modal identification using the frequency scale domain decomposition technique of ambient vibration responses abstract this paper proposes a new modal identification method of ambient vibration responses the application of the singular value decomposition to continuous wavelet transform of power spectral density matrix gives singular values and singular vectors in frequency scale domain analytical development shows a direct relation between local maxima in frequency scale representation of singular values and modal parameters this relation is then carried on for the identification of modal parameters via a complete practical procedure the main novelties of this work involve the new formulation in frequency scale domain and the capacity for the identification of modal parameters without the step of ridges extraction in comparison with previous wavelet based modal identification methods

multi frequency nonlinear energy transfer from linear oscillators to mdof essentially nonlinear attachments abstract we report on multi frequency energy transfer from a two mode initially excited linear system to a multi degree of freedom mdof essentially nonlinear attachment this occurs through simultaneous resonance interactions of both linear modes with a set of nonlinear normal modes nnms of the attachment and is studied utilizing numerical wavelet transforms the multi frequency nonlinear energy transfer discussed herein differs from multi frequency energy transfer caused by resonance capture cascading where sequential energy transfer from a set of linear modes to single dof nonlinear attachments takes place

recurrence plots revisited abstract we show that recurrence plots rps give detailed characterizations of time series generated by dynamical systems driven by slowly varying external forces for deterministic systems we show that rps of the time series can be used to reconstruct the rp of the driving force if it varies sufficiently slowly if the driving force is one dimensional its functional form can then be inferred up to an invertible coordinate transformation the same results hold for stochastic systems if the rp of the time series is suitably averaged and transformed these results are used to investigate the nonlinear prediction of time series generated by dynamical systems driven by slowly varying external forces we also consider the problem of detecting a small change in the driving force and propose a surrogate data technique for assessing statistical significance numerically simulated time series and a time series of respiration rates recorded from a subject with sleep apnea are used as illustrative examples

nonlinear structures in electroencephalogram signals abstract we apply a nonlinear prediction algorithm to investigate the presence of nonlinear structure in electroencephalogram eeg recordings the eeg signal could be modeled as a realization of a nonlinear model plus a residual noise uncorrelated gaussian noise using linear and nonlinear models we analyze the statistical nature of these residual noises in the case of epileptic patients and normal subjects we found that the residual noise presents gaussian distribution for epileptic patients if a nonlinear model is used whereas in the case of normal subjects the residual noise will exhibit a gaussian distribution only if a linear model autoregressive is used these results provide another evidence of the nonlinear character of the epileptic seizure recordings while the normal eeg seems to be better described as linearly correlated noise

wavelet analysis for hopf bifurcations with aeroelastic applications abstract a wavelet analysis on the output signal of a non linear system in the neighbourhood of a hopf bifurcation i e a limit cycle oscillation has been performed to point out the linear and non linear signatures of the system indeed this kind of non linear behaviour is characterized not only by a simple harmonic oscillation in developed steady state condition but also by an initial transitory phase with a complex time evolution of the spectral signal content both these issues could be described in an analytical way via a singular perturbation analysis but they could be also directly analyzed by a signal processing tool via wavelet analysis continuous wavelet transform cwt this is obtained by using the wavelet capability in describing efficiently the time evolution of the spectrum of the signal i e a non linear signature of a hopf bifurcation furthermore the analytical results given by the singular perturbation analysis for the same class of non linear problems have allowed one to interpret correctly the results obtained by the wavelet analysis in this paper this theoretical link between the wavelet analysis and the output signal of a dynamical system recently achieved for linear mechanical damped systems has been extended to non linear systems in the neighbourhood of a hopf bifurcation this kind of analysis is of natural interest in aeroelastic applications where an efficient and noise insensitive analysis of the output signal recorded during the flight tests performed in the neighbourhood of the critical condition flutter may be desirable together with the capability to record the non linear system signature the time scale decompositions cwt have given the opportunity to analyze pre and post critical transient behaviour of a non linear aeroelastic system and thus upon considering the analytical tool given by the singular perturbation analysis to identify its linear and non linear features applications include either two non linear coupled oscillators or a typical section in a supersonic flow

