This webpage is dedicated to the RankFactorizationProblem (click here) package dedicated to the effective study of the rank factorization problem.

The rank factorization problem aims at solving the following problem: Let K be a field, M ∈ Km × n, and D1, ..., Dr ∈ Km × m, find a column vector u ∈ Km × 1 and r row vectors v1, ..., vr ∈ K1 × n such that M = D1 u v1 + ... + Dr u vr.

This rank factorization problem arises in gearbox vibration analysis as a demodulation problem. For more details, see:  
 
Elisa Hubert, Amplitude and phase demodulation of multi-carrier signals: Application to gear vibration signals, PhD thesis, University of Lyon, France, 2019.

This problem was studied in:

  1. Hubert, E., Barrau, A., Badaoui, M. E., "New multi-carrier demodulation method applied to gearbox vibration analysis", Proceedings of ICASSP, 2018.

  2. Hubert, E., Amplitude and phase demodulation of multi-carrier signals: Application to gear vibration signals, PhD thesis, University of Lyon, France, 2019.

  3. Hubert, E., Bouzidi, Y., Dagher, R., Barrau, A., Quadrat, A. (2019). "Algebraic aspects of the exact signal demodulation problem", Proceedings of SSSC & TDS , Sinaia (Romania), 09-11/09/2019 ( paper.pdf ).

  4. Hubert, E., Barrau, A., Bouzidi, Y., Dagher, R., Quadrat, A. (2020). "On a rank factorisation problem arising in gearbox vibration analysis", Proceedings of the 21st IFAC World Congress , Germany, 12-17/07/2020 ( paper.pdf ).

  5. Hubert, E., Bouzidi, Y., Dagher, R., Quadrat, A. (2021). "Centrohermitian solutions of a factorization problem arising in vibration analysis. Part I: Lee's transformation", Proceedings of the European Control Conference 2021 ( paper.pdf ).

  6. Hubert, E., Bouzidi, Y., Dagher, R., Quadrat, A. (2021). "Centrohermitian solutions of a factorization problem arising in vibration analysis. Part II: A coninvolutory matrix approach", Proceedings of the European Control Conference 2021 ( paper.pdf ).

  7. Hubert, E., Bouzidi, Y., Dagher, R., Quadrat, A. (2021). "Algebraic aspects of a rank factorization problem arising in vibration analysis", Maple in Mathematics Education and Research, Communications in Computer and Information Science, vol. 1414, Springer, 104--118 ( paper.pdf , Maple and pdf files of the examples).

  8. Dagher, R., Hubert, E., Quadrat, A. (2023). "On the general solutions of a rank factorization problem arising in vibration analysis", INRIA Research Report n. 9438, submitted for publication ( Inria Report 9438).

For an example handled by CapAndHomalg (GAP), see Appendix of:  
 
Dagher, R., Hubert, E., Quadrat, A. (2021). "On the general solutions of a rank factorization problem arising in vibration analysis", INRIA Research Report n. 9438, version 1 ( Inria Report 9438).

The corresponding CapAndHomalg file can be downloaded here RR9438.ipynb

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