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

• Published in: Mechanical systems and signal processing Vol. 169; p. 108759
• Main Authors: Shi, Yuanfeng, Li, Binbin, Au, Siu-Kui
• Format: Journal Article
• Language: English
• Published: Berlin Elsevier Ltd 15.04.2022; Elsevier BV
• Subjects: Clustering; Computation; Cramér-Rao bound; Damage detection; Damping ratio; Error analysis; Finite element method; Lower bounds; Maximum likelihood estimator; Maximum likelihood estimators; Modal analysis; Model updating; Monte Carlo simulation; Noise measurement; Operational modal analysis; Parameter identification; Parameterization; Resonant frequencies; State space models; State-space model; Uncertainty analysis; Uncertainty quantification; Maximum likelihood estimator; Uncertainty quantification; State-space model; Cramér-Rao bound; Operational modal analysis
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2021.108759

•Cramér-Rao bound of modal parameters is constructed in OMA.•A modal-form stochastic state-space model is proposed for calculating CRB.•Fast evaluation of Fisher information matrix is provided assuming stationary measurements.•Cluster-mode approximation of FIM accelerates computation while retaining accuracy. 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 Cramér-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.