Efficient two-stage modal identification for structures with closely spaced modes by Bayesian FFT and joint approximate diagonalization

Abstract

Modal parameter identification plays a crucial role in structural health monitoring and vibration analysis, as it provides key insights into the dynamic characteristics of structures. While Bayesian statistics effectively address uncertainties in measurement and system identification; however existing methods face challenges with closely spaced modes. A recently developed expectation–maximization (EM) algorithm has shown promise in most scenarios. However, the Bayesian goal function has multiple local extrema, especially for closely spaced mode shapes, and selecting an appropriate initial guess to obtain accurate and fast identification remains a challenge. To circumvent the limitation, an innovative two-stage Bayesian method is proposed with improved efficiency and robustness for modal parameter identification on structures with closely spaced modes. In doing so, the posterior distribution is established via the Bayesian FFT analysis and then, the most probable modal parameters are searched in two sequential stages. In the first stage, the closely spaced mode shapes are found pertaining to a joint approximate diagonalization problem, which can be quickly solved by the Jacobi rotation algorithm, without the need to specify an initial guess. Subsequently in the second stage, the natural frequencies and damping ratios are simply obtained through Newton iteration. The two-stage method decouples the optimization procedure and therefore, can substantially improve the identification efficiency. Numerical simulations and experimental data are analyzed to validate our method, demonstrating its superior efficiency and accuracy modal identification in the presence of closely spaced modes.