Fast computation of uncertainty lower bounds for state-space model-based operational modal analysis

In operational modal analysis, identified modal parameters, e.g., natural frequencies, damping ratios, and mode shapes, are subject to uncertainties due to effects such as limited data, measurement noise, modelling error and unknown excitations. It becomes relevant to quantify the associated uncertainty for downstream analyses, e.g., finite element model updating and damage detection. Fast computation of uncertainty lower bounds of modal parameters via the Crame & PRIME;r-Rao bound is addressed in this study for an (asymptotically) unbiased estimator of the stochastic state space model (SSM). Starting with a modal-form SSM, the Fisher information matrix (FIM) of the SSM parameters can be obtained analytically. Direct evaluation of such FIM is computationally prohibitive for a high-dimensional parameter space and long data, however, rendering it infeasible in practical applications. Various approximation schemes are proposed to accelerate the computation of the FIM, including a re-parameterisation via the innovations form to remove the singularity of FIM, introducing stationarity assumption to eliminate recursive calculations and mode clustering for a further speedup. The proposed methodology is applied to synthetic and field data, and verified by direct Monte Carlo simulation. Although the methodology is demonstrated for the uncertainty analysis of modal parameters based on the maximum likelihood estimator of SSM, it can also be used to lower bound the identification uncertainty of any unbiased estimator of SSM.