estimating time evolving partial coherence between signals via multivariate locally stationary wavelet processes we consider the problem of estimating time localized cross dependence in a collection of nonstationary signals to this end we develop the multivariate locally stationary wavelet framework which provides a time scale decomposition of the signals and thus naturally captures the time evolving scale specific cross dependence between components of the signals under the proposed model we rigorously define and estimate two forms of cross dependence measures wavelet coherence and wavelet partial coherence these dependence measures differ in a subtle but important way the former is a broad measure of dependence which may include indirect associations i e dependence between a pair of signals that is driven by another signal conversely wavelet partial coherence measures direct linear association between a pair of signals i e it removes the linear effect of other observed signals our time scale wavelet partial coherence estimation scheme thus provides a mechanism for identifying hidden dynamic relationships within a network of nonstationary signals as we demonstrate on electroencephalograms recorded in a visual motor experiment

a test for second order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series summary many time series are not second order stationary and it is not appropriate to analyse them by using methods designed for stationary series the paper introduces a new test for second order stationarity that detects kinds of departures from stationarity that are different from those based on fourier methods the new test is also computationally fast designed to work with gaussian and a wide range of non gaussian time series and can locate non stationarities in time and scale the test is demonstrated on earthquake explosion infant electrocardiogram and simulated time series showing varying degrees of stationarity the second main contribution develops approximate confidence intervals for time varying autocovariances for locally stationary series as the usual bands computed for stationary series are not appropriate our new bands enable practitioners to assess time varying autocovariances statistically and are exhibited on localized autocovariances of explosion and simulated time series

most recent changepoint detection in panel data detecting recent changepoints in time series can be important for short term prediction as we can then base predictions just on the data since the changepoint in many applications we have panel

variance change point detection under a smoothly changing mean trend with application to liver procurement literature on change point analysis mostly requires a sudden change in the data distribution either in a few parameters or the distribution as a whole we are interested in the scenario where the

analysis of subspace fitting and ml techniques for parameter estimation from sensor array data it is shown that the multidimensional signal subspace method termed weighted subspace fitting wsf is asymptotically efficient this results in a novel compact matrix expression for the cramer rao bound crb on the estimation error variance the asymptotic analysis of the maximum likelihood ml and wsf methods is extended to deterministic emitter signals the asymptotic properties of the estimates for this case are shown to be identical to the gaussian emitter signal case i e independent of the actual signal waveforms conclusions concerning the modeling aspect of the sensor array problem are drawn

detecting a shift in location some robust tests abstract the test statistic w suggested by hawkins 1977 and worsley 1979 for testing a sequence of observations for a shift in location is sensitive to the assumption that the distribution of the population being sampled is normal a modification of this statistic is proposed which is robust against heavy tailed distributions we also study the performance of several alternative testing procedures by means of a simulation experiment the farley hinich test 1975 and the homogeneity test discussed in brown durbin and evans 1975 perform well in the simulation experiment against heavy tailed distributions some applications to economic data are also discussed in the paper

maximum likelihood identification of non stationary operational data abstract in operation modal analysis has become a valid alternative for structures where a classic input output test would be difficult if not impossible to conduct due to practical considerations measurements are sometimes performed in patches roving sensor setups instead of covering the entire structure at once in practice one is often confronted with non stationary ambient excitation sources e g wind traffic waves etc since the scaling of operational mode shape estimates depends on the unknown level of the ambient excitation an extra effort is required in order to correctly merge the different parts of the mode shapes in this contribution two different approaches for merging operational mode shapes from non stationary data are proposed both methods are based upon a single maximum likelihood estimation procedure for comparison and validation both techniques were applied to non stationary data sets obtained by scanning laser vibrometry as well as the z24 bridge bench mark data

wild binary segmentation for multiple change point detection we propose a new technique called wild binary segmentation wbs for consistent estimation of the number and locations of multiple change points in data we assume that the number of change points can increase to infinity with the sample size due to a certain random localisation mechanism wbs works even for very short spacings between the change points and or very small jump magnitudes unlike standard binary segmentation on the other hand despite its use of localisation wbs does not require the choice of a window or span parameter and does not lead to a significant increase in computational complexity wbs is also easy to code we propose two stopping criteria for wbs one based on thresholding and the other based on what we term the strengthened schwarz information criterion we provide default recommended values of the parameters of the procedure and show that it offers very good practical performance in comparison with the state of the art the wbs methodology is implemented in the r package wbs available on cran in addition we provide a new proof of consistency of binary segmentation with improved rates of convergence as well as a corresponding result for wbs

