A Fully Multivariate Multifractal Detrended Fluctuation Analysis Method for Fault Diagnosis

TL;DR

This paper introduces a novel multivariate multifractal analysis method, FM-MFDFA, combined with MVMD, to improve fault diagnosis in multichannel vibration data, outperforming traditional approaches especially in noisy environments.

Contribution

It presents a fully multivariate generalization of MFDFA using a new covariance-weighted norm and integrates MVMD for enhanced fault feature extraction.

Findings

Outperforms conventional MFDFA in fault detection accuracy

Effectively distinguishes healthy and faulty states in wind turbine data

Robust under noisy measurement conditions

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.