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Conference Papers Year : 2020

On a rank factorisation problem arising in gearbox vibration analysis

Abstract

Given a field $K$, a matrix $M \in K^{n \times m}$ of rank at most $r$, $r$ matrices $D_i \in K^{n \times n}$, 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 can be used to characterize when this polynomial problem is solvable and if so, how to explicitly compute the solutions of the problem.
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Dates and versions

hal-03070702 , version 1 (15-12-2020)
hal-03070702 , version 2 (16-12-2020)

Identifiers

  • HAL Id : hal-03070702 , version 1

Cite

Elisa Hubert, Axel Barrau, Yacine Bouzidi, Roudy Dagher, Alban Quadrat. On a rank factorisation problem arising in gearbox vibration analysis. 21st IFAC World Congress, Jul 2020, Berlin / Virtual, Germany. ⟨hal-03070702v1⟩
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