Tensor Singular Spectrum Decomposition: Multisensor Denoising Algorithm and Application

Abstract

Realising multi-sensor signal fusion and weak feature adaptive extraction is a challenging task. Therefore, a new algorithm called tensor singular spectrum decomposition is proposed in this study for the adaptive decomposition of multi-sensor time series. Traditional tensor decomposition algorithms, such as CP, HOSVD and Tucker decomposition, are derived from <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> -mode product. The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> -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 non-pseudodiagonal core tensor and nonunique decomposition results in traditional tensor decomposition algorithms. To this end, decomposition of the original tensor signal and reconstruction of multi-sensor component signals are realised in this study by combining the trajectory tensor construction, superposition of the Gaussian function spectral model, adaptive iterative optimisation 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 singular value decomposition in processing single-sensor signals whilst retaining the inherent structure and coupling relationship between multi-sensor data and realising the organic fusion and adaptive decomposition of multi-sensor 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 multi-sensor signals compared with existing methods.