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

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Elisa Hubert
• Function : Author
• PersonId : 1050972
Axel Barrau
• Function : Author
• PersonId : 941948
Yacine Bouzidi
• Function : Author
• PersonId : 955292
Roudy Dagher
• Function : Author
• PersonId : 833444

#### 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.

### Dates and versions

hal-03070709 , version 1 (15-12-2020)

### Identifiers

• HAL Id : hal-03070709 , version 1

### Cite

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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