Empowering Advanced Parametric Modes Clustering from Topological Data Analysis
| Autor: | Tarek Frahi, Baptiste Vinh Mau, Antonio Falcó, Francisco Chinesta, Jean Louis Duval |
|---|---|
| Přispěvatelé: | UCH. Departamento de Matemáticas, Física y Ciencias Tecnológicas, Producción Científica UCH 2021, Laboratoire Procédés et Ingénierie en Mécanique et Matériaux (PIMM), Conservatoire National des Arts et Métiers [CNAM] (CNAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM), Universidad Cardenal Herrera-CEU (CEU-UCH), ESI Group (ESI Group) |
| Rok vydání: | 2021 |
| Předmět: |
Optimal design
Technology Topology Dynamical systems theory QH301-705.5 Superficies (Matemáticas) Deformaciones (Mecánica) Computer science QC1-999 Modal analysis Data analysis 02 engineering and technology Topología Sciences de l'ingénieur 01 natural sciences topological data analysis [SPI]Engineering Sciences [physics] 0203 mechanical engineering Surfaces Applied mathematics General Materials Science Biology (General) 0101 mathematics QD1-999 Instrumentation Eigenvalues and eigenvectors Parametric statistics Fluid Flow and Transfer Processes Basis (linear algebra) Physics Process Chemistry and Technology General Engineering Análisis de datos structural dynamics Engineering (General). Civil engineering (General) modal analysis Orthogonal basis Computer Science Applications 010101 applied mathematics Chemistry Deformations (Mechanics) 020303 mechanical engineering & transports NVH Topological data analysis TA1-2040 |
| Zdroj: | CEU Repositorio Institucional Fundación Universitaria San Pablo CEU (FUSPCEU) Applied Sciences, Vol 11, Iss 6554, p 6554 (2021) Applied Sciences Applied Sciences, MDPI, 2021, 11 (14), pp.6554. ⟨10.3390/app11146554⟩ Volume 11 Issue 14 |
| ISSN: | 2076-3417 |
| DOI: | 10.3390/app11146554 |
| Popis: | Este artículo se encuentra disponible en la siguiente URL: https://www.mdpi.com/2076-3417/11/14/6554 Modal analysis is widely used for addressing NVH—Noise, Vibration, and Hardness—in automotive engineering. The so-called principal modes constitute an orthogonal basis, obtained from the eigenvectors related to the dynamical problem. When this basis is used for expressing the displacement field of a dynamical problem, the model equations become uncoupled. Moreover, a reduced basis can be defined according to the eigenvalues magnitude, leading to an uncoupled reduced model, especially appealing when solving large dynamical systems. However, engineering looks for optimal designs and therefore it focuses on parametric designs needing the efficient solution of parametric dynamical models. Solving parametrized eigenproblems remains a tricky issue, and, therefore, nonintrusive approaches are privileged. In that framework, a reduced basis consisting of the most significant eigenmodes is retained for each choice of the model parameters under consideration. Then, one is tempted to create a parametric reduced basis, by simply expressing the reduced basis parametrically by using an appropriate regression technique. However, an issue remains that limits the direct application of the just referred approach, the one related to the basis ordering. In order to order the modes before interpolating them, different techniques were proposed in the past, being the Modal Assurance Criterion—MAC—one of the most widely used. In the present paper, we proposed an alternative technique that, instead of operating at the eigenmodes level, classify the modes with respect to the deformed structure shapes that the eigenmodes induce, by invoking the so-called Topological Data Analysis—TDA—that ensures the invariance properties that topology ensure. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|