# A Multivariate Blaschke-Based Mode Decomposition Approach for Gear Fault Diagnosis

## TL;DR

This paper introduces a new method for diagnosing gear faults by decomposing multivariate signals using Blaschke products and adaptive techniques.

## Contribution

The novel MBMD method integrates multivariate vibration signals using Blaschke-based decomposition and joint spectral segmentation for improved fault diagnosis.

## Key findings

- MBMD efficiently integrates multivariate information for gear fault diagnosis.
- The method outperforms existing techniques in fault feature extraction accuracy.
- Blaschke multi-spectra reformulate decomposition as a spectrum segmentation task.

## Abstract

Existing multivariate signal decomposition methods insufficiently account for the mechanical characteristics of gear systems, limiting their capability in fault feature extraction. To address this limitation, we propose a novel method, Multivariate Blaschke-based Mode Decomposition (MBMD). In MBMD, multivariate vibration signals are modeled as multi-dimensional responses of the gear system. Using Stochastic Adaptive Fourier Decomposition (SAFD), these signals are represented as a unified combination of Blaschke products, enabling adaptive multi-channel information fusion. To achieve modal alignment, we introduce the concept of Blaschke multi-spectra, reformulating the decomposition problem as a spectrum segmentation task, which is solved via a joint spectral segmentation algorithm. Furthermore, a voting-based filter bank, designed according to gear fault mechanisms, is employed to suppress noise and enhance fault feature extraction. Experimental validation on gear fault signals demonstrates the effectiveness of MBMD, showing that it can efficiently integrate multivariate information and achieve more accurate fault diagnosis than existing methods, providing a new perspective for mechanical fault diagnosis.