linear quadratic differential games with cheap control abstract this paper considers a linear quadratic differential game in which the weighting on the minimizing control is allowed to approach zero it is shown that if a certain minimum phase condition is satisfied then the value of the game will approach zero as the weighting on the minimizing control approaches zero

minimizing error in the logarithmic decrement method through uncertainty propagation abstract logarithmic decrement is a well known approach for estimating the damping ratio from a time history this paper uses uncertainty propagation to unveil how uncertainties in different quantities can impact damping ratio estimates more specifically the trade off between the number of periods n between the first and final peaks and measurement noise is addressed the insights gained from this analysis are condensed into a single graphic or guide which provides the ideal number of periods n to use for a common range of measurement uncertainties and damping ratios the guide is then applied to experimental data derived from image processing to estimate the damping ratio

poms analysis of randomly vibrating systems obtained from karhunen loeve expansion abstract the karhunen loeve kl decomposition establishes that a 2d random field can be expanded as a series involving a sequence of deterministic orthogonal functions with orthogonal random coefficients the proper orthogonal decomposition pod method consists in detecting spatially coherent modes in the dynamics of a spatio temporally varying system by diagonalizing the spatial correlation function given by an averaging operator the kl expansion is applied here to the responses of randomly excited vibrating systems with a view to performing a pod in separated variables time and space form discrete and continuous mechanical systems are considered in this study as well as stationary and transient non stationary responses an averaging operator involving time and ensemble averages is proposed to draw up the pod in separated variables form from the associated kl expansion the result obtained using this approach agrees with the classical pod in the case of deterministic or ergodic random signals the associated proper orthogonal modes are interpreted in case of linear and nonlinear vibrating systems subjected to white noise excitation in terms of normal modes

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

dynamics of linear discrete systems connected to local essentially non linear attachments the dynamics of a linear periodic substructure weakly coupled to an essentially non linear attachment are studied the essential non linearizable non linearity of the attachment enables it to resonate with any of the linearized modes of the subtructure leading to energy pumping phenomena e g passive one way irreversible transfer of energy from the substructure to the attachment as a specific application the dynamics of a finite linear chain of coupled oscillators with a non linear end attachment is examined in the absence of damping it is found that the dynamical effect of the non linear attachment is predominant in neighborhoods of internal resonances between the attachment and the chain when damping exists energy pumping phenomena are realized in the system it is shown that energy pumping strongly depends on the topological structure of the non linear normal modes nnms of the underlying undamped system this is due to the fact that energy pumping is caused by the excitation of certain damped invariant nnm manifolds that are analytic continuations for weak damping of nnms of the underlying undamped system the bifurcations of the nnms of the undamped system help explain resonance capture cascades in the damped system this is a series of energy pumping phenomena occurring at different frequencies with sudden lower frequency transitions between sequential events the observed multi frequency energy pumping cascades are particularly interesting from a practical point of view since they indicate that non linear attachments can be designed to resonate and extract energy from an a priori specified set of modes of a linear structure in compatibility with the design objectives

model misspecification tests model building and predictability in complex systems abstract in this paper we show that significant advantages can be realized by using functions of simple variables such as time lags as directions in reconstruction spaces for complicated time series first we show that more sensitive model misspecification tests can be constructed when the candidate model is used as one of the directions in the reconstruction space this naturally results in misspecification tests based on the construction of conditional probabilities which can reveal misspecified models even when other powerful methods such as the bds test applied to a sequence of residuals fails second we show that model building and predictability of the time series can be substantially improved by using an informational criterion to determine the functions with which to associate the directions of the reconstruction space this criterion is of the form of a conditional probability and is related to a measure of the short term predictability of the time series we consider specifically an example in which the search space of functions is linear combinations of time lags and we compare the resulting model with a linear least squares fit to the data we also show that this optimized reconstruction space can improve longer term predictability we demonstrate this by comparing longer term predictions made using the optimized space with predictions made using a simple time lagged reconstruction space

