{"ID":2837180,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.20831","arxiv_id":"2511.20831","title":"A Fully Multivariate Multifractal Detrended Fluctuation Analysis Method for Fault Diagnosis","abstract":"We propose a fully multivariate generalization of multifractal detrended fluctuation analysis (MFDFA) and leverage it to develop a fault diagnosis framework for multichannel machine vibration data. We introduce a novel covariance-weighted $L_{pq}$ matrix norm based on Mahalanobis distance to define a fully multivariate fluctuation function that uniquely captures cross-channel dependencies and variance biases in multichannel vibration data. This formulation, termed FM-MFDFA, allows for a more accurate characterization of the multiscale structure of multivariate signals. To enhance feature relevance, the proposed framework integrates multivariate variational mode decomposition (MVMD) to isolate fault-relevant components before applying FM-MFDFA. Results on wind turbine gearbox data demonstrate that the proposed method outperforms conventional MFDFA approaches by effectively distinguishing between healthy and faulty machine states, even under noisy conditions.","short_abstract":"We propose a fully multivariate generalization of multifractal detrended fluctuation analysis (MFDFA) and leverage it to develop a fault diagnosis framework for multichannel machine vibration data. We introduce a novel covariance-weighted $L_{pq}$ matrix norm based on Mahalanobis distance to define a fully multivariate...","url_abs":"https://arxiv.org/abs/2511.20831","url_pdf":"https://arxiv.org/pdf/2511.20831v1","authors":"[\"Khuram Naveed\",\"Naveed ur Rehman\"]","published":"2025-11-25T20:30:57Z","proceeding":"eess.SP","tasks":"[\"eess.SP\"]","methods":"[]","has_code":false}