Fault diagnosis of rotor based on Semi-supervised Multi-Graph Joint Embedding

Traditional graph embedding methods only consider the pairwise relationship between fault data. But in practical applications, the relationship of high-dimensional fault data usually is multiple classes corresponding to multiple samples. Therefore, the hypergraph structure is introduced to fully portray the complex structural relationship of high-dimensional fault data. However, during the construction of the hypergraph, the hyperedge weight is usually set as the sum of the similarities between every two vertices contained within the hyperedge, and this "averaging effect" causes the relationship between data sample points with high similarity to be weakened, while the relationship between data sample points with low similarity to be strengthened. This phenomenon also leads to the hypergraph cannot accurately portray the relationship of high-dimensional data, which reduces the fault classification accuracy. To address this issue, a novel dimensionality reduction method named Semi-supervised Multi-Graph Joint Embedding (SMGJE) is proposed and applied to rotor fault diagnosis. SMGJE constructs simple graphs and hypergraphs with the same sample points and characterizes the structure of high-dimensional data in a multi-graph joint embedding. The edges of the simple graph are the direct description of the similarity between sample points so that SMGJE can overcome this "averaging effect" of the hypergraph. The effectiveness of the proposed method is verified by two different fault datasets.