hilbert transform and its engineering applications the hilbert transform is useful in calculating instantaneous attributes of a time series especially the envelope amplitude and instantaneous frequency the instantaneous envelope is the amplitude of the complex hilbert transform the instantaneous frequency is the time rate of change of the instantaneous phase angle these properties can be applied to identify dynamic characteristics of a linear as well as a nonlinear system however the conventional discrete hilbert transform which is based on fast fourier transform and inverse fourier transform has shown the lack of accuracy for time derivative calculations in this paper we first introduce the hilbert transform and its applications to the nonlinear system parameter identification then we address the practical issues in applying the hilbert transform to engineering applications to increase the accuracy of the envelope detection we propose a hilbert transform technique based on local maxima interpolation analyses and simulations are carried out to demonstrate the advantages of the proposed technique finally we employ the proposed local maxima interpolation technique in identifying the nonlinear dynamic characteristics of industrial examples

high gain observer approach to disturbance attenuation using measurement feedback a procedure is developed for disturbance attenuation in a linear system via the use of measurement feedback a high gain observer is used to recover the disturbance attenuation properties asymptotically which can be achieved using full state feedback it is thus shown that the problem of disturbance attenuation via measurement feedback can be decomposed into two problems of disturbance attenuation via state feedback these problems of disturbance via state feedback can then be solved using existing methods based on the algebraic riccati equation

linear control theory with an h 0e optimality criterion this expository paper sets out the principal results in bf h infty control theory in the context of continuous time linear systems the focus is on the mathematical theory rather than computational methods

time series and dependent variables we present a new method for analyzing time series which is designed to extract inherent deterministic dependencies in the series the method is particularly suited to series with broad band spectra such as chaotic series with or without noise we derive quantities j e based on conditional probabilities whose magnitude roughly speaking is an indicator of the extent to which the kth element in the series is a deterministic function of the k j th element to within a measurement uncertainty e we apply our method to a number of deterministic time series generated by chaotic processes such as the tent logistic and h non maps as well as to sequences of quasi random numbers in all cases the 6j correctly indicate the expected dependencies we also show that the j are robust to the addition of substantial noise in a deterministic process in addition we derive a predictability index which is a measure of the extent to which a time series is predictable given some tolerance e finally we discuss the behavior of the 6i as e approaches zero

identification of weak nonlinearities on damping and stiffness by the continuous wavelet transform we consider the free response of a nonlinear vibrating system using the ridges and skeletons of the continuous wavelet transform we identify weak nonlinearities on damping and stiffness and estimate their physical parameters the crucial choice of the son wavelet function is obtained using an optimization technique based on the entropy of the continuous wavelet transform the method is applied to simulated single degree of freedom systems and multi degree of freedom systems with nonlinearities on damping and stiffness experimental validation of the nonlinear identification and parameter estimation method is presented the experimental system is a clamped beam with nonlinearities on damping and stiffness and these nonlinearities are identified and quantified from a displacement sensor

a weighted least squares method for circle fitting to frequency response data abstract despite the recent development of powerful multi degree of freedom curve fitting programs the advent of the microcomputer has meant that there is still scope for improvement of simpler single degree of freedom models a weighted least squares curves fitting method based on a well known conformal mapping is described this method is shown to have important theoretical advantages over some established methods

using surrogate data to detect nonlinearity in time series we address the issue of reliably discriminating between chaos and noise from a time series in particular we are interested in avoiding claims of chaos when simpler models such as linearly correlated noise can explain the data we take a statistical approach and use a form of bootstrapping to detect nonlinearity by showing that a given linear model is unlikely to have produced the data our method requires the careful statement of a null hypothesis which characterizes a candidate linear process the generation of an ensemble of surrogate data sets which are similar to the original time series but consistent with the null hypothesis and the computation of a discriminating statistic for the original and for each of the surrogate data sets the idea is to test the original time series against the null hypothesis by checking whether the discriminating statistic computed for the original time series differs significantly from the statistics computed for each of the surrogate sets we present algorithms for generating surrogate data under various null hypotheses and we show the results of numerical experiments on artificial data using correlation dimension lyapunov exponent and forecasting error as discriminating statistics finally we consider a number of experimental timemore series including sunspots electroencephalogram eeg signals and fluid convection and evaluate the statistical significance of the evidence for nonlinear structure in each case 52 refs 10 figs less

