Physical interpretation of the proper orthogonal modes using the singular value decomposition
31 Jan 2002-Journal of Sound and Vibration (Academic Press Ltd Elsevier Science Ltd)-Vol. 249, Iss: 5, pp 849-865
TL;DR: In this paper, the authors provide insights into the physical interpretation of the proper orthogonal modes using the singular value decomposition (SVD) in the field of structural dynamics.
About: This article is published in Journal of Sound and Vibration.The article was published on 2002-01-31. It has received 284 citations till now. The article focuses on the topics: Orthogonal basis & Principal component analysis.
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TL;DR: In this article, a review of the past and recent developments in system identification of nonlinear dynamical structures is presented, highlighting their assets and limitations and identifying future directions in this research area.
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TL;DR: In this article, a different approach is adopted, and proper orthogonal decomposition is considered, and modes extracted from the decomposition may serve two purposes, namely order reduction by projecting high-dimensional data into a lower-dimensional space and feature extraction by revealing relevant but unexpected structure hidden in the data.
Abstract: Modal analysis is used extensively for understanding the dynamic behavior of structures. However, a major concern for structural dynamicists is that its validity is limited to linear structures. New developments have been proposed in order to examine nonlinear systems, among which the theory based on nonlinear normal modes is indubitably the most appealing. In this paper, a different approach is adopted, and proper orthogonal decomposition is considered. The modes extracted from the decomposition may serve two purposes, namely order reduction by projecting high-dimensional data into a lower-dimensional space and feature extraction by revealing relevant but unexpected structure hidden in the data. The utility of the method for dynamic characterization and order reduction of linear and nonlinear mechanical systems is demonstrated in this study.
838 citations
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28 Feb 2019TL;DR: In this paper, the authors bring together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science, and highlight many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy.
Abstract: Data-driven discovery is revolutionizing the modeling, prediction, and control of complex systems. This textbook brings together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science. It highlights many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy. Aimed at advanced undergraduate and beginning graduate students in the engineering and physical sciences, the text presents a range of topics and methods from introductory to state of the art.
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TL;DR: In this article, the relation between the vibration modes of mechanical systems and the modes computed through a blind source separation technique called independent component analysis (ICA) was investigated for free and random vibrations of weakly damped systems.
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"Physical interpretation of the prop..." refers background in this paper
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TL;DR: In this article, a text designed to make multivariate techniques available to behavioural, social, biological and medical students is presented, which includes an approach to multivariate inference based on the union-intersection and generalized likelihood ratio principles.
Abstract: A text designed to make multivariate techniques available to behavioural, social, biological and medical students. Special features include an approach to multivariate inference based on the union-intersection and generalized likelihood ratio principles.
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01 Jan 1996TL;DR: In this article, the authors present a review of rigor properties of low-dimensional models and their applications in the field of fluid mechanics. But they do not consider the effects of random perturbation on models.
Abstract: Preface Part I. Turbulence: 1. Introduction 2. Coherent structures 3. Proper orthogonal decomposition 4. Galerkin projection Part II. Dynamical Systems: 5. Qualitative theory 6. Symmetry 7. One-dimensional 'turbulence' 8. Randomly perturbed systems Part III. 9. Low-dimensional Models: 10. Behaviour of the models Part IV. Other Applications and Related Work: 11. Some other fluid problems 12. Review: prospects for rigor Bibliography.
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01 Oct 1979TL;DR: This best-selling text focuses on the analysis and design of complicated dynamics systems and is recommended by engineers, applied mathematicians, and undergraduates.
Abstract: This best-selling text focuses on the analysis and design of complicated dynamics systems CHOICE called it "a high-level, concise book that could well be used as a reference by engineers, applied mathematicians, and undergraduates The format is good, the presentation clear, the diagrams instructive, the examples and problems helpfulReferences and a multiple-choice examination are included"
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