Adaptive Embedded Flexible Tensor Singular Spectrum Decomposition

To address the difficulty in extracting fault features from dual-channel signals, this work proposes a multichannel signal fusion processing method based on Flexible Tensor Singular Spectrum Decomposition (FTSSD) with adaptive embedding dimension selection. Firstly, the optimal embedding dimension of the trajectory tensor is adaptively determined using the proposed Trajectory Dimension Ratio (TDR) index. Once the optimal embedding dimension is obtained, the multichannel signals are represented as an optimal trajectory tensor. Then, FTSSD is employed to decompose the tensor and extract feature component signals. Moreover, by setting a residual threshold or maximum number of components to control the iterative process, the precision and rationality of the decomposition are ensured. Finally, all component signals are reconstructed, and their waveforms and spectra are comprehensively analyzed. The experimental results demonstrate that the proposed adaptive embedding FTSSD algorithm achieves a high accuracy and robustness in multichannel signal decomposition and feature extraction, making it suitable for the multicomponent analysis of complex dynamic signals such as mechanical fault diagnosis and vibration analysis.