# Algebraic aspects of a rank factorization problem arising in vibration analysis

Abstract : This paper continues the study of a factorization problem arising in gear fault surveillance. The structure of a class of solutions -- interesting in practice -- of this factorization problem is studied. We show that these solutions can be parametrized. The parameter space ${\mathcal P}$ is proved to be the complementary of an algebraic set that is explicitly characterized based on module theory and computer algebra. A finite open cover of ${\mathcal P}$ is obtained and for each basic open subset of the cover, a closed-form solution is computed using computer algebra. Hence, the local structure of the solution space can be finely studied. Finally, we show that the existence of a single closed-form solution defined on the whole parameter space ${\mathcal P}$ is related to difficult problems in module theory.
Document type :
Conference papers
Domain :

https://hal.inria.fr/hal-03070709
Submitted on : Tuesday, December 15, 2020 - 10:12:35 PM
Last modification on : Friday, December 18, 2020 - 11:40:50 AM

### Identifiers

• HAL Id : hal-03070709, version 1

### Citation

Elisa Hubert, Axel Barrau, Yacine Bouzidi, Roudy Dagher, Alban Quadrat. Algebraic aspects of a rank factorization problem arising in vibration analysis. Maple Conference, Nov 2020, Waterloo / Virtual, Canada. ⟨hal-03070709⟩

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