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 ‘-order 〈, 〉-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 -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(2K-FTSSD). 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 multi-sensor signal attributes.

中文翻译：

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柔性张量奇异值分解及其在多传感器信号融合处理中的应用


张量以多维数组的形式表示，在图像处理和高维数据挖掘等各个领域具有重要的应用。这项研究定义了张量-张量乘法的新概念，即“阶<,>模积”，为高级张量运算奠定了基础框架。在此基础上，还提出了矩阵 SVD 到张量的新颖扩展，称为灵活张量 SVD (FTSVD)。 FTSVD 克服了在 模乘积上运行的流行张量 SVD 的固有限制，特别是非唯一优化结果和非伪对角核心张量。基于FTSVD和迭代分解原理的基础上，本研究提出了一种自适应信号分解技术，称为第二类张量奇异谱分解（2K-FTSSD）。该技术非常适合多传感器信息融合处理。通过动态仿真和实验信号分析，已对所提出技术的有效性进行了彻底评估。比较分析表明，该方法在多传感器信号融合处理、特征提取、早期故障检测以及多传感器信号属性之间内在相互关系的保存方面优于传统方法。