Journal ArticleDOI
An eigensystem realization algorithm for modal parameter identification and model reduction
Jer-Nan Juang,Richard S. Pappa +1 more
TLDR
A new approach is introduced in conjunction with the singular value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm.Abstract:
A method, called the Eigensystem Realization Algorithm (ERA), is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system modes and noise modes. For illustration of the algorithm, examples are shown using simulation data and experimental data for a rectangular grid structure.read more
Citations
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A review of structural health monitoring literature 1996-2001
TL;DR: An updated review covering the years 1996 2001 will summarize the outcome of an updated review of the structural health monitoring literature, finding that although there are many more SHM studies being reported, the investigators, in general, have not yet fully embraced the well-developed tools from statistical pattern recognition.
Journal ArticleDOI
Modal identification of output-only systems using frequency domain decomposition
TL;DR: By introducing a decomposition of the spectral density function matrix, the response spectra can be separated into a set of single degree of freedom systems, each corresponding to an individual mode, and close modes can be identified with high accuracy even in the case of strong noise contamination of the signals.
Book
Optimal Estimation of Dynamic Systems
TL;DR: In this paper, Kronecker Factorization and Levenberg-Marquardt method for least square estimation is used to estimate the probability of an error in a prior state estimate.
Journal ArticleDOI
On dynamic mode decomposition: Theory and applications
TL;DR: In this paper, the authors define dynamic mode decomposition (DMD) as the eigendecomposition of an approximating linear operator, and propose sampling strategies that increase computational efficiency and mitigate the effects of noise.
Journal ArticleDOI
Modal Analysis of Fluid Flows: An Overview
Kunihiko Taira,Steven L. Brunton,Scott T. M. Dawson,Clarence W. Rowley,Tim Colonius,Beverley McKeon,Oliver T. Schmidt,Stanislav Gordeyev,Vassilios Theofilis,Lawrence Ukeiley +9 more
TL;DR: The intent of this document is to provide an introduction to modal analysis that is accessible to the larger fluid dynamics community and presents a brief overview of several of the well-established techniques.
References
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Book
The Theory of Matrices
TL;DR: In this article, the Routh-Hurwitz problem of singular pencils of matrices has been studied in the context of systems of linear differential equations with variable coefficients, and its applications to the analysis of complex matrices have been discussed.
Journal ArticleDOI
Principal component analysis in linear systems: Controllability, observability, and model reduction
TL;DR: In this paper, it is shown that principal component analysis (PCA) is a powerful tool for coping with structural instability in dynamic systems, and it is proposed that the first step in model reduction is to apply the mechanics of minimal realization using these working subspaces.
Journal ArticleDOI
Singular value decomposition and least squares solutions
Gene H. Golub,C. Reinsch +1 more
TL;DR: The decomposition of A is called the singular value decomposition (SVD) and the diagonal elements of ∑ are the non-negative square roots of the eigenvalues of A T A; they are called singular values.
Journal ArticleDOI
Mathematical description of linear dynamical systems
TL;DR: In this paper, it is shown that the input/output relations determine only one part of a system, that which is completely observable and completely controllable, and methods are given for calculating irreducible realization of a given impulse-response matrix.
Journal ArticleDOI
The singular value decomposition: Its computation and some applications
TL;DR: This work provides a tutorial introduction to certain numerical computations both in linear algebra and linear systems in the context of bounded arithmetic and the singular value decomposition (SVD).