slex analysis of multivariate nonstationary time series we develop a procedure for analyzing multivariate nonstationary time series using the slex library smooth localized complex exponentials which is a collection of bases each basis consisting of waveforms that are orthogonal and time localized versions of the fourier complex exponentials under the slex framework we build a family of multivariate models that can explicitly characterize the time varying spectral and coherence properties every model has a spectral representation in terms of a unique slex basis before selecting a model we first decompose the multivariate time series into nonstationary components with uncorrelated nonredundant spectral information the best slex model is selected using the penalized log energy criterion which we derive in this article to be the kullback leibler distance between a model and the slex principal components of the multivariate time series the model selection criterion takes into account all of the pairwise cross correlation simultaneously in the multivar

automatic choice of measurement locations for dynamic testing this paper examines the problem of choosing an optimum set of measurement locations for experimental modal testing and suggests criteria whereby the suitability of the chosen locations can be assessed two methods of coordinate selection are used one based on guyan reduction and the other on the fisher information matrix each begins with a detailed finite element model of the structure being tested both procedures reduce this model by one degree of freedom at a time until the number of degrees of freedom in the reduced model equals the number of measurement locations required the choice of the eliminated coordinates is generally automatic and the coordinates of the reduced model are those used for modal testing

detection of change in the spatiotemporal mean function summary the paper develops inferential methodology for detecting a change in the annual pattern of an environmental variable measured at fixed locations in a spatial region using a framework built on functional data analysis we model observations as a collection of function valued time sequences available at many sites each sequence is modelled as an annual mean function which may change plus a sequence of error functions which are spatially correlated the tests statistics extend the cumulative sum paradigm to this more complex setting their asymptotic distributions are not parameter free because of the spatial dependence but can be effectively approximated by monte carlo simulations the new methodology is applied to precipitation data its finite sample performance is assessed by a simulation study

detection of changes in multivariate time series with application to eeg data the primary contributions of this article are rigorously developed novel statistical methods for detecting change points in multivariate time series we extend the class of score type change point statistics considered in 2007 by huskova praskova and steinebach to the vector autoregressive var case and the epidemic change alternative our proposed procedures do not require the observed time series to actually follow the var model instead following the strategy implicitly employed by practitioners our approach takes model misspecification into account so that our detection procedure uses the model background merely for feature extraction we derive the asymptotic distributions of our test statistics and show that our procedure has asymptotic power of 1 the proposed test statistics require the estimation of the inverse of the long run covariance matrix which is particularly difficult in higher dimensional settings i e where the dimension of the time series and the dimension of the parameter vecto

merging sensor data from multiple measurement set ups for non stationary subspace based modal analysis processing sensor data from multiple non simultaneously recorded measurement set ups for structural analysis is often achieved by merging identification results obtained from records corresponding to different sensor pools since pole matching and eigenvector gluing might not be consistent in some cases the question arises to merge the data first and then process them globally subspace identification algorithms have proven efficient for performing output only modal analysis of mechanical systems subject to uncontrolled unmeasured and non stationary excitation the purpose of this paper is to investigate as to how subspace based output only modal analysis algorithms can be adapted to handle the multi patch measurements set up numerical results obtained on both laboratory and real application examples are reported which show the relevance and usefulness of the proposed algorithm

wavelet processes and adaptive estimation of the evolutionary wavelet spectrum this article defines and studies a new class of non stationary random processes constructed from discrete non decimated wavelets which generalizes the cramer fourier representation of stationary time series we define an evolutionary wavelet spectrum ews which quantifies how process power varies locally over time and scale we show how the ews may be rigorously estimated by a smoothed wavelet periodogram and how both these quantities may be inverted to provide an estimable time localized autocovariance we illustrate our theory with a pedagogical example based on discrete non decimated haar wavelets and also a real medical time series example

