Uncertainty calculation for modal parameters used with stochastic subspace identification: an application to a bridge structure
2015
Stochastic subspace identification method (SSI) has been proven to be an efficient algorithm for the identification of
liner-time-invariant system using multivariate measurements. Generally, the estimated modal parameters through SSI
may be afflicted with statistical uncertainty, e.g. undefined measurement noises, non-stationary excitation, finite number
of data samples etc. Therefore, the identified results are subjected to variance errors. Accordingly, the concept of the
stabilization diagram can help users to identify the correct model, i.e. through removing the spurious modes. Modal
parameters are estimated at successive model orders where the physical modes of the system are extracted and separated
from the spurious modes. Besides, an uncertainty computation scheme was derived for the calculation of uncertainty
bounds for modal parameters at some given model order. The uncertainty bounds of damping ratios are particularly
interesting, as the estimation of damping ratios are difficult to obtain. In this paper, an automated stochastic subspace
identification algorithm is addressed. First, the identification of modal parameters through covariance-driven stochastic
subspace identification from the output-only measurements is used for discussion. A systematic way of investigation on
the criteria for the stabilization diagram is presented. Secondly, an automated algorithm of post-processing on
stabilization diagram is demonstrated. Finally, the computation of uncertainty bounds for each mode with all model order
in the stabilization diagram is utilized to determine system natural frequencies and damping ratios. Demonstration of this
study on the system identification of a three-span steel bridge under operation condition is presented. It is shown that the
proposed new operation procedure for the automated covariance-driven stochastic subspace identification can enhance
the robustness and reliability in structural health monitoring.
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