parameter identification of nonlinear aeroelastic system with time delayed feedback control in this paper an enhanced response sensitivity approach is proposed for parameter identification of nonlinear time delay aeroelastic systems two common aeroelastic models are investigated namely

development and validation of a new experimental method to identify damping matrices of a dynamic system as demonstrated in the authors previous work damping matrices in the equation of motion of a dynamics system can be identified from the frequency response function matrix frm of the system a newly developed method with a much simpler algorithm is proposed in this paper for more effective damping matrices identification theoretical validation of the method and related noise study are conducted using a simple example which reveals the method s improved features a set of specially designed measurements are conducted for a qualitative experimental validation of the identification method important measurement issues learned from the experiment which include needs for phase matching and frm conditioning are explained possible significant applications of the method are also discussed

melnikov method for discontinuous planar systems abstract this paper treats the occurrence of homoclinic solutions in planar systems with discontinuous right hand side more precisely we deal with a t periodic perturbed system such that the unperturbed system is an autonomous possessing homoclinic orbit by means of the so called non smooth melnikov function there is shown the existence of a homoclinic solution for a perturbed system the non smooth melnikov function is derived and the method of how to find it in concrete problems is also introduced

linear damping models for structural vibration abstract linear damping models for structural vibration are examined first the familiar dissipation matrix model then the general linear model in both cases an approximation of small damping is used to obtain simple expressions for damped natural frequencies complex mode shapes and transfer functions results for transfer functions can be expressed in the form of very direct extensions of the familiar expression for the undamped case this allows a detailed discussion of the implications of the various damping models for the interpretation of measured transfer functions especially in the context of experimental modal analysis in the case of a dissipation matrix model it would be possible in principle to determine all the model parameters from measurements in the case of the general model however there is a fundamental ambiguity which prevents full determination of the model from measurements on a single structure

realization of stable models with subspace methods abstract subspace methods for system identification estimate the dynamics of state space models either by using the shiftinvariance property of an estimated observability or controllability matrix or by estimating a state sequence and then solving a least squares problem to obtain the system matrices in either case it is possible for the estimated system to be unstable we present algorithms to find stable approximants to a least squares problem which can then be applied to subspace methods to ensure stability either asymptotic or marginal stability can be ensured in the latter case a pole or a pair of poles being forced to lie on the unit circle in addition some results on a sufficient condition for stability for least squares solutions obtained by the shift invariance approach are derived

analysis of grazing bifurcations of quasiperiodic system attractors this paper presents the first application of the discontinuity mapping approach to the study of near grazing bifurcations of originally quasiperiodic co dimension two system attractors the paper establishes an exact formulation for the discontinuity mapping methodology under the assumption that a poincare section can be found that is everywhere transversal to the grazing attractor in particular it is shown that while a reduced formulation may be employed successfully in the case of co dimension one attractors it fails to capture dynamics in directions transversal to the original quasiperiodic attractor this shortcoming necessitates the full machinery presented here the generality of the proposed approach is illustrated through numerical analysis of two nonlinear dynamical systems of dimension three and four

extraction of structural system matrices from an identified state space system using the combined measurements of dva a time domain method for the extraction of the structural system matrices mass damping and stiffness matrices from an identified state space system is proposed in this paper using the combined measurements of displacement velocity and acceleration dva together with the input excitations the method is based on the invariance of continuous time markov parameters an explicit expression of the relationship between the continuous time markov parameters the structural system matrices and the influence matrices for output dva as well as the input force has been derived the determination of structural system matrices is also valid when only the displacement velocity or acceleration responses are measured in this paper the equivalent state system matrices are obtained by an algorithm which combines the eigensystem realization algorithm era and the autoregressive with exogeneous arx model the arx model provides the necessary discrete time markov parameters from the measured input and output data and then the equivalent state system matrices are identified from discrete time markov parameters by using the era a lumped mass model with three degrees of freedom is employed to illustrate the accuracy and feasibility of the presented method

periodic occurrence of chaotic behavior of homoclinic tangles abstract in this article we illustrate through numerical simulations some important aspects of the dynamics of the periodically perturbed homoclinic solutions for a dissipative saddle more explicitly we demonstrate that when homoclinic tangles are created three different dynamical phenomena namely horseshoes periodic sinks and attractors with sinai ruelle bowen measures manifest themselves periodically with respect to the magnitude of the forcing function in addition when the stable and the unstable manifolds are pulled apart so as not to intersect first rank 1 attractors then quasi periodic attractors are added to the dynamical scene

a wavelet based approach for the identification of linear time varying dynamical systems a novel procedure is developed for the identification of linear discrete models of dynamical systems from noisy data of particular interest is the application of the methodology to time varying systems the procedure is based on a representation of the governing differential equations with respect to a wavelet basis and the formulation of an inverse algebraic problem in the associated subspace the effect of noisy data is considered and numerical simulations demonstrating the applicability of the method to single and multi degree of freedom dynamical systems are presented

the backus gilbert method and their minimum norm solution abstractthis paper has two objectives one is to review the backus gilbert bg method backus and gilbert investigate continuous inverse problems in a radially symmetric earth using an approach completely different from that of standard inversion methods if m is an earth property of interest the bg method provides average values of m over some radial intervals if an interval w is relatively short and centered near a particular radius r0 the bg average will be a local average of m near r0 with a resolving length of w backus and gilbert also introduce the concept of trade off between resolution and error which is essential in inverse theory regardless of the inversion method in spite of its importance inverse theory texts neither describe the bg method in full nor show how to apply it in all its generality because the three papers that introduce the bg method are mathematically difficult this paper provides background material and a detailed derivation of the method as well as two completely wor

projected gradient methods for nonnegative matrix factorization nonnegative matrix factorization nmf can be formulated as a minimization problem with bound constraints although bound constrained optimization has been studied extensively in both theory and practice so far no study has formally applied its techniques to nmf in this letter we propose two projected gradient methods for nmf both of which exhibit strong optimization properties we discuss efficient implementations and demonstrate that one of the proposed methods converges faster than the popular multiplicative update approach a simple matlab code is also provided