a test for second order stationarity of a multivariate time series it is well known that the discrete fourier transforms dft of a second order stationary time series between two distinct fourier frequencies are asymptotically uncorrelated in contrast for a large class of second order nonstationary time series including locally stationary time series this property does not hold in this paper these starkly differing properties are used to define a global test for stationarity based on the dft of a vector time series it is shown that the test statistic under the null of stationarity asymptotically has a chi squared distribution whereas under the alternative of local stationarity asymptotically it has a noncentral chi squared distribution further if the time series is gaussian and stationary the test statistic is pivotal however in many econometric applications the assumption of gaussianity can be too strong but under weaker conditions the test statistic involves an unknown variance that is extremely difficult to directly estimate from the data to overcome this issue a scheme to estimate the unknown variance based on the stationary bootstrap is proposed the properties of the stationary bootstrap under both stationarity and nonstationarity are derived these results are used to show consistency of the bootstrap estimator under stationarity and to derive the power of the test under nonstationarity the method is illustrated with some simulations the test is also used to test for stationarity of ftse 100 and dax 30 stock indexes from january 2011 december 2012

consistent and powerful graph based change point test for high dimensional data a change point detection is proposed by using a bayesian type statistic based on the shortest hamiltonian path and the change point is estimated by using ratio cut a permutation procedure is applied to approximate the significance of bayesian type statistics the change point test is proven to be consistent and an error probability in change point estimation is provided the test is very powerful against alternatives with a shift in variance and is accurate in change point estimation as shown in simulation studies its applicability in tracking cell division is illustrated

testing and locating variance changepoints with application to stock prices abstract this article explores testing and locating multiple variance changepoints in a sequence of independent gaussian random variables assuming known and common mean this type of problem is very common in applied economics and finance a binary procedure combined with the schwarz information criterion sic is used to search all of the possible variance changepoints existing in the sequence the simulated power of the proposed procedure is compared to that of the cusum procedure used by inclan and tiao to cope with variance changepoints the sic and unbiased sic for this problem are derived to obtain the percentage points of the sic criterion the asymptotic null distribution of a function of the sic is obtained and then the approximate percentage points of the sic are tabulated finally the results are applied to the weekly stock prices the unknown but common mean case is also outlined at the end

statistical model based damage detection and localization subspace based residuals and damage to noise sensitivity ratios the vibration based structural health monitoring problem is addressed as the double task of detecting damages modeled as changes in the eigenstructure of a linear dynamic system and localizing the detected damages within a fem of the monitored structure the proposed damage detection algorithm is based on a residual generated from a stochastic subspace based covariance driven identification method and on the statistical local approach to the design of detection algorithms this algorithm basically computes a global test which performs a sensitivity analysis of the residuals to the damages relative to uncertainties and noises how this residual relates to some residuals for damage localization and model updating is discussed damage localization is stated as a detection problem this problem is addressed by plugging aggregated sensitivities of the modes and mode shapes w r t fem structural parameters in the above setting this results in directional tests which perform the same type of damage to noise sensitivity analysis of the residual as for damage detection how the sensitivity aggregation mechanism relates to sub structuring is outlined numerical results obtained on one example are reported

selection of noisy measurement locations for error reduction in static parameter identification an incomplete set of noisy static force and displacement measurements is used for parameter identification of structures at the element level measurement location and the level of accuracy in the measured data can drastically affect the accuracy of the identified parameters a heuristic method is presented to select a limited number of degrees of freedom dof to perform a successful parameter identification and to reduce the impact of measurement errors on the identified parameters this pretest simulation uses an error sensitivity analysis to determine the effect of measurement errors on the parameter estimates the selected dof can be used for nondestructive testing and health monitoring of structures two numerical examples one for a truss and one for a frame are presented to demonstrate that using the measurements at the selected subset of dof can limit the error in the parameter estimates