dependent variables in broad band continuous time series in this paper we continue our development of new methods for the analysis of broad band time series by deriving quantities which are able to indicate deterministic dependence of an element in one time series on elements in other time series these methods are very broadly applicable and are particularly well suited to the study of continuous time series in which the value of the function may depend on derivatives of the function itself or on other quantities we apply our methods to a number of mathematical examples including the lorentz equation the h6non heiles equations the forced brusselator and the mackey glass equation we show that our methods are very successful at indicating deterministic dependencies in these systems even if the time series are highly chaotic statistical aspects of our procedure are discussed as are a number of interesting and surprising epistomological implications

analysis of wavelets in chaotic states for a one degree of freedom system with viscoelastic restraints a qualitative numerical technique is presented for identifying chaotic states of a non linear one sided constrained one degree of freedom 1 d o f deterministic system under a dynamic non conservative load discrete wavelet analysis in its classic and packet versions was used to search for the boundaries of chaotic and non chaotic solutions the results obtained were verified by an analysis of the lyapunov exponents of the investigated system on the basis of numerical tests one can state that wavelet analysis may be a fast and reliable tool suitable for searching for the boundaries of chaotic and non chaotic solutions

stochastic processes evolutionary spectrum estimation via harmonic wavelets the problem of estimating the power spectrum of non stationary stochastic processes using dyadic generalized and filtered harmonic wavelets is addressed explicit relationships between the statistical moments of the coefficients of the wavelets based representation of the process and of its evolving spectral values are given it is shown that the popular concept of a separable evolutionary spectrum involving a deterministic modulating envelope is subject to interpretation further mathematical expressions elucidating the analogy between the wavelets based spectral representation and the traditional one involving trigonometric functions are derived finally the applicability and the physical soundness of the developed procedure are demonstrated by applying it to records of the kocaeli turkey earthquake 8 17 1999

damping identification in multi degree of freedom systems via a wavelet logarithmic decrement part 1 theory a wavelet based formula similar to the logarithmic decrement formula is introduced to estimate damping in multi degree of freedom systems from time domain responses both analytical and numerical approaches are investigated

continuous wavelet transform for modal identification using free decay response abstract this paper deals with the use of the continuous wavelet transform for system identification purposes the wavelet analysis of the free responses of a linear mechanical system allows the estimation of its natural frequencies viscous damping ratios and mode shapes using either the modulus or the phase of the wavelet transform a complete procedure for modal identification from free responses based on the continuous wavelet transform is presented two difficulties during the implementation of this technique are highlighted the edge effect and the choice of the time frequency localization of the wavelet transform some upper and lower bounds for the mother wavelet s parameters are given in order to improve the numerical computation three complex valued mother wavelets are studied and the full procedure is applied to a damped discrete system the correct choice of the mother wavelet s parameters leads to an accurate identification of the modal parameters

analytical 3 d p element for quadrilateral plates part 1 thick isotropic plate structures an analytical three dimensional 3 d p version element for the vibration analysis of arbitrary quadrilateral thick plates is presented with the additional hierarchical shape functions and analytically integrated element matrices the computed accuracy is considerably improved the computed natural frequencies of cantilever and simply supported square plates show that the convergence rate of the present element is very fast with respect to the number of hierarchical terms and it can predict very accurate modes the element is applicable to the free vibration analysis of quadrilateral polygonal plates as well as 3 d space structures the continuous wavelet transform cwt is applied for the identification of damping ratios based on the rayleigh damping model the damped vibration response is obtained a simple experiment is performed to verify the predicted vibration responses the results show that the proposed element is also efficient for the vibration response analysis of plates

disturbance attenuation and h optimization a design method based on the algebraic riccati equation this note presents a method for designing a state feedback control law to reduce the effect of disturbances on the output of a given linear system the problem under consideration involves attenuating the disturbances to a prespecified level the construction of the state feedback control law requires the solution of a certain algebraic riccati equation by applying the procedure with successively smaller values of the prespecifled disturbance level the result also provides an approach to the h infty optimization problem for the state feedback case

