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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2511.20831 |
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| _version_ | 1866918218263691264 |
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| author | Naveed, Khuram Rehman, Naveed ur |
| author_facet | Naveed, Khuram Rehman, Naveed ur |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20831 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Fully Multivariate Multifractal Detrended Fluctuation Analysis Method for Fault Diagnosis Naveed, Khuram Rehman, Naveed ur Signal Processing 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. |
| title | A Fully Multivariate Multifractal Detrended Fluctuation Analysis Method for Fault Diagnosis |
| topic | Signal Processing |
| url | https://arxiv.org/abs/2511.20831 |