A Robust Probabilistic Approach to Stochastic Subspace Identification
Brandon J. O'Connell Timothy J. Rogers
Modal parameter estimation of operational structures is often a challenging
task when confronted with unwanted distortions (outliers) in field
measurements. Atypical observations present a problem to operational modal
analysis (OMA) algorithms, such as stochastic subspace identification (SSI),
severely biasing parameter estimates and resulting in misidentification of the
system. Despite this predicament, no simple mechanism currently exists capable
of dealing with such anomalies in SSI. Addressing this problem, this paper
first introduces a novel probabilistic formulation of stochastic subspace
identification (Prob-SSI), realised using probabilistic projections.
Mathematically, the equivalence between this model and the classic algorithm is
demonstrated. This fresh perspective, viewing SSI as a problem in probabilistic
inference, lays the necessary mathematical foundation to enable a plethora of
new, more sophisticated OMA approaches. To this end, a statistically robust SSI
algorithm (robust Prob-SSI) is developed, capable of providing a principled and
automatic way of handling outlying or anomalous data in the measured
timeseries, such as may occur in field recordings, e.g. intermittent sensor
dropout. Robust Prob-SSI is shown to outperform conventional SSI when
confronted with 'corrupted' data, exhibiting improved identification
performance and higher levels of confidence in the found poles when viewing
consistency (stabilisation) diagrams. Similar benefits are also demonstrated on
the Z24 Bridge benchmark dataset, highlighting enhanced performance on measured
systems.