Principal Component Stochastic Subspace Identification for Output-Only Modal Analysis

Abstract

Stochastic Subspace Identification (SSI) is widely used in modal analysis of engineering structures, known for its numerical stability and high accuracy in modal parameter identification. SSI methods are generally classified into two types: Data-Driven (SSI-Data) and Covariance-Driven (SSI-Cov), which have been considered to originate from different theoretical foundations and computational principles. In contrast, this study demonstrates that SSI-Cov and SSI-Data converge to the same solution under the condition of infinite observations, by establishing a unified framework incorporating instrumental variable analysis. Further, a novel modal identification approach, Principal Component Stochastic Subspace Identification (PCSSI), is proposed based on this framework. This method employs Principal Component Analysis (PCA) to extract key components of the signal subspace and project the observed data onto this space, enhancing modal identification stability while significantly reducing computational complexity. Through 5000 Monte Carlo numerical simulations, the statistical analysis shows that PCSSI consistently outperforms traditional SSI methods in terms of numerical stability and noise reduction, demonstrating clear advantages over both SSI-Cov and SSI-Data. Its effectiveness is further validated using experimental data from a scaled bridge model. Compared to conventional SSI approaches, PCSSI demonstrates superior robustness under complex engineering conditions, especially when dealing with limited data or high noise levels, underscoring its strong potential for practical applications.