Complex Eigenvalue Analysis for Structures with Viscoelastic Behavior

This document deals with a method for eigenvalue extraction for the analysis of structures with viscoelastic materials. A generalized Maxwell model is used to model linear viscoelasticity. Such kind of model necessitates a state-space formulation to perform eigenvalue analysis with standard solvers. This formulation is very close to ADF formulation. The use of several materials on the same structure and during the same analysis may lead to a large number of internal states. This article purpose is to identify simultaneously all the viscoelastic materials and to constrain them to have the same time-constants. As it is usually possible, the size of the state-space problem is therefore widely reduced. Moreover, an accurate method for reducing mass and stiffness operators is proposed; The enhancement of the modal basis allows to obtain good results with large reduction. As the length of the paper is limited, only theoretical development are presented in the present paper while numerical results will be presented in the conference.Comment: ASME 2011 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference (IDETC/CIE2011), Washington : France (2011

On errors-in-variables estimation with unknown noise variance ratio

We propose an estimation method for an errors-in-variables model with unknown input and output noise variances. The main assumption that allows identifiability of the model is clustering of the data into two clusters that are distinct in a certain specified sense. We show an application of the proposed method for system identification

Outliers in dynamic factor models

Dynamic factor models have a wide range of applications in econometrics and applied economics. The basic motivation resides in their capability of reducing a large set of time series to only few indicators (factors). If the number of time series is large compared to the available number of observations then most information may be conveyed to the factors. This way low dimension models may be estimated for explaining and forecasting one or more time series of interest. It is desirable that outlier free time series be available for estimation. In practice, outlying observations are likely to arise at unknown dates due, for instance, to external unusual events or gross data entry errors. Several methods for outlier detection in time series are available. Most methods, however, apply to univariate time series while even methods designed for handling the multivariate framework do not include dynamic factor models explicitly. A method for discovering outliers occurrences in a dynamic factor model is introduced that is based on linear transforms of the observed data. Some strategies to separate outliers that add to the model and outliers within the common component are discussed. Applications to simulated and real data sets are presented to check the effectiveness of the proposed method.Comment: Published in at http://dx.doi.org/10.1214/07-EJS082 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of Mathematical Statistics (http://www.imstat.org

Significance Regression: A Statistical Approach to Biased Linear Regression and Partial Least Squares

This paper first examines the properties of biased regressors that proceed by restricting the search for the optimal regressor to a subspace. These properties suggest features such biased regression methods should incorporate. Motivated by these observations, this work proposes a new formulation for biased regression derived from the principle of statistical significance. This new formulation, significance regression (SR), leads to partial least squares (PLS) under certain model assumptions and to more general methods under various other model kumptions. For models with multiple outputs, SR will be shown to have certain advantages over PLS. Using the new formulation a significance test is advanced for determining the number of directions to be used; for PLS, cross-validation has been the primary method for determining this quantity. The prediction and estimation properties of SR are discussed. A brief numerical example illustrates the relationship between SR and PLS

Sensitivity analysis and approximation methods for general eigenvalue problems

Optimization of dynamic systems involving complex non-hermitian matrices is often computationally expensive. Major contributors to the computational expense are the sensitivity analysis and reanalysis of a modified design. The present work seeks to alleviate this computational burden by identifying efficient sensitivity analysis and approximate reanalysis methods. For the algebraic eigenvalue problem involving non-hermitian matrices, algorithms for sensitivity analysis and approximate reanalysis are classified, compared and evaluated for efficiency and accuracy. Proper eigenvector normalization is discussed. An improved method for calculating derivatives of eigenvectors is proposed based on a more rational normalization condition and taking advantage of matrix sparsity. Important numerical aspects of this method are also discussed. To alleviate the problem of reanalysis, various approximation methods for eigenvalues are proposed and evaluated. Linear and quadratic approximations are based directly on the Taylor series. Several approximation methods are developed based on the generalized Rayleigh quotient for the eigenvalue problem. Approximation methods based on trace theorem give high accuracy without needing any derivatives. Operation counts for the computation of the approximations are given. General recommendations are made for the selection of appropriate approximation technique as a function of the matrix size, number of design variables, number of eigenvalues of interest and the number of design points at which approximation is sought

Solving nonlinear rational expectations models by eigenvalue-eigenvector decompositions

We provide a summarized presentation of solution methods for rational expectations models, based on eigenvalue/eigenvector decompositions. These methods solve systems of stochastic linear difference equations by relying on the use of stability conditions derived from the eigenvectors associated to unstable eigenvalues of the coefficient matrices in the system. For nonlinear models, a linear approximation must be obtained, and the stability conditions are approximate, This is however, the only source of approximation error, since the nonlinear structure of the original model is used to produce the numerical solution. After applying the method to a baseline stochastic growth model, we explain how it can be used: i) to salve some identification problems that may arise in standard growth models, and ii) to solve endogenous growth models