The flexible tensor singular value decomposition and its applications in multisensor signal fusion processing

A tensor, represented as a multidimensional array, has crucial applications in various fields such as image processing and high-dimensional data mining. This study defines a novel concept of tensor-tensor multiplication, the 'o-order < p, q >-mode product', laying a foundational framework for advanced tensor operations. Building on this, a novel extension of matrix SVD to tensors, termed the flexible tensor SVD (FTSVD), is also proposed. The FTSVD overcomes the inherent limitations of the popular tensor SVD that operates on the n-mode product, notably non-unique optimization results, and non-pseudo-diagonal core tensors. Building upon the foundations of the FTSVD and iterative decomposition principles, this study presents an adaptive signal decomposition technique named the second-kind tensor singular spectrum decomposition(2KFTSSD). This technique is well-suited for multisensor information fusion processing. The effectiveness of the presented technique has been thoroughly evaluated through both dynamic simulation and experimental signal analyses. Comparative analyses suggest that the proposed method outperforms traditional approaches in multisensor signal fusion processing, feature extraction, early fault detection, and the preservation of intrinsic interrelationships among multisensor signal attributes.