# On a rank factorisation problem arising in gearbox vibration analysis

Abstract : 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.
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Conference papers
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https://hal.inria.fr/hal-03070702
Contributor : Alban Quadrat Connect in order to contact the contributor
Submitted on : Wednesday, December 16, 2020 - 11:41:58 AM
Last modification on : Friday, January 21, 2022 - 3:17:33 AM

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IFAC_2020_final.pdf
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• HAL Id : hal-03070702, version 2

### Citation

Elisa Hubert, Axel Barrau, Yacine Bouzidi, Roudy Dagher, Alban Quadrat. On a rank factorisation problem arising in gearbox vibration analysis. IFAC 2020 - 21st World Congress, Jul 2020, Berlin / Virtual, Germany. ⟨hal-03070702v2⟩

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