Tensor Singular Spectrum Decomposition: Multisensor Denoising Algorithm and Application

Realizing multisensor signal fusion and weak feature adaptive extraction is a challenging task. Therefore, a new algorithm called tensor singular spectrum decomposition (SSD) is proposed in this study for the adaptive decomposition of multisensor time series. Traditional tensor decomposition algorithms, such as CANDECOMP/PARAFAC (CP), high-order singular value decomposition (HOSVD), and Tucker decomposition, are derived from $n$ -mode product. The $n$ -mode product essentially uses the idea of matrices to deal with tensors, given that it defines the multiplication between matrix and higher order tensor, thereby creating problems of nonpseudodiagonal core tensor and nonunique decomposition results in traditional tensor decomposition algorithms. To this end, the decomposition of the original tensor signal and the reconstruction of multisensor component signals are realized in this study by combining the trajectory tensor construction, superposition of the Gaussian function spectral model, adaptive iterative optimization of embedding dimension, and diagonal average method on the basis of the principle of tensor–tensor order-preserving multiplication. The proposed algorithm inherits the perfect mathematical theory and excellent properties of matrix SVD in processing single-sensor signals, while retaining the inherent structure and coupling relationship between multisensor data and realizing the organic fusion and adaptive decomposition of multisensor signals. The analysis results of simulation, experimental, and engineering signals showed that the proposed method can effectively extract weak fault quantification features hidden in original multisensor signals compared with the existing methods.