damping identification using a continuous wavelet transform application to real data a continuous wavelet transform cwt based on the gabor wavelet function is used to identify the damping of a multi degree of freedom system the common procedures are already known especially the identification with a morlet cwt this study gives special attention to the following a description of the instantaneous noise the edge effect of the cwt the frequency shift of the cwt the bandwidth of the wavelet function and the selection of the parameter of the gabor wavelet function of the cwt the procedures are demonstrated using several numerical examples and on signals acquired from the lateral vibration of a uniform beam the study demonstrates the advantages of using the amplitude and phase methods both of which provide information about the instantaneous noise the procedures presented are appropriate for automating the identification process

quasi random initial population for genetic algorithms the selection of the initial population in a population based heuristic optimizationmethod is important since it affects the search for several iterations and often has an influence on the final solution if no a priori information about the optima is available the initial population is often selected randomly using pseudorandom numbers usually however it is more important that the points are as evenly distributed as possible than that they imitate random points in this paper we study the use of quasi random sequences in the initial population of a genetic algorithm sample points in a quasi random sequence are designed to have good distribution properties here a modified genetic algorithm using quasi random sequences in the initial population is tested by solving a large number of continuous benchmark problems from the literature the numerical results of two implementations of genetic algorithms using different quasi random sequences are compared to those of a traditional implementation using pseudorandom numbers the results obtained are promising

contrast source inversion methods in elastodynamics in this paper a nonlinear inversion method is presented for determining the mass density of an elastic inclusion from the knowledge of how the inclusion scatters known incident elastic waves the algorithm employed is an extension of the multiplicative regularized contrast source inversion method mr csi to elasticity this method involves alternate determination of the mass density contrast and the contrast sources the product of the contrast and the fields in each iterative step the simple updating schemes of the method allow the introduction of an extra regularization term to the cost functional as a multiplicative constraint this so called mr csi method mr csi has been proven to be very effective for the acoustic and electromagnetic inverse scattering problems numerical examples demonstrate that the mr csi method shows excellent edge preserving properties by robustly handling noisy data very well even for more complicated elastodynamic problems

local analysis of co dimension one and co dimension two grazing bifurcations in impact microactuators impact microactuators rely on repeated collisions to generate gross displacements of a microelectromechanical machine element without the need for large applied forces their design and control rely on an understanding of the critical transition between non impacting and impacting long term system dynamics and the associated changes in system behavior in this paper we present three co dimension one characteristically distinct transition scenarios associated with grazing conditions for a periodic response of an impact microactuator a discontinuous jump to an impacting periodic response associated with parameter hysteresis a continuous transition to an impacting chaotic attractor and a discontinuous jump to an impacting chaotic attractor using the concept of discontinuity mappings a theoretical analysis is presented that predicts the character of each transition from a set of quantities that are computable in terms of system properties at grazing specifically we show how this analysis can be applied to predict the bifurcation behavior on neighborhoods of two co dimension two bifurcation points that separate the co dimension one bifurcation scenarios the predictions are validated against results from numerical simulations of a model impact microactuator

bifurcations of subharmonics abstract we consider a piecewise linear second order ordinary differential equation which is topologically equivalent to the sine gordon equation the system is subjected to a time harmonic disturbance and the behavior of the periodic solutions is examined it is shown that subharmonic motions with period n times that of the disturbance appear via saddle node bifurcations for all n 1 2 3 these motions then undergo period doubling or pitchfork bifurcations as parameters are varied beyond the saddle node bifurcation values the limit n is considered and is compared with a melnikov calculation for the system due to the piecewise linear nature of the system no approximations are necessary and thus the results are valid for nonsmall parameter values furthermore this provides an answer to the uniformity question in the study of stability of subharmonics

a robust parameter design for multi response problems most real world search and optimization problems naturally involve multiple responses in this paper we investigate a multiple response problem within desirability function framework and try to determine values of input variables that achieve a target value for each response through three meta heuristic algorithms such as genetic algorithm ga simulated annealing sa and tabu search ts each algorithm has some parameters that need to be accurately calibrated to ensure the best performance for this purpose a robust calibration is applied to the parameters by means of taguchi method the computational results of these three algorithms are compared against each others the superior performance of sa over ts and ts over ga is inferred from the obtained results in various situations

modifications of real code genetic algorithm for global optimization a series of modifications to the real coded genetic algorithm for the task of locating the global minimum of multidimensional functions are presented here these modifications include a new stopping rule a novel mutation mechanism and a periodically application of a local search procedure the proposed modifications are tested on a series of optimization problems and the results are reported

sirt and cg type methods for the iterative solution of sparse linear least squares problems abstract sirt and cg type methods have been successfully employed for the approximate solution of least squares problems arising in tomography in this paper we study and compare their convergence and regularization properties it is pointed out that sirt methods apply an uncontrollable implicit rescaling which affects the statistical characteristics of the system whereas cg type methods do not for a large class of model problems it is shown that virtually the same solutions as obtained by sirt methods can be obtained by applying a cg type method to a properly rescaled system but with an amount of work proportional to the square root of the amount of work with sirt

mean square error criteria to multiresponse process optimization by a new genetic algorithm the recent push for quality in industry has brought response surface methodology to the attention of many users most of the published literature on robust design methodology is basically concerned with optimization of a single response or quality characteristic which is often most critical to consumers for most products however quality is multidimensional so it is common to observe multiple responses in an experimental situation in this paper we present a methodology for analyzing several quality characteristics simultaneously using the mean square error mse criterion when data are collected from a combined array problems with highly nonlinear or multimodal objective functions are extremely difficult to solve and are further complicated by the presence of multiple objectives an alternative approach is to use a heuristic search procedure such as a genetic algorithm ga the ga generates a string of solutions using genetics like operators such as selection crossover and mutation in this paper a genetic algorithm based on arithmetic crossover for the multiresponse problem is proposed the string of solutions highlight the trade offs that one needs to consider in order to obtain a compromise solution a numerical example has been presented to illustrate the performance and the applicability of the proposed method

