Bayesian FFT modal identification for multi-setup experimental modal analysis

Abstract

In full-scale forced vibration tests, the demand often arises to capture high-spatial-resolution and high-precision mode shapes with a limited number of sensors and shakers. Such detailed mode shapes are valuable for applications such as damage localization and high-dimensional finite element model updating. Multi-setup experimental modal analysis (EMA) addresses this challenge by roving sensors and shakers across multiple setups. To enable fast and accurate multi-setup EMA, this paper develops a Bayesian modal identification strategy by extending the existing single-setup algorithm. Specifically, a frequency-domain probabilistic model is first formulated using multiple sets of structural multiple-input, multiple-output (MIMO) vibration data. A constrained Laplace method is then employed for Bayesian posterior approximation, providing the maximum a posteriori estimate of modal parameters along with a posterior covariance matrix (PCM) for uncertainty quantification. Utilizing complex matrix calculus, analytical expressions are derived for parameter updates in the coordinate descent optimization, as well as for PCM computation, enhancing both coding simplicity and computational efficiency. The proposed algorithm is intensively validated with synthetic and field data from bridge and building structures. It demonstrates that the proposed method yields highly consistent results compared to scenarios with adequate test equipment. The resulting high-fidelity MIMO model enables structural response prediction under future loading conditions and supports condition assessment.