From EM to Newton: fast and reliable computation for Bayesian FFT modal identification

This paper develops a modified Newton algorithm for efficient Bayesian inference of modal parameters in operational modal analysis (OMA). The proposed approach builds upon an existing Expectation-Maximization (EM) algorithm for Bayesian FFT modal identification. The gradient vector and Hessian matrix are derived using Fisher’s identity and Louis’ identity, forming the core components of the Newton’s method. To craft an efficient and robust algorithm, the paper then presents critical implementation strategies, such as pseudo-inversion of the Hessian matrix, constraints handling, data normalization, and parameter initialization. Validation of the proposed approach is then conducted using synthetic and field data acquired from two different structures, demonstrating its accuracy and efficiency. Moreover, the performance is shown to be superior to state-of-the-art algorithms and is an order of magnitude faster than the previously implemented EM algorithm. The proposed algorithm unifies the most probable value optimization and the uncertainty quantification, distinguished by its programming simplicity and an ease of extension to other OMA cases, e.g., with multiple setups.