Accelerating convergence in Bayesian operational modal analysis with Fisher information matrix

Abstract

Bayesian operational modal analysis (BAYOMA) has been increasingly applied to ambient vibration tests, providing a fundamental means for estimating modal properties as well as quantifying their identification uncertainty consistent with probability rules and modelling assumptions. Computing the most probable value of modal parameters in BAYOMA involves a high-dimensional numerical optimisation of the negative log-likelihood function (NLLF). Brute-force optimisation using generic algorithms treating the NLLF as a black box is computationally prohibitive and often non-converging. Efficient iterative algorithms have been developed over the past decade, but challenges still exist, e.g., for very close modes that may require significantly more iterations or (in some cases) may not be converging. Leveraging on recent advance in the mathematics and understanding of the Fisher Information Matrix (FIM) of modal parameters, an efficient method based on Newton-type iterations is proposed in this work to improve computational efficiency and convergence robustness. The MPV estimate in each iteration is updated based on two characteristic types of principal directions of the FIM. Move of the first type involves mode shapes only and is orthogonal to the subspace spanned by the current mode shape estimates. The second type involves updates of all modal parameters, where the mode shapes move within the subspace. Compact analytical expressions are derived for the gradient of NLLF to ensure accurate and efficient use in determining each iteration move. The performance of the proposed method is investigated with a comprehensive study based on synthetic, laboratory and field data. Results reveal that the proposed algorithm generally outperforms existing ones in terms of computational time by an order of magnitude, and it has better convergence robustness especially for challenging cases with very close modes and high modal force coherence.