regularization parameter selection for nonlinear iterative image restoration and mri reconstruction using gcv and sure based methods regularized iterative reconstruction algorithms for imaging inverse problems require selection of appropriate regularization parameter values we focus on the challenging problem of tuning regularization parameters for nonlinear algorithms for the case of additive possibly complex gaussian noise generalized cross validation gcv and weighted mean squared error mse approaches based on stein s unbiased risk estimate sure need the jacobian matrix of the nonlinear reconstruction operator representative of the iterative algorithm with respect to the data we derive the desired jacobian matrix for two types of nonlinear iterative algorithms a fast variant of the standard iterative reweighted least squares method and the contemporary split bregman algorithm both of which can accommodate a wide variety of analysis and synthesis type regularizers the proposed approach iteratively computes two weighted sure type measures predicted sure and projected sure which require knowledge of noise variance 2 and gcv which does not need 2 for these algorithms we apply the methods to image restoration and to magnetic resonance image mri reconstruction using total variation and an analysis type l1 regularization we demonstrate through simulations and experiments with real data that minimizing predicted sure and projected sure consistently lead to near mse optimal reconstructions we also observe that minimizing gcv yields reconstruction results that are near mse optimal for image restoration and slightly suboptimal for mri theoretical derivations in this paper related to jacobian matrix evaluations can be extended in principle to other types of regularizers and reconstruction algorithms

time domain galerkin method for dynamic load identification summary this paper proposes a new method called time domain galerkin method tdgm for investigating the structural dynamic load identification problems firstly the shape functions are adopted to approximate three parameters such as the dynamic load kernel function response and measured structural response secondly defining a residual function could be expressed as the difference of the measured response and the computational response thirdly select an appropriate weighting function to multiply the defined residual function and make integral operation with respect to time to be zero finally when the shape functions are chosen as the weighting function it establishes the forward model called tdgm furthermore the regularization method could have effectiveness in solving the ill posed matrix of load reconstruction and obtaining the accurate identified results of the dynamic load compared with the traditional green kernel function method gkfm tdgm can effectively overcome the influences of noise and improve the accuracy of the dynamic load identification three numerical examples are provided to demonstrate the correctness and advantages of tdgm copyright 2015 john wiley sons ltd

a unifying theorem for three subspace system identification algorithms the aim of this paper is to indicate and explore the similarities between three different subspace algorithms for the identification of combined deterministic stochastic systems the similarities between these algorithms have been obscured due to different notations and backgrounds it is shown that all three algorithms are special cases of one unifying theorem the comparison also reveals that the three algorithms use exactly the same subspace to determine the order and the extended observability matrix but that the weighting matrix used to calculate a basis for the column space of the observability matrix is different in the three cases

identification and model reduction of time varying discrete time systems abstract linear discrete time variable systems are considered and an important class of uniform realizations is defined the necessary and sufficient conditions for a pulse response to be uniformly realizable are obtained two model reduction schemes one via balanced realizations and the other via hankel matrix are proposed the latter approach can be considered as an identification algorithm for the two dimensional pulse response sequence h k i it is shown that the two approaches yield an identical reduced model which is always asymptotically stable

identification of damping part 3 symmetry preserving methods abstract in two recent papers adhikari and woodhouse 2001 journal of sound and vibration243 43 61 63 88 methods were proposed to identify viscous and non viscous damping models for vibrating systems using measured complex frequencies and mode shapes in many cases the identified damping matrix becomes asymmetric a non physical result methods are presented here to identify damping models which preserve symmetry of the system both viscous and non viscous models are considered the procedure is based on a constrained error minimization approach and uses only experimentally identified complex modes and complex natural frequencies together with for the non viscous model the mass matrix of the system the methods are illustrated by numerical examples

the 2 norm of random matrices abstract numerical experiments show that it is possible to derive simple estimates for the expected 2 norm of random matrices a with elements from a normal distribution with zero mean and standard deviation and from a poisson distribution with mean value these estimates are max m n 2 max m n and e 2 mn respectively where m and n are the dimensions of a

on computing first and second order derivative spectra enhancing resolution in spectral response and an ability to differentiate spectral mixing in delineating the endmembers from the spectral response are central to the spectral data analysis first and higher order derivatives analysis of absorbance and reflectance spectral data is commonly used techniques in differentiating the spectral mixing but high sensitivity of derivative to the noise in data is a major problem in the robust estimation of derivative of spectral data an algorithm of robust estimation of first and second order derivative spectra from evenly spaced noisy normal spectral data is proposed the algorithm is formalized in the framework of an inverse problem where based on the fundamental theorem of calculus a matrix equation is formed using a volterra type integral equation of first kind a regularization technique where the balancing principle is used in selecting a posteriori optimal regularization parameter is designed to solve the inverse problem for robust estimation of first order derivative spectra the higher order derivative spectra are obtained while using the algorithm in sequel the algorithm is tested successfully with synthetically generated spectral data contaminated with additive white gaussian noise and also with real absorbance and reflectance spectral data for fresh and sea water respectively robust and efficient algorithm of computing first and second orders derivative spectra is designed the algorithm is based on the premise of inverse problem where a robust solution is achieved via regularization it couples discrepancy and balancing principles to determine regularization parameter and implement stopping rule respectively numerical experiments on noisy data suggest superiority of the method over finite difference and fourier transform based techniques the proposed method is applied on absorbance and reflectance spectral data for fresh and sea water

dynamics of homoclinic tangles in periodically perturbed second order equations we obtain a comprehensive description on the overall geometrical and dynamical structures of homoclinic tangles in periodically perturbed second order ordinary differential equations with dissipation let be the size of perturbation and be the entire homoclinic tangle we prove in particular that i for infinitely many disjoint open sets of contains nothing else but a horseshoe of infinitely many branches ii for infinitely many disjoint open sets of contains nothing else but one sink and one horseshoe of infinitely many branches and iii there are positive measure sets of so that admits strange attractors with sinai ruelle bowen measure we also use the equation d2qdt2 q2 dqdt q q2 q2sin t to illustrate how to apply our theory to the analysis and to the numerical simulations of a given equation

neuro fuzzy and genetic algorithm in multiple response optimization abstract optimization of a multiple output system whose function is only approximately known and is represented in tabular form is modeled and optimized by the combined use of a neuro fuzzy network and optimization techniques which do not require the explicit representation of the function neuro fuzzy network is useful for learning the approximate original tabular system however the results obtained by the neuro fuzzy network are represented implicitly in the network the manfis neuro fuzzy network which is an extension of the anfis network is used to model the multiple output system and a genetic algorithm is used to optimize the resulting multiple objective decision making problem a chemical process whose function is represented approximately in tabular form is solved to illustrate the approach

