Dimensionality reduction using local-global standard hypergraph embedding for rotor fault diagnosis

The vibration signal contains a lot of state information, and its time domain, frequency domain, and time-frequency domain features are extracted to describe the rotor's operational state in detail. However, multi-domain and multi-angle feature extraction can lead to information redundancy, causing the 'dimensionality catastrophe' problem, which also makes fault classification more difficult. Dimensionality reduction (DR) is a technique that can help with this issue, but the majority of current DR algorithms are based on a simple intrinsic structure. To accurately characterize the intrinsic structure of high-dimensional fault dataset, this study proposed a novel DR algorithm that considers local information, global information, and the hypergraph model, named local-global standard hypergraph embedding (LGSHE). LGSHE redefines the hypergraph weight matrix's calculation formula and constructs the local intra-class standard hypergraph, local inter-class standard hypergraph, global intra-class standard hypergraph, and global inter-class standard hypergraph to characterize the fault data structure. LGSHE can accurately characterize the intrinsic structure of high-dimensional fault dataset and increase fault classification accuracy. The performance of LGSHE is validated on two different structures of double-span rotor experimental benches, and the results show that the algorithm can achieve good fault classification accuracy.