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      Dimensionality reduction for studying physical phenomena : Dimensionality reduction for studying physical phenomena

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      ScienceOpen Posters
      ScienceOpen
      Numerical Algebra, Matrix Theory, Differential-Algebraic Equations, and Control Theory
      parametric study, dimensionality reduction, stability analysis, supervised learning
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            Abstract

            We explore dimensionality reduction in the context of model based and model free approaches. In the model based approach there is a governing equation or a set of rules relating quantities of interest, whereas in a model free setting there are no rules or equations, only data is available. As an example consider the problem of squealing noise in a brake. The model based approach relates quantities of interest like mass distribution within the brake, damping, stiffness and other properties of a brake material, speed of rotation etc with a dynamical equation, the steady state behaviour can be obtained by converting it to an eigenvalue problem and finding eigenvalues and eigenvectors (which are related to squeal frequency and mode shapes of a disc brake). The model reduction problem could be posed as projecting the eigenvalue problem to a lower dimensional space, while preserving important eigenvalues and eigenvectors. In contrast, the model free approach starts with data, i.e., a set of parameter values which correspond to squeal and the values which correspond to no-squeal. If the number of parameters responsible for squeal is very large, then dimensionality reduction is concerned with reducing the number of these parameters or ranking these parameters in order of importance. We illustrate pros and cons of model based and model free dimensionality reduction with some numerical examples.

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            Conference
            ScienceOpen Posters
            ScienceOpen
            September 1 2015
            Author information
            https://orcid.org/0000-0002-7958-5915
            Article
            10.14293/P2199-8442.1.SOP-PHYS.P7FSU7.v1
            dd652daa-18ea-4db4-9ef7-418a94b0cb55

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .

            Numerical Algebra, Matrix Theory, Differential-Algebraic Equations, and Control Theory
            History

            Nonlinear & Complex systems
            parametric study, dimensionality reduction, stability analysis, supervised learning

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