A novel variational Bayesian approach to stochastic subspace identification

Covariance-driven stochastic subspace identification (SSI) is a frequently employed modal analysis technique, often used in operational modal analysis (OMA) applications, as a reliable means of recovering the modal properties of a structural dynamic system. At its core, this method relies on a mathematical concept known as canonical correlation analysis (CCA) that seeks to find the correlation between Hankel matrices of the future and the past observations, from a set of response sensors, measuring a dynamic system. In previous work by the authors, a probabilistic formulation of SSI was presented that saw the replacement of traditional CCA with its probabilistic equivalent, using the theory of latent variable models. This change in formulation provides new insight into this well established approach. Subsequently, the probabilistic method was further extended by the authors to a so-called, fully Bayesian approach and solved using Markov Chain Monte Carlo (MCMC) sampling to recover the posterior distributions over the modal properties. The availability of the posterior uncertainty provides additional information to the user which can impact future decision making or modelling exercises. This paper presents a continuation of the Bayesian SSI formulation in the form of a novel variational Bayesian SSI approach, capable of approximating a surrogate posterior distribution over the modal properties. It is shown on a simple case study how suitable approximations to the posterior distributions over the modal properties can be recovered that show good agreement with the truth, whilst also encompassing the SSI estimate in the posterior. This is also followed by a brief discussion on its overall performance and the possible limitations and how these could be addressed.