identification of linear time varying mdof dynamic systems from forced excitation using hilbert transform and emd method an algorithm is developed for the identification of linear time varying ltv multiple degrees of freedom systems it is based on the hilbert transform and the empirical mode decomposition with forced vibration response data the proposed identification algorithm is applied to single degree of freedom and multi degrees of freedom dynamic systems three ideal cases of ltv systems with smoothly varying abruptly varying and periodically varying stiffness and damping are studied to illustrate the capability of the algorithm to track the variations of the system simulation results demonstrate the effectiveness and the robustness of the proposed identification algorithm and the lack of complete orthogonality for any two intrinsic mode functions is one of the sources of error in the identification

melnikov method for homoclinic bifurcation in nonlinear impact oscillators based on an inverted pendulum impacting on rigid walls under external periodic excitation a class of nonlinear impact oscillators is discussed for its homoclinic bifurcation the melnikov method established for smooth dynamical systems is extended to be applicable to the nonsmooth one for nonlinear impact systems closed form solutions between impacts are generally unavailable the absence of closed form solutions makes difficulties in estimation of the gap between the stable manifold and unstable manifold in this paper we give a method to compute the melnikov functions up to the n t h order so as to obtain conditions of parameters for the persistence of homoclinic cycles which are formed via the identification given by the impact rule

normal form maps for grazing bifurcations in n dimensional piecewise smooth dynamical systems abstract this paper presents a unified framework for performing local analysis of grazing bifurcations in n dimensional piecewise smooth systems of odes these occur when a periodic orbit has a point of tangency with a smooth n 1 dimensional boundary dividing distinct regions in phase space where the vector field is smooth it is shown under quite general circumstances that this leads to a normal form map that contains to lowest order either a square root or a 3 2 type singularity according to whether the vector field is discontinuous or not at the grazing point in particular contrary to what has been reported in the literature piecewise linear local maps do not occur generically first the concept of a grazing bifurcation is carefully defined using appropriate non degeneracy conditions next complete expressions are derived for calculating the leading order term in the normal form poincare map at a grazing bifurcation point in arbitrary systems using the concept of a discontinuity mapping finally the theory is compared with numerical examples including bilinear oscillators a relay feedback controller and general third order systems

meshless thin plate spline methods for the modified helmholtz equation in this paper we investigate the application of the meshless radial basis function method for solving the helmholtz equation using thin plate splines we use a meshless method mixed with a boundary and a fundamental solution methods the numerical computation is achieved by using the generalized minimal residual gmres the least square lsqr methods associated with tikhonov regularization

border collision bifurcations including period two to period three for piecewise smooth systems abstract we examine bifurcation phenomena for maps that are piecewise smooth and depend continuously on a parameter in the simplest case there is a surface in phase space along which the map has no derivative or has two one sided derivatives is the border of two regions in which the map is smooth as the parameter is varied a fixed point e may collide with the border and we may assume that this collision occurs at 0 a variety of bifurcations occur frequently in such situations but never or almost never occur in smooth systems in particular e may cross the border and so will exist for 0 but it may be a saddle in one case say 0 for 0 there may be a stable period 3 orbit which similarly shrinks to e0 as 0 hence one observes the following stable periodic orbits a stable period 2 orbit collapses to a point and is reborn as a stable period 3 orbit we also see analogously stable period 2 to stable period p orbit bifurcations with p 5 11 52 or period 2 to quasi periodic or even to a chaotic attractor we believe this phenomenon will be seen in many applications

full waveform static corrections using blind channel identification near surface wavefield perturbations can be very complex and completely mask the target reflections despite this complexity conventional methods rely on parameterizations characterized by simple time and amplitude anomalies to compensate for these perturbations determining and compensating for time shifts is generally referred to as residual static corrections whereas surface consistent deconvolution techniques deal with amplitude anomalies we present an approach that uses the full waveform to parameterize near surface perturbations therefore we refer to this method as waveform statics important differences from conventional static corrections are that this approachallowstimeshiftstovarywithfrequencyandtakesamplitudevariationsdirectlyintoaccount furthermore theprocedure is fully automated and does not rely on near surface velocity information the waveform static corrections are obtained using blind channel identification and applied to the recordings using multichannel deconvolution as a result the method implicitly incorporates array forming the developed method is validated onsyntheticdataandappliedtopartofafielddatasetacquiredin an area with significant near surface heterogeneity the source and receiver responses obtained are strongly correlated to the near surfaceconditionsandshowchanges bothinphaseandfrequency content along the spread the application of the waveform statics demonstrates that they not only correct for near surface wavefield perturbations but also strongly reduce coherent noise this results in substantial improvements both in trace totrace coherency and in depth resolution in addition the procedure delineates reflection events that are difficult to detect prior to our proposed correction based on these results we conclude that complex near surface perturbations can be successfully dealt with using the multichannel full waveform static correctionprocedure

analysis of discrete ill posed problems by means of the l curve when discrete ill posed problems are analyzed and solved by various numerical regularization techniques a very convenient way to display information about the regularized solution is to plot the norm or seminorm of the solution versus the norm of the residual vector in particular the graph associated with tikhonov regularization plays a central role the main purpose of this paper is to advocate the use of this graph in the numerical treatment of discrete ill posed problems the graph is characterized quantitatively and several important relations between regularized solutions and the graph are derived it is also demonstrated that several methods for choosing the regularization parameter are related to locating a characteristic l shaped corner of the graph

spatial damping identification in the frequency domain a theoretical and experimental comparison abstract this paper deals with spatial damping identification methods in contrast to the commonly used damping methods modal proportional the spatial damping information improves structural models with a known location of the damping sources the lee kim chen ju tsuei fritzen iv and local equation of motion methods were theoretically and experimentally compared experimentally the spatial damping identification was tested against modal and spatial incompleteness differences in viscous and hysteretic damping models the performance of identification methods and the effect of damping treatments it was found that for a structure with a known equation of motion beam plate the local equation of motion method is more efficient and gives a more precise location of the damping full frequency response function frf matrix methods can also identify the spatial damping but are more demanding because the numerical and measurement effort increases with n2 where n is the number of measurement points and consequently the size of the frf matrix