detecting relevant changes in time series models summary most of the literature on change point analysis by means of hypothesis testing considers hypotheses of the form h0 1 2versush1 1 2 where 1 and 2 denote parameters of the process before and after a change point the paper takes a different perspective and investigates the null hypotheses of no relevant changes i e h0 1 2 where is an appropriate norm this formulation of the testing problem is motivated by the fact that in many applications a modification of the statistical analysis might not be necessary if the difference between the parameters before and after the change point is small a general approach to problems of this type is developed which is based on the cumulative sum principle for the asymptotic analysis weak convergence of the sequential empirical process must be established under the alternative of non stationarity and it is shown that the resulting test statistic is asymptotically normally distributed the results can also be used to establish similarity of the parameters i e h1 1 2 at a controlled type 1 error and to estimate the magnitude 1 2 of the change with a corresponding confidence interval several applications of the methodology are given including tests for relevant changes in the mean variance parameter in a linear regression model and distribution function among others the finite sample properties of the new tests are investigated by means of a simulation study and illustrated by analysing a data example from portfolio management

a tree based model for homogeneous groupings of multinomials the motivation of this paper is to provide a tree based method for grouping multinomial data according to their classification probability vectors we produce an initial tree by binary recursive partitioning whereby multinomials are successively split into two subsets and the splits are determined by maximizing the likelihood function if the number of multinomials k is too large we propose to order the multinomials and then build the initial tree based on a dramatically smaller number k 1 of possible splits the tree is then pruned from the bottom up the pruning process involves a sequence of hypothesis tests of a single homogeneous group against the alternative that there are two distinct internally homogeneous groups as pruning criteria the bayesian information criterion and the wilcoxon rank sum test are proposed the tree based model is illustrated on genetic sequence data homogeneous groupings of genetic sequences present new opportunities to understand and align these sequences copyright 2005 john wiley sons ltd

estimating a change point in a sequence of very high dimensional covariance matrices this article considers the problem of estimating a change point in the covariance matrix in a sequence of high dimensional vectors where the dimension is substantially larger than the sample size

variance change point detection for fractional brownian motion based on the likelihood ratio test abstract fractional brownian motion is one of the main stochastic processes used for describing the long range dependence phenomenon for self similar processes it appears that for many real time series characteristics of the data change significantly over time such behaviour one can observe in many applications including physical and biological experiments in this paper we present a new technique for the critical change point detection for cases where the data under consideration are driven by fractional brownian motion with a time changed diffusion coefficient the proposed methodology is based on the likelihood ratio approach and represents an extension of a similar methodology used for brownian motion the process with independent increments here we also propose a statistical test for testing the significance of the estimated critical point in addition to that an extensive simulation study is provided to test the performance of the proposed method

multiple change point detection for high dimensional time series via sparsified binary segmentation time series segmentation a k a multiple change point detection is a well established problem however few solutions are designed specifically for high dimensional situations in this paper our interest is in segmenting the second order structure of a high dimensional time series in a generic step of a binary segmentation algorithm for multivariate time series one natural solution is to combine cusum statistics obtained from local periodograms and cross periodograms of the components of the input time series however the standard maximum and average methods for doing so often fail in high dimensions when for example the change points are sparse across the panel or the cusum statistics are spuriously large in this paper we propose the sparsified binary segmentation sbs algorithm which aggregates the cusum statistics by adding only those that pass a certain threshold this sparsifying step reduces the impact of irrelevant noisy contributions which is particularly beneficial in high dimensions in order to show the consistency of sbs we introduce the multivariate locally stationary wavelet model for time series which is a separate contribution of this work

structural break estimation for nonstationary time series models this article considers the problem of modeling a class of nonstationary time series using piecewise autoregressive ar processes the number and locations of the piecewise ar segments as well as the orders of the respective ar processes are assumed unknown the minimum description length principle is applied to compare various segmented ar fits to the data the goal is to find the best combination of the number of segments the lengths of the segments and the orders of the piecewise ar processes such a best combination is implicitly defined as the optimizer of an objective function and a genetic algorithm is implemented to solve this difficult optimization problem numerical results from simulation experiments and real data analyses show that the procedure has excellent empirical properties the segmentation of multivariate time series is also considered assuming that the true underlying model is a segmented autoregression this procedure is shown to be consistent for estimating the location of

