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 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 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.

The working environment of seawater axial piston hydraulic pump is harsh, and it is difficult to diagnose due to insufficient fault database. In contrast, pumps of the same type but using hydraulic oil have an adequate fault database and are easy to diagnose. In view of the above situation, a fault diagnosis method of seawater hydraulic piston pump based on transfer learning is proposed. The method decomposes the original sampled fault signal by complementary ensemble empirical mode decomposition (CEEMD) to obtain the intrinsic mode function (IMF) that can characterize the original signal. The singular value decomposition (SVD) is performed on the IMF. Then, the obtained singular value is used as a feature parameter to construct a feature vector. The feature data of seawater hydraulic pump and oil pump are used as target data and auxiliary data to form training data. The training data is trained based on the iterative adjustment of the weight through the TrAdaBoost transfer learning algorithm. Finally, the results of diagnosis and classification are compared with traditional machine learning. When the number of training data is 5 groups, the accuracy of transfer learning is 30.5% higher than that of traditional machine learning. The results show that transfer learning has great advantages in the case of a small number of samples.

Convolutional neural networks and transformers have both achieved remarkable success in the field of fault diagnosis owing to their proficiency in extracting local and global features. However, in real industrial production, the diagnostic performance of many methods is often limited by factors such as environmental noise and sample quantity. To address these challenges, this article presents a novel fault diagnosis framework called MFSFormer. First, it employs embedded convolutional layers with kernels of various sizes to extract multiscale receptive field features from vibration signals. Second, a Fuse-Shuffle attention block is employed to capture dependencies between feature channels and windows, facilitating the implementation of subfeature flow. The case studies conducted on two public datasets demonstrate that the proposed method achieves an average diagnostic accuracy that surpasses the suboptimal method by 3.91% and 7.00% in noisy environments and small-sample conditions, respectively. The results indicate that the proposed method not only enhances the robustness of fault diagnosis in noisy environments, but also improves diagnostic accuracy under limited sample conditions, and the method has practical value.