dynamics of a two degree of freedom periodically forced system with a rigid stop diversity and evolution of periodic impact motions abstract a two degree of freedom periodically forced system with a clearance is considered the correlation between dynamic performance and system parameters is studied to find their feasible matching law the fundamental group of impact motions is defined which have the excitation period and differ by the number p of impacts the generation mechanism of complete and incomplete chattering impact vibration of the system is studied a series of singular points between any two adjacent fundamental impact motions are found at which real grazing and bare grazing bifurcation boundaries of one of them saddle node and period doubling bifurcation boundaries of the other alternately intersect and create two types of transition regions hysteresis and tongue shaped regions subharmonic impact motions are found to regularly appear in the tongue shaped regions based on the sampling ranges of parameters dynamics of the system is studied with emphasis on the influence of system parameters on impact velocities existence regions and correlative distribution of single impact periodic motions by multi parameter and multi performance co simulation analysis

recovering the density of a string from only lowest frequency data a classical inverse problem is can you hear the density of a string clamped at both ends the answer as narrowly stated is negative one has to give an additional data sequence such as the energy in each mode norming constants or information on the string slope at the endpoints or alternatively change the boundary conditions and obtain the new frequencies what if neither of these options is possible one solution recently proposed was to add a known mass density and remeasure the dirichlet spectrum w rundell and p e sacks siam j appl math 73 2013 pp 1020 1037 in this work we take a related approach we are able to add any number of known mass densities but we can only measure the fundamental frequency that is the lowest eigenvalue in each case we will show that our problem can be closely approximated by a related problem for which there is uniqueness and we discuss a suite of reconstruction methods

n4sid subspace algorithms for the identification of combined deterministic stochastic systems abstract recently a great deal of attention has been given to numerical algorithms for subspace state space system identification n4sid in this paper we derive two new n4sid algorithms to identify mixed deterministic stochastic systems both algorithms determine state sequences through the projection of input and output data these state sequences are shown to be outputs of non steady state kalman filter banks from these it is easy to determine the state space system matrices the n4sid algorithms are always convergent non iterative and numerically stable since they only make use of qr and singular value decompositions both n4sid algorithms are similar but the second one trades off accuracy for simplicity these new algorithms are compared with existing subspace algorithms in theory and in practice

identification of damping part 4 error analysis in previous papers s adhikari and j woodhouse 2001 journal of sound and vibration243 43 61 63 88 s adhikari and j woodhouse 2002 journal of sound and vibration251 477 490 methods were proposed to obtain the coefficient matrix for a viscous damping model or a non viscous damping model with an exponential relaxation function from measured complex natural frequencies and modes in all these works it has been assumed that exact complex natural frequencies and complex modes are known in reality this will not be the case the purpose of this paper is to analyze the sensitivity of the identified damping matrices to measurement errors by using numerical and analytical studies it is shown that the proposed methods can indeed be expected to give useful results from moderately noisy data provided a correct damping model is selected for fitting indications are also given of what level of noise in the measured modal properties is needed to mask the true physical behaviour

extension of modal analysis to linear time varying systems linear time varying ltv systems have been often dealt with on a case by case basis many well developed concepts and analytic methods of linear time invariant lti systems cannot be applied to ltv systems for example the conventional definition of modal parameters is invalid for ltv systems the first part of this paper explores the possibility of extending the modal concept of ltv systems the discrete time state space model is used to represent ltv systems by analogy to lti systems the pseudo modal parameters are defined using the eigenvalues of the discrete time state transition matrix the paper shows that the pseudo modal parameters preserve certain properties of the conventional modal parameters defined for lti systems the second part of the paper extends a previously developed algorithm to identify the pseudo modal parameters using forced responses and forcing inputs for a general ltv system the input and output hankel matrices formed by an ensemble of data satisfy a matrix facotrization relation the key step of the method is to modify the output matrix in such a way that the range space of the observability matrix can be extracted a robotic manipulator with varying inertia links is used as an example the first part of the numerical simulation illustrates the applications of the pseudo modal parameters the second part of the simulation tests the identification algorithm under different conditions several practical issues are addressed

bifurcations in piecewise smooth feedback systems this paper is concerned with the analysis and classification of non standard bifurcations in piecewise smooth feedback systems bifurcations involving fixed points in maps equilibria and limit cycles in flows are considered with particular attention to border collisions of fixed points in maps non smooth bifurcations of equilibria grazing bifurcations and sliding bifurcations of limit cycles in flows the aim is to describe existing and novel results to form the basis of a consistent theory of bifurcations in such systems in so doing a novel approach to classify non smooth bifurcations of equilibria in flows is presented experimental results on pulse width modulated voltage mode controlled dc dc power converters motivates the relevance to applications of the analysis proposed

asymptotic theory of filtering for linear operator equations with discrete noisy data on considere les equations integrales de fredholm de premiere espece a noyaux continus avec echantillonnage des donnees et alteration par le bruit blanc on etablit une condition suffisante de convergence des methodes de filtrage

an assessment of damping identification methods a study is carried out into the philosophy and performance of different approaches for the determination of linear viscous damping in elasto mechanical systems the methods studied include a closed form solution identification methods based on inverting the matrix of receptances energy expressions developed from single frequency excitation and responses as well as first order perturbation methods the work is concentrated particularly upon modal truncation and how this affects the distribution of matrix terms and the ability of the identified damping together with known mass and stiffness terms to reproduce the complex eigenvalues and eigenvectors of the full order system a simulated example is used to illustrate various points covered in the theoretical discussion of the methods considered

bifurcation and chaos near sliding homoclinics we study the chaotic behaviour of a time dependent perturbation of a discontinuous differential equation whose unperturbed part has a sliding homoclinic orbit that is a solution homoclinic to a hyperbolic fixed point with a part belonging to a discontinuity surface we assume the time dependent perturbation satisfies a kind of recurrence condition which is satisfied by almost periodic perturbations following a functional analytic approach we construct a melnikov like function m in such a way that if m has a simple zero at some point then the system has solutions that behave chaotically applications of this result to quasi periodic systems are also given