state space reconstruction in the presence of noise takens theorem demonstrates that in the absence of noise a multidimensional state space can be reconstructed from a scalar time series this theorem gives little guidance however about practical considerations for reconstructing a good state space we extend takens treatment applying statistical methods to incorporate the effects of observational noise and estimation error we define the distortion matrix which is proportional to the conditional covariance of a state given a series of noisy measurements and the noise amplification which is proportional to root mean square time series prediction errors with an ideal model we derive explicit formulae for these quantities and we prove that in the low noise limit minimizing the distortion is equivalent to minimizing the noise amplification we identify several different scaling regimes for distortion and noise amplification and derive asymptotic scaling laws when the dimension and lyapunov exponents are sufficiently large these scaling laws show that no matter how the state space is reconstructed there is an explosion in the noise amplification from a practical point of view determinism is lost and the time series is effectively a random process in the low noise large data limit we show that the technique of local singular value decomposition is an optimal coordinate transformation in the sense that it achieves the minimum distortion in a state space of the lowest possible dimension however in numerical experiments we find that estimation error complicates this issue for local approximation methods we analyze the effect of reconstruction on estimation error derive a scaling law and suggest an algorithm for reducing estimation errors

computation of normal modes from identified complex modes a technique is presented to compute a set of normal modes from a set of measured damped complex modes the number of elements in the modal vectors which is equal to the number of measurements can be larger than the number of modes under consideration it is also shown in this paper that the practice of normal mode approximation to complex modes can lead to considerably large errors when the modes are too complex a numerical example and a simulated experiment are presented to illustrate the concepts discussed and to support the theory presented

natural frequencies and damping estimation using wavelet transform of a frequency response function this paper deals with a general wavelet transform of frfs for linear systems complex fractional functions are used as wavelets and properties of the wavelet transform are studied then an efficient method for estimating natural frequencies and dampings is proposed the efficiency of the method is illustrated with both analytical and experimental data of frequency response functions

a high order purely frequency based harmonic balance formulation for continuation of periodic solutions combining the harmonic balance method hbm and a continuation method is a well known technique to follow the periodic solutions of dynamical systems when a control parameter is varied however since deriving the algebraic system containing the fourier coefficients can be a highly cumbersome procedure the classical hbm is often limited to polynomial quadratic and cubic nonlinearities and or a few harmonics several variations on the classical hbm such as the incremental hbm or the alternating frequency time domain hbm have been presented in the literature to overcome this shortcoming here we present an alternative approach that can be applied to a very large class of dynamical systems autonomous or forced with smooth equations the main idea is to systematically recast the dynamical system in quadratic polynomial form before applying the hbm once the equations have been rendered quadratic it becomes obvious to derive the algebraic system and solve it by the so called asymptotic numerical method anm continuation technique several classical examples are presented to illustrate the use of this numerical approach

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

a complex orthogonal decomposition for wave motion analysis a method is presented for decomposing wave motion into its principle components the basic idea is a complex generalization of proper orthogonal decomposition the method involves the representation of real oscillatory signals as complex analytic signals the relationship between complex modes and wave motion is explored from an ensemble of complex signals a complex correlation matrix is formed and its complex eigensolution is the basis of the decomposition like a complex singular value decomposition the complex eigenvectors contain standing and traveling characteristics a traveling index is proposed to quantify the relative degree of traveling and standing in a waveform a method of dissecting a wave mode into its traveling and standing parts is also proposed from the complex modes and modal coordinates frequencies wavelengths and characteristic wave speeds can be obtained the method is applied to traveling and standing wave examples

disturbance decoupling by measurement feedback with stability or pole placement in this paper we solve the disturbance decoupling problem by measurement feedback and requiring stability or pole placement on the closed loop system the problem is attacked using the geometric approach through the concepts of a bmod mathcal b invariant and controllability subspaces and their duals a mid k invariant and complementary observability subspaces the solution of this problem has an interesting structure consisting of a feedback processor which decomposes into i a disturbance decoupling loop ii a disturbance input stabilization or pole placement loop and iii a controlled output stabilization or pole placement loop

