A new perspective on Bayesian operational modal analysis

The quantification of uncertainty is of particular interest to the dynamics community, which increasingly desires a measure of uncertainty for greater insight, allowing for more informed and confident decision-making. In the field of operational modal analysis (OMA), obtained modal information is frequently used to assess the current state of aerospace, mechanical, offshore and civil structures. However, the stochasticity of operational systems and the lack of forcing information can lead to inconsistent results. Quantifying the uncertainty of the recovered modal parameters through OMA is therefore of significant value. In this article, a new perspective on Bayesian OMA is proposed — a Bayesian stochastic subspace identification (SSI) algorithm. Distinct from existing approaches to Bayesian OMA, a hierarchical probabilistic model is embedded at the core of canonical variate-weighted, covariance-driven SSI. Through substitution of canonical correlation analysis with its Bayesian equivalent, posterior distributions over the modal characteristics are obtained. Two inference schemes are presented for the proposed Bayesian formulation: Markov Chain Monte Carlo and variational Bayes. Two case studies are then explored. The first is benchmark study using data from a simulated, multi degree-of-freedom, linear system. Following application of Bayesian SSI using both forms of inference, it is shown that the same posterior is targeted and recovered by both schemes, with good agreement between the mean of the posterior and the conventional SSI result. The second study applies the variational form of Bayesian SSI to data obtained from an in-service structure — the Z24 bridge. The Z24 is chosen given its familiarity in the fields of OMA and structural health monitoring. The results of this study are first presented at a single model order, and then at multiple model orders using a stabilisation diagram. In both cases, the recovered posterior uncertainty is included and compared to the conventional SSI result. It is observed that the posterior distributions with mean values coinciding with the natural frequencies exhibit much lower variance than posteriors situated away from the natural frequencies.