impact oscillators with homoclinic orbit tangent to the wall abstract homoclinic bifurcation for a nonlinear inverted pendulum impacting between two rigid walls under external periodic excitation is analyzed under the hypothesis that the unperturbed system has a homoclinc orbit tangent to the wall consequently the impact surface cannot be chosen as the poincare section to measure the distance between the perturbed stable and unstable manifolds furthermore compared to the case that the unperturbed homoclinic orbit intersects the wall transversally more cases are involved as the parameters vary thus the analysis of the homoclinic orbit tangent to the wall is much more difficult in this paper by using a method of melnikov type we derive sufficient conditions under which the perturbed stable and unstable manifolds intersect transversally as an application an impact oscillator of duffing type is studied in detail

identification of damping part 1 viscous damping abstract characterization of damping forces in a vibrating structure has long been an active area of research in structural dynamics the most common approach is to use viscous damping where the instantaneous generalized velocities are the only relevant state variables that affect damping forces however viscous damping is by no means the only damping model within the scope of linear analysis any model which makes the energy dissipation functional non negative is a possible candidate for a valid damping model this paper and its companion see pp 63 88 of this issue are devoted to developing methodologies for identification of such general damping models responsible for energy dissipation in a vibrating structure this paper considers identification of viscous damping under circumstances when the actual damping model in the structure is non viscous a method is presented to obtain a full non proportional viscous damping matrix from complex modes and complex natural frequencies it is assumed that the damping is small so that a first order perturbation method is applicable the proposed method and several related issues are discussed by considering numerical examples based on a linear array of damped spring mass oscillators it is shown that the method can predict the spatial location of damping with good accuracy and also give some indication of the correct mechanism of damping

planar crack identification in 3d linear elasticity by the reciprocity gap method abstract we study the reciprocity gap method andrieux et al 1999 for the identification of planar cracks in the framework of three dimensional linear elasticity in order to achieve better accuracy on thick domains we propose to use polynomial test functions instead of fourier series we also propose to improve the solution by various regularization techniques that are tested and compared numerical assessments are provided in 2d and 3d

damping identification in frequency domain using integral method abstract a new method for damping identification of linear system in frequency domain is presented by using frequency response function frf with integral method the frf curve is firstly transformed to other type of frequency related curve by changing the representations of horizontal and vertical axes for the newly constructed frequency related curve integral is conducted and the area forming from the new curve is used to determine the damping three different methods based on integral are proposed in this paper which are called fdi 1 fdi 2 and fdi 3 method respectively for a single degree of freedom sdof system the formulated relation of each method between integrated area and loss factor is derived theoretically the numeral simulation and experiment results show that the proposed integral methods have high precision strong noise resistance and are very stable in repeated measurements among the three integral methods fdi 3 method is the most recommended because of its higher accuracy and simpler algorithm the new methods are limited to linear system in which modes are well separated and for closely spaced mode system mode decomposition process should be conducted firstly

on the origin and bifurcations of stick slip oscillations a recently proposed model of macroscopic friction is investigated using methods of dynamical systems analysis particular emphasis is put on the bifurcations associated with the appearance of stick

an approach for reducing computational requirements in modal identification references unningham h j and desmarais r n generalization of the subsonic kernel function in the s plane with applications to flutter analysis nasa tp 2292 march 1984 vepa r on the use of fade approximants to represent unsteady aerodynamic loads for arbitrary small motions of wings aiaa paper 76 17 jan 1976 jones w p aerodynamic forces on wings in non uniform motion arc r m 2117 aug 1945 hounjet m h l arspns a method to calculate steady and unsteady potential flow about fixed and rotating lifting and nonlifting bodies nlr tr 85114 l sept 1985

homoclinic solutions for autonomous ordinary differential equations with nonautonomous perturbations nonautomonous ordinary differential equations depending on two parameters 1 and 2 are considered in rn it is assumed that when both parameters are zero the differential equation is autonomous with a hyperbolic equilibrium and a homoclinic solution no restriction is placed on the dimension of the phase space rn or on the dimension of intersection of the stable and unstable manifolds by means of the method of lyapunov schmidt a bifurcation function h is constructed between two finite dimensional spaces where the zeros of h correspond to homoclinic solutions at nonzero parameter values the independent variables of h consist of scalars 1 2 and a vector where is a phase angle and corresponds to directions other than along the original homoclinic solution tangent to both the stable and unstable manifolds when is fixed the equation h 0 yields in general several bifurcation curves through the origin in the 1 2 plane along which there exists a homoclinic solution when is varied these become a number of wedge shaped regions the theory is applied to two examples one in r6 where the invariant manifolds meet in dimension three and a second in r4 where these manifolds agree

a state space force identification method based on markov parameters precise computation and regularization technique a time domain force identification approach for linear system is proposed this approach can found a highly precise force identification model within the scope of general computer precision while it does not cost much computing time although the force identification model is accurate the force identification process like other inverse methods is still ill posed due to the inversion process and the white noise in measured structural responses the singular value decomposition is used to reveal the intrinsically matter of the ill posedness of force identification problem and a regularization technique is utilized to deal with this issue finally the proposed method with the aid of regularization technique is successfully applied to identify the input forces in two numerical simulations

a generalized approach to q markov covariance equivalent realizations for discrete systems abstract a new algorithm is developed which constructs q markov covariance equivalent realizations q markov covers of multivariable linear discrete time systems a q markov cover is a state realization which matches exactly a finite portion of the impulse response sequence markov parameters and output autocorrelation sequence covariance parameters of a linear system the algorithm generates the q markov covers starting with only the basic data namely the q markov parameters and the q covariance parameters the algorithm leads to a parameterization of all minimal stable q markov covers which can be constructed since the data are easily computed from a given state space model the algorithm presented will be useful for both realization and model reduction of multivariable linear discrete time systems an example is presented to demonstrate the algorithm