modal parameter identification through gabor expansion of response signals abstract a new method of identifying modal parameters by decomposing response signals with gabor transform is presented in this paper to estimate natural frequencies damping ratios and mode shapes of linear time invariant systems according to gabor expansion theory responses of a multi degree of freedom system can be decomposed into uncoupled signal components each vibrating at a single natural frequency from these uncoupled signals modal parameters are subsequently extracted with common methods the proposed method can process stationary and non stationary responses and requires no input signal except for the response signals generated by unknown excitation acting on a system in the sense of less restriction on the in out signals the approach based on time frequency decomposition is very general a simulation study on a simply supported beam under non stationary excitation has demonstrated that the proposed method is effective in parameter estimation

monotonicity of maximal solutions of algebraic riccati equations abstract a monotonicity result for the maximal solution of the equation xbb x a x xa q 0 q q a b stabilizable is proved

modal identification based on continuous wavelet transform and ambient excitation tests abstract this paper deals with the use of the continuous wavelet transform for modal identification from ambient vibration tests the wavelet analysis of the free responses of a linear mechanical system has been used to estimate its natural frequencies viscous damping ratios and mode shapes using either the modulus or the phase of the wavelet transform with ridge and skeleton notions this technique is extended in this paper to the response from ambient excitation tests based on the equivalent formulation between the free response and the correlation function of a linear mechanical system under stationary stochastic excitation the main novelties involve the new formulation of continuous wavelet transform and the use of the singular value decomposition algorithm for ridges and skeleton detection under the noisy conditions of ambient vibration tests a complete procedure for modal identification of ambient response including these new formulations is presented and then applied to numerical examples and experimental test to illustrate its validity

sliding window proper orthogonal decomposition application to linear and nonlinear modal identification abstract the proper orthogonal decomposition pod method is a tool well adapted to analyze vector signals whereas continuous gabor transform cgt is suitable for scalar signal with multi frequency components in this paper a method named sliding window proper orthogonal decomposition swpod combining pod and cgt to analyze multi degrees of freedom mdof vibration system responses is presented swpod gives access to the evolution of the coherent spacial structures and their frequency components versus time the method is of principal interest in the case of swept sine excitation of linear or nonlinear systems to access the resonance frequencies mode shapes and modal damping ratios a procedure is proposed to extract the linear and nonlinear normal modes of weakly damped mdof mechanical systems and illustrated using numerical examples

some new results on algebraic riccati equations arising in linear quadratic differential games and the stabilization of uncertain linear systems abstract this paper presents some new results on algebraic riccati equations arising in linear quadratic differential games the first result is a uniqueness result for solutions of the riccati equations under consideration the second result is concerned with riccati equations which arise in differential games in which the weighting on the minimizing control is allowed to approach zero it is shown that if a certain minimum phase condition is satisfied then the corresponding solution to the riccati equation will also approach zero

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

transfer function synthesis using frequency response data an improved method for transfer function synthesis from measured frequency response data is presented the improvement is due to a new scheme of matrix adaptation that eliminates measurement dependent inaccuracies step by step arbitrary coefficients can be set to any preassigned values so that account can be taken of previous knowledge of the investigated system an extension to integrating systems is developed the efficiency of the proposed method is demonstrated for an example taken from the literature

identification of coupled non linear modes from free vibration using time frequency representations abstract a new method based on time frequency representations is presented for identifying the non linear modal parameters of a multi degree of freedom non linear lightly damped mechanical system the coupled non linear modes are first introduced it is shown that by using the coupled non linear modes the free response can be expressed as a linear combination of frequency and amplitude modulated components this suggests the use of time frequency methods to characterize these modulation laws and then identify the coupled non linear modes these modulation laws are extracted by using an extended definition of the so called ridges of the continuous gabor transform which enables a more accurate estimation an identification procedure of the coupled non linear modes is proposed and the validity of the whole process is confirmed by performing computer simulations of different types of non linear elastic dynamic systems

testing for nonlinearity in time series the method of surrogate data we describe a statistical approach for identifying nonlinearity in time series the method first specifies some linear process as a null hypothesis then generates surrogate data sets which are consistent with this null hypothesis and finally computes a discriminating statistic for the original and for each of the surrogate data sets if the value computed for the original data is significantly different than the ensemble of values computed for the surrogate data then the null hypothesis is rejected and nonlinearity is detected we discuss various null hypotheses and discriminating statistics the method is demonstrated for numerical data generated by known chaotic systems and applied to a number of experimental time series which arise in the measurement of superfluids brain waves and sunspots we evaluate the statistical significance of the evidence for nonlinear structure in each case and illustrate aspects of the data which this approach identifies

physical interpretation of the proper orthogonal modes using the singular value decomposition abstract proper orthogonal decomposition is a statistical pattern analysis technique for finding the dominant structures called the proper orthogonal modes in an ensemble of spatially distributed data while the proper orthogonal modes are obtained through a statistical formulation they can be physically interpreted in the field of structural dynamics the purpose of this paper is thus to provide some insights into the physical interpretation of the proper orthogonal modes using the singular value decomposition

a new integral transform for linear systems identification the powerful multi degree of freedom curve fitting procedures necessitate relatively large computer storages hence it is interesting to seek linear system identification methods for implementation on a standard micro computer the present method introduces a new transform based on the cauchy weierstrass theorem such a transformation allows an increase in the influence of the poles and the zeros on a transfer function the introduction of a damping parameter permits the definition of a procedure for the precise identification of the parameters

asymptotic h sup infinity disturbance attenuation based on perfect observation a design method of controllers which ensure internal stability and attain asymptotically h sup infinity disturbance attenuation is presented the design procedure consists of two steps 1 to design an h sup infinity state feedback control via an algebraic riccati equation approach and 2 under a certain minimum phase condition to recover the achievable performance asymptotically by applying high gain observers it makes use of the perfect observation for the design of high gain observers it is shown that the asymptotic recovery can be attained by using reduced order observers provided there is no direct feedthrough of controls and disturbances in observations

statistical tests for deterministic effects in broad band time series we derive a normalized version of the indicators of savit and green and prove that these normalized statistics have asymptotically a normal distribution with a mean of zero and standard deviation of one if the time series is random in the sense of being lid independent and identically distributed we verify this result numerically and study the magnitude of the finite size effects we also show that these statistics are very sensitive to the existence of deterministic effects in the series even if the underlying deterministic structure is complex such as those generated by a chaotic system we show that with moderate amounts of data the statistics can easily indicate the presence of an underlying attractor even in the presence of iid noise which is as large as or greater than the signal finally we discuss the generalization of our approach to include 1 other null hypotheses besides lid which express assumptions of specific dependencies and 2 the study of deterministic effects between more than one time series

transient resonant interactions of finite linear chains with essentially nonlinear end attachments leading to passive energy pumping we study resonance capture phenomena leading to energy pumping in systems with multiple degrees of freedom dof composed of n linear oscillators weakly coupled to strongly nonlinear attachments possessing essential nonlinearizable cubic stiffness nonlinearities first we present numerical evidence of energy pumping in the systems under consideration i e of passive one way irreversible transfer of externally imparted energy to the nonlinear attachments provided that the energy is above a critical level to obtain a better understanding of the energy pumping phenomenon we reduce the dynamics governing the chain attachment interaction to a single nonlinear integro differential equation that governs exactly the transient dynamics of the strongly nonlinear attachment by introducing an approximation based on jacobian elliptic functions we derive an approximate set of two nonlinear integro differential modulation equations that govern the time evolution of the amplitude and phase of the motion of the attachment this set of modulation equations is studied both analytically and numerically we then perform a perturbation analysis in an neighborhood of a 1 1 resonant manifold of the system in order to study the attracting region in the reduced phase space of the system that is responsible for resonance capture and nonlinear energy pumping this analysis provides a justification of the numerical findings

reconstructing attractors from scalar time series a comparison of singular system and redundancy criteria abstract a delay vector phase space reconstruction in which the delay time satisfiesa minimum redundancy criterion is compared with a reconstruction obtained using a singular system approach minimum redundancy produces the better reconstruction the reconstructions are compared using a distortion functional d which measures how well the location of a point in the original phase space can be determined on the basis of its image under the reconstruction process the superiority of the redundancy analysis over the singular system analysis is found to arise from the former s foundation on the notion of general independence as opposed to the latter s foundation on the notion of linear independence