method is presented to improve the robustness of current damage detection methodologies measured statistical changes in natural frequencies and mode shapes along with a correlated analytical stochastic finite element model are used to assess the integrity of a structure the approach accounts for variations in the modal properties of a structure due to experimental errors in the test procedure a perturbation of the healthy eigenvalue problem is performed to yield the relationship between the changes in eigenvalues and in the global stiffness matrix this stiffness change is represented as a sum over every structural member by a product of a stiffness reduction factor and a stiffness submatrix the determination of damaged stiffness statistics permits the comparison of probability density functions between the healthy and estimated damaged stiffnesses a set of graphical and statistical probability damage quotients are then found that indicate a confidence level on the existence of damage the effectiveness of the proposed technique is illustrated using simulated data on a three degree of freedom spring mass system and on an euler bernoulli cantilever aluminum beam

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

damage assessment of structures using modal test data abstract system health monitoring of structures is important not only for conducting safe operation but also maintaining system performance in this paper two identification algorithms for assessing structural damages using the modal test data have been developed an important characteristic in the present approaches is that the employment of the global numerical models e g fem model and some important information e g young s modulus of structures are avoided to a great extent as the first step of the damage identification two algorithms for the detection of damage location are proposed which are similar in concept to the subspace rotation algorithm or best achievable eigenvector technique furthermore a quadratic programming model is set up for the two approaches to predict the damage extent to demonstrate the capability of the proposed approaches an example of a 10 bay planar truss structure is employed for checking the present approaches numerically furthermore the experimental data from the vibration test of a beam with two fixed ends are used directly in the present approaches the final results show that the present techniques perform quite well in spite of the little structural information and measurement inaccuracies

improved damage detection method based on element modal strain damage index using sparse measurement an improved damage detection method based on the concept of element modal strain damage index is introduced the proposed methods attempts to address some of the weaknesses of the damage detection method based on modal curvatures the use of numerical differentiation procedures is identified as the main cause for the poor performance of the modal curvature method under sparse and noisy measurement an improved damage index that does not rely on numerical differentiation is then formulated the proposed damage index can be calculated using only modal displacement and modal rotation a penalty based minimization approach is then used to find the unknown modal rotation using sparse and noisy modal displacement measurement numerical simulation and experiment validation confirm the relative advantage of the proposed method compared with modal curvature based approaches

chaotic saddles at the onset of intermittent spatiotemporal chaos in a recent study rempel and chian phys rev lett 98 014101 2007 it has been shown that nonattracting chaotic sets chaotic saddles are responsible for intermittency in the regularized long wave equation that undergoes a transition to spatiotemporal chaos stc via quasiperiodicity and temporal chaos in the present paper it is demonstrated that a similar mechanism is present in the damped kuramoto sivashinsky equation prior to the onset of stc a spatiotemporally chaotic saddle coexists with a spatially regular attractor after the transition to stc the chaotic saddle merges with the attractor generating intermittent bursts of stc that dominate the post transition dynamics

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

structural change localization and monitoring through a perturbation based inverse problem structural change detection and characterization or structural health monitoring is generally based on modal analysis for detection localization and quantification of changes in structure classical methods combine both variations in frequencies and mode shapes which require accurate and spatially distributed measurements in this study the detection and localization of a local perturbation are assessed by analysis of frequency changes in the fundamental mode and overtones that are combined with a perturbation based linear inverse method and a deconvolution process this perturbation method is applied first to a bending beam with the change considered as a local perturbation of the young s modulus using a one dimensional finite element model for modal analysis localization is successful even for extended and multiple changes in a second step the method is numerically tested under ambient noise vibration from the beam support with local changes that are shifted step by step along the beam the frequency values are revealed using the random decrement technique that is applied to the time evolving vibrations recorded by one sensor at the free extremity of the beam finally the inversion method is experimentally demonstrated at the laboratory scale with data recorded at the free end of a plexiglas beam attached to a metallic support