boundary identification for a 3d laplace equation using a genetic algorithm in this paper we consider the identification of the geometric structure of the boundary of the solution domain for the three dimensional laplace equation we investigate the determination of the shape of an unknown portion of the boundary of a solution domain from cauchy data on the remaining portion of the boundary this problem arises in the study of quantitative non destructive evaluation of corrosion in materials in which boundary measurements of currents and voltages are used to determine the material loss caused by corrosion the domain identification problem is considered as a variational problem to minimize a defect functional which utilises some additional data on certain known parts of the boundary a real coded genetic algorithm rcga is used in order to minimise the objective functional the unknown boundary is parameterized using b splines the laplace equation is discretised using the method of fundamental solutions mfs numerical results are presented and discussed for several test examples

optimally scaled vector regularization method to solve ill posed linear problems instead of the tikhonov regularization method which with a scalar being the regularization parameter liu et al 1 have proposed a novel regularization method with a vector as being the regularization parameter as a continuation we further propose an optimally scaled vector regularization method osvrm to solve the ill posed linear problems which is better than the tikhonov regularization method the presently proposed vector regularization method is shown to be well conditioning to overcome the ill posedness of the linear equations system the osvrm causes a significant improvement of stability and accuracy in the numerical solution of ill posed linear problem and its convergence speed is as fast as by solving the well posed linear problem some tests of the linear inverse problems confirm the efficiency and accuracy of the osvrm

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

multi response simulation optimization using genetic algorithm within desirability function framework this paper presents a new methodology to solve multi response statistical optimization problems this methodology integrates desirability function and simulation approach with a genetic algorithm the desirability function is responsible for modeling the multi response statistical problem the simulation approach generates required input data from a simulated system and finally the genetic algorithm tries to optimize the model this methodology includes four methods the methods differ from each other in controlling the randomness of the problem in the first and second methods replications control this randomness while in the third and fourth methods we control the variation by statistical tests furthermore we compare the performances of these methods by numerical examples and designed experiments and report the results

nonsmooth homoclinic orbits melnikov functions and chaos in discontinuous systems abstract we first study the problem of chaotic behaviour in time perturbed discontinuous systems whose unperturbed part has a piecewise c 1 homoclinic solution transversally crossing the discontinuity manifolds we show that if a certain melnikov function has a simple zero at some point then the system has solutions that behave chaotically the melnikov function is explicitly constructed for two dimensional systems and extends the usual melnikov function for the smooth case in the second part we extend these results to sliding homoclinic bifurcations we also mention some possibilities for further research

on hopf bifurcation in non smooth planar systems abstract as we know for non smooth planar systems there are foci of three different types called focus focus ff focus parabolic fp and parabolic parabolic pp type respectively the poincare map with its analytical property and the problem of hopf bifurcation have been studied in coll et al 2001 3 and filippov 1988 6 for general systems and in zou et al 2006 13 for piecewise linear systems in this paper we also study the problem of hopf bifurcation for non smooth planar systems obtaining new results more precisely we prove that one or two limit cycles can be produced from an elementary focus of the least order order 1 for foci of ff or fp type and order 2 for foci of pp type theorem 2 3 different from the case of smooth systems for piecewise linear systems we prove that 2 limit cycles can appear near a focus of either ff fp or pp type theorem 3 3

identification of damping in mdof systems using time scale decomposition abstract a method of damping identification in multi degree of freedom systems is presented the method is based on the time scale decomposition of the system impulse response the continuous wavelet transform is used to decompose the impulse response into the time scale domain three techniques based on the wavelet tranform are used to estimate damping these are the wavelet transform cross section procedure the impulse response recovery procedure based on wavelet domain filtering and the wavelet ridge detection procedure the methods are applied to simulated multi degree of freedom systems

subspace based methods for the identification of linear time invariant systems subspace based methods for system identification have attracted much attention during the past few years this interest is due to the ability of providing accurate state space models for multivariable linear systems directly from input output data the methods have their origin in classical state space realization theory as developed in the 1960s the main computational tools are the qr and the singular value decompositions here an overview of existing subspace based techniques for system identification is given the methods are grouped into the classes of realization based and direct techniques similarities between different algorithms are pointed out and their applicability is commented upon we also discuss some recent ideas for improving and extending the methods a simulation example is included for comparing different algorithms the subspace based approach is found to perform competitive with respect to prediction error methods provided the system is properly excited

identification of linear time varying systems abstract this paper is concerned with the identification of linear time varying systems the discrete time state space model of freely vibrating systems is used as an identification model the focus is placed on identifying successive discrete transition matrices that have the same eigenvalues as the original transition matrices first a typical subspace based method is presented to illustrate the extraction of the observability range space using the singular value decomposition svd of a general hankel matrix then the identification of varying transition matrices is approached by using an ensemble of response sequences for arbitrarily varying systems a series of the hankel matrices are formed by an ensemble set of responses which are obtained through multiple experiments on the system with the same time varying behaviour the varying transition matrix at each moment is estimated through the svd of two successive hankel matrices the proposed algorithm is applied to two special cases that require only a single response series i e periodically varying systems and slowly varying systems the use of the eigenvalues of the transition matrices is discussed and the pseudomodal parameters are defined finally a two link manipulator subjected to a varying end force is used as an example to illustrate the tracking capability and performance of the proposed algorithm

subspace based identification of linear time varying system a physical parameter identification method for the linear time varying system is presented in this paper for an arbitrarily time varying system a series of hankel matrices are established directly from the combined measurements of displacement velocity and acceleration together with the input excitations from a single experiment with the system the time varying equivalent state space system matrices of the structure at each time instance are then identified by singular value decomposition using the free or random responses a time varying transformation matrix for transforming the identified equivalent system matrices into the physical system matrices is developed to determine the mass stiffness and damping matrices details of the proposed approach are investigated with a two degrees of freedom spring mass damper system with three kinds of time varying parameters numerical results show that the proposed method is accurate and effective in identifying time varying physical parameters

