Algebraic Aspects of a Rank Factorization Problem Arising in Vibration Analysis

Autor:	Elisa Hubert, Roudy Dagher, Alban Quadrat, Yacine Bouzidi
Rok vydání:	2021
Předmět:	Vibration Class (set theory) Pure mathematics Cover (topology) Rank factorization Structure (category theory) Parameter space Algebraic number Symbolic computation Mathematics
Zdroj:	Communications in Computer and Information Science ISBN: 9783030816971 MC
Popis:	This paper continues the study of a rank factorization problem arising in gear fault surveillance [10, 11, 12, 13]. The structure of a class of solutions − important in practice − of the rank factorization problem is studied. We show that these solutions can be parametrized. Using module theory and computer algebra methods, the parameter space \({\mathcal P}\) is explicitly characterized and is shown to be the complementary of an algebraic set. Finally, a finite open cover of \({\mathcal P}\) is obtained and for each basic open subset of the cover of \({\mathcal P}\), a closed-form solution is characterized.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::30e9fd8ea3801fd5309afea2d778556b https://doi.org/10.1007/978-3-030-81698-8_8 Zobrazit plný text záznamu