Abstract Summary
The importance of uncertainty quantification has become increasingly more apparent, particularly in the field of system identification and modal analysis. The stochastic nature of the forcing in operational modal analysis (OMA) lends itself to variable identification performance. The need to quantify the uncertainty and therefore encapsulate this variability introduced by the data and the method itself, is highly sought by many a modern dynamicist to aid decision making. Often atypical observations in time series data can further compound this issue and even lead to the misidentification of the system. At time of writing, no method currently exists capable of quantifying the uncertainty in a Bayesian sense, whilst remaining statistically robust to outliers. Covariance-driven stochastic subspace identification (SSI) is frequently employed in OMA applications as a reliable means of recovering the modal properties of a structural dynamic system. At the heart of this method lies a mathematical concept known as canonical correlation analysis (CCA) which 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 earlier work by the authors, a probabilistic formulation of SSI was presented that saw the replacement of traditional CCA with a probabilistic equivalent, using the theory of latent variable models. This change in formulation provides new insight into this well established technique. Subsequently, the authors extended this to a statistically robust approach, with the inclusion of a Student’s-T distributed noise model. This robust extension saw improved identification performance over standard SSI when confronted with atypical observations in time series responses. Following the success of this work, the probabilistic interpretation of SSI was further extended to a, so-called, fully Bayesian approach, capable of recovering the posterior distributions over the modal properties. The availability of this posterior uncertainty provides additional information to the dynamicist, which can impact future decision making or modelling exercises. This paper combines the two work packages and presents a Robust Bayesian formulation of SSI using a statistically robust, variational Bayesian approach capable of approximating the posterior distributions over the modal properties. This robust Bayseian approach demonstrates a number of improvements, most notably the ability to recover posterior distributions over the modal properties, whilst remaining statistically robust to atypical observations.