a class of subspace model identification algorithms to identify periodically and arbitrarily time varying systems abstract subspace model identification algorithms that allow the identification of a linear time varying ltv state space model from an ensemble set of input output measurements are presented in this paper each pair of input and output sequences in this ensemble is recorded when the underlying system to be identified undergoes the same time varying behavior the algorithms operate directly on the available ensemble of input output data and are a generalization of the recently proposed multivariable output error state space moesp class of algorithms to this ensemble type of identification problems a special case is considered in this paper where the repetition of this time varying behavior is intrinsic namely in periodically time varying systems an example of identifying a multirate sampled data system from a recorded input and output sequence demonstrates some of the capabilities of the presented subspace model identification algorithms

modal parameter estimation using the state space method abstract in modal parameter identification the damped complex exponential response methods extract modal parameters using free decay responses although there are several different complex exponential methods they are based on the prony method the prony method has some limitations such as poor robustness to noise computational burden and the unstable nature of root solver routines recent developments in signal processing indicate that model based eigendecomposition methods are very viable alternatives in this paper one of the model based eigendecomposition methods the state space method is first introduced the state space method makes use of the singular value decomposition svd to form a well conditioned data matrix and obtains the modal parameters through the eigendecomposition of the data matrix the paper then focuses on an analytical derivation of the svd of the data matrix in order to present a theoretical base for the method a simulation is used to illustrate important properties of the svd and performance of the state space method finally more applications of the svd of the data matrix are explored and the proposed applications are demonstrated by modal testing example it is shown that the state space method provides an elegant and robust tool for extracting modal parameters the svd of the data matrix offers significant information about the system order and mode participation of a free response

relations between svd and gsvd of discrete regularization problems in standard and general form abstract we consider an algorithm due to elden that transforms general discrete regularization problems into standard form we derive a simple relationship between the svd associated with the standard form problem and the gsvd associated with the general problem and we discuss the accuracy of the gsvd computed via this transformation

blind separation of sound sources from the principle of least spatial entropy abstract the aim of the paper is to offer a method for separating incoherent and compact sound sources which may overlap in both the space and frequency domains this is found of interest in acoustical applications involving the identification and ranking of sound sources stemming from different physical origins the principle proceeds in two steps the first one being reminiscent to source reconstruction e g as in near field acoustical holography and the second one to blind source separation specifically the source mixture is first expanded into a linear combination of spatial basis functions whose coefficients are set by backpropagating the pressures measured by an array of microphones to the source domain this leads to a formulation similar but no identical to blind source separation in the second step these coefficients are blindly separated into uncorrelated latent variables assigned to incoherent virtual sources these are shown to be defined up to an arbitrary rotation a unique set of sound sources is finally recovered by searching for that rotation by conjugate gradient descent in the stiefel manifold of unitary matrices which maximizes their spatial compactness as measured either by their spatial variance or their spatial entropy this results in the proposal of two separation criteria coined least spatial variance and least spatial entropy respectively the same concept of spatial entropy which is central to the paper is also exploited in defining a new criterion the entropic l curve dedicated to determining the number of active sound sources the idea consists in considering the number of sources that achieves the best compromise between a low spatial entropy as expected from compact sources and a low statistical entropy as expected from a low residual error the proposed methodology is validated on both laboratory experiments and numerical data and illustrated on an industrial example concerned with the ranking of sound sources on a diesel engine at the same time its robustness to the estimated number of active sources is demonstrated

structural damping identification based on an iterative regularization method a time domain structural damping identification method is presented in this paper the damping of a structure is assumed to be time invariant rayleigh damping time variant rayleigh damping and modal damping respectively and an iterative regularization method is proposed to identify these three types of damping in turn a sensitivity approach is adopted in the formulation of the ill posed inverse problem a new constraint is imposed on the identified iterative increment as well as on the unknown structural parameters to ensure their physical meaning in the identification process is not lost the proposed method is verified in numerical studies with a space frame structure and laboratory measurements of accelerations with accurate results

a new method for nmr data inversion based on double parameter regularization nuclear magnetic resonance nmr technology plays a significant role in petroleum exploration nmr data can be processed using inversion methods to reflect the relaxation information of all the components a new double parameter regularization dpr method was proposed for the inversion of nmr data whose regularization terms consist of tikhonov regularization and maximum entropy regularization the objective function for the dpr method was solved using the levenberg marquardt method the proportional coefficient of the regularization parameter was obtained using an iteration procedure the optimum regularization parameter of the dpr method was selected using an s curve the relationship between the optimum regularization parameter and the signal to noise ratio snr of the data was evaluated moreover we compared the results of the nmr inversion obtained from the norm smooth method the maximum entropy method and the dpr method for simulated data we evaluated how the proportional coefficient of the re

continuous and discontinuous grazing bifurcations in impacting oscillators this paper seeks to formulate conditions for the persistence of a local attractor in the immediate vicinity of periodic and quasiperiodic grazing trajectories in an impacting mechanical system a local analysis based on the discontinuity mapping approach is employed to derive a normal form description of the dynamics near the grazing trajectory in agreement with previous studies of grazing periodic trajectories it is found that the catastrophic loss of a local attractor and strong instability characteristic of grazing bifurcations is directly associated with the repeated application of a square root term that appears to lowest order in the normal form expansion specifically it is found that the square root term is absent in the description of the dynamics normal to a quasiperiodic trajectory covering a co dimension one invariant torus resulting in a piecewise linear description of the normal dynamics and at most a weak instability in contrast for co dimension two or higher the square root term is generically present in the normal dynamics here however the quasiperiodicity of the grazing motion implies that there is no upper limit to the time between impacts on nearby trajectories suggesting the persistence of a local attractor for some interval about the parameter value corresponding to grazing the results of the analysis are illustrated through a series of model examples

exponential dichotomies heteroclinic orbits and melnikov functions the interest in the behaviour of the solutions to perturbed autonomous systems with bounded perturbative term like

control of near grazing dynamics in impact oscillators a method is presented for controlling the persistence of a local attractor near a grazing periodic trajectory in a piecewise smooth dynamical system in the presence of discontinuous jumps in the state associated with intersections with system discontinuities in particular it is shown that a discrete linear feedback strategy may be employed to retain the existence of an attractor near the grazing trajectory such that the deviation of the attractor from the grazing trajectory goes to zero as the system parameters approach those corresponding to grazing contact the implementation relies on a local analysis of the near grazing dynamics using the concept of discontinuity mappings numerical results are presented for a linear and a nonlinear oscillator