A Non-Euclidean Method for Open-Circuit Fault Diagnosis in Back-to-Back Converters Leveraging SPD Manifold and Mathematical Morphological Filtering

Fault diagnosis for back-to-back converters with multiple switch combinations is challenging due to strong nonlinearity and high dimensionality, which limits traditional Euclidean-based methods for accurate diagnosis. This paper proposes a novel diagnosis method on the symmetric positive definite (SPD) manifold. First, fault signals are embedded in a high-dimensional phase space and mapped to the SPD tangent space to improve efficiency by avoiding expensive Riemannian kernel computations. Then, an adaptive weighted multi-scale morphological filtering (AWMMF) approach tailored to the SPD manifold is performed in tangent space to suppress noise and enhance discriminative structures. Next, local regularized Fisher discriminant analysis (LRFDA) is used to further improves the separability of the fault features. Finally, the minimum Riemannian distance mean (MRDM) classifier enables accurate diagnosis in SPD manifold under varying conditions. Simulations and experiments demonstrate that the proposed method achieves the highest accuracy among five state-of-the-art baselines, while maintaining robustness, real-time suitability, and low hyperparameter sensitivity, highlighting its practicality for real-world fault diagnosis.