Fault Evolution Trajectory Reconstruction and Manifold Interpolation Method based on Parallel Transport Mechanism

Abstract

In industrial intelligent operation and maintenance, the bearing fault signals, after dimensionality reduction through manifold learning, tend to exhibit discontinuous "fragmented" characteristics, making it difficult to depict the continuous evolution pattern of the fault. Moreover, the absence of intermediate state samples can easily lead to diagnostic errors. Therefore, this paper proposes a fault evolution trajectory reconstruction and manifold interpolation method based on parallel transport mechanism (TR-MIPT). This method utilizes local principal component analysis to construct the manifold topology, and generates pseudo-time degradation sequences based on geodesic metric; through tangent space estimation, orthogonal Procrustes alignment and discrete Riemannian connection, it realizes the distortion-free transmission of evolution gradients across coordinate systems; and combines local normal curvature and second-order geometric retract mapping to generate virtual samples and continuous evolution trajectories. Experimental results on the datasets from Case Western Reserve University and Northeast Petroleum University show that TR-MIPT can effectively reconstruct the degradation path, reduce the reconstruction error of intermediate states, and improve the diagnostic accuracy for small sample sizes and unseen intermediate-state faults.