sensor placement methodologies for dynamic testing two methods are presented for structural sensor placement the first scheme selects the most linearly independent impulse responses at all candidate sensor locations from a gram schmidt orthogonalization procedure the second scheme is based on a principal component analysis and iteratively removes sensors that do not contribute significant information to the fisher information matrix furthermore use of a model reduction criterion is proposed to address the optimality issue several sensor placement methods were implemented to compare results and were applied to an euler bernoulli beam and a cantilevered frame structure it is shown that the proposed frequency criterion appears to be a selective criterion for choosing optimum sensor locations finally the optimum measurement locations from several of the methods studied yield acceptable results based on data from an experimental study on the frame structure

multiple change point analysis fast implementation and strong consistency one of the main challenges in identifying structural changes in stochastic processes is to carry out analysis for time series with dependency structure in a computationally tractable way another challenge is that the number of true change points is usually unknown requiring a suitable model selection criterion to arrive at informative conclusions to address the first challenge we model the data generating process as a segment wise autoregression which is composed of several segments time epochs each of which modeled by an autoregressive model we propose a multiwindow method that is both effective and efficient for discovering the structural changes the proposed approach was motivated by transforming a segment wise autoregression into a multivariate time series that is asymptotically segment wise independent and identically distributed to address the second challenge we derive theoretical guarantees for almost surely selecting the true number of change points of segment wise independent multivariate time series specifically under mild assumptions we show that a bayesian information criterion like criterion gives a strongly consistent selection of the optimal number of change points while an akaike information criterion like criterion cannot finally we demonstrate the theory and strength of the proposed algorithms by experiments on both synthetic and real world data including the eastern u s temperature data and the el nino data the experiment leads to some interesting discoveries about temporal variability of the summer time temperature over the eastern u s and about the most dominant factor of ocean influence on climate which were also discovered by environmental scientists

automatic statistical analysis of bivariate nonstationary time series we propose a new method for analyzing bivariate nonstationary time series the proposed method is a statistical procedure that automatically segments the time series into approximately stationary blocks and selects the span to be used to obtain the smoothed estimates of the time varying spectra and coherence it is based on the smooth localized complex exponential slex transform which forms a library of orthogonal complex valued transforms that are simultaneously localized in time and frequency we show that the smoothed slex periodograms are consistent estimators report simulation results and apply the method to a two channel electroencephalogram dataset recorded during an epileptic seizure

an improved bayesian information criterion for multiple change point models in multiple change point analysis inferring the number of change points is often achieved by minimizing a selection criterion that trades off data fidelity with complexity we address the open problem of defining a selection criterion adapted to the context of multiple change point analysis our approach is inspired by the schwarz seminal formulation of the bayesian information criterion bic similarly we introduce priors here describing the occurrence of change points and we use the laplace approximation to derive a closed form expression of the criterion differently from this previous work we take advantage of the a priori information introduced instead of asymptotically eliminating the dependence on priors results obtained on simulated series show a substantial gain in performance versus recent alternative criteria used in multiple change point analysis results also show that the a priori information introduced in our criterion on the regularity of interevent times is the main driver of this s

modular subspace based system identification from multi setup measurements subspace identification algorithms are efficient for output only eigenstructure identification of linear mimo systems the problem of merging sensor data obtained from moving and nonsimultaneously recorded measurement setups under varying excitation is considered to address the problem of dimension explosion when retrieving the system matrices of the complete system a modular and scalable approach is proposed adapted to a large class of subspace methods observability matrices are normalized and merged to retrieve global system matrices

use of cumulative sums of squares for retrospective detection of changes of variance abstract this article studies the problem of multiple change points in the variance of a sequence of independent observations we propose a procedure to detect variance changes based on an iterated cumulative sums of squares icss algorithm we study the properties of the centered cumulative sum of squares function and give an intuitive basis for the icss algorithm for series of moderate size i e 200 observations and beyond the icss algorithm offers results comparable to those obtained by a bayesian approach or by likelihood ratio tests without the heavy computational burden required by these approaches simulation results comparing the icss algorithm to other approaches are presented

optimal sensor location for detecting changes in dynamical behavior we address the problem of optimal sensor location for monitoring the eigenstructure of a multivariable dynamical system the criterions which are optimized are the power of new tests designed for detecting and diagnosing changes in the eigencharacteristics of a system 3 12 the key points are the choice of the parameterization for computing the criterion and the comparison of designs with a different number of sensors the discussion of the numerical results for sensor location includes the analysis of the effect of the geometry of the unknown excitation