a pseudo excitation approach for structural damage identification from strong to weak modality a damage characterization framework based on the pseudo excitation pe approach has recently been established aimed at quantitatively identifying damage in beam plate and shell like structural components however it is envisaged that the effectiveness of the pe approach can be restricted in practical implementation due to the involvement of high order derivatives of structural dynamic deflections in which measurement noise and uncertainties can overwhelm the damage associated signal features upon mathematical differentiation in this study the pe approach was revamped by introducing the weighted integration whereby the prerequisite of satisfying the local equilibrium conditions was relaxed from point by point to region by region the revamped modality was thus colloquially referred to as weak formulation of the pe approach as opposed to its original version which is contrastively termed as strong formulation by properly configuring a weight function noise immunity of the pe approach was enhanced giving rise to improved detection accuracy and precision even under noisy measurement conditions furthermore the weak formulation was extended to a series of coherent variants through partial integration rendering a multitude of detection strategies by selecting measurement parameters and configurations this endowed the pe approach with flexibility in experimental manipulability so as to accommodate various detection requirements as an application of the weak formulation a continuous gauss smoothing cgs based detection scheme was developed and validated by localizing multiple cracks in a beam structure showing fairly improved noise tolerance

symmetry as a continuous feature symmetry is treated as a continuous feature and a continuous measure of distance from symmetry in shapes is defined the symmetry distance sd of a shape is defined to be the minimum mean squared distance required to move points of the original shape in order to obtain a symmetrical shape this general definition of a symmetry measure enables a comparison of the amount of symmetry of different shapes and the amount of different symmetries of a single shape this measure is applicable to any type of symmetry in any dimension the symmetry distance gives rise to a method of reconstructing symmetry of occluded shapes the authors extend the method to deal with symmetries of noisy and fuzzy data finally the authors consider grayscale images as 3d shapes and use the symmetry distance to find the orientation of symmetric objects from their images and to find locally symmetric regions in images

repellers semi attractors and long lived chaotic transients abstract we study the chaotic transients observed in many deterministic systems in general they are related to strange repellers or semi attractors if they are repelling in some and attracting in other directions we propose formulas relating the average life time of the transient to dimensions of the repeller and to lyapunov exponents of the flow on it the formulas are tested numerically in a number of cases

reactions in flows with nonhyperbolic dynamics we study the reaction dynamics of active particles that are advected passively by 2d incompressible open flows whose motion is nonhyperbolic this nonhyperbolicity is associated with the presence of persistent vortices near the wake wherein fluid is trapped we show that the fractal equilibrium distribution of the reactants is described by an effective dimension d mathit eff which is a finite resolution approximation to the fractal dimension furthermore d mathit eff depends on the resolution and on the reaction rate 1 ensuremath tau as ensuremath tau is increased the equilibrium distribution goes through a series of transitions where the effective dimension increases abruptly these transitions are determined by the complex structure of cantori surrounding the kolmogorov arnold moser kam islands

continuous extension of the geometric control method in this paper we give a continuous version valid for flows of the geometric control method introduced by toroczkai et al 1994 and constructed for mappings on 2d poincare sections this method does not require explicit knowledge of the dynamics just a rough location of the periodic orbit and a single parameter easily computed from four data points applicability in numerical and real experiments is discussed

fisher information based optimal input locations for modal identification abstract a method is proposed to determine optimal locations of input forces for experimental modal analysis the input locations are optimal in a sense that the measured vibration responses under inputs thus located contain maximum information about unknown modal parameters of interest these optimal input locations are obtained by maximizing the trace of the associated fisher information matrix fim analytical expressions are obtained for the different derivatives involved by expressing acceleration responses in terms of pseudo modal responses a dimensionless scaling is introduced to normalize the effect of different types of modal parameters an explicit relation is also derived between the fim and the mode shape components at input locations it is shown that in certain experimental scenarios this relation may be used to directly obtain the optimal input locations from only the mode shapes an extensive series of numerical simulations including situations of single multiple inputs and single multiple modes of interest is used to illustrate the proposed approach it is observed that the modal parameters identified using any suitable modal identification technique have the lowest estimation uncertainty when the inputs are optimally located as an application in damage detection it is shown that modal parameters estimated from experiments with non optimally located inputs may lead to incorrect damage localization the proposed method is also applied to data from experiments performed on a laboratory scale truss model

new formulas for the legendre fenchel transform we present new formulas for the legendre fenchel transform of functions they concern the following three operations inverting a strictly monotone convex function post composing an arbitrary function with a strictly monotone concave function multiplying two positively valued strictly monotone convex functions