Underdetermined modal parameter identification for time-invariant structures via autocorrelation-optimized CP decomposition

In recent years, operational modal parameter identification has become crucial in fields such as engineering, aerospace, mechanics, and civil infrastructure, as well as in analyzing complex structures. However, when the number of sensors is fewer than the modal parameters to be identified, the system becomes underdetermined, meaning that the limited sensor data cannot fully capture the system’s modal information. This often results in uncertainties and challenges in the identification process. Current methods for underdetermined operational modal parameter identification typically rely on signal sparsity or statistical independence assumptions, often requiring signal preprocessing to enforce sparsity, which restricts their applicability. To address these limitations, this study presents a novel underdetermined operational modal parameter identification method based on autocorrelation-optimized principal component tensor decomposition. This approach first establishes a connection between operational modal parameter identification and CP tensor decomposition, then introduces a new tensor construction technique that combines statistical characteristics of the data with time-series analysis. By decomposing the constructed tensor, the method extracts the modal shape matrix along with a set of sub-tensors representing modal responses, enabling the estimation of modal parameters. The method’s effectiveness is verified through experiments on a three-degree-of-freedom spring oscillator and a uniform cantilever beam structure, even under underdetermined and noisy conditions. Results demonstrate that the proposed method outperforms existing techniques in both recognition accuracy and noise resistance, providing a stable and precise identification of operational modal parameters.