convergence acceleration of iterative modal reduction methods an accelerated method is presented for the iterative condensation of eigenproblems the present study was motivated by the improved reduction system and the succession level approximate reduction sar the reduction procedures are supplemented with the second order approximation in the series expansion of the system transformation the reduced equation of an equivalent system and the transformation matrix are updated in an iterative manner in addition systematicderivation andcomparisonoftheequationsinvolvedin variouscondensationshave been sought thematrixupdateincorporatesnotonlyinverseiteration butalsosubspacetransformation implicitly theseriesexpansion canbeconsideredasrepeatedupdatesofthetransformationmatrixthroughinverseiteration the solution accuracy is sensitive to the selection of the degrees of freedom for which sequential elimination or energy method may be preferable when a poor selection causes a sudden failure of the updatemethod the hybrid dynamic condensation can be used the method of sar is closely related to the hybrid dynamic condensation nomenclature as kss i 1 mss in eq 10 bpp bsp submatrices for inertia force in eq 68 dg mg i 1 kg dynamic matrix in eq 13 ke me equivalent structural matrices in eq 26 kg mg reduced matrices in guyan s condensation kr mr structural matrices reduced through tr kx mx structural matrices reduced through tx k ka b stiffness matrix and submatrices m ma b mass matrix and submatrices p number of primary degrees of freedom q pp modal matrix for generalized coordinates r residual error in eigenproblem s number of secondary degrees of freedom t exact transformation matrix in eq 22 ti matrices in series of eqs 15 and 18 tp system transformation matrix tr approximate transformation matrix tx improved transformation matrix in eq 40 t0 transformation in guyan s condensation t k frequency dependent transformation in eq 3 x p improved modal matrix x pp xsp submatrices of x p e convergence tolerance k p

sensor array processing based on subspace fitting algorithms for estimating unknown signal parameters from the measured output of a sensor array are considered in connection with the subspace fitting problem the methods considered are the deterministic maximum likelihood method ml esprit and a recently proposed multidimensional signal subspace method these methods are formulated in a subspace fitting based framework which provides insight into their algebraic and asymptotic relations it is shown that by introducing a specific weighting matrix the multidimensional signal subspace method can achieve the same asymptotic properties as the ml method the asymptotic distribution of the estimation error is derived for a general subspace weighting and the weighting that provides minimum variance estimates is identified the resulting optimal technique is termed the weighted subspace fitting wsf method numerical examples indicate that the asymptotic variance of the wsf estimates coincides with the cramer rao bound the performance improvement compared to the other techniques is found to be most prominent for highly correlated signals

a semiparametric changepoint model a semiparametric changepoint model is considered and the empirical likelihood method is applied to detect the change from a distribution to a weighted distribution in a sequence of independent random variables the maximum likelihood changepoint estimator is shown to be consistent the empirical likelihood ratio test statistic is proved to have the same limit null distribution as that with parametric models a data based test for the validity of the models is also proposed simulation shows the sensitivity and robustness of the semiparametric approach the methods are applied to some classical datasets such as the nile river data and stock price data

how much information does dependence between wavelet coefficients contain abstractthis article is motivated by several articles that propose statistical inference where the independence of wavelet coefficients for both short as well as long range dependent time series is assumed we focus on the sample variance and investigate the influence of the dependence between wavelet coefficients and this statistic to this end we derive asymptotic distributional properties of the sample variance for a time series that is synthesized ignoring some or all dependence between wavelet coefficients we show that the second order properties differ from the those of the true time series whose wavelet coefficients have the same marginal distribution except in the independent gaussian case this holds true even if the dependency is correct within each level and only the dependence between levels is ignored in the case of sample autocovariances and sample autocorrelations at lag one we indicate that first order properties are erroneous in a second step we investigate several nonparametric b

simultaneous multiple change point and factor analysis for high dimensional time series abstract we propose the first comprehensive treatment of high dimensional time series factor models with multiple change points in their second order structure we operate under the most flexible definition of piecewise stationarity and estimate the number and locations of change points consistently as well as identifying whether they originate in the common or idiosyncratic components through the use of wavelets we transform the problem of change point detection in the second order structure of a high dimensional time series into the relatively easier problem of change point detection in the means of high dimensional panel data also our methodology circumvents the difficult issue of the accurate estimation of the true number of factors in the presence of multiple change points by adopting a screening procedure we further show that consistent factor analysis is achieved over each segment defined by the change points estimated by the proposed methodology in extensive simulation studies we observe that factor analysis prior to change point detection improves the detectability of change points and identify and describe an interesting spillover effect in which substantial breaks in the idiosyncratic components get naturally enough identified as change points in the common components which prompts us to regard the corresponding change points as also acting as a form of factors our methodology is implemented in the r package factorcpt available from cran

single sample modal identification of a nonstationary stochastic process gauss markov processes excited by nonstationary noises are encountered in the modeling of vibrating systems we prove that the classical instrumental variable method as well as the ho kalman realization algorithm for identifying the pole part modal characteristics of the model are consistent when used on a single sample of the nonstationary signal

haar fisz estimation of evolutionary wavelet spectra summary we propose a new haar fisz technique for estimating the time varying piecewise constant local variance of a locally stationary gaussian time series we apply our technique to the estimation of the spectral structure in the locally stationary wavelet model our method combines haar wavelets and the variance stabilizing fisz transform the resulting estimator is mean square consistent rapidly computable and easy to implement and performs well in practice we also introduce the haar fisz transform a device for stabilizing the variance of scaled x2 data and bringing their distribution close to gaussianity

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

state space formulation a solution to modal parameter estimation abstract as an alternative to fourier techniques based on transfer function fitting modal parameters identification methods derived from a state space formulation of the dynamic equation have been recently studied and developed this formulation leads to the solution of the modal problem via multi dimensional arma model parameters identification in this paper the transition from the dynamic equation to the arma model is described and the algorithms of identification are explained for the very common case of uncontrolled and unmeasured excitation these techniques the qualities of which have been established during extensive processing of offshore structures measurements have been generalized to more complex excitation models such as those of turbo alternators several examples illustrate these different application domains

break detection in the covariance structure of multivariate time series models in this paper we introduce an asymptotic test procedure to assess the stability of volatilities and cross volatilites of linear and nonlinear multivariate time series models the test is very flexible as it can be applied for example to many of the multivariate garch models established in the literature and also works well in the case of high dimensionality of the underlying data since it is nonparametric the procedure avoids the difficulties associated with parametric model selection model fitting and parameter estimation we provide the theoretical foundation for the test and demonstrate its applicability via a simulation study and an analysis of financial data extensions to multiple changes and the case of infinite fourth moments are also discussed

direct approach in inverse problems for dynamic systems a direct and effective approach is presented for the inverse problem of dynamic structural systems which is related to structural optimization system identification and damage detection the structural modifications are sought for the characteristic changes assigned from the design goals or modal measurements a finite element method is used for the system analysis and inverse problem mathematical programming techniques are applied for the minimization of the deviation of the finite element model from the desired inverse system along with an objective function of least structural change the modal method is based on the perturbation equations of a set of selected degrees of freedom and the energy equation associated with the frequency change the mode shape change is expressed as the sum of the baseline mode shape and complementary vector which plays a very important role in the search for the inverse solution the linear perturbation equation is employed to get an initial approximation which can be improved through iterations with the nonlinear perturbation equation the proposed method does not involve the system reduction therefore it is believed to be superior to conventional methods which suffer from the residual error due to transformation of the eigenproblem

a unified matrix polynomial approach to modal identification abstract one important current focus of modal identification is a reformulation of modal parameter estimation algorithms into a single consistent mathematical formulation with a corresponding set of definitions and unifying concepts particularly a matrix polynomial approach is used to unify the presentation with respect to current algorithms such as the least squares complex exponential lsce the polyreference time domain ptd ibrahim time domain itd eigensystem realization algorithm era rational fraction polynomial rfp polyreference frequency domain pfd and the complex mode indication function cmif methods using this unified matrix polynomial approach umpa allows a discussion of the similarities and differences of the commonly used methods the use of least squares ls total least squares tls double least squares dls and singular value decomposition svd methods is discussed in order to take advantage of redundant measurement data eigenvalue and svd transformation methods are utilized to reduce the effective size of the resulting eigenvalue eigenvector problem as well