On a rank factorisation problem arising in gearbox vibration analysis
| Autor: | Alban Quadrat, Roudy Dagher, Axel Barrau, Yacine Bouzidi, Elisa Hubert |
|---|---|
| Přispěvatelé: | Laboratoire d'Analyse des Signaux et des Processus Industriels (LASPI), Université Jean Monnet [Saint-Étienne] (UJM), SAFRAN Group, Géométrie, Algèbre, Informatique, Applications (GAIA), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Service Expérimentation et Développement (SED [Lille]), Institut National de Recherche en Informatique et en Automatique (Inria), OUtils de Résolution Algébriques pour la Géométrie et ses ApplicatioNs (OURAGAN), Inria de Paris, Université Jean Monnet - Saint-Étienne (UJM) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
0209 industrial biotechnology
Pure mathematics Polynomial Rank (linear algebra) [MATH.MATH-OA]Mathematics [math]/Operator Algebras [math.OA] Field (mathematics) 02 engineering and technology [SPI.AUTO]Engineering Sciences [physics]/Automatic Matrix (mathematics) 020901 industrial engineering & automation Factorization Demodulation 0202 electrical engineering electronic engineering information engineering [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Linear algebra Mathematics Modulation [INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC] Vibration analysis 020208 electrical & electronic engineering Linear system [MATH.MATH-RA]Mathematics [math]/Rings and Algebras [math.RA] Control and Systems Engineering Factorisation methods [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Phase modulation |
| Zdroj: | IFAC 2020-21st World Congress IFAC 2020-21st World Congress, Jul 2020, Berlin / Virtual, Germany |
| Popis: | International audience; Given a field $K$, $r$ matrices $D_i \in K^{n \times n}$, a matrix $M \in K^{n \times m}$ of rank at most $r$, in this paper, we study the problem of factoring $M$ as follows $M=\sum_{i=1}^r D_i \, u \, v_i$, where $u \in K^{n \times 1}$ and $v_i \in K^{1 \times m}$ for $i=1, \ldots, r$. This problem arises in modulation-based mechanical models studied in gearbox vibration analysis (e.g., amplitude and phase modulation). We show how linear algebra methods combined with linear system theory ideas can be used to characterize when this polynomial problem is solvable and if so, how to explicitly compute the solutions. |
| Databáze: | OpenAIRE |
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