Robust probabilistic canonical correlations for stochastic subspace identification

Stochastic subspace identification (SSI) has become one of the key algorithms for the identification of linear structural dynamic systems. Commonly used in operational modal analysis, SSI is an efficient method for recovering the modal properties of a structure from measured data. When formed as “covariance-driven SSI” (Cov-SSI) the method relies on the computation of the canonical correlations and canonical directions between the past and future responses of the dynamic system, across a set of measured sensors. The mathematical tool that recovers this information is known as canonical correlation analysis (CCA). Using this knowledge, this paper presents two novel contributions. The first is a probabilistic interpretation of Cov-SSI, through the substitution of traditional CCA with its probabilistic interpretation. The second is an extension to the probabilistic SSI formulation, a robust form using the latent variable interpretation of the Students' T-distribution and robust CCA. This robust probabilistic SSI method is first benchmarked against Cov-SSI on a simple simulated dataset. Both identification procedures are then assessed on their resistance to noise and outliers in a corrupted dataset, typically caused by practically encountered scenarios such as sensor drop-out or partial detachment. Cov-SSI is shown to perform poorly, producing unrealistic results, whilst robust probabilistic SSI remains capable of confidently identifying the system in the presence of outliers. This evidence may lead to suggest that this new robust method could be more regularly used over classical Cov-SSI when the practitioner is worried